- FindStat

Identifier

Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000097: Graphs ⟶ ℤ

Values

[1] => {{1}} => [1] => ([],1) => 1

[1,2] => {{1},{2}} => [1,1] => ([(0,1)],2) => 2

[2,1] => {{1,2}} => [2] => ([],2) => 1

[1,2,3] => {{1},{2},{3}} => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3

[1,3,2] => {{1},{2,3}} => [1,2] => ([(1,2)],3) => 2

[2,1,3] => {{1,2},{3}} => [2,1] => ([(0,2),(1,2)],3) => 2

[2,3,1] => {{1,2,3}} => [3] => ([],3) => 1

[3,1,2] => {{1,3},{2}} => [2,1] => ([(0,2),(1,2)],3) => 2

[3,2,1] => {{1,3},{2}} => [2,1] => ([(0,2),(1,2)],3) => 2

[1,2,3,4] => {{1},{2},{3},{4}} => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[1,2,4,3] => {{1},{2},{3,4}} => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3

[1,3,2,4] => {{1},{2,3},{4}} => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3

[1,3,4,2] => {{1},{2,3,4}} => [1,3] => ([(2,3)],4) => 2

[1,4,2,3] => {{1},{2,4},{3}} => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3

[1,4,3,2] => {{1},{2,4},{3}} => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 3

[2,1,3,4] => {{1,2},{3},{4}} => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3

[2,1,4,3] => {{1,2},{3,4}} => [2,2] => ([(1,3),(2,3)],4) => 2

[2,3,1,4] => {{1,2,3},{4}} => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2

[2,3,4,1] => {{1,2,3,4}} => [4] => ([],4) => 1

[2,4,1,3] => {{1,2,4},{3}} => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2

[2,4,3,1] => {{1,2,4},{3}} => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2

[3,1,2,4] => {{1,3},{2},{4}} => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3

[3,1,4,2] => {{1,3,4},{2}} => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2

[3,2,1,4] => {{1,3},{2},{4}} => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3

[3,2,4,1] => {{1,3,4},{2}} => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2

[3,4,1,2] => {{1,3},{2,4}} => [2,2] => ([(1,3),(2,3)],4) => 2

[3,4,2,1] => {{1,3},{2,4}} => [2,2] => ([(1,3),(2,3)],4) => 2

[4,1,2,3] => {{1,4},{2},{3}} => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3

[4,1,3,2] => {{1,4},{2},{3}} => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3

[4,2,1,3] => {{1,4},{2},{3}} => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3

[4,2,3,1] => {{1,4},{2},{3}} => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3

[4,3,1,2] => {{1,4},{2,3}} => [2,2] => ([(1,3),(2,3)],4) => 2

[4,3,2,1] => {{1,4},{2,3}} => [2,2] => ([(1,3),(2,3)],4) => 2

[1,2,3,4,5] => {{1},{2},{3},{4},{5}} => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[1,2,3,5,4] => {{1},{2},{3},{4,5}} => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[1,2,4,3,5] => {{1},{2},{3,4},{5}} => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[1,2,4,5,3] => {{1},{2},{3,4,5}} => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3

[1,2,5,3,4] => {{1},{2},{3,5},{4}} => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[1,2,5,4,3] => {{1},{2},{3,5},{4}} => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[1,3,2,4,5] => {{1},{2,3},{4},{5}} => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[1,3,2,5,4] => {{1},{2,3},{4,5}} => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3

[1,3,4,2,5] => {{1},{2,3,4},{5}} => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3

[1,3,4,5,2] => {{1},{2,3,4,5}} => [1,4] => ([(3,4)],5) => 2

[1,3,5,2,4] => {{1},{2,3,5},{4}} => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3

[1,3,5,4,2] => {{1},{2,3,5},{4}} => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3

[1,4,2,3,5] => {{1},{2,4},{3},{5}} => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[1,4,2,5,3] => {{1},{2,4,5},{3}} => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3

[1,4,3,2,5] => {{1},{2,4},{3},{5}} => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[1,4,3,5,2] => {{1},{2,4,5},{3}} => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3

[1,4,5,2,3] => {{1},{2,4},{3,5}} => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3

[1,4,5,3,2] => {{1},{2,4},{3,5}} => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3

[1,5,2,3,4] => {{1},{2,5},{3},{4}} => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[1,5,2,4,3] => {{1},{2,5},{3},{4}} => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[1,5,3,2,4] => {{1},{2,5},{3},{4}} => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[1,5,3,4,2] => {{1},{2,5},{3},{4}} => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[1,5,4,2,3] => {{1},{2,5},{3,4}} => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3

[1,5,4,3,2] => {{1},{2,5},{3,4}} => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 3

[2,1,3,4,5] => {{1,2},{3},{4},{5}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[2,1,3,5,4] => {{1,2},{3},{4,5}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[2,1,4,3,5] => {{1,2},{3,4},{5}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[2,1,4,5,3] => {{1,2},{3,4,5}} => [2,3] => ([(2,4),(3,4)],5) => 2

[2,1,5,3,4] => {{1,2},{3,5},{4}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[2,1,5,4,3] => {{1,2},{3,5},{4}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[2,3,1,4,5] => {{1,2,3},{4},{5}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[2,3,1,5,4] => {{1,2,3},{4,5}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

[2,3,4,1,5] => {{1,2,3,4},{5}} => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[2,3,4,5,1] => {{1,2,3,4,5}} => [5] => ([],5) => 1

[2,3,5,1,4] => {{1,2,3,5},{4}} => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[2,3,5,4,1] => {{1,2,3,5},{4}} => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[2,4,1,3,5] => {{1,2,4},{3},{5}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[2,4,1,5,3] => {{1,2,4,5},{3}} => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[2,4,3,1,5] => {{1,2,4},{3},{5}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[2,4,3,5,1] => {{1,2,4,5},{3}} => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[2,4,5,1,3] => {{1,2,4},{3,5}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

[2,4,5,3,1] => {{1,2,4},{3,5}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

[2,5,1,3,4] => {{1,2,5},{3},{4}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[2,5,1,4,3] => {{1,2,5},{3},{4}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[2,5,3,1,4] => {{1,2,5},{3},{4}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[2,5,3,4,1] => {{1,2,5},{3},{4}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[2,5,4,1,3] => {{1,2,5},{3,4}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

[2,5,4,3,1] => {{1,2,5},{3,4}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

[3,1,2,4,5] => {{1,3},{2},{4},{5}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[3,1,2,5,4] => {{1,3},{2},{4,5}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[3,1,4,2,5] => {{1,3,4},{2},{5}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[3,1,4,5,2] => {{1,3,4,5},{2}} => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[3,1,5,2,4] => {{1,3,5},{2},{4}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[3,1,5,4,2] => {{1,3,5},{2},{4}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[3,2,1,4,5] => {{1,3},{2},{4},{5}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[3,2,1,5,4] => {{1,3},{2},{4,5}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[3,2,4,1,5] => {{1,3,4},{2},{5}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[3,2,4,5,1] => {{1,3,4,5},{2}} => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[3,2,5,1,4] => {{1,3,5},{2},{4}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[3,2,5,4,1] => {{1,3,5},{2},{4}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[3,4,1,2,5] => {{1,3},{2,4},{5}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[3,4,1,5,2] => {{1,3},{2,4,5}} => [2,3] => ([(2,4),(3,4)],5) => 2

[3,4,2,1,5] => {{1,3},{2,4},{5}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[3,4,2,5,1] => {{1,3},{2,4,5}} => [2,3] => ([(2,4),(3,4)],5) => 2

[3,4,5,1,2] => {{1,3,5},{2,4}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

[3,4,5,2,1] => {{1,3,5},{2,4}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

[3,5,1,2,4] => {{1,3},{2,5},{4}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[3,5,1,4,2] => {{1,3},{2,5},{4}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

>>> Load all 10194 entries. <<<

[3,5,2,1,4] => {{1,3},{2,5},{4}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[3,5,2,4,1] => {{1,3},{2,5},{4}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[3,5,4,1,2] => {{1,3,4},{2,5}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

[3,5,4,2,1] => {{1,3,4},{2,5}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

[4,1,2,3,5] => {{1,4},{2},{3},{5}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[4,1,2,5,3] => {{1,4,5},{2},{3}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,1,3,2,5] => {{1,4},{2},{3},{5}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[4,1,3,5,2] => {{1,4,5},{2},{3}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,1,5,2,3] => {{1,4},{2},{3,5}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,1,5,3,2] => {{1,4},{2},{3,5}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,2,1,3,5] => {{1,4},{2},{3},{5}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[4,2,1,5,3] => {{1,4,5},{2},{3}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,2,3,1,5] => {{1,4},{2},{3},{5}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[4,2,3,5,1] => {{1,4,5},{2},{3}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,2,5,1,3] => {{1,4},{2},{3,5}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,2,5,3,1] => {{1,4},{2},{3,5}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,3,1,2,5] => {{1,4},{2,3},{5}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,3,1,5,2] => {{1,4,5},{2,3}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

[4,3,2,1,5] => {{1,4},{2,3},{5}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,3,2,5,1] => {{1,4,5},{2,3}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

[4,3,5,1,2] => {{1,4},{2,3,5}} => [2,3] => ([(2,4),(3,4)],5) => 2

[4,3,5,2,1] => {{1,4},{2,3,5}} => [2,3] => ([(2,4),(3,4)],5) => 2

[4,5,1,2,3] => {{1,4},{2,5},{3}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,5,1,3,2] => {{1,4},{2,5},{3}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,5,2,1,3] => {{1,4},{2,5},{3}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,5,2,3,1] => {{1,4},{2,5},{3}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,5,3,1,2] => {{1,4},{2,5},{3}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[4,5,3,2,1] => {{1,4},{2,5},{3}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,1,2,3,4] => {{1,5},{2},{3},{4}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[5,1,2,4,3] => {{1,5},{2},{3},{4}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[5,1,3,2,4] => {{1,5},{2},{3},{4}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[5,1,3,4,2] => {{1,5},{2},{3},{4}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[5,1,4,2,3] => {{1,5},{2},{3,4}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,1,4,3,2] => {{1,5},{2},{3,4}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,2,1,3,4] => {{1,5},{2},{3},{4}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[5,2,1,4,3] => {{1,5},{2},{3},{4}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[5,2,3,1,4] => {{1,5},{2},{3},{4}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[5,2,3,4,1] => {{1,5},{2},{3},{4}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

[5,2,4,1,3] => {{1,5},{2},{3,4}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,2,4,3,1] => {{1,5},{2},{3,4}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,3,1,2,4] => {{1,5},{2,3},{4}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,3,1,4,2] => {{1,5},{2,3},{4}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,3,2,1,4] => {{1,5},{2,3},{4}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,3,2,4,1] => {{1,5},{2,3},{4}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,3,4,1,2] => {{1,5},{2,3,4}} => [2,3] => ([(2,4),(3,4)],5) => 2

[5,3,4,2,1] => {{1,5},{2,3,4}} => [2,3] => ([(2,4),(3,4)],5) => 2

[5,4,1,2,3] => {{1,5},{2,4},{3}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,4,1,3,2] => {{1,5},{2,4},{3}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,4,2,1,3] => {{1,5},{2,4},{3}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,4,2,3,1] => {{1,5},{2,4},{3}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,4,3,1,2] => {{1,5},{2,4},{3}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[5,4,3,2,1] => {{1,5},{2,4},{3}} => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

[1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6

[1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}} => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}} => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}} => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,2,3,6,4,5] => {{1},{2},{3},{4,6},{5}} => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,2,3,6,5,4] => {{1},{2},{3},{4,6},{5}} => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}} => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}} => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}} => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,2,4,5,6,3] => {{1},{2},{3,4,5,6}} => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3

[1,2,4,6,3,5] => {{1},{2},{3,4,6},{5}} => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,2,4,6,5,3] => {{1},{2},{3,4,6},{5}} => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,2,5,3,4,6] => {{1},{2},{3,5},{4},{6}} => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,2,5,3,6,4] => {{1},{2},{3,5,6},{4}} => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,2,5,4,3,6] => {{1},{2},{3,5},{4},{6}} => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,2,5,4,6,3] => {{1},{2},{3,5,6},{4}} => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,2,5,6,3,4] => {{1},{2},{3,5},{4,6}} => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,2,5,6,4,3] => {{1},{2},{3,5},{4,6}} => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,2,6,3,4,5] => {{1},{2},{3,6},{4},{5}} => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,2,6,3,5,4] => {{1},{2},{3,6},{4},{5}} => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,2,6,4,3,5] => {{1},{2},{3,6},{4},{5}} => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,2,6,4,5,3] => {{1},{2},{3,6},{4},{5}} => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,2,6,5,3,4] => {{1},{2},{3,6},{4,5}} => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,2,6,5,4,3] => {{1},{2},{3,6},{4,5}} => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}} => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,3,2,5,6,4] => {{1},{2,3},{4,5,6}} => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,3,2,6,4,5] => {{1},{2,3},{4,6},{5}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,3,2,6,5,4] => {{1},{2,3},{4,6},{5}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,3,4,2,6,5] => {{1},{2,3,4},{5,6}} => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,3,4,5,2,6] => {{1},{2,3,4,5},{6}} => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,3,4,5,6,2] => {{1},{2,3,4,5,6}} => [1,5] => ([(4,5)],6) => 2

[1,3,4,6,2,5] => {{1},{2,3,4,6},{5}} => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,3,4,6,5,2] => {{1},{2,3,4,6},{5}} => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,3,5,2,4,6] => {{1},{2,3,5},{4},{6}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,3,5,2,6,4] => {{1},{2,3,5,6},{4}} => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,3,5,4,2,6] => {{1},{2,3,5},{4},{6}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,3,5,4,6,2] => {{1},{2,3,5,6},{4}} => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,3,5,6,2,4] => {{1},{2,3,5},{4,6}} => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,3,5,6,4,2] => {{1},{2,3,5},{4,6}} => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,3,6,2,4,5] => {{1},{2,3,6},{4},{5}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,3,6,2,5,4] => {{1},{2,3,6},{4},{5}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,3,6,4,2,5] => {{1},{2,3,6},{4},{5}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,3,6,4,5,2] => {{1},{2,3,6},{4},{5}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,3,6,5,2,4] => {{1},{2,3,6},{4,5}} => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,3,6,5,4,2] => {{1},{2,3,6},{4,5}} => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,4,2,3,5,6] => {{1},{2,4},{3},{5},{6}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,4,2,3,6,5] => {{1},{2,4},{3},{5,6}} => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,2,5,3,6] => {{1},{2,4,5},{3},{6}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,2,5,6,3] => {{1},{2,4,5,6},{3}} => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,4,2,6,3,5] => {{1},{2,4,6},{3},{5}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,2,6,5,3] => {{1},{2,4,6},{3},{5}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,3,2,5,6] => {{1},{2,4},{3},{5},{6}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,4,3,2,6,5] => {{1},{2,4},{3},{5,6}} => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,3,5,2,6] => {{1},{2,4,5},{3},{6}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,3,5,6,2] => {{1},{2,4,5,6},{3}} => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,4,3,6,2,5] => {{1},{2,4,6},{3},{5}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,3,6,5,2] => {{1},{2,4,6},{3},{5}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,5,2,3,6] => {{1},{2,4},{3,5},{6}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,5,2,6,3] => {{1},{2,4},{3,5,6}} => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,4,5,3,2,6] => {{1},{2,4},{3,5},{6}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,5,3,6,2] => {{1},{2,4},{3,5,6}} => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,4,5,6,2,3] => {{1},{2,4,6},{3,5}} => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,4,5,6,3,2] => {{1},{2,4,6},{3,5}} => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,4,6,2,3,5] => {{1},{2,4},{3,6},{5}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,6,2,5,3] => {{1},{2,4},{3,6},{5}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,6,3,2,5] => {{1},{2,4},{3,6},{5}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,6,3,5,2] => {{1},{2,4},{3,6},{5}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,4,6,5,2,3] => {{1},{2,4,5},{3,6}} => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,4,6,5,3,2] => {{1},{2,4,5},{3,6}} => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,5,2,3,4,6] => {{1},{2,5},{3},{4},{6}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,5,2,3,6,4] => {{1},{2,5,6},{3},{4}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,2,4,3,6] => {{1},{2,5},{3},{4},{6}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,5,2,4,6,3] => {{1},{2,5,6},{3},{4}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,2,6,3,4] => {{1},{2,5},{3},{4,6}} => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,2,6,4,3] => {{1},{2,5},{3},{4,6}} => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,3,2,4,6] => {{1},{2,5},{3},{4},{6}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,5,3,2,6,4] => {{1},{2,5,6},{3},{4}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,3,4,2,6] => {{1},{2,5},{3},{4},{6}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,5,3,4,6,2] => {{1},{2,5,6},{3},{4}} => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,3,6,2,4] => {{1},{2,5},{3},{4,6}} => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,3,6,4,2] => {{1},{2,5},{3},{4,6}} => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,4,2,3,6] => {{1},{2,5},{3,4},{6}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,4,2,6,3] => {{1},{2,5,6},{3,4}} => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,5,4,3,2,6] => {{1},{2,5},{3,4},{6}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,4,3,6,2] => {{1},{2,5,6},{3,4}} => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,5,4,6,2,3] => {{1},{2,5},{3,4,6}} => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,5,4,6,3,2] => {{1},{2,5},{3,4,6}} => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,5,6,2,3,4] => {{1},{2,5},{3,6},{4}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,6,2,4,3] => {{1},{2,5},{3,6},{4}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,6,3,2,4] => {{1},{2,5},{3,6},{4}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,6,3,4,2] => {{1},{2,5},{3,6},{4}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,6,4,2,3] => {{1},{2,5},{3,6},{4}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,5,6,4,3,2] => {{1},{2,5},{3,6},{4}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,2,3,4,5] => {{1},{2,6},{3},{4},{5}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,6,2,3,5,4] => {{1},{2,6},{3},{4},{5}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,6,2,4,3,5] => {{1},{2,6},{3},{4},{5}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,6,2,4,5,3] => {{1},{2,6},{3},{4},{5}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,6,2,5,3,4] => {{1},{2,6},{3},{4,5}} => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,2,5,4,3] => {{1},{2,6},{3},{4,5}} => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,3,2,4,5] => {{1},{2,6},{3},{4},{5}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,6,3,2,5,4] => {{1},{2,6},{3},{4},{5}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,6,3,4,2,5] => {{1},{2,6},{3},{4},{5}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,6,3,4,5,2] => {{1},{2,6},{3},{4},{5}} => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[1,6,3,5,2,4] => {{1},{2,6},{3},{4,5}} => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,3,5,4,2] => {{1},{2,6},{3},{4,5}} => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,4,2,3,5] => {{1},{2,6},{3,4},{5}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,4,2,5,3] => {{1},{2,6},{3,4},{5}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,4,3,2,5] => {{1},{2,6},{3,4},{5}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,4,3,5,2] => {{1},{2,6},{3,4},{5}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,4,5,2,3] => {{1},{2,6},{3,4,5}} => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,6,4,5,3,2] => {{1},{2,6},{3,4,5}} => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,6,5,2,3,4] => {{1},{2,6},{3,5},{4}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,5,2,4,3] => {{1},{2,6},{3,5},{4}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,5,3,2,4] => {{1},{2,6},{3,5},{4}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,5,3,4,2] => {{1},{2,6},{3,5},{4}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,5,4,2,3] => {{1},{2,6},{3,5},{4}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[1,6,5,4,3,2] => {{1},{2,6},{3,5},{4}} => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,1,3,5,6,4] => {{1,2},{3},{4,5,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,1,3,6,4,5] => {{1,2},{3},{4,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,1,3,6,5,4] => {{1,2},{3},{4,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,1,4,3,6,5] => {{1,2},{3,4},{5,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,1,4,5,3,6] => {{1,2},{3,4,5},{6}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,1,4,5,6,3] => {{1,2},{3,4,5,6}} => [2,4] => ([(3,5),(4,5)],6) => 2

[2,1,4,6,3,5] => {{1,2},{3,4,6},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,1,4,6,5,3] => {{1,2},{3,4,6},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,1,5,3,4,6] => {{1,2},{3,5},{4},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,1,5,3,6,4] => {{1,2},{3,5,6},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,1,5,4,3,6] => {{1,2},{3,5},{4},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,1,5,4,6,3] => {{1,2},{3,5,6},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,1,5,6,3,4] => {{1,2},{3,5},{4,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,1,5,6,4,3] => {{1,2},{3,5},{4,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,1,6,3,4,5] => {{1,2},{3,6},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,1,6,3,5,4] => {{1,2},{3,6},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,1,6,4,3,5] => {{1,2},{3,6},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,1,6,4,5,3] => {{1,2},{3,6},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,1,6,5,3,4] => {{1,2},{3,6},{4,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,1,6,5,4,3] => {{1,2},{3,6},{4,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,3,1,4,6,5] => {{1,2,3},{4},{5,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,3,1,5,4,6] => {{1,2,3},{4,5},{6}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,3,1,5,6,4] => {{1,2,3},{4,5,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[2,3,1,6,4,5] => {{1,2,3},{4,6},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,3,1,6,5,4] => {{1,2,3},{4,6},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,3,4,1,6,5] => {{1,2,3,4},{5,6}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,3,4,5,6,1] => {{1,2,3,4,5,6}} => [6] => ([],6) => 1

[2,3,4,6,1,5] => {{1,2,3,4,6},{5}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,3,4,6,5,1] => {{1,2,3,4,6},{5}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,3,5,1,4,6] => {{1,2,3,5},{4},{6}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,3,5,1,6,4] => {{1,2,3,5,6},{4}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,3,5,4,1,6] => {{1,2,3,5},{4},{6}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,3,5,4,6,1] => {{1,2,3,5,6},{4}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,3,5,6,1,4] => {{1,2,3,5},{4,6}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,3,5,6,4,1] => {{1,2,3,5},{4,6}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,3,6,1,4,5] => {{1,2,3,6},{4},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,3,6,1,5,4] => {{1,2,3,6},{4},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,3,6,4,1,5] => {{1,2,3,6},{4},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,3,6,4,5,1] => {{1,2,3,6},{4},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,3,6,5,1,4] => {{1,2,3,6},{4,5}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,3,6,5,4,1] => {{1,2,3,6},{4,5}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,4,1,3,5,6] => {{1,2,4},{3},{5},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,4,1,3,6,5] => {{1,2,4},{3},{5,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,1,5,3,6] => {{1,2,4,5},{3},{6}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,1,5,6,3] => {{1,2,4,5,6},{3}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,4,1,6,3,5] => {{1,2,4,6},{3},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,1,6,5,3] => {{1,2,4,6},{3},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,3,1,5,6] => {{1,2,4},{3},{5},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,4,3,1,6,5] => {{1,2,4},{3},{5,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,3,5,1,6] => {{1,2,4,5},{3},{6}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,3,5,6,1] => {{1,2,4,5,6},{3}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,4,3,6,1,5] => {{1,2,4,6},{3},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,3,6,5,1] => {{1,2,4,6},{3},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,5,1,3,6] => {{1,2,4},{3,5},{6}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,5,1,6,3] => {{1,2,4},{3,5,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[2,4,5,3,1,6] => {{1,2,4},{3,5},{6}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,5,3,6,1] => {{1,2,4},{3,5,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[2,4,5,6,1,3] => {{1,2,4,6},{3,5}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,4,5,6,3,1] => {{1,2,4,6},{3,5}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,4,6,1,3,5] => {{1,2,4},{3,6},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,6,1,5,3] => {{1,2,4},{3,6},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,6,3,1,5] => {{1,2,4},{3,6},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,6,3,5,1] => {{1,2,4},{3,6},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,4,6,5,1,3] => {{1,2,4,5},{3,6}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,4,6,5,3,1] => {{1,2,4,5},{3,6}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,5,1,3,4,6] => {{1,2,5},{3},{4},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,5,1,3,6,4] => {{1,2,5,6},{3},{4}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,1,4,3,6] => {{1,2,5},{3},{4},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,5,1,4,6,3] => {{1,2,5,6},{3},{4}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,1,6,3,4] => {{1,2,5},{3},{4,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,1,6,4,3] => {{1,2,5},{3},{4,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,3,1,4,6] => {{1,2,5},{3},{4},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,5,3,1,6,4] => {{1,2,5,6},{3},{4}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,3,4,1,6] => {{1,2,5},{3},{4},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,5,3,4,6,1] => {{1,2,5,6},{3},{4}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,3,6,1,4] => {{1,2,5},{3},{4,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,3,6,4,1] => {{1,2,5},{3},{4,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,4,1,3,6] => {{1,2,5},{3,4},{6}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,4,1,6,3] => {{1,2,5,6},{3,4}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,5,4,3,1,6] => {{1,2,5},{3,4},{6}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,4,3,6,1] => {{1,2,5,6},{3,4}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[2,5,4,6,1,3] => {{1,2,5},{3,4,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[2,5,4,6,3,1] => {{1,2,5},{3,4,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[2,5,6,1,3,4] => {{1,2,5},{3,6},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,6,1,4,3] => {{1,2,5},{3,6},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,6,3,1,4] => {{1,2,5},{3,6},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,6,3,4,1] => {{1,2,5},{3,6},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,6,4,1,3] => {{1,2,5},{3,6},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,5,6,4,3,1] => {{1,2,5},{3,6},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,1,3,4,5] => {{1,2,6},{3},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,6,1,3,5,4] => {{1,2,6},{3},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,6,1,4,3,5] => {{1,2,6},{3},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,6,1,4,5,3] => {{1,2,6},{3},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,6,1,5,3,4] => {{1,2,6},{3},{4,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,1,5,4,3] => {{1,2,6},{3},{4,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,3,1,4,5] => {{1,2,6},{3},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,6,3,1,5,4] => {{1,2,6},{3},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,6,3,4,1,5] => {{1,2,6},{3},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,6,3,4,5,1] => {{1,2,6},{3},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[2,6,3,5,1,4] => {{1,2,6},{3},{4,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,3,5,4,1] => {{1,2,6},{3},{4,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,4,1,3,5] => {{1,2,6},{3,4},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,4,1,5,3] => {{1,2,6},{3,4},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,4,3,1,5] => {{1,2,6},{3,4},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,4,3,5,1] => {{1,2,6},{3,4},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,4,5,1,3] => {{1,2,6},{3,4,5}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[2,6,4,5,3,1] => {{1,2,6},{3,4,5}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[2,6,5,1,3,4] => {{1,2,6},{3,5},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,5,1,4,3] => {{1,2,6},{3,5},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,5,3,1,4] => {{1,2,6},{3,5},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,5,3,4,1] => {{1,2,6},{3,5},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,5,4,1,3] => {{1,2,6},{3,5},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[2,6,5,4,3,1] => {{1,2,6},{3,5},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,1,2,4,5,6] => {{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[3,1,2,4,6,5] => {{1,3},{2},{4},{5,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,1,2,5,4,6] => {{1,3},{2},{4,5},{6}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,1,2,5,6,4] => {{1,3},{2},{4,5,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,1,2,6,4,5] => {{1,3},{2},{4,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,1,2,6,5,4] => {{1,3},{2},{4,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,1,4,2,5,6] => {{1,3,4},{2},{5},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,1,4,2,6,5] => {{1,3,4},{2},{5,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,1,4,5,2,6] => {{1,3,4,5},{2},{6}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,1,4,5,6,2] => {{1,3,4,5,6},{2}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[3,1,4,6,2,5] => {{1,3,4,6},{2},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,1,4,6,5,2] => {{1,3,4,6},{2},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,1,5,2,4,6] => {{1,3,5},{2},{4},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,1,5,2,6,4] => {{1,3,5,6},{2},{4}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,1,5,4,2,6] => {{1,3,5},{2},{4},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,1,5,4,6,2] => {{1,3,5,6},{2},{4}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,1,5,6,2,4] => {{1,3,5},{2},{4,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,1,5,6,4,2] => {{1,3,5},{2},{4,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,1,6,2,4,5] => {{1,3,6},{2},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,1,6,2,5,4] => {{1,3,6},{2},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,1,6,4,2,5] => {{1,3,6},{2},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,1,6,4,5,2] => {{1,3,6},{2},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,1,6,5,2,4] => {{1,3,6},{2},{4,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,1,6,5,4,2] => {{1,3,6},{2},{4,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,2,1,4,5,6] => {{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[3,2,1,4,6,5] => {{1,3},{2},{4},{5,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,2,1,5,4,6] => {{1,3},{2},{4,5},{6}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,2,1,5,6,4] => {{1,3},{2},{4,5,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,2,1,6,4,5] => {{1,3},{2},{4,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,2,1,6,5,4] => {{1,3},{2},{4,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,2,4,1,5,6] => {{1,3,4},{2},{5},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,2,4,1,6,5] => {{1,3,4},{2},{5,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,2,4,5,1,6] => {{1,3,4,5},{2},{6}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,2,4,5,6,1] => {{1,3,4,5,6},{2}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[3,2,4,6,1,5] => {{1,3,4,6},{2},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,2,4,6,5,1] => {{1,3,4,6},{2},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,2,5,1,4,6] => {{1,3,5},{2},{4},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,2,5,1,6,4] => {{1,3,5,6},{2},{4}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,2,5,4,1,6] => {{1,3,5},{2},{4},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,2,5,4,6,1] => {{1,3,5,6},{2},{4}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,2,5,6,1,4] => {{1,3,5},{2},{4,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,2,5,6,4,1] => {{1,3,5},{2},{4,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,2,6,1,4,5] => {{1,3,6},{2},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,2,6,1,5,4] => {{1,3,6},{2},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,2,6,4,1,5] => {{1,3,6},{2},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,2,6,4,5,1] => {{1,3,6},{2},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,2,6,5,1,4] => {{1,3,6},{2},{4,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,2,6,5,4,1] => {{1,3,6},{2},{4,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,1,2,5,6] => {{1,3},{2,4},{5},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,4,1,2,6,5] => {{1,3},{2,4},{5,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,1,5,2,6] => {{1,3},{2,4,5},{6}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,1,5,6,2] => {{1,3},{2,4,5,6}} => [2,4] => ([(3,5),(4,5)],6) => 2

[3,4,1,6,2,5] => {{1,3},{2,4,6},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,1,6,5,2] => {{1,3},{2,4,6},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,2,1,5,6] => {{1,3},{2,4},{5},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,4,2,1,6,5] => {{1,3},{2,4},{5,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,2,5,1,6] => {{1,3},{2,4,5},{6}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,2,5,6,1] => {{1,3},{2,4,5,6}} => [2,4] => ([(3,5),(4,5)],6) => 2

[3,4,2,6,1,5] => {{1,3},{2,4,6},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,2,6,5,1] => {{1,3},{2,4,6},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,5,1,2,6] => {{1,3,5},{2,4},{6}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,5,1,6,2] => {{1,3,5,6},{2,4}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[3,4,5,2,1,6] => {{1,3,5},{2,4},{6}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,5,2,6,1] => {{1,3,5,6},{2,4}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[3,4,5,6,1,2] => {{1,3,5},{2,4,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[3,4,5,6,2,1] => {{1,3,5},{2,4,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[3,4,6,1,2,5] => {{1,3,6},{2,4},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,6,1,5,2] => {{1,3,6},{2,4},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,6,2,1,5] => {{1,3,6},{2,4},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,6,2,5,1] => {{1,3,6},{2,4},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,4,6,5,1,2] => {{1,3,6},{2,4,5}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[3,4,6,5,2,1] => {{1,3,6},{2,4,5}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[3,5,1,2,4,6] => {{1,3},{2,5},{4},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,5,1,2,6,4] => {{1,3},{2,5,6},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,1,4,2,6] => {{1,3},{2,5},{4},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,5,1,4,6,2] => {{1,3},{2,5,6},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,1,6,2,4] => {{1,3},{2,5},{4,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,1,6,4,2] => {{1,3},{2,5},{4,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,2,1,4,6] => {{1,3},{2,5},{4},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,5,2,1,6,4] => {{1,3},{2,5,6},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,2,4,1,6] => {{1,3},{2,5},{4},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,5,2,4,6,1] => {{1,3},{2,5,6},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,2,6,1,4] => {{1,3},{2,5},{4,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,2,6,4,1] => {{1,3},{2,5},{4,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,4,1,2,6] => {{1,3,4},{2,5},{6}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,4,1,6,2] => {{1,3,4},{2,5,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[3,5,4,2,1,6] => {{1,3,4},{2,5},{6}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,4,2,6,1] => {{1,3,4},{2,5,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[3,5,4,6,1,2] => {{1,3,4,6},{2,5}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[3,5,4,6,2,1] => {{1,3,4,6},{2,5}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[3,5,6,1,2,4] => {{1,3,6},{2,5},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,6,1,4,2] => {{1,3,6},{2,5},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,6,2,1,4] => {{1,3,6},{2,5},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,6,2,4,1] => {{1,3,6},{2,5},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,6,4,1,2] => {{1,3,6},{2,5},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,5,6,4,2,1] => {{1,3,6},{2,5},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,1,2,4,5] => {{1,3},{2,6},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,6,1,2,5,4] => {{1,3},{2,6},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,6,1,4,2,5] => {{1,3},{2,6},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,6,1,4,5,2] => {{1,3},{2,6},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,6,1,5,2,4] => {{1,3},{2,6},{4,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,1,5,4,2] => {{1,3},{2,6},{4,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,2,1,4,5] => {{1,3},{2,6},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,6,2,1,5,4] => {{1,3},{2,6},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,6,2,4,1,5] => {{1,3},{2,6},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,6,2,4,5,1] => {{1,3},{2,6},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[3,6,2,5,1,4] => {{1,3},{2,6},{4,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,2,5,4,1] => {{1,3},{2,6},{4,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,4,1,2,5] => {{1,3,4},{2,6},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,4,1,5,2] => {{1,3,4},{2,6},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,4,2,1,5] => {{1,3,4},{2,6},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,4,2,5,1] => {{1,3,4},{2,6},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,4,5,1,2] => {{1,3,4,5},{2,6}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[3,6,4,5,2,1] => {{1,3,4,5},{2,6}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[3,6,5,1,2,4] => {{1,3,5},{2,6},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,5,1,4,2] => {{1,3,5},{2,6},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,5,2,1,4] => {{1,3,5},{2,6},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,5,2,4,1] => {{1,3,5},{2,6},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,5,4,1,2] => {{1,3,5},{2,6},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[3,6,5,4,2,1] => {{1,3,5},{2,6},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,1,2,3,5,6] => {{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[4,1,2,3,6,5] => {{1,4},{2},{3},{5,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,2,5,3,6] => {{1,4,5},{2},{3},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,2,5,6,3] => {{1,4,5,6},{2},{3}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,1,2,6,3,5] => {{1,4,6},{2},{3},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,2,6,5,3] => {{1,4,6},{2},{3},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,3,2,5,6] => {{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[4,1,3,2,6,5] => {{1,4},{2},{3},{5,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,3,5,2,6] => {{1,4,5},{2},{3},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,3,5,6,2] => {{1,4,5,6},{2},{3}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,1,3,6,2,5] => {{1,4,6},{2},{3},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,3,6,5,2] => {{1,4,6},{2},{3},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,5,2,3,6] => {{1,4},{2},{3,5},{6}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,5,2,6,3] => {{1,4},{2},{3,5,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,1,5,3,2,6] => {{1,4},{2},{3,5},{6}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,5,3,6,2] => {{1,4},{2},{3,5,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,1,5,6,2,3] => {{1,4,6},{2},{3,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,1,5,6,3,2] => {{1,4,6},{2},{3,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,1,6,2,3,5] => {{1,4},{2},{3,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,6,2,5,3] => {{1,4},{2},{3,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,6,3,2,5] => {{1,4},{2},{3,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,6,3,5,2] => {{1,4},{2},{3,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,1,6,5,2,3] => {{1,4,5},{2},{3,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,1,6,5,3,2] => {{1,4,5},{2},{3,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,2,1,3,5,6] => {{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[4,2,1,3,6,5] => {{1,4},{2},{3},{5,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,1,5,3,6] => {{1,4,5},{2},{3},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,1,5,6,3] => {{1,4,5,6},{2},{3}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,2,1,6,3,5] => {{1,4,6},{2},{3},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,1,6,5,3] => {{1,4,6},{2},{3},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,3,1,5,6] => {{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[4,2,3,1,6,5] => {{1,4},{2},{3},{5,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,3,5,1,6] => {{1,4,5},{2},{3},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,3,5,6,1] => {{1,4,5,6},{2},{3}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,2,3,6,1,5] => {{1,4,6},{2},{3},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,3,6,5,1] => {{1,4,6},{2},{3},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,5,1,3,6] => {{1,4},{2},{3,5},{6}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,5,1,6,3] => {{1,4},{2},{3,5,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,2,5,3,1,6] => {{1,4},{2},{3,5},{6}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,5,3,6,1] => {{1,4},{2},{3,5,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,2,5,6,1,3] => {{1,4,6},{2},{3,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,2,5,6,3,1] => {{1,4,6},{2},{3,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,2,6,1,3,5] => {{1,4},{2},{3,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,6,1,5,3] => {{1,4},{2},{3,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,6,3,1,5] => {{1,4},{2},{3,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,6,3,5,1] => {{1,4},{2},{3,6},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,2,6,5,1,3] => {{1,4,5},{2},{3,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,2,6,5,3,1] => {{1,4,5},{2},{3,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,1,2,5,6] => {{1,4},{2,3},{5},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,3,1,2,6,5] => {{1,4},{2,3},{5,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,1,5,2,6] => {{1,4,5},{2,3},{6}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,1,5,6,2] => {{1,4,5,6},{2,3}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[4,3,1,6,2,5] => {{1,4,6},{2,3},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,1,6,5,2] => {{1,4,6},{2,3},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,2,1,5,6] => {{1,4},{2,3},{5},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,3,2,1,6,5] => {{1,4},{2,3},{5,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,2,5,1,6] => {{1,4,5},{2,3},{6}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,2,5,6,1] => {{1,4,5,6},{2,3}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

[4,3,2,6,1,5] => {{1,4,6},{2,3},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,2,6,5,1] => {{1,4,6},{2,3},{5}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,5,1,2,6] => {{1,4},{2,3,5},{6}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,5,1,6,2] => {{1,4},{2,3,5,6}} => [2,4] => ([(3,5),(4,5)],6) => 2

[4,3,5,2,1,6] => {{1,4},{2,3,5},{6}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,5,2,6,1] => {{1,4},{2,3,5,6}} => [2,4] => ([(3,5),(4,5)],6) => 2

[4,3,5,6,1,2] => {{1,4,6},{2,3,5}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[4,3,5,6,2,1] => {{1,4,6},{2,3,5}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[4,3,6,1,2,5] => {{1,4},{2,3,6},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,6,1,5,2] => {{1,4},{2,3,6},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,6,2,1,5] => {{1,4},{2,3,6},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,6,2,5,1] => {{1,4},{2,3,6},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,3,6,5,1,2] => {{1,4,5},{2,3,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[4,3,6,5,2,1] => {{1,4,5},{2,3,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[4,5,1,2,3,6] => {{1,4},{2,5},{3},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,5,1,2,6,3] => {{1,4},{2,5,6},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,1,3,2,6] => {{1,4},{2,5},{3},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,5,1,3,6,2] => {{1,4},{2,5,6},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,1,6,2,3] => {{1,4,6},{2,5},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,1,6,3,2] => {{1,4,6},{2,5},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,2,1,3,6] => {{1,4},{2,5},{3},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,5,2,1,6,3] => {{1,4},{2,5,6},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,2,3,1,6] => {{1,4},{2,5},{3},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,5,2,3,6,1] => {{1,4},{2,5,6},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,2,6,1,3] => {{1,4,6},{2,5},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,2,6,3,1] => {{1,4,6},{2,5},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,3,1,2,6] => {{1,4},{2,5},{3},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,5,3,1,6,2] => {{1,4},{2,5,6},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,3,2,1,6] => {{1,4},{2,5},{3},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,5,3,2,6,1] => {{1,4},{2,5,6},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,3,6,1,2] => {{1,4,6},{2,5},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,3,6,2,1] => {{1,4,6},{2,5},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,6,1,2,3] => {{1,4},{2,5},{3,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,6,1,3,2] => {{1,4},{2,5},{3,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,6,2,1,3] => {{1,4},{2,5},{3,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,6,2,3,1] => {{1,4},{2,5},{3,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,6,3,1,2] => {{1,4},{2,5},{3,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,5,6,3,2,1] => {{1,4},{2,5},{3,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,6,1,2,3,5] => {{1,4},{2,6},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,6,1,2,5,3] => {{1,4},{2,6},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,6,1,3,2,5] => {{1,4},{2,6},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,6,1,3,5,2] => {{1,4},{2,6},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,6,1,5,2,3] => {{1,4,5},{2,6},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,6,1,5,3,2] => {{1,4,5},{2,6},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,6,2,1,3,5] => {{1,4},{2,6},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,6,2,1,5,3] => {{1,4},{2,6},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,6,2,3,1,5] => {{1,4},{2,6},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,6,2,3,5,1] => {{1,4},{2,6},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,6,2,5,1,3] => {{1,4,5},{2,6},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,6,2,5,3,1] => {{1,4,5},{2,6},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,6,3,1,2,5] => {{1,4},{2,6},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,6,3,1,5,2] => {{1,4},{2,6},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,6,3,2,1,5] => {{1,4},{2,6},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,6,3,2,5,1] => {{1,4},{2,6},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[4,6,3,5,1,2] => {{1,4,5},{2,6},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,6,3,5,2,1] => {{1,4,5},{2,6},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,6,5,1,2,3] => {{1,4},{2,6},{3,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,6,5,1,3,2] => {{1,4},{2,6},{3,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,6,5,2,1,3] => {{1,4},{2,6},{3,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,6,5,2,3,1] => {{1,4},{2,6},{3,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,6,5,3,1,2] => {{1,4},{2,6},{3,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[4,6,5,3,2,1] => {{1,4},{2,6},{3,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,1,2,3,4,6] => {{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[5,1,2,3,6,4] => {{1,5,6},{2},{3},{4}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,2,4,3,6] => {{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[5,1,2,4,6,3] => {{1,5,6},{2},{3},{4}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,2,6,3,4] => {{1,5},{2},{3},{4,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,2,6,4,3] => {{1,5},{2},{3},{4,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,3,2,4,6] => {{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[5,1,3,2,6,4] => {{1,5,6},{2},{3},{4}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,3,4,2,6] => {{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[5,1,3,4,6,2] => {{1,5,6},{2},{3},{4}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,3,6,2,4] => {{1,5},{2},{3},{4,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,3,6,4,2] => {{1,5},{2},{3},{4,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,4,2,3,6] => {{1,5},{2},{3,4},{6}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,4,2,6,3] => {{1,5,6},{2},{3,4}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,1,4,3,2,6] => {{1,5},{2},{3,4},{6}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,4,3,6,2] => {{1,5,6},{2},{3,4}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,1,4,6,2,3] => {{1,5},{2},{3,4,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,1,4,6,3,2] => {{1,5},{2},{3,4,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,1,6,2,3,4] => {{1,5},{2},{3,6},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,6,2,4,3] => {{1,5},{2},{3,6},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,6,3,2,4] => {{1,5},{2},{3,6},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,6,3,4,2] => {{1,5},{2},{3,6},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,6,4,2,3] => {{1,5},{2},{3,6},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,1,6,4,3,2] => {{1,5},{2},{3,6},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,1,3,4,6] => {{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[5,2,1,3,6,4] => {{1,5,6},{2},{3},{4}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,1,4,3,6] => {{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[5,2,1,4,6,3] => {{1,5,6},{2},{3},{4}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,1,6,3,4] => {{1,5},{2},{3},{4,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,1,6,4,3] => {{1,5},{2},{3},{4,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,3,1,4,6] => {{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[5,2,3,1,6,4] => {{1,5,6},{2},{3},{4}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,3,4,1,6] => {{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[5,2,3,4,6,1] => {{1,5,6},{2},{3},{4}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,3,6,1,4] => {{1,5},{2},{3},{4,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,3,6,4,1] => {{1,5},{2},{3},{4,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,4,1,3,6] => {{1,5},{2},{3,4},{6}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,4,1,6,3] => {{1,5,6},{2},{3,4}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,2,4,3,1,6] => {{1,5},{2},{3,4},{6}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,4,3,6,1] => {{1,5,6},{2},{3,4}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,2,4,6,1,3] => {{1,5},{2},{3,4,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,2,4,6,3,1] => {{1,5},{2},{3,4,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,2,6,1,3,4] => {{1,5},{2},{3,6},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,6,1,4,3] => {{1,5},{2},{3,6},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,6,3,1,4] => {{1,5},{2},{3,6},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,6,3,4,1] => {{1,5},{2},{3,6},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,6,4,1,3] => {{1,5},{2},{3,6},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,2,6,4,3,1] => {{1,5},{2},{3,6},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,3,1,2,4,6] => {{1,5},{2,3},{4},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,3,1,2,6,4] => {{1,5,6},{2,3},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,1,4,2,6] => {{1,5},{2,3},{4},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,3,1,4,6,2] => {{1,5,6},{2,3},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,1,6,2,4] => {{1,5},{2,3},{4,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,1,6,4,2] => {{1,5},{2,3},{4,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,2,1,4,6] => {{1,5},{2,3},{4},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,3,2,1,6,4] => {{1,5,6},{2,3},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,2,4,1,6] => {{1,5},{2,3},{4},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,3,2,4,6,1] => {{1,5,6},{2,3},{4}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,2,6,1,4] => {{1,5},{2,3},{4,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,2,6,4,1] => {{1,5},{2,3},{4,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,4,1,2,6] => {{1,5},{2,3,4},{6}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,4,1,6,2] => {{1,5,6},{2,3,4}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[5,3,4,2,1,6] => {{1,5},{2,3,4},{6}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,4,2,6,1] => {{1,5,6},{2,3,4}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

[5,3,4,6,1,2] => {{1,5},{2,3,4,6}} => [2,4] => ([(3,5),(4,5)],6) => 2

[5,3,4,6,2,1] => {{1,5},{2,3,4,6}} => [2,4] => ([(3,5),(4,5)],6) => 2

[5,3,6,1,2,4] => {{1,5},{2,3,6},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,6,1,4,2] => {{1,5},{2,3,6},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,6,2,1,4] => {{1,5},{2,3,6},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,6,2,4,1] => {{1,5},{2,3,6},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,6,4,1,2] => {{1,5},{2,3,6},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,3,6,4,2,1] => {{1,5},{2,3,6},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,1,2,3,6] => {{1,5},{2,4},{3},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,4,1,2,6,3] => {{1,5,6},{2,4},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,1,3,2,6] => {{1,5},{2,4},{3},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,4,1,3,6,2] => {{1,5,6},{2,4},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,1,6,2,3] => {{1,5},{2,4,6},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,1,6,3,2] => {{1,5},{2,4,6},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,2,1,3,6] => {{1,5},{2,4},{3},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,4,2,1,6,3] => {{1,5,6},{2,4},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,2,3,1,6] => {{1,5},{2,4},{3},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,4,2,3,6,1] => {{1,5,6},{2,4},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,2,6,1,3] => {{1,5},{2,4,6},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,2,6,3,1] => {{1,5},{2,4,6},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,3,1,2,6] => {{1,5},{2,4},{3},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,4,3,1,6,2] => {{1,5,6},{2,4},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,3,2,1,6] => {{1,5},{2,4},{3},{6}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,4,3,2,6,1] => {{1,5,6},{2,4},{3}} => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,3,6,1,2] => {{1,5},{2,4,6},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,3,6,2,1] => {{1,5},{2,4,6},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,6,1,2,3] => {{1,5},{2,4},{3,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,6,1,3,2] => {{1,5},{2,4},{3,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,6,2,1,3] => {{1,5},{2,4},{3,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,6,2,3,1] => {{1,5},{2,4},{3,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,6,3,1,2] => {{1,5},{2,4},{3,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,4,6,3,2,1] => {{1,5},{2,4},{3,6}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,6,1,2,3,4] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,1,2,4,3] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,1,3,2,4] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,1,3,4,2] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,1,4,2,3] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,1,4,3,2] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,2,1,3,4] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,2,1,4,3] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,2,3,1,4] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,2,3,4,1] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,2,4,1,3] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,2,4,3,1] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,3,1,2,4] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,3,1,4,2] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,3,2,1,4] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,3,2,4,1] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,3,4,1,2] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,3,4,2,1] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[5,6,4,1,2,3] => {{1,5},{2,6},{3,4}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,6,4,1,3,2] => {{1,5},{2,6},{3,4}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,6,4,2,1,3] => {{1,5},{2,6},{3,4}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,6,4,2,3,1] => {{1,5},{2,6},{3,4}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,6,4,3,1,2] => {{1,5},{2,6},{3,4}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[5,6,4,3,2,1] => {{1,5},{2,6},{3,4}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,1,2,3,4,5] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,1,2,3,5,4] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,1,2,4,3,5] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,1,2,4,5,3] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,1,2,5,3,4] => {{1,6},{2},{3},{4,5}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,1,2,5,4,3] => {{1,6},{2},{3},{4,5}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,1,3,2,4,5] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,1,3,2,5,4] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,1,3,4,2,5] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,1,3,4,5,2] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,1,3,5,2,4] => {{1,6},{2},{3},{4,5}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,1,3,5,4,2] => {{1,6},{2},{3},{4,5}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,1,4,2,3,5] => {{1,6},{2},{3,4},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,1,4,2,5,3] => {{1,6},{2},{3,4},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,1,4,3,2,5] => {{1,6},{2},{3,4},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,1,4,3,5,2] => {{1,6},{2},{3,4},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,1,4,5,2,3] => {{1,6},{2},{3,4,5}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,1,4,5,3,2] => {{1,6},{2},{3,4,5}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,1,5,2,3,4] => {{1,6},{2},{3,5},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,1,5,2,4,3] => {{1,6},{2},{3,5},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,1,5,3,2,4] => {{1,6},{2},{3,5},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,1,5,3,4,2] => {{1,6},{2},{3,5},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,1,5,4,2,3] => {{1,6},{2},{3,5},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,1,5,4,3,2] => {{1,6},{2},{3,5},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,1,3,4,5] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,2,1,3,5,4] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,2,1,4,3,5] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,2,1,4,5,3] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,2,1,5,3,4] => {{1,6},{2},{3},{4,5}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,1,5,4,3] => {{1,6},{2},{3},{4,5}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,3,1,4,5] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,2,3,1,5,4] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,2,3,4,1,5] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,2,3,4,5,1] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

[6,2,3,5,1,4] => {{1,6},{2},{3},{4,5}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,3,5,4,1] => {{1,6},{2},{3},{4,5}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,4,1,3,5] => {{1,6},{2},{3,4},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,4,1,5,3] => {{1,6},{2},{3,4},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,4,3,1,5] => {{1,6},{2},{3,4},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,4,3,5,1] => {{1,6},{2},{3,4},{5}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,4,5,1,3] => {{1,6},{2},{3,4,5}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,2,4,5,3,1] => {{1,6},{2},{3,4,5}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,2,5,1,3,4] => {{1,6},{2},{3,5},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,5,1,4,3] => {{1,6},{2},{3,5},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,5,3,1,4] => {{1,6},{2},{3,5},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,5,3,4,1] => {{1,6},{2},{3,5},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,5,4,1,3] => {{1,6},{2},{3,5},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,2,5,4,3,1] => {{1,6},{2},{3,5},{4}} => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,3,1,2,4,5] => {{1,6},{2,3},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,3,1,2,5,4] => {{1,6},{2,3},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,3,1,4,2,5] => {{1,6},{2,3},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,3,1,4,5,2] => {{1,6},{2,3},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,3,1,5,2,4] => {{1,6},{2,3},{4,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,3,1,5,4,2] => {{1,6},{2,3},{4,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,3,2,1,4,5] => {{1,6},{2,3},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,3,2,1,5,4] => {{1,6},{2,3},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,3,2,4,1,5] => {{1,6},{2,3},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,3,2,4,5,1] => {{1,6},{2,3},{4},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,3,2,5,1,4] => {{1,6},{2,3},{4,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,3,2,5,4,1] => {{1,6},{2,3},{4,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,3,4,1,2,5] => {{1,6},{2,3,4},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,3,4,1,5,2] => {{1,6},{2,3,4},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,3,4,2,1,5] => {{1,6},{2,3,4},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,3,4,2,5,1] => {{1,6},{2,3,4},{5}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,3,4,5,1,2] => {{1,6},{2,3,4,5}} => [2,4] => ([(3,5),(4,5)],6) => 2

[6,3,4,5,2,1] => {{1,6},{2,3,4,5}} => [2,4] => ([(3,5),(4,5)],6) => 2

[6,3,5,1,2,4] => {{1,6},{2,3,5},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,3,5,1,4,2] => {{1,6},{2,3,5},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,3,5,2,1,4] => {{1,6},{2,3,5},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,3,5,2,4,1] => {{1,6},{2,3,5},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,3,5,4,1,2] => {{1,6},{2,3,5},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,3,5,4,2,1] => {{1,6},{2,3,5},{4}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,4,1,2,3,5] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,4,1,2,5,3] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,4,1,3,2,5] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,4,1,3,5,2] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,4,1,5,2,3] => {{1,6},{2,4,5},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,4,1,5,3,2] => {{1,6},{2,4,5},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,4,2,1,3,5] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,4,2,1,5,3] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,4,2,3,1,5] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,4,2,3,5,1] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,4,2,5,1,3] => {{1,6},{2,4,5},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,4,2,5,3,1] => {{1,6},{2,4,5},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,4,3,1,2,5] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,4,3,1,5,2] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,4,3,2,1,5] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,4,3,2,5,1] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,4,3,5,1,2] => {{1,6},{2,4,5},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,4,3,5,2,1] => {{1,6},{2,4,5},{3}} => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,4,5,1,2,3] => {{1,6},{2,4},{3,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,4,5,1,3,2] => {{1,6},{2,4},{3,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,4,5,2,1,3] => {{1,6},{2,4},{3,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,4,5,2,3,1] => {{1,6},{2,4},{3,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,4,5,3,1,2] => {{1,6},{2,4},{3,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,4,5,3,2,1] => {{1,6},{2,4},{3,5}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,5,1,2,3,4] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,1,2,4,3] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,1,3,2,4] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,1,3,4,2] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,1,4,2,3] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,1,4,3,2] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,2,1,3,4] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,2,1,4,3] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,2,3,1,4] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,2,3,4,1] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,2,4,1,3] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,2,4,3,1] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,3,1,2,4] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,3,1,4,2] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,3,2,1,4] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,3,2,4,1] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,3,4,1,2] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,3,4,2,1] => {{1,6},{2,5},{3},{4}} => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

[6,5,4,1,2,3] => {{1,6},{2,5},{3,4}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,5,4,1,3,2] => {{1,6},{2,5},{3,4}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,5,4,2,1,3] => {{1,6},{2,5},{3,4}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,5,4,2,3,1] => {{1,6},{2,5},{3,4}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,5,4,3,1,2] => {{1,6},{2,5},{3,4}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[6,5,4,3,2,1] => {{1,6},{2,5},{3,4}} => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

[1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7

[1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}} => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}} => [1,1,1,1,2,1] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,3,4,6,7,5] => {{1},{2},{3},{4},{5,6,7}} => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,3,4,7,5,6] => {{1},{2},{3},{4},{5,7},{6}} => [1,1,1,1,2,1] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,3,4,7,6,5] => {{1},{2},{3},{4},{5,7},{6}} => [1,1,1,1,2,1] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}} => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}} => [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,3,5,6,4,7] => {{1},{2},{3},{4,5,6},{7}} => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,3,5,6,7,4] => {{1},{2},{3},{4,5,6,7}} => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,3,5,7,4,6] => {{1},{2},{3},{4,5,7},{6}} => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,3,5,7,6,4] => {{1},{2},{3},{4,5,7},{6}} => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,3,6,4,5,7] => {{1},{2},{3},{4,6},{5},{7}} => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,3,6,4,7,5] => {{1},{2},{3},{4,6,7},{5}} => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,3,6,5,4,7] => {{1},{2},{3},{4,6},{5},{7}} => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,3,6,5,7,4] => {{1},{2},{3},{4,6,7},{5}} => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,3,6,7,4,5] => {{1},{2},{3},{4,6},{5,7}} => [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,3,6,7,5,4] => {{1},{2},{3},{4,6},{5,7}} => [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,3,7,4,5,6] => {{1},{2},{3},{4,7},{5},{6}} => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,3,7,4,6,5] => {{1},{2},{3},{4,7},{5},{6}} => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,3,7,5,4,6] => {{1},{2},{3},{4,7},{5},{6}} => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,3,7,5,6,4] => {{1},{2},{3},{4,7},{5},{6}} => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,3,7,6,4,5] => {{1},{2},{3},{4,7},{5,6}} => [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,3,7,6,5,4] => {{1},{2},{3},{4,7},{5,6}} => [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}} => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,4,3,6,7,5] => {{1},{2},{3,4},{5,6,7}} => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,7},{6}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,4,3,7,6,5] => {{1},{2},{3,4},{5,7},{6}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,4,5,3,6,7] => {{1},{2},{3,4,5},{6},{7}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,4,5,3,7,6] => {{1},{2},{3,4,5},{6,7}} => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,4,5,6,3,7] => {{1},{2},{3,4,5,6},{7}} => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,4,5,6,7,3] => {{1},{2},{3,4,5,6,7}} => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 3

[1,2,4,5,7,3,6] => {{1},{2},{3,4,5,7},{6}} => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,4,5,7,6,3] => {{1},{2},{3,4,5,7},{6}} => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,4,6,3,5,7] => {{1},{2},{3,4,6},{5},{7}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,4,6,3,7,5] => {{1},{2},{3,4,6,7},{5}} => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,4,6,5,3,7] => {{1},{2},{3,4,6},{5},{7}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,4,6,5,7,3] => {{1},{2},{3,4,6,7},{5}} => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,4,6,7,3,5] => {{1},{2},{3,4,6},{5,7}} => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,4,6,7,5,3] => {{1},{2},{3,4,6},{5,7}} => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,4,7,3,5,6] => {{1},{2},{3,4,7},{5},{6}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,4,7,3,6,5] => {{1},{2},{3,4,7},{5},{6}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,4,7,5,3,6] => {{1},{2},{3,4,7},{5},{6}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,4,7,5,6,3] => {{1},{2},{3,4,7},{5},{6}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,4,7,6,3,5] => {{1},{2},{3,4,7},{5,6}} => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,4,7,6,5,3] => {{1},{2},{3,4,7},{5,6}} => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,5,3,4,6,7] => {{1},{2},{3,5},{4},{6},{7}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,5,3,4,7,6] => {{1},{2},{3,5},{4},{6,7}} => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,3,6,4,7] => {{1},{2},{3,5,6},{4},{7}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,3,6,7,4] => {{1},{2},{3,5,6,7},{4}} => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,5,3,7,4,6] => {{1},{2},{3,5,7},{4},{6}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,3,7,6,4] => {{1},{2},{3,5,7},{4},{6}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,4,3,6,7] => {{1},{2},{3,5},{4},{6},{7}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,5,4,3,7,6] => {{1},{2},{3,5},{4},{6,7}} => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,4,6,3,7] => {{1},{2},{3,5,6},{4},{7}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,4,6,7,3] => {{1},{2},{3,5,6,7},{4}} => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,5,4,7,3,6] => {{1},{2},{3,5,7},{4},{6}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,4,7,6,3] => {{1},{2},{3,5,7},{4},{6}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,6,3,4,7] => {{1},{2},{3,5},{4,6},{7}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,6,3,7,4] => {{1},{2},{3,5},{4,6,7}} => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,5,6,4,3,7] => {{1},{2},{3,5},{4,6},{7}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,6,4,7,3] => {{1},{2},{3,5},{4,6,7}} => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,5,6,7,3,4] => {{1},{2},{3,5,7},{4,6}} => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,5,6,7,4,3] => {{1},{2},{3,5,7},{4,6}} => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,5,7,3,4,6] => {{1},{2},{3,5},{4,7},{6}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,7,3,6,4] => {{1},{2},{3,5},{4,7},{6}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,7,4,3,6] => {{1},{2},{3,5},{4,7},{6}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,7,4,6,3] => {{1},{2},{3,5},{4,7},{6}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,5,7,6,3,4] => {{1},{2},{3,5,6},{4,7}} => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,5,7,6,4,3] => {{1},{2},{3,5,6},{4,7}} => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,6,3,4,5,7] => {{1},{2},{3,6},{4},{5},{7}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,6,3,4,7,5] => {{1},{2},{3,6,7},{4},{5}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,3,5,4,7] => {{1},{2},{3,6},{4},{5},{7}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,6,3,5,7,4] => {{1},{2},{3,6,7},{4},{5}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,3,7,4,5] => {{1},{2},{3,6},{4},{5,7}} => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,3,7,5,4] => {{1},{2},{3,6},{4},{5,7}} => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,4,3,5,7] => {{1},{2},{3,6},{4},{5},{7}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,6,4,3,7,5] => {{1},{2},{3,6,7},{4},{5}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,4,5,3,7] => {{1},{2},{3,6},{4},{5},{7}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,6,4,5,7,3] => {{1},{2},{3,6,7},{4},{5}} => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,4,7,3,5] => {{1},{2},{3,6},{4},{5,7}} => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,4,7,5,3] => {{1},{2},{3,6},{4},{5,7}} => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,5,3,4,7] => {{1},{2},{3,6},{4,5},{7}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,5,3,7,4] => {{1},{2},{3,6,7},{4,5}} => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,6,5,4,3,7] => {{1},{2},{3,6},{4,5},{7}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,5,4,7,3] => {{1},{2},{3,6,7},{4,5}} => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,6,5,7,3,4] => {{1},{2},{3,6},{4,5,7}} => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,6,5,7,4,3] => {{1},{2},{3,6},{4,5,7}} => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,6,7,3,4,5] => {{1},{2},{3,6},{4,7},{5}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,7,3,5,4] => {{1},{2},{3,6},{4,7},{5}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,7,4,3,5] => {{1},{2},{3,6},{4,7},{5}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,7,4,5,3] => {{1},{2},{3,6},{4,7},{5}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,7,5,3,4] => {{1},{2},{3,6},{4,7},{5}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,6,7,5,4,3] => {{1},{2},{3,6},{4,7},{5}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,3,4,5,6] => {{1},{2},{3,7},{4},{5},{6}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,7,3,4,6,5] => {{1},{2},{3,7},{4},{5},{6}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,7,3,5,4,6] => {{1},{2},{3,7},{4},{5},{6}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,7,3,5,6,4] => {{1},{2},{3,7},{4},{5},{6}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,7,3,6,4,5] => {{1},{2},{3,7},{4},{5,6}} => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,3,6,5,4] => {{1},{2},{3,7},{4},{5,6}} => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,4,3,5,6] => {{1},{2},{3,7},{4},{5},{6}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,7,4,3,6,5] => {{1},{2},{3,7},{4},{5},{6}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,7,4,5,3,6] => {{1},{2},{3,7},{4},{5},{6}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,7,4,5,6,3] => {{1},{2},{3,7},{4},{5},{6}} => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,2,7,4,6,3,5] => {{1},{2},{3,7},{4},{5,6}} => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,4,6,5,3] => {{1},{2},{3,7},{4},{5,6}} => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,5,3,4,6] => {{1},{2},{3,7},{4,5},{6}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,5,3,6,4] => {{1},{2},{3,7},{4,5},{6}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,5,4,3,6] => {{1},{2},{3,7},{4,5},{6}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,5,4,6,3] => {{1},{2},{3,7},{4,5},{6}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,5,6,3,4] => {{1},{2},{3,7},{4,5,6}} => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,7,5,6,4,3] => {{1},{2},{3,7},{4,5,6}} => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,2,7,6,3,4,5] => {{1},{2},{3,7},{4,6},{5}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,6,3,5,4] => {{1},{2},{3,7},{4,6},{5}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,6,4,3,5] => {{1},{2},{3,7},{4,6},{5}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,6,4,5,3] => {{1},{2},{3,7},{4,6},{5}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,6,5,3,4] => {{1},{2},{3,7},{4,6},{5}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,2,7,6,5,4,3] => {{1},{2},{3,7},{4,6},{5}} => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,2,4,5,6,7] => {{1},{2,3},{4},{5},{6},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,2,4,6,7,5] => {{1},{2,3},{4},{5,6,7}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,2,4,7,6,5] => {{1},{2,3},{4},{5,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,2,5,6,4,7] => {{1},{2,3},{4,5,6},{7}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,2,5,6,7,4] => {{1},{2,3},{4,5,6,7}} => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,2,5,7,4,6] => {{1},{2,3},{4,5,7},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,2,5,7,6,4] => {{1},{2,3},{4,5,7},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,2,6,4,5,7] => {{1},{2,3},{4,6},{5},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,2,6,4,7,5] => {{1},{2,3},{4,6,7},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,2,6,5,4,7] => {{1},{2,3},{4,6},{5},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,2,6,5,7,4] => {{1},{2,3},{4,6,7},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,2,6,7,4,5] => {{1},{2,3},{4,6},{5,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,2,6,7,5,4] => {{1},{2,3},{4,6},{5,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,2,7,4,5,6] => {{1},{2,3},{4,7},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,2,7,4,6,5] => {{1},{2,3},{4,7},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,2,7,5,4,6] => {{1},{2,3},{4,7},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,2,7,5,6,4] => {{1},{2,3},{4,7},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,2,7,6,4,5] => {{1},{2,3},{4,7},{5,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,2,7,6,5,4] => {{1},{2,3},{4,7},{5,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,4,2,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,4,2,5,7,6] => {{1},{2,3,4},{5},{6,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,4,2,6,5,7] => {{1},{2,3,4},{5,6},{7}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,4,2,6,7,5] => {{1},{2,3,4},{5,6,7}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,4,2,7,5,6] => {{1},{2,3,4},{5,7},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,4,2,7,6,5] => {{1},{2,3,4},{5,7},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,4,5,2,6,7] => {{1},{2,3,4,5},{6},{7}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,4,5,2,7,6] => {{1},{2,3,4,5},{6,7}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,4,5,6,2,7] => {{1},{2,3,4,5,6},{7}} => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,4,5,6,7,2] => {{1},{2,3,4,5,6,7}} => [1,6] => ([(5,6)],7) => 2

[1,3,4,5,7,2,6] => {{1},{2,3,4,5,7},{6}} => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,4,5,7,6,2] => {{1},{2,3,4,5,7},{6}} => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,4,6,2,5,7] => {{1},{2,3,4,6},{5},{7}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,4,6,2,7,5] => {{1},{2,3,4,6,7},{5}} => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,4,6,5,2,7] => {{1},{2,3,4,6},{5},{7}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,4,6,5,7,2] => {{1},{2,3,4,6,7},{5}} => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,4,6,7,2,5] => {{1},{2,3,4,6},{5,7}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,4,6,7,5,2] => {{1},{2,3,4,6},{5,7}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,4,7,2,5,6] => {{1},{2,3,4,7},{5},{6}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,4,7,2,6,5] => {{1},{2,3,4,7},{5},{6}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,4,7,5,2,6] => {{1},{2,3,4,7},{5},{6}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,4,7,5,6,2] => {{1},{2,3,4,7},{5},{6}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,4,7,6,2,5] => {{1},{2,3,4,7},{5,6}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,4,7,6,5,2] => {{1},{2,3,4,7},{5,6}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,5,2,4,6,7] => {{1},{2,3,5},{4},{6},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,5,2,4,7,6] => {{1},{2,3,5},{4},{6,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,2,6,4,7] => {{1},{2,3,5,6},{4},{7}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,2,6,7,4] => {{1},{2,3,5,6,7},{4}} => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,5,2,7,4,6] => {{1},{2,3,5,7},{4},{6}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,2,7,6,4] => {{1},{2,3,5,7},{4},{6}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,4,2,6,7] => {{1},{2,3,5},{4},{6},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,5,4,2,7,6] => {{1},{2,3,5},{4},{6,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,4,6,2,7] => {{1},{2,3,5,6},{4},{7}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,4,6,7,2] => {{1},{2,3,5,6,7},{4}} => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,5,4,7,2,6] => {{1},{2,3,5,7},{4},{6}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,4,7,6,2] => {{1},{2,3,5,7},{4},{6}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,6,2,4,7] => {{1},{2,3,5},{4,6},{7}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,6,2,7,4] => {{1},{2,3,5},{4,6,7}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,5,6,4,2,7] => {{1},{2,3,5},{4,6},{7}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,6,4,7,2] => {{1},{2,3,5},{4,6,7}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,5,6,7,2,4] => {{1},{2,3,5,7},{4,6}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,5,6,7,4,2] => {{1},{2,3,5,7},{4,6}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,5,7,2,4,6] => {{1},{2,3,5},{4,7},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,7,2,6,4] => {{1},{2,3,5},{4,7},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,7,4,2,6] => {{1},{2,3,5},{4,7},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,7,4,6,2] => {{1},{2,3,5},{4,7},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,5,7,6,2,4] => {{1},{2,3,5,6},{4,7}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,5,7,6,4,2] => {{1},{2,3,5,6},{4,7}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,6,2,4,5,7] => {{1},{2,3,6},{4},{5},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,6,2,4,7,5] => {{1},{2,3,6,7},{4},{5}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,2,5,4,7] => {{1},{2,3,6},{4},{5},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,6,2,5,7,4] => {{1},{2,3,6,7},{4},{5}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,2,7,4,5] => {{1},{2,3,6},{4},{5,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,2,7,5,4] => {{1},{2,3,6},{4},{5,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,4,2,5,7] => {{1},{2,3,6},{4},{5},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,6,4,2,7,5] => {{1},{2,3,6,7},{4},{5}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,4,5,2,7] => {{1},{2,3,6},{4},{5},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,6,4,5,7,2] => {{1},{2,3,6,7},{4},{5}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,4,7,2,5] => {{1},{2,3,6},{4},{5,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,4,7,5,2] => {{1},{2,3,6},{4},{5,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,5,2,4,7] => {{1},{2,3,6},{4,5},{7}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,5,2,7,4] => {{1},{2,3,6,7},{4,5}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,6,5,4,2,7] => {{1},{2,3,6},{4,5},{7}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,5,4,7,2] => {{1},{2,3,6,7},{4,5}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,6,5,7,2,4] => {{1},{2,3,6},{4,5,7}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,6,5,7,4,2] => {{1},{2,3,6},{4,5,7}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,6,7,2,4,5] => {{1},{2,3,6},{4,7},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,7,2,5,4] => {{1},{2,3,6},{4,7},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,7,4,2,5] => {{1},{2,3,6},{4,7},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,7,4,5,2] => {{1},{2,3,6},{4,7},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,7,5,2,4] => {{1},{2,3,6},{4,7},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,6,7,5,4,2] => {{1},{2,3,6},{4,7},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,2,4,5,6] => {{1},{2,3,7},{4},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,7,2,4,6,5] => {{1},{2,3,7},{4},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,7,2,5,4,6] => {{1},{2,3,7},{4},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,7,2,5,6,4] => {{1},{2,3,7},{4},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,7,2,6,4,5] => {{1},{2,3,7},{4},{5,6}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,2,6,5,4] => {{1},{2,3,7},{4},{5,6}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,4,2,5,6] => {{1},{2,3,7},{4},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,7,4,2,6,5] => {{1},{2,3,7},{4},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,7,4,5,2,6] => {{1},{2,3,7},{4},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,7,4,5,6,2] => {{1},{2,3,7},{4},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,3,7,4,6,2,5] => {{1},{2,3,7},{4},{5,6}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,4,6,5,2] => {{1},{2,3,7},{4},{5,6}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,5,2,4,6] => {{1},{2,3,7},{4,5},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,5,2,6,4] => {{1},{2,3,7},{4,5},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,5,4,2,6] => {{1},{2,3,7},{4,5},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,5,4,6,2] => {{1},{2,3,7},{4,5},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,5,6,2,4] => {{1},{2,3,7},{4,5,6}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,7,5,6,4,2] => {{1},{2,3,7},{4,5,6}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,3,7,6,2,4,5] => {{1},{2,3,7},{4,6},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,6,2,5,4] => {{1},{2,3,7},{4,6},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,6,4,2,5] => {{1},{2,3,7},{4,6},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,6,4,5,2] => {{1},{2,3,7},{4,6},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,6,5,2,4] => {{1},{2,3,7},{4,6},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,3,7,6,5,4,2] => {{1},{2,3,7},{4,6},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,2,3,5,6,7] => {{1},{2,4},{3},{5},{6},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,4,2,3,5,7,6] => {{1},{2,4},{3},{5},{6,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,2,3,6,5,7] => {{1},{2,4},{3},{5,6},{7}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,2,3,6,7,5] => {{1},{2,4},{3},{5,6,7}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,2,3,7,5,6] => {{1},{2,4},{3},{5,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,2,3,7,6,5] => {{1},{2,4},{3},{5,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,2,5,3,6,7] => {{1},{2,4,5},{3},{6},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,2,5,3,7,6] => {{1},{2,4,5},{3},{6,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,2,5,6,3,7] => {{1},{2,4,5,6},{3},{7}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,2,5,6,7,3] => {{1},{2,4,5,6,7},{3}} => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,2,5,7,3,6] => {{1},{2,4,5,7},{3},{6}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,2,5,7,6,3] => {{1},{2,4,5,7},{3},{6}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,2,6,3,5,7] => {{1},{2,4,6},{3},{5},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,2,6,3,7,5] => {{1},{2,4,6,7},{3},{5}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,2,6,5,3,7] => {{1},{2,4,6},{3},{5},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,2,6,5,7,3] => {{1},{2,4,6,7},{3},{5}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,2,6,7,3,5] => {{1},{2,4,6},{3},{5,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,2,6,7,5,3] => {{1},{2,4,6},{3},{5,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,2,7,3,5,6] => {{1},{2,4,7},{3},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,2,7,3,6,5] => {{1},{2,4,7},{3},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,2,7,5,3,6] => {{1},{2,4,7},{3},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,2,7,5,6,3] => {{1},{2,4,7},{3},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,2,7,6,3,5] => {{1},{2,4,7},{3},{5,6}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,2,7,6,5,3] => {{1},{2,4,7},{3},{5,6}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,3,2,5,6,7] => {{1},{2,4},{3},{5},{6},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,4,3,2,5,7,6] => {{1},{2,4},{3},{5},{6,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,3,2,6,5,7] => {{1},{2,4},{3},{5,6},{7}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,3,2,6,7,5] => {{1},{2,4},{3},{5,6,7}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,3,2,7,5,6] => {{1},{2,4},{3},{5,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,3,2,7,6,5] => {{1},{2,4},{3},{5,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,3,5,2,6,7] => {{1},{2,4,5},{3},{6},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,3,5,2,7,6] => {{1},{2,4,5},{3},{6,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,3,5,6,2,7] => {{1},{2,4,5,6},{3},{7}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,3,5,6,7,2] => {{1},{2,4,5,6,7},{3}} => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,3,5,7,2,6] => {{1},{2,4,5,7},{3},{6}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,3,5,7,6,2] => {{1},{2,4,5,7},{3},{6}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,3,6,2,5,7] => {{1},{2,4,6},{3},{5},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,3,6,2,7,5] => {{1},{2,4,6,7},{3},{5}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,3,6,5,2,7] => {{1},{2,4,6},{3},{5},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,3,6,5,7,2] => {{1},{2,4,6,7},{3},{5}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,3,6,7,2,5] => {{1},{2,4,6},{3},{5,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,3,6,7,5,2] => {{1},{2,4,6},{3},{5,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,3,7,2,5,6] => {{1},{2,4,7},{3},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,3,7,2,6,5] => {{1},{2,4,7},{3},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,3,7,5,2,6] => {{1},{2,4,7},{3},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,3,7,5,6,2] => {{1},{2,4,7},{3},{5},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,3,7,6,2,5] => {{1},{2,4,7},{3},{5,6}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,3,7,6,5,2] => {{1},{2,4,7},{3},{5,6}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,2,3,6,7] => {{1},{2,4},{3,5},{6},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,5,2,3,7,6] => {{1},{2,4},{3,5},{6,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,2,6,3,7] => {{1},{2,4},{3,5,6},{7}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,2,6,7,3] => {{1},{2,4},{3,5,6,7}} => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,5,2,7,3,6] => {{1},{2,4},{3,5,7},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,2,7,6,3] => {{1},{2,4},{3,5,7},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,3,2,6,7] => {{1},{2,4},{3,5},{6},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,5,3,2,7,6] => {{1},{2,4},{3,5},{6,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,3,6,2,7] => {{1},{2,4},{3,5,6},{7}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,3,6,7,2] => {{1},{2,4},{3,5,6,7}} => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,5,3,7,2,6] => {{1},{2,4},{3,5,7},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,3,7,6,2] => {{1},{2,4},{3,5,7},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,6,2,3,7] => {{1},{2,4,6},{3,5},{7}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,6,2,7,3] => {{1},{2,4,6,7},{3,5}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,5,6,3,2,7] => {{1},{2,4,6},{3,5},{7}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,6,3,7,2] => {{1},{2,4,6,7},{3,5}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,5,6,7,2,3] => {{1},{2,4,6},{3,5,7}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,5,6,7,3,2] => {{1},{2,4,6},{3,5,7}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,5,7,2,3,6] => {{1},{2,4,7},{3,5},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,7,2,6,3] => {{1},{2,4,7},{3,5},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,7,3,2,6] => {{1},{2,4,7},{3,5},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,7,3,6,2] => {{1},{2,4,7},{3,5},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,5,7,6,2,3] => {{1},{2,4,7},{3,5,6}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,5,7,6,3,2] => {{1},{2,4,7},{3,5,6}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,6,2,3,5,7] => {{1},{2,4},{3,6},{5},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,6,2,3,7,5] => {{1},{2,4},{3,6,7},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,2,5,3,7] => {{1},{2,4},{3,6},{5},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,6,2,5,7,3] => {{1},{2,4},{3,6,7},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,2,7,3,5] => {{1},{2,4},{3,6},{5,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,2,7,5,3] => {{1},{2,4},{3,6},{5,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,3,2,5,7] => {{1},{2,4},{3,6},{5},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,6,3,2,7,5] => {{1},{2,4},{3,6,7},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,3,5,2,7] => {{1},{2,4},{3,6},{5},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,6,3,5,7,2] => {{1},{2,4},{3,6,7},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,3,7,2,5] => {{1},{2,4},{3,6},{5,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,3,7,5,2] => {{1},{2,4},{3,6},{5,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,5,2,3,7] => {{1},{2,4,5},{3,6},{7}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,5,2,7,3] => {{1},{2,4,5},{3,6,7}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,6,5,3,2,7] => {{1},{2,4,5},{3,6},{7}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,5,3,7,2] => {{1},{2,4,5},{3,6,7}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,6,5,7,2,3] => {{1},{2,4,5,7},{3,6}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,6,5,7,3,2] => {{1},{2,4,5,7},{3,6}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,6,7,2,3,5] => {{1},{2,4,7},{3,6},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,7,2,5,3] => {{1},{2,4,7},{3,6},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,7,3,2,5] => {{1},{2,4,7},{3,6},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,7,3,5,2] => {{1},{2,4,7},{3,6},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,7,5,2,3] => {{1},{2,4,7},{3,6},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,6,7,5,3,2] => {{1},{2,4,7},{3,6},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,2,3,5,6] => {{1},{2,4},{3,7},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,7,2,3,6,5] => {{1},{2,4},{3,7},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,7,2,5,3,6] => {{1},{2,4},{3,7},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,7,2,5,6,3] => {{1},{2,4},{3,7},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,7,2,6,3,5] => {{1},{2,4},{3,7},{5,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,2,6,5,3] => {{1},{2,4},{3,7},{5,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,3,2,5,6] => {{1},{2,4},{3,7},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,7,3,2,6,5] => {{1},{2,4},{3,7},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,7,3,5,2,6] => {{1},{2,4},{3,7},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,7,3,5,6,2] => {{1},{2,4},{3,7},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,4,7,3,6,2,5] => {{1},{2,4},{3,7},{5,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,3,6,5,2] => {{1},{2,4},{3,7},{5,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,5,2,3,6] => {{1},{2,4,5},{3,7},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,5,2,6,3] => {{1},{2,4,5},{3,7},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,5,3,2,6] => {{1},{2,4,5},{3,7},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,5,3,6,2] => {{1},{2,4,5},{3,7},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,5,6,2,3] => {{1},{2,4,5,6},{3,7}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,7,5,6,3,2] => {{1},{2,4,5,6},{3,7}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,4,7,6,2,3,5] => {{1},{2,4,6},{3,7},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,6,2,5,3] => {{1},{2,4,6},{3,7},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,6,3,2,5] => {{1},{2,4,6},{3,7},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,6,3,5,2] => {{1},{2,4,6},{3,7},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,6,5,2,3] => {{1},{2,4,6},{3,7},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,4,7,6,5,3,2] => {{1},{2,4,6},{3,7},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,2,3,4,6,7] => {{1},{2,5},{3},{4},{6},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,5,2,3,4,7,6] => {{1},{2,5},{3},{4},{6,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,3,6,4,7] => {{1},{2,5,6},{3},{4},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,3,6,7,4] => {{1},{2,5,6,7},{3},{4}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,2,3,7,4,6] => {{1},{2,5,7},{3},{4},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,3,7,6,4] => {{1},{2,5,7},{3},{4},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,4,3,6,7] => {{1},{2,5},{3},{4},{6},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,5,2,4,3,7,6] => {{1},{2,5},{3},{4},{6,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,4,6,3,7] => {{1},{2,5,6},{3},{4},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,4,6,7,3] => {{1},{2,5,6,7},{3},{4}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,2,4,7,3,6] => {{1},{2,5,7},{3},{4},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,4,7,6,3] => {{1},{2,5,7},{3},{4},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,6,3,4,7] => {{1},{2,5},{3},{4,6},{7}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,6,3,7,4] => {{1},{2,5},{3},{4,6,7}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,2,6,4,3,7] => {{1},{2,5},{3},{4,6},{7}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,6,4,7,3] => {{1},{2,5},{3},{4,6,7}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,2,6,7,3,4] => {{1},{2,5,7},{3},{4,6}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,2,6,7,4,3] => {{1},{2,5,7},{3},{4,6}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,2,7,3,4,6] => {{1},{2,5},{3},{4,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,7,3,6,4] => {{1},{2,5},{3},{4,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,7,4,3,6] => {{1},{2,5},{3},{4,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,7,4,6,3] => {{1},{2,5},{3},{4,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,2,7,6,3,4] => {{1},{2,5,6},{3},{4,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,2,7,6,4,3] => {{1},{2,5,6},{3},{4,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,3,2,4,6,7] => {{1},{2,5},{3},{4},{6},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,5,3,2,4,7,6] => {{1},{2,5},{3},{4},{6,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,2,6,4,7] => {{1},{2,5,6},{3},{4},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,2,6,7,4] => {{1},{2,5,6,7},{3},{4}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,3,2,7,4,6] => {{1},{2,5,7},{3},{4},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,2,7,6,4] => {{1},{2,5,7},{3},{4},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,4,2,6,7] => {{1},{2,5},{3},{4},{6},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,5,3,4,2,7,6] => {{1},{2,5},{3},{4},{6,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,4,6,2,7] => {{1},{2,5,6},{3},{4},{7}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,4,6,7,2] => {{1},{2,5,6,7},{3},{4}} => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,3,4,7,2,6] => {{1},{2,5,7},{3},{4},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,4,7,6,2] => {{1},{2,5,7},{3},{4},{6}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,6,2,4,7] => {{1},{2,5},{3},{4,6},{7}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,6,2,7,4] => {{1},{2,5},{3},{4,6,7}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,3,6,4,2,7] => {{1},{2,5},{3},{4,6},{7}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,6,4,7,2] => {{1},{2,5},{3},{4,6,7}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,3,6,7,2,4] => {{1},{2,5,7},{3},{4,6}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,3,6,7,4,2] => {{1},{2,5,7},{3},{4,6}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,3,7,2,4,6] => {{1},{2,5},{3},{4,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,7,2,6,4] => {{1},{2,5},{3},{4,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,7,4,2,6] => {{1},{2,5},{3},{4,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,7,4,6,2] => {{1},{2,5},{3},{4,7},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,3,7,6,2,4] => {{1},{2,5,6},{3},{4,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,3,7,6,4,2] => {{1},{2,5,6},{3},{4,7}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,2,3,6,7] => {{1},{2,5},{3,4},{6},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,4,2,3,7,6] => {{1},{2,5},{3,4},{6,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,2,6,3,7] => {{1},{2,5,6},{3,4},{7}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,2,6,7,3] => {{1},{2,5,6,7},{3,4}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,5,4,2,7,3,6] => {{1},{2,5,7},{3,4},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,2,7,6,3] => {{1},{2,5,7},{3,4},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,3,2,6,7] => {{1},{2,5},{3,4},{6},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,4,3,2,7,6] => {{1},{2,5},{3,4},{6,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,3,6,2,7] => {{1},{2,5,6},{3,4},{7}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,3,6,7,2] => {{1},{2,5,6,7},{3,4}} => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,5,4,3,7,2,6] => {{1},{2,5,7},{3,4},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,3,7,6,2] => {{1},{2,5,7},{3,4},{6}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,6,2,3,7] => {{1},{2,5},{3,4,6},{7}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,6,2,7,3] => {{1},{2,5},{3,4,6,7}} => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,5,4,6,3,2,7] => {{1},{2,5},{3,4,6},{7}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,6,3,7,2] => {{1},{2,5},{3,4,6,7}} => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,5,4,6,7,2,3] => {{1},{2,5,7},{3,4,6}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,5,4,6,7,3,2] => {{1},{2,5,7},{3,4,6}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,5,4,7,2,3,6] => {{1},{2,5},{3,4,7},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,7,2,6,3] => {{1},{2,5},{3,4,7},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,7,3,2,6] => {{1},{2,5},{3,4,7},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,7,3,6,2] => {{1},{2,5},{3,4,7},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,4,7,6,2,3] => {{1},{2,5,6},{3,4,7}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,5,4,7,6,3,2] => {{1},{2,5,6},{3,4,7}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,5,6,2,3,4,7] => {{1},{2,5},{3,6},{4},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,6,2,3,7,4] => {{1},{2,5},{3,6,7},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,2,4,3,7] => {{1},{2,5},{3,6},{4},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,6,2,4,7,3] => {{1},{2,5},{3,6,7},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,2,7,3,4] => {{1},{2,5,7},{3,6},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,2,7,4,3] => {{1},{2,5,7},{3,6},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,3,2,4,7] => {{1},{2,5},{3,6},{4},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,6,3,2,7,4] => {{1},{2,5},{3,6,7},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,3,4,2,7] => {{1},{2,5},{3,6},{4},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,6,3,4,7,2] => {{1},{2,5},{3,6,7},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,3,7,2,4] => {{1},{2,5,7},{3,6},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,3,7,4,2] => {{1},{2,5,7},{3,6},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,4,2,3,7] => {{1},{2,5},{3,6},{4},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,6,4,2,7,3] => {{1},{2,5},{3,6,7},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,4,3,2,7] => {{1},{2,5},{3,6},{4},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,6,4,3,7,2] => {{1},{2,5},{3,6,7},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,4,7,2,3] => {{1},{2,5,7},{3,6},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,4,7,3,2] => {{1},{2,5,7},{3,6},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,7,2,3,4] => {{1},{2,5},{3,6},{4,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,7,2,4,3] => {{1},{2,5},{3,6},{4,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,7,3,2,4] => {{1},{2,5},{3,6},{4,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,7,3,4,2] => {{1},{2,5},{3,6},{4,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,7,4,2,3] => {{1},{2,5},{3,6},{4,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,6,7,4,3,2] => {{1},{2,5},{3,6},{4,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,7,2,3,4,6] => {{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,7,2,3,6,4] => {{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,7,2,4,3,6] => {{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,7,2,4,6,3] => {{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,7,2,6,3,4] => {{1},{2,5,6},{3,7},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,7,2,6,4,3] => {{1},{2,5,6},{3,7},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,7,3,2,4,6] => {{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,7,3,2,6,4] => {{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,7,3,4,2,6] => {{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,7,3,4,6,2] => {{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,7,3,6,2,4] => {{1},{2,5,6},{3,7},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,7,3,6,4,2] => {{1},{2,5,6},{3,7},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,7,4,2,3,6] => {{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,7,4,2,6,3] => {{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,7,4,3,2,6] => {{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,7,4,3,6,2] => {{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,5,7,4,6,2,3] => {{1},{2,5,6},{3,7},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,7,4,6,3,2] => {{1},{2,5,6},{3,7},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,7,6,2,3,4] => {{1},{2,5},{3,7},{4,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,7,6,2,4,3] => {{1},{2,5},{3,7},{4,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,7,6,3,2,4] => {{1},{2,5},{3,7},{4,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,7,6,3,4,2] => {{1},{2,5},{3,7},{4,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,7,6,4,2,3] => {{1},{2,5},{3,7},{4,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,5,7,6,4,3,2] => {{1},{2,5},{3,7},{4,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,2,3,4,5,7] => {{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,6,2,3,4,7,5] => {{1},{2,6,7},{3},{4},{5}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,3,5,4,7] => {{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,6,2,3,5,7,4] => {{1},{2,6,7},{3},{4},{5}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,3,7,4,5] => {{1},{2,6},{3},{4},{5,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,3,7,5,4] => {{1},{2,6},{3},{4},{5,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,4,3,5,7] => {{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,6,2,4,3,7,5] => {{1},{2,6,7},{3},{4},{5}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,4,5,3,7] => {{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,6,2,4,5,7,3] => {{1},{2,6,7},{3},{4},{5}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,4,7,3,5] => {{1},{2,6},{3},{4},{5,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,4,7,5,3] => {{1},{2,6},{3},{4},{5,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,5,3,4,7] => {{1},{2,6},{3},{4,5},{7}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,5,3,7,4] => {{1},{2,6,7},{3},{4,5}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,2,5,4,3,7] => {{1},{2,6},{3},{4,5},{7}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,5,4,7,3] => {{1},{2,6,7},{3},{4,5}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,2,5,7,3,4] => {{1},{2,6},{3},{4,5,7}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,2,5,7,4,3] => {{1},{2,6},{3},{4,5,7}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,2,7,3,4,5] => {{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,7,3,5,4] => {{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,7,4,3,5] => {{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,7,4,5,3] => {{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,7,5,3,4] => {{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,2,7,5,4,3] => {{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,2,4,5,7] => {{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,6,3,2,4,7,5] => {{1},{2,6,7},{3},{4},{5}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,2,5,4,7] => {{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,6,3,2,5,7,4] => {{1},{2,6,7},{3},{4},{5}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,2,7,4,5] => {{1},{2,6},{3},{4},{5,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,2,7,5,4] => {{1},{2,6},{3},{4},{5,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,4,2,5,7] => {{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,6,3,4,2,7,5] => {{1},{2,6,7},{3},{4},{5}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,4,5,2,7] => {{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,6,3,4,5,7,2] => {{1},{2,6,7},{3},{4},{5}} => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,4,7,2,5] => {{1},{2,6},{3},{4},{5,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,4,7,5,2] => {{1},{2,6},{3},{4},{5,7}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,5,2,4,7] => {{1},{2,6},{3},{4,5},{7}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,5,2,7,4] => {{1},{2,6,7},{3},{4,5}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,3,5,4,2,7] => {{1},{2,6},{3},{4,5},{7}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,5,4,7,2] => {{1},{2,6,7},{3},{4,5}} => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,3,5,7,2,4] => {{1},{2,6},{3},{4,5,7}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,3,5,7,4,2] => {{1},{2,6},{3},{4,5,7}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,3,7,2,4,5] => {{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,7,2,5,4] => {{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,7,4,2,5] => {{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,7,4,5,2] => {{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,7,5,2,4] => {{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,3,7,5,4,2] => {{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,4,2,3,5,7] => {{1},{2,6},{3,4},{5},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,4,2,3,7,5] => {{1},{2,6,7},{3,4},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,2,5,3,7] => {{1},{2,6},{3,4},{5},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,4,2,5,7,3] => {{1},{2,6,7},{3,4},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,2,7,3,5] => {{1},{2,6},{3,4},{5,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,2,7,5,3] => {{1},{2,6},{3,4},{5,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,3,2,5,7] => {{1},{2,6},{3,4},{5},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,4,3,2,7,5] => {{1},{2,6,7},{3,4},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,3,5,2,7] => {{1},{2,6},{3,4},{5},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,4,3,5,7,2] => {{1},{2,6,7},{3,4},{5}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,3,7,2,5] => {{1},{2,6},{3,4},{5,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,3,7,5,2] => {{1},{2,6},{3,4},{5,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,5,2,3,7] => {{1},{2,6},{3,4,5},{7}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,5,2,7,3] => {{1},{2,6,7},{3,4,5}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,6,4,5,3,2,7] => {{1},{2,6},{3,4,5},{7}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,5,3,7,2] => {{1},{2,6,7},{3,4,5}} => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,6,4,5,7,2,3] => {{1},{2,6},{3,4,5,7}} => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,6,4,5,7,3,2] => {{1},{2,6},{3,4,5,7}} => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,6,4,7,2,3,5] => {{1},{2,6},{3,4,7},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,7,2,5,3] => {{1},{2,6},{3,4,7},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,7,3,2,5] => {{1},{2,6},{3,4,7},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,7,3,5,2] => {{1},{2,6},{3,4,7},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,7,5,2,3] => {{1},{2,6},{3,4,7},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,4,7,5,3,2] => {{1},{2,6},{3,4,7},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,2,3,4,7] => {{1},{2,6},{3,5},{4},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,5,2,3,7,4] => {{1},{2,6,7},{3,5},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,2,4,3,7] => {{1},{2,6},{3,5},{4},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,5,2,4,7,3] => {{1},{2,6,7},{3,5},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,2,7,3,4] => {{1},{2,6},{3,5,7},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,2,7,4,3] => {{1},{2,6},{3,5,7},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,3,2,4,7] => {{1},{2,6},{3,5},{4},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,5,3,2,7,4] => {{1},{2,6,7},{3,5},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,3,4,2,7] => {{1},{2,6},{3,5},{4},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,5,3,4,7,2] => {{1},{2,6,7},{3,5},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,3,7,2,4] => {{1},{2,6},{3,5,7},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,3,7,4,2] => {{1},{2,6},{3,5,7},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,4,2,3,7] => {{1},{2,6},{3,5},{4},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,5,4,2,7,3] => {{1},{2,6,7},{3,5},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,4,3,2,7] => {{1},{2,6},{3,5},{4},{7}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,5,4,3,7,2] => {{1},{2,6,7},{3,5},{4}} => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,4,7,2,3] => {{1},{2,6},{3,5,7},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,4,7,3,2] => {{1},{2,6},{3,5,7},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,7,2,3,4] => {{1},{2,6},{3,5},{4,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,7,2,4,3] => {{1},{2,6},{3,5},{4,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,7,3,2,4] => {{1},{2,6},{3,5},{4,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,7,3,4,2] => {{1},{2,6},{3,5},{4,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,7,4,2,3] => {{1},{2,6},{3,5},{4,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,5,7,4,3,2] => {{1},{2,6},{3,5},{4,7}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,7,2,3,4,5] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,2,3,5,4] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,2,4,3,5] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,2,4,5,3] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,2,5,3,4] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,2,5,4,3] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,3,2,4,5] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,3,2,5,4] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,3,4,2,5] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,3,4,5,2] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,3,5,2,4] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,3,5,4,2] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,4,2,3,5] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,4,2,5,3] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,4,3,2,5] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,4,3,5,2] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,4,5,2,3] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,4,5,3,2] => {{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,6,7,5,2,3,4] => {{1},{2,6},{3,7},{4,5}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,7,5,2,4,3] => {{1},{2,6},{3,7},{4,5}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,7,5,3,2,4] => {{1},{2,6},{3,7},{4,5}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,7,5,3,4,2] => {{1},{2,6},{3,7},{4,5}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,7,5,4,2,3] => {{1},{2,6},{3,7},{4,5}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,6,7,5,4,3,2] => {{1},{2,6},{3,7},{4,5}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,2,3,4,5,6] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,2,3,4,6,5] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,2,3,5,4,6] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,2,3,5,6,4] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,2,3,6,4,5] => {{1},{2,7},{3},{4},{5,6}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,2,3,6,5,4] => {{1},{2,7},{3},{4},{5,6}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,2,4,3,5,6] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,2,4,3,6,5] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,2,4,5,3,6] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,2,4,5,6,3] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,2,4,6,3,5] => {{1},{2,7},{3},{4},{5,6}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,2,4,6,5,3] => {{1},{2,7},{3},{4},{5,6}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,2,5,3,4,6] => {{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,2,5,3,6,4] => {{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,2,5,4,3,6] => {{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,2,5,4,6,3] => {{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,2,5,6,3,4] => {{1},{2,7},{3},{4,5,6}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,2,5,6,4,3] => {{1},{2,7},{3},{4,5,6}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,2,6,3,4,5] => {{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,2,6,3,5,4] => {{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,2,6,4,3,5] => {{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,2,6,4,5,3] => {{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,2,6,5,3,4] => {{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,2,6,5,4,3] => {{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,2,4,5,6] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,3,2,4,6,5] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,3,2,5,4,6] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,3,2,5,6,4] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,3,2,6,4,5] => {{1},{2,7},{3},{4},{5,6}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,2,6,5,4] => {{1},{2,7},{3},{4},{5,6}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,4,2,5,6] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,3,4,2,6,5] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,3,4,5,2,6] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,3,4,5,6,2] => {{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[1,7,3,4,6,2,5] => {{1},{2,7},{3},{4},{5,6}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,4,6,5,2] => {{1},{2,7},{3},{4},{5,6}} => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,5,2,4,6] => {{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,5,2,6,4] => {{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,5,4,2,6] => {{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,5,4,6,2] => {{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,5,6,2,4] => {{1},{2,7},{3},{4,5,6}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,3,5,6,4,2] => {{1},{2,7},{3},{4,5,6}} => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,3,6,2,4,5] => {{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,6,2,5,4] => {{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,6,4,2,5] => {{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,6,4,5,2] => {{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,6,5,2,4] => {{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,3,6,5,4,2] => {{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,4,2,3,5,6] => {{1},{2,7},{3,4},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,4,2,3,6,5] => {{1},{2,7},{3,4},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,4,2,5,3,6] => {{1},{2,7},{3,4},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,4,2,5,6,3] => {{1},{2,7},{3,4},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,4,2,6,3,5] => {{1},{2,7},{3,4},{5,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,4,2,6,5,3] => {{1},{2,7},{3,4},{5,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,4,3,2,5,6] => {{1},{2,7},{3,4},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,4,3,2,6,5] => {{1},{2,7},{3,4},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,4,3,5,2,6] => {{1},{2,7},{3,4},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,4,3,5,6,2] => {{1},{2,7},{3,4},{5},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,4,3,6,2,5] => {{1},{2,7},{3,4},{5,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,4,3,6,5,2] => {{1},{2,7},{3,4},{5,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,4,5,2,3,6] => {{1},{2,7},{3,4,5},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,4,5,2,6,3] => {{1},{2,7},{3,4,5},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,4,5,3,2,6] => {{1},{2,7},{3,4,5},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,4,5,3,6,2] => {{1},{2,7},{3,4,5},{6}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,4,5,6,2,3] => {{1},{2,7},{3,4,5,6}} => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,7,4,5,6,3,2] => {{1},{2,7},{3,4,5,6}} => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 3

[1,7,4,6,2,3,5] => {{1},{2,7},{3,4,6},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,4,6,2,5,3] => {{1},{2,7},{3,4,6},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,4,6,3,2,5] => {{1},{2,7},{3,4,6},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,4,6,3,5,2] => {{1},{2,7},{3,4,6},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,4,6,5,2,3] => {{1},{2,7},{3,4,6},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,4,6,5,3,2] => {{1},{2,7},{3,4,6},{5}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,5,2,3,4,6] => {{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,5,2,3,6,4] => {{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,5,2,4,3,6] => {{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,5,2,4,6,3] => {{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,5,2,6,3,4] => {{1},{2,7},{3,5,6},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,5,2,6,4,3] => {{1},{2,7},{3,5,6},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,5,3,2,4,6] => {{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,5,3,2,6,4] => {{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,5,3,4,2,6] => {{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,5,3,4,6,2] => {{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,5,3,6,2,4] => {{1},{2,7},{3,5,6},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,5,3,6,4,2] => {{1},{2,7},{3,5,6},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,5,4,2,3,6] => {{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,5,4,2,6,3] => {{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,5,4,3,2,6] => {{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,5,4,3,6,2] => {{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,5,4,6,2,3] => {{1},{2,7},{3,5,6},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,5,4,6,3,2] => {{1},{2,7},{3,5,6},{4}} => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,5,6,2,3,4] => {{1},{2,7},{3,5},{4,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,5,6,2,4,3] => {{1},{2,7},{3,5},{4,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,5,6,3,2,4] => {{1},{2,7},{3,5},{4,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,5,6,3,4,2] => {{1},{2,7},{3,5},{4,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,5,6,4,2,3] => {{1},{2,7},{3,5},{4,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,5,6,4,3,2] => {{1},{2,7},{3,5},{4,6}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,6,2,3,4,5] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,2,3,5,4] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,2,4,3,5] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,2,4,5,3] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,2,5,3,4] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,2,5,4,3] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,3,2,4,5] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,3,2,5,4] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,3,4,2,5] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,3,4,5,2] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,3,5,2,4] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,3,5,4,2] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,4,2,3,5] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,4,2,5,3] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,4,3,2,5] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,4,3,5,2] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,4,5,2,3] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,4,5,3,2] => {{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[1,7,6,5,2,3,4] => {{1},{2,7},{3,6},{4,5}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,6,5,2,4,3] => {{1},{2,7},{3,6},{4,5}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,6,5,3,2,4] => {{1},{2,7},{3,6},{4,5}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,6,5,3,4,2] => {{1},{2,7},{3,6},{4,5}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,6,5,4,2,3] => {{1},{2,7},{3,6},{4,5}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[1,7,6,5,4,3,2] => {{1},{2,7},{3,6},{4,5}} => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,3,4,5,6,7] => {{1,2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[2,1,3,4,5,7,6] => {{1,2},{3},{4},{5},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,3,4,6,5,7] => {{1,2},{3},{4},{5,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,3,4,6,7,5] => {{1,2},{3},{4},{5,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,3,4,7,5,6] => {{1,2},{3},{4},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,3,4,7,6,5] => {{1,2},{3},{4},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,3,5,4,6,7] => {{1,2},{3},{4,5},{6},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,3,5,6,4,7] => {{1,2},{3},{4,5,6},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,3,5,6,7,4] => {{1,2},{3},{4,5,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,3,5,7,4,6] => {{1,2},{3},{4,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,3,5,7,6,4] => {{1,2},{3},{4,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,3,6,4,5,7] => {{1,2},{3},{4,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,3,6,4,7,5] => {{1,2},{3},{4,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,3,6,5,4,7] => {{1,2},{3},{4,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,3,6,5,7,4] => {{1,2},{3},{4,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,3,6,7,4,5] => {{1,2},{3},{4,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,3,6,7,5,4] => {{1,2},{3},{4,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,3,7,4,5,6] => {{1,2},{3},{4,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,3,7,4,6,5] => {{1,2},{3},{4,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,3,7,5,4,6] => {{1,2},{3},{4,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,3,7,5,6,4] => {{1,2},{3},{4,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,3,7,6,4,5] => {{1,2},{3},{4,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,3,7,6,5,4] => {{1,2},{3},{4,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,4,3,5,6,7] => {{1,2},{3,4},{5},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,4,3,6,7,5] => {{1,2},{3,4},{5,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,4,3,7,5,6] => {{1,2},{3,4},{5,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,4,3,7,6,5] => {{1,2},{3,4},{5,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,4,5,3,6,7] => {{1,2},{3,4,5},{6},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,4,5,3,7,6] => {{1,2},{3,4,5},{6,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,4,5,6,3,7] => {{1,2},{3,4,5,6},{7}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,4,5,6,7,3] => {{1,2},{3,4,5,6,7}} => [2,5] => ([(4,6),(5,6)],7) => 2

[2,1,4,5,7,3,6] => {{1,2},{3,4,5,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,4,5,7,6,3] => {{1,2},{3,4,5,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,4,6,3,5,7] => {{1,2},{3,4,6},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,4,6,3,7,5] => {{1,2},{3,4,6,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,4,6,5,3,7] => {{1,2},{3,4,6},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,4,6,5,7,3] => {{1,2},{3,4,6,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,4,6,7,3,5] => {{1,2},{3,4,6},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,4,6,7,5,3] => {{1,2},{3,4,6},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,4,7,3,5,6] => {{1,2},{3,4,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,4,7,3,6,5] => {{1,2},{3,4,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,4,7,5,3,6] => {{1,2},{3,4,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,4,7,5,6,3] => {{1,2},{3,4,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,4,7,6,3,5] => {{1,2},{3,4,7},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,4,7,6,5,3] => {{1,2},{3,4,7},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,5,3,4,6,7] => {{1,2},{3,5},{4},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,5,3,4,7,6] => {{1,2},{3,5},{4},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,3,6,4,7] => {{1,2},{3,5,6},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,3,6,7,4] => {{1,2},{3,5,6,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,5,3,7,4,6] => {{1,2},{3,5,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,3,7,6,4] => {{1,2},{3,5,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,4,3,6,7] => {{1,2},{3,5},{4},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,5,4,3,7,6] => {{1,2},{3,5},{4},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,4,6,3,7] => {{1,2},{3,5,6},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,4,6,7,3] => {{1,2},{3,5,6,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,5,4,7,3,6] => {{1,2},{3,5,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,4,7,6,3] => {{1,2},{3,5,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,6,3,4,7] => {{1,2},{3,5},{4,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,6,3,7,4] => {{1,2},{3,5},{4,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,5,6,4,3,7] => {{1,2},{3,5},{4,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,6,4,7,3] => {{1,2},{3,5},{4,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,5,6,7,3,4] => {{1,2},{3,5,7},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,5,6,7,4,3] => {{1,2},{3,5,7},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,5,7,3,4,6] => {{1,2},{3,5},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,7,3,6,4] => {{1,2},{3,5},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,7,4,3,6] => {{1,2},{3,5},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,7,4,6,3] => {{1,2},{3,5},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,5,7,6,3,4] => {{1,2},{3,5,6},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,5,7,6,4,3] => {{1,2},{3,5,6},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,6,3,4,5,7] => {{1,2},{3,6},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,6,3,4,7,5] => {{1,2},{3,6,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,3,5,4,7] => {{1,2},{3,6},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,6,3,5,7,4] => {{1,2},{3,6,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,3,7,4,5] => {{1,2},{3,6},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,3,7,5,4] => {{1,2},{3,6},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,4,3,5,7] => {{1,2},{3,6},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,6,4,3,7,5] => {{1,2},{3,6,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,4,5,3,7] => {{1,2},{3,6},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,6,4,5,7,3] => {{1,2},{3,6,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,4,7,3,5] => {{1,2},{3,6},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,4,7,5,3] => {{1,2},{3,6},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,5,3,4,7] => {{1,2},{3,6},{4,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,5,3,7,4] => {{1,2},{3,6,7},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,6,5,4,3,7] => {{1,2},{3,6},{4,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,5,4,7,3] => {{1,2},{3,6,7},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,6,5,7,3,4] => {{1,2},{3,6},{4,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,6,5,7,4,3] => {{1,2},{3,6},{4,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,6,7,3,4,5] => {{1,2},{3,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,7,3,5,4] => {{1,2},{3,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,7,4,3,5] => {{1,2},{3,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,7,4,5,3] => {{1,2},{3,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,7,5,3,4] => {{1,2},{3,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,6,7,5,4,3] => {{1,2},{3,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,3,4,5,6] => {{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,7,3,4,6,5] => {{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,7,3,5,4,6] => {{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,7,3,5,6,4] => {{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,7,3,6,4,5] => {{1,2},{3,7},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,3,6,5,4] => {{1,2},{3,7},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,4,3,5,6] => {{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,7,4,3,6,5] => {{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,7,4,5,3,6] => {{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,7,4,5,6,3] => {{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,1,7,4,6,3,5] => {{1,2},{3,7},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,4,6,5,3] => {{1,2},{3,7},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,5,3,4,6] => {{1,2},{3,7},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,5,3,6,4] => {{1,2},{3,7},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,5,4,3,6] => {{1,2},{3,7},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,5,4,6,3] => {{1,2},{3,7},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,5,6,3,4] => {{1,2},{3,7},{4,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,7,5,6,4,3] => {{1,2},{3,7},{4,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,1,7,6,3,4,5] => {{1,2},{3,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,6,3,5,4] => {{1,2},{3,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,6,4,3,5] => {{1,2},{3,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,6,4,5,3] => {{1,2},{3,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,6,5,3,4] => {{1,2},{3,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,1,7,6,5,4,3] => {{1,2},{3,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,1,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,3,1,4,5,7,6] => {{1,2,3},{4},{5},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,1,4,6,5,7] => {{1,2,3},{4},{5,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,1,4,6,7,5] => {{1,2,3},{4},{5,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,1,4,7,5,6] => {{1,2,3},{4},{5,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,1,4,7,6,5] => {{1,2,3},{4},{5,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,1,5,4,6,7] => {{1,2,3},{4,5},{6},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,1,5,4,7,6] => {{1,2,3},{4,5},{6,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,1,5,6,4,7] => {{1,2,3},{4,5,6},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,1,5,6,7,4] => {{1,2,3},{4,5,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[2,3,1,5,7,4,6] => {{1,2,3},{4,5,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,1,5,7,6,4] => {{1,2,3},{4,5,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,1,6,4,5,7] => {{1,2,3},{4,6},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,1,6,4,7,5] => {{1,2,3},{4,6,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,1,6,5,4,7] => {{1,2,3},{4,6},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,1,6,5,7,4] => {{1,2,3},{4,6,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,1,6,7,4,5] => {{1,2,3},{4,6},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,1,6,7,5,4] => {{1,2,3},{4,6},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,1,7,4,5,6] => {{1,2,3},{4,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,1,7,4,6,5] => {{1,2,3},{4,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,1,7,5,4,6] => {{1,2,3},{4,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,1,7,5,6,4] => {{1,2,3},{4,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,1,7,6,4,5] => {{1,2,3},{4,7},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,1,7,6,5,4] => {{1,2,3},{4,7},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,4,1,5,6,7] => {{1,2,3,4},{5},{6},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,4,1,5,7,6] => {{1,2,3,4},{5},{6,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,4,1,6,5,7] => {{1,2,3,4},{5,6},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,4,1,6,7,5] => {{1,2,3,4},{5,6,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,4,1,7,5,6] => {{1,2,3,4},{5,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,4,1,7,6,5] => {{1,2,3,4},{5,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,4,5,1,6,7] => {{1,2,3,4,5},{6},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,4,5,1,7,6] => {{1,2,3,4,5},{6,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,4,5,6,1,7] => {{1,2,3,4,5,6},{7}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}} => [7] => ([],7) => 1

[2,3,4,5,7,1,6] => {{1,2,3,4,5,7},{6}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,4,5,7,6,1] => {{1,2,3,4,5,7},{6}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,4,6,1,5,7] => {{1,2,3,4,6},{5},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,4,6,1,7,5] => {{1,2,3,4,6,7},{5}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,4,6,5,1,7] => {{1,2,3,4,6},{5},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,4,6,5,7,1] => {{1,2,3,4,6,7},{5}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,4,6,7,1,5] => {{1,2,3,4,6},{5,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,4,6,7,5,1] => {{1,2,3,4,6},{5,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,4,7,1,5,6] => {{1,2,3,4,7},{5},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,4,7,1,6,5] => {{1,2,3,4,7},{5},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,4,7,5,1,6] => {{1,2,3,4,7},{5},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,4,7,5,6,1] => {{1,2,3,4,7},{5},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,4,7,6,1,5] => {{1,2,3,4,7},{5,6}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,4,7,6,5,1] => {{1,2,3,4,7},{5,6}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,5,1,4,6,7] => {{1,2,3,5},{4},{6},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,5,1,4,7,6] => {{1,2,3,5},{4},{6,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,1,6,4,7] => {{1,2,3,5,6},{4},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,1,6,7,4] => {{1,2,3,5,6,7},{4}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,5,1,7,4,6] => {{1,2,3,5,7},{4},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,1,7,6,4] => {{1,2,3,5,7},{4},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,4,1,6,7] => {{1,2,3,5},{4},{6},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,5,4,1,7,6] => {{1,2,3,5},{4},{6,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,4,6,1,7] => {{1,2,3,5,6},{4},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,4,6,7,1] => {{1,2,3,5,6,7},{4}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,5,4,7,1,6] => {{1,2,3,5,7},{4},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,4,7,6,1] => {{1,2,3,5,7},{4},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,6,1,4,7] => {{1,2,3,5},{4,6},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,6,1,7,4] => {{1,2,3,5},{4,6,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,5,6,4,1,7] => {{1,2,3,5},{4,6},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,6,4,7,1] => {{1,2,3,5},{4,6,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,5,6,7,1,4] => {{1,2,3,5,7},{4,6}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,5,6,7,4,1] => {{1,2,3,5,7},{4,6}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,5,7,1,4,6] => {{1,2,3,5},{4,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,7,1,6,4] => {{1,2,3,5},{4,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,7,4,1,6] => {{1,2,3,5},{4,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,7,4,6,1] => {{1,2,3,5},{4,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,5,7,6,1,4] => {{1,2,3,5,6},{4,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,5,7,6,4,1] => {{1,2,3,5,6},{4,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,6,1,4,5,7] => {{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,6,1,4,7,5] => {{1,2,3,6,7},{4},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,1,5,4,7] => {{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,6,1,5,7,4] => {{1,2,3,6,7},{4},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,1,7,4,5] => {{1,2,3,6},{4},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,1,7,5,4] => {{1,2,3,6},{4},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,4,1,5,7] => {{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,6,4,1,7,5] => {{1,2,3,6,7},{4},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,4,5,1,7] => {{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,6,4,5,7,1] => {{1,2,3,6,7},{4},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,4,7,1,5] => {{1,2,3,6},{4},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,4,7,5,1] => {{1,2,3,6},{4},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,5,1,4,7] => {{1,2,3,6},{4,5},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,5,1,7,4] => {{1,2,3,6,7},{4,5}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,6,5,4,1,7] => {{1,2,3,6},{4,5},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,5,4,7,1] => {{1,2,3,6,7},{4,5}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,6,5,7,1,4] => {{1,2,3,6},{4,5,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,6,5,7,4,1] => {{1,2,3,6},{4,5,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,6,7,1,4,5] => {{1,2,3,6},{4,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,7,1,5,4] => {{1,2,3,6},{4,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,7,4,1,5] => {{1,2,3,6},{4,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,7,4,5,1] => {{1,2,3,6},{4,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,7,5,1,4] => {{1,2,3,6},{4,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,6,7,5,4,1] => {{1,2,3,6},{4,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,1,4,5,6] => {{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,7,1,4,6,5] => {{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,7,1,5,4,6] => {{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,7,1,5,6,4] => {{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,7,1,6,4,5] => {{1,2,3,7},{4},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,1,6,5,4] => {{1,2,3,7},{4},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,4,1,5,6] => {{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,7,4,1,6,5] => {{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,7,4,5,1,6] => {{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,7,4,5,6,1] => {{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,3,7,4,6,1,5] => {{1,2,3,7},{4},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,4,6,5,1] => {{1,2,3,7},{4},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,5,1,4,6] => {{1,2,3,7},{4,5},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,5,1,6,4] => {{1,2,3,7},{4,5},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,5,4,1,6] => {{1,2,3,7},{4,5},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,5,4,6,1] => {{1,2,3,7},{4,5},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,5,6,1,4] => {{1,2,3,7},{4,5,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,7,5,6,4,1] => {{1,2,3,7},{4,5,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,3,7,6,1,4,5] => {{1,2,3,7},{4,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,6,1,5,4] => {{1,2,3,7},{4,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,6,4,1,5] => {{1,2,3,7},{4,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,6,4,5,1] => {{1,2,3,7},{4,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,6,5,1,4] => {{1,2,3,7},{4,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,3,7,6,5,4,1] => {{1,2,3,7},{4,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,1,3,5,6,7] => {{1,2,4},{3},{5},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,4,1,3,5,7,6] => {{1,2,4},{3},{5},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,1,3,6,5,7] => {{1,2,4},{3},{5,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,1,3,6,7,5] => {{1,2,4},{3},{5,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,1,3,7,5,6] => {{1,2,4},{3},{5,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,1,3,7,6,5] => {{1,2,4},{3},{5,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,1,5,3,6,7] => {{1,2,4,5},{3},{6},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,1,5,3,7,6] => {{1,2,4,5},{3},{6,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,1,5,6,3,7] => {{1,2,4,5,6},{3},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,1,5,6,7,3] => {{1,2,4,5,6,7},{3}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,1,5,7,3,6] => {{1,2,4,5,7},{3},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,1,5,7,6,3] => {{1,2,4,5,7},{3},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,1,6,3,5,7] => {{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,1,6,3,7,5] => {{1,2,4,6,7},{3},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,1,6,5,3,7] => {{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,1,6,5,7,3] => {{1,2,4,6,7},{3},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,1,6,7,3,5] => {{1,2,4,6},{3},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,1,6,7,5,3] => {{1,2,4,6},{3},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,1,7,3,5,6] => {{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,1,7,3,6,5] => {{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,1,7,5,3,6] => {{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,1,7,5,6,3] => {{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,1,7,6,3,5] => {{1,2,4,7},{3},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,1,7,6,5,3] => {{1,2,4,7},{3},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,3,1,5,6,7] => {{1,2,4},{3},{5},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,4,3,1,5,7,6] => {{1,2,4},{3},{5},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,3,1,6,5,7] => {{1,2,4},{3},{5,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,3,1,6,7,5] => {{1,2,4},{3},{5,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,3,1,7,5,6] => {{1,2,4},{3},{5,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,3,1,7,6,5] => {{1,2,4},{3},{5,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,3,5,1,6,7] => {{1,2,4,5},{3},{6},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,3,5,1,7,6] => {{1,2,4,5},{3},{6,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,3,5,6,1,7] => {{1,2,4,5,6},{3},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,3,5,6,7,1] => {{1,2,4,5,6,7},{3}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,3,5,7,1,6] => {{1,2,4,5,7},{3},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,3,5,7,6,1] => {{1,2,4,5,7},{3},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,3,6,1,5,7] => {{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,3,6,1,7,5] => {{1,2,4,6,7},{3},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,3,6,5,1,7] => {{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,3,6,5,7,1] => {{1,2,4,6,7},{3},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,3,6,7,1,5] => {{1,2,4,6},{3},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,3,6,7,5,1] => {{1,2,4,6},{3},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,3,7,1,5,6] => {{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,3,7,1,6,5] => {{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,3,7,5,1,6] => {{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,3,7,5,6,1] => {{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,3,7,6,1,5] => {{1,2,4,7},{3},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,3,7,6,5,1] => {{1,2,4,7},{3},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,1,3,6,7] => {{1,2,4},{3,5},{6},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,5,1,3,7,6] => {{1,2,4},{3,5},{6,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,1,6,3,7] => {{1,2,4},{3,5,6},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,1,6,7,3] => {{1,2,4},{3,5,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[2,4,5,1,7,3,6] => {{1,2,4},{3,5,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,1,7,6,3] => {{1,2,4},{3,5,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,3,1,6,7] => {{1,2,4},{3,5},{6},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,5,3,1,7,6] => {{1,2,4},{3,5},{6,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,3,6,1,7] => {{1,2,4},{3,5,6},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,3,6,7,1] => {{1,2,4},{3,5,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[2,4,5,3,7,1,6] => {{1,2,4},{3,5,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,3,7,6,1] => {{1,2,4},{3,5,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,6,1,3,7] => {{1,2,4,6},{3,5},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,6,1,7,3] => {{1,2,4,6,7},{3,5}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,5,6,3,1,7] => {{1,2,4,6},{3,5},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,6,3,7,1] => {{1,2,4,6,7},{3,5}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,5,6,7,1,3] => {{1,2,4,6},{3,5,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,5,6,7,3,1] => {{1,2,4,6},{3,5,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,5,7,1,3,6] => {{1,2,4,7},{3,5},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,7,1,6,3] => {{1,2,4,7},{3,5},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,7,3,1,6] => {{1,2,4,7},{3,5},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,7,3,6,1] => {{1,2,4,7},{3,5},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,5,7,6,1,3] => {{1,2,4,7},{3,5,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,5,7,6,3,1] => {{1,2,4,7},{3,5,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,6,1,3,5,7] => {{1,2,4},{3,6},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,6,1,3,7,5] => {{1,2,4},{3,6,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,1,5,3,7] => {{1,2,4},{3,6},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,6,1,5,7,3] => {{1,2,4},{3,6,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,1,7,3,5] => {{1,2,4},{3,6},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,1,7,5,3] => {{1,2,4},{3,6},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,3,1,5,7] => {{1,2,4},{3,6},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,6,3,1,7,5] => {{1,2,4},{3,6,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,3,5,1,7] => {{1,2,4},{3,6},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,6,3,5,7,1] => {{1,2,4},{3,6,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,3,7,1,5] => {{1,2,4},{3,6},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,3,7,5,1] => {{1,2,4},{3,6},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,5,1,3,7] => {{1,2,4,5},{3,6},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,5,1,7,3] => {{1,2,4,5},{3,6,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,6,5,3,1,7] => {{1,2,4,5},{3,6},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,5,3,7,1] => {{1,2,4,5},{3,6,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,6,5,7,1,3] => {{1,2,4,5,7},{3,6}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,6,5,7,3,1] => {{1,2,4,5,7},{3,6}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,6,7,1,3,5] => {{1,2,4,7},{3,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,7,1,5,3] => {{1,2,4,7},{3,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,7,3,1,5] => {{1,2,4,7},{3,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,7,3,5,1] => {{1,2,4,7},{3,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,7,5,1,3] => {{1,2,4,7},{3,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,6,7,5,3,1] => {{1,2,4,7},{3,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,1,3,5,6] => {{1,2,4},{3,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,7,1,3,6,5] => {{1,2,4},{3,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,7,1,5,3,6] => {{1,2,4},{3,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,7,1,5,6,3] => {{1,2,4},{3,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,7,1,6,3,5] => {{1,2,4},{3,7},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,1,6,5,3] => {{1,2,4},{3,7},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,3,1,5,6] => {{1,2,4},{3,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,7,3,1,6,5] => {{1,2,4},{3,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,7,3,5,1,6] => {{1,2,4},{3,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,7,3,5,6,1] => {{1,2,4},{3,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,4,7,3,6,1,5] => {{1,2,4},{3,7},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,3,6,5,1] => {{1,2,4},{3,7},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,5,1,3,6] => {{1,2,4,5},{3,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,5,1,6,3] => {{1,2,4,5},{3,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,5,3,1,6] => {{1,2,4,5},{3,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,5,3,6,1] => {{1,2,4,5},{3,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,5,6,1,3] => {{1,2,4,5,6},{3,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,7,5,6,3,1] => {{1,2,4,5,6},{3,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,4,7,6,1,3,5] => {{1,2,4,6},{3,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,6,1,5,3] => {{1,2,4,6},{3,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,6,3,1,5] => {{1,2,4,6},{3,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,6,3,5,1] => {{1,2,4,6},{3,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,6,5,1,3] => {{1,2,4,6},{3,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,4,7,6,5,3,1] => {{1,2,4,6},{3,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,1,3,4,6,7] => {{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,5,1,3,4,7,6] => {{1,2,5},{3},{4},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,3,6,4,7] => {{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,3,6,7,4] => {{1,2,5,6,7},{3},{4}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,1,3,7,4,6] => {{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,3,7,6,4] => {{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,4,3,6,7] => {{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,5,1,4,3,7,6] => {{1,2,5},{3},{4},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,4,6,3,7] => {{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,4,6,7,3] => {{1,2,5,6,7},{3},{4}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,1,4,7,3,6] => {{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,4,7,6,3] => {{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,6,3,4,7] => {{1,2,5},{3},{4,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,6,3,7,4] => {{1,2,5},{3},{4,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,1,6,4,3,7] => {{1,2,5},{3},{4,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,6,4,7,3] => {{1,2,5},{3},{4,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,1,6,7,3,4] => {{1,2,5,7},{3},{4,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,1,6,7,4,3] => {{1,2,5,7},{3},{4,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,1,7,3,4,6] => {{1,2,5},{3},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,7,3,6,4] => {{1,2,5},{3},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,7,4,3,6] => {{1,2,5},{3},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,7,4,6,3] => {{1,2,5},{3},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,1,7,6,3,4] => {{1,2,5,6},{3},{4,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,1,7,6,4,3] => {{1,2,5,6},{3},{4,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,3,1,4,6,7] => {{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,5,3,1,4,7,6] => {{1,2,5},{3},{4},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,1,6,4,7] => {{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,1,6,7,4] => {{1,2,5,6,7},{3},{4}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,3,1,7,4,6] => {{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,1,7,6,4] => {{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,4,1,6,7] => {{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,5,3,4,1,7,6] => {{1,2,5},{3},{4},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,4,6,1,7] => {{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,4,6,7,1] => {{1,2,5,6,7},{3},{4}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,3,4,7,1,6] => {{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,4,7,6,1] => {{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,6,1,4,7] => {{1,2,5},{3},{4,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,6,1,7,4] => {{1,2,5},{3},{4,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,3,6,4,1,7] => {{1,2,5},{3},{4,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,6,4,7,1] => {{1,2,5},{3},{4,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,3,6,7,1,4] => {{1,2,5,7},{3},{4,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,3,6,7,4,1] => {{1,2,5,7},{3},{4,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,3,7,1,4,6] => {{1,2,5},{3},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,7,1,6,4] => {{1,2,5},{3},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,7,4,1,6] => {{1,2,5},{3},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,7,4,6,1] => {{1,2,5},{3},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,3,7,6,1,4] => {{1,2,5,6},{3},{4,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,3,7,6,4,1] => {{1,2,5,6},{3},{4,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,1,3,6,7] => {{1,2,5},{3,4},{6},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,4,1,3,7,6] => {{1,2,5},{3,4},{6,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,1,6,3,7] => {{1,2,5,6},{3,4},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,1,6,7,3] => {{1,2,5,6,7},{3,4}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,5,4,1,7,3,6] => {{1,2,5,7},{3,4},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,1,7,6,3] => {{1,2,5,7},{3,4},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,3,1,6,7] => {{1,2,5},{3,4},{6},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,4,3,1,7,6] => {{1,2,5},{3,4},{6,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,3,6,1,7] => {{1,2,5,6},{3,4},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,3,6,7,1] => {{1,2,5,6,7},{3,4}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,5,4,3,7,1,6] => {{1,2,5,7},{3,4},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,3,7,6,1] => {{1,2,5,7},{3,4},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,6,1,3,7] => {{1,2,5},{3,4,6},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,6,1,7,3] => {{1,2,5},{3,4,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[2,5,4,6,3,1,7] => {{1,2,5},{3,4,6},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,6,3,7,1] => {{1,2,5},{3,4,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[2,5,4,6,7,1,3] => {{1,2,5,7},{3,4,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,5,4,6,7,3,1] => {{1,2,5,7},{3,4,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,5,4,7,1,3,6] => {{1,2,5},{3,4,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,7,1,6,3] => {{1,2,5},{3,4,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,7,3,1,6] => {{1,2,5},{3,4,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,7,3,6,1] => {{1,2,5},{3,4,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,4,7,6,1,3] => {{1,2,5,6},{3,4,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,5,4,7,6,3,1] => {{1,2,5,6},{3,4,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,5,6,1,3,4,7] => {{1,2,5},{3,6},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,6,1,3,7,4] => {{1,2,5},{3,6,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,1,4,3,7] => {{1,2,5},{3,6},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,6,1,4,7,3] => {{1,2,5},{3,6,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,1,7,3,4] => {{1,2,5,7},{3,6},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,1,7,4,3] => {{1,2,5,7},{3,6},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,3,1,4,7] => {{1,2,5},{3,6},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,6,3,1,7,4] => {{1,2,5},{3,6,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,3,4,1,7] => {{1,2,5},{3,6},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,6,3,4,7,1] => {{1,2,5},{3,6,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,3,7,1,4] => {{1,2,5,7},{3,6},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,3,7,4,1] => {{1,2,5,7},{3,6},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,4,1,3,7] => {{1,2,5},{3,6},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,6,4,1,7,3] => {{1,2,5},{3,6,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,4,3,1,7] => {{1,2,5},{3,6},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,6,4,3,7,1] => {{1,2,5},{3,6,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,4,7,1,3] => {{1,2,5,7},{3,6},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,4,7,3,1] => {{1,2,5,7},{3,6},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,7,1,3,4] => {{1,2,5},{3,6},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,7,1,4,3] => {{1,2,5},{3,6},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,7,3,1,4] => {{1,2,5},{3,6},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,7,3,4,1] => {{1,2,5},{3,6},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,7,4,1,3] => {{1,2,5},{3,6},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,6,7,4,3,1] => {{1,2,5},{3,6},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,7,1,3,4,6] => {{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,7,1,3,6,4] => {{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,7,1,4,3,6] => {{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,7,1,4,6,3] => {{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,7,1,6,3,4] => {{1,2,5,6},{3,7},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,7,1,6,4,3] => {{1,2,5,6},{3,7},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,7,3,1,4,6] => {{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,7,3,1,6,4] => {{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,7,3,4,1,6] => {{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,7,3,4,6,1] => {{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,7,3,6,1,4] => {{1,2,5,6},{3,7},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,7,3,6,4,1] => {{1,2,5,6},{3,7},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,7,4,1,3,6] => {{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,7,4,1,6,3] => {{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,7,4,3,1,6] => {{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,7,4,3,6,1] => {{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,5,7,4,6,1,3] => {{1,2,5,6},{3,7},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,7,4,6,3,1] => {{1,2,5,6},{3,7},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,7,6,1,3,4] => {{1,2,5},{3,7},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,7,6,1,4,3] => {{1,2,5},{3,7},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,7,6,3,1,4] => {{1,2,5},{3,7},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,7,6,3,4,1] => {{1,2,5},{3,7},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,7,6,4,1,3] => {{1,2,5},{3,7},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,5,7,6,4,3,1] => {{1,2,5},{3,7},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,1,3,4,5,7] => {{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,6,1,3,4,7,5] => {{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,3,5,4,7] => {{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,6,1,3,5,7,4] => {{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,3,7,4,5] => {{1,2,6},{3},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,3,7,5,4] => {{1,2,6},{3},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,4,3,5,7] => {{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,6,1,4,3,7,5] => {{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,4,5,3,7] => {{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,6,1,4,5,7,3] => {{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,4,7,3,5] => {{1,2,6},{3},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,4,7,5,3] => {{1,2,6},{3},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,5,3,4,7] => {{1,2,6},{3},{4,5},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,5,3,7,4] => {{1,2,6,7},{3},{4,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,1,5,4,3,7] => {{1,2,6},{3},{4,5},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,5,4,7,3] => {{1,2,6,7},{3},{4,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,1,5,7,3,4] => {{1,2,6},{3},{4,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,1,5,7,4,3] => {{1,2,6},{3},{4,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,1,7,3,4,5] => {{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,7,3,5,4] => {{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,7,4,3,5] => {{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,7,4,5,3] => {{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,7,5,3,4] => {{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,1,7,5,4,3] => {{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,1,4,5,7] => {{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,6,3,1,4,7,5] => {{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,1,5,4,7] => {{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,6,3,1,5,7,4] => {{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,1,7,4,5] => {{1,2,6},{3},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,1,7,5,4] => {{1,2,6},{3},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,4,1,5,7] => {{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,6,3,4,1,7,5] => {{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,4,5,1,7] => {{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,6,3,4,5,7,1] => {{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,4,7,1,5] => {{1,2,6},{3},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,4,7,5,1] => {{1,2,6},{3},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,5,1,4,7] => {{1,2,6},{3},{4,5},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,5,1,7,4] => {{1,2,6,7},{3},{4,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,3,5,4,1,7] => {{1,2,6},{3},{4,5},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,5,4,7,1] => {{1,2,6,7},{3},{4,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,3,5,7,1,4] => {{1,2,6},{3},{4,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,3,5,7,4,1] => {{1,2,6},{3},{4,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,3,7,1,4,5] => {{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,7,1,5,4] => {{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,7,4,1,5] => {{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,7,4,5,1] => {{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,7,5,1,4] => {{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,3,7,5,4,1] => {{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,4,1,3,5,7] => {{1,2,6},{3,4},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,4,1,3,7,5] => {{1,2,6,7},{3,4},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,1,5,3,7] => {{1,2,6},{3,4},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,4,1,5,7,3] => {{1,2,6,7},{3,4},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,1,7,3,5] => {{1,2,6},{3,4},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,1,7,5,3] => {{1,2,6},{3,4},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,3,1,5,7] => {{1,2,6},{3,4},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,4,3,1,7,5] => {{1,2,6,7},{3,4},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,3,5,1,7] => {{1,2,6},{3,4},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,4,3,5,7,1] => {{1,2,6,7},{3,4},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,3,7,1,5] => {{1,2,6},{3,4},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,3,7,5,1] => {{1,2,6},{3,4},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,5,1,3,7] => {{1,2,6},{3,4,5},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,5,1,7,3] => {{1,2,6,7},{3,4,5}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,6,4,5,3,1,7] => {{1,2,6},{3,4,5},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,5,3,7,1] => {{1,2,6,7},{3,4,5}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[2,6,4,5,7,1,3] => {{1,2,6},{3,4,5,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[2,6,4,5,7,3,1] => {{1,2,6},{3,4,5,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[2,6,4,7,1,3,5] => {{1,2,6},{3,4,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,7,1,5,3] => {{1,2,6},{3,4,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,7,3,1,5] => {{1,2,6},{3,4,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,7,3,5,1] => {{1,2,6},{3,4,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,7,5,1,3] => {{1,2,6},{3,4,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,4,7,5,3,1] => {{1,2,6},{3,4,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,1,3,4,7] => {{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,5,1,3,7,4] => {{1,2,6,7},{3,5},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,1,4,3,7] => {{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,5,1,4,7,3] => {{1,2,6,7},{3,5},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,1,7,3,4] => {{1,2,6},{3,5,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,1,7,4,3] => {{1,2,6},{3,5,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,3,1,4,7] => {{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,5,3,1,7,4] => {{1,2,6,7},{3,5},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,3,4,1,7] => {{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,5,3,4,7,1] => {{1,2,6,7},{3,5},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,3,7,1,4] => {{1,2,6},{3,5,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,3,7,4,1] => {{1,2,6},{3,5,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,4,1,3,7] => {{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,5,4,1,7,3] => {{1,2,6,7},{3,5},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,4,3,1,7] => {{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,5,4,3,7,1] => {{1,2,6,7},{3,5},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,4,7,1,3] => {{1,2,6},{3,5,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,4,7,3,1] => {{1,2,6},{3,5,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,7,1,3,4] => {{1,2,6},{3,5},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,7,1,4,3] => {{1,2,6},{3,5},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,7,3,1,4] => {{1,2,6},{3,5},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,7,3,4,1] => {{1,2,6},{3,5},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,7,4,1,3] => {{1,2,6},{3,5},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,5,7,4,3,1] => {{1,2,6},{3,5},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,7,1,3,4,5] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,1,3,5,4] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,1,4,3,5] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,1,4,5,3] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,1,5,3,4] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,1,5,4,3] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,3,1,4,5] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,3,1,5,4] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,3,4,1,5] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,3,4,5,1] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,3,5,1,4] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,3,5,4,1] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,4,1,3,5] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,4,1,5,3] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,4,3,1,5] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,4,3,5,1] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,4,5,1,3] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,4,5,3,1] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,6,7,5,1,3,4] => {{1,2,6},{3,7},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,7,5,1,4,3] => {{1,2,6},{3,7},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,7,5,3,1,4] => {{1,2,6},{3,7},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,7,5,3,4,1] => {{1,2,6},{3,7},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,7,5,4,1,3] => {{1,2,6},{3,7},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,6,7,5,4,3,1] => {{1,2,6},{3,7},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,1,3,4,5,6] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,1,3,4,6,5] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,1,3,5,4,6] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,1,3,5,6,4] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,1,3,6,4,5] => {{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,1,3,6,5,4] => {{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,1,4,3,5,6] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,1,4,3,6,5] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,1,4,5,3,6] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,1,4,5,6,3] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,1,4,6,3,5] => {{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,1,4,6,5,3] => {{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,1,5,3,4,6] => {{1,2,7},{3},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,1,5,3,6,4] => {{1,2,7},{3},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,1,5,4,3,6] => {{1,2,7},{3},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,1,5,4,6,3] => {{1,2,7},{3},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,1,5,6,3,4] => {{1,2,7},{3},{4,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,1,5,6,4,3] => {{1,2,7},{3},{4,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,1,6,3,4,5] => {{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,1,6,3,5,4] => {{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,1,6,4,3,5] => {{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,1,6,4,5,3] => {{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,1,6,5,3,4] => {{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,1,6,5,4,3] => {{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,1,4,5,6] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,3,1,4,6,5] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,3,1,5,4,6] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,3,1,5,6,4] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,3,1,6,4,5] => {{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,1,6,5,4] => {{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,4,1,5,6] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,3,4,1,6,5] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,3,4,5,1,6] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,3,4,5,6,1] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[2,7,3,4,6,1,5] => {{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,4,6,5,1] => {{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,5,1,4,6] => {{1,2,7},{3},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,5,1,6,4] => {{1,2,7},{3},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,5,4,1,6] => {{1,2,7},{3},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,5,4,6,1] => {{1,2,7},{3},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,5,6,1,4] => {{1,2,7},{3},{4,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,3,5,6,4,1] => {{1,2,7},{3},{4,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,3,6,1,4,5] => {{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,6,1,5,4] => {{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,6,4,1,5] => {{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,6,4,5,1] => {{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,6,5,1,4] => {{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,3,6,5,4,1] => {{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,4,1,3,5,6] => {{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,4,1,3,6,5] => {{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,4,1,5,3,6] => {{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,4,1,5,6,3] => {{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,4,1,6,3,5] => {{1,2,7},{3,4},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,4,1,6,5,3] => {{1,2,7},{3,4},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,4,3,1,5,6] => {{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,4,3,1,6,5] => {{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,4,3,5,1,6] => {{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,4,3,5,6,1] => {{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,4,3,6,1,5] => {{1,2,7},{3,4},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,4,3,6,5,1] => {{1,2,7},{3,4},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,4,5,1,3,6] => {{1,2,7},{3,4,5},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,4,5,1,6,3] => {{1,2,7},{3,4,5},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,4,5,3,1,6] => {{1,2,7},{3,4,5},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,4,5,3,6,1] => {{1,2,7},{3,4,5},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,4,5,6,1,3] => {{1,2,7},{3,4,5,6}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[2,7,4,5,6,3,1] => {{1,2,7},{3,4,5,6}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[2,7,4,6,1,3,5] => {{1,2,7},{3,4,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,4,6,1,5,3] => {{1,2,7},{3,4,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,4,6,3,1,5] => {{1,2,7},{3,4,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,4,6,3,5,1] => {{1,2,7},{3,4,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,4,6,5,1,3] => {{1,2,7},{3,4,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,4,6,5,3,1] => {{1,2,7},{3,4,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,5,1,3,4,6] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,5,1,3,6,4] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,5,1,4,3,6] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,5,1,4,6,3] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,5,1,6,3,4] => {{1,2,7},{3,5,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,5,1,6,4,3] => {{1,2,7},{3,5,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,5,3,1,4,6] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,5,3,1,6,4] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,5,3,4,1,6] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,5,3,4,6,1] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,5,3,6,1,4] => {{1,2,7},{3,5,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,5,3,6,4,1] => {{1,2,7},{3,5,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,5,4,1,3,6] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,5,4,1,6,3] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,5,4,3,1,6] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,5,4,3,6,1] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,5,4,6,1,3] => {{1,2,7},{3,5,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,5,4,6,3,1] => {{1,2,7},{3,5,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,5,6,1,3,4] => {{1,2,7},{3,5},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,5,6,1,4,3] => {{1,2,7},{3,5},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,5,6,3,1,4] => {{1,2,7},{3,5},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,5,6,3,4,1] => {{1,2,7},{3,5},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,5,6,4,1,3] => {{1,2,7},{3,5},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,5,6,4,3,1] => {{1,2,7},{3,5},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,6,1,3,4,5] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,1,3,5,4] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,1,4,3,5] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,1,4,5,3] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,1,5,3,4] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,1,5,4,3] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,3,1,4,5] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,3,1,5,4] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,3,4,1,5] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,3,4,5,1] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,3,5,1,4] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,3,5,4,1] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,4,1,3,5] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,4,1,5,3] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,4,3,1,5] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,4,3,5,1] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,4,5,1,3] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,4,5,3,1] => {{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[2,7,6,5,1,3,4] => {{1,2,7},{3,6},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,6,5,1,4,3] => {{1,2,7},{3,6},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,6,5,3,1,4] => {{1,2,7},{3,6},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,6,5,3,4,1] => {{1,2,7},{3,6},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,6,5,4,1,3] => {{1,2,7},{3,6},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[2,7,6,5,4,3,1] => {{1,2,7},{3,6},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,2,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[3,1,2,4,5,7,6] => {{1,3},{2},{4},{5},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,2,4,6,5,7] => {{1,3},{2},{4},{5,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,2,4,6,7,5] => {{1,3},{2},{4},{5,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,2,4,7,5,6] => {{1,3},{2},{4},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,2,4,7,6,5] => {{1,3},{2},{4},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,2,5,4,6,7] => {{1,3},{2},{4,5},{6},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,2,5,4,7,6] => {{1,3},{2},{4,5},{6,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,2,5,6,4,7] => {{1,3},{2},{4,5,6},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,2,5,6,7,4] => {{1,3},{2},{4,5,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,2,5,7,4,6] => {{1,3},{2},{4,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,2,5,7,6,4] => {{1,3},{2},{4,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,2,6,4,5,7] => {{1,3},{2},{4,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,2,6,4,7,5] => {{1,3},{2},{4,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,2,6,5,4,7] => {{1,3},{2},{4,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,2,6,5,7,4] => {{1,3},{2},{4,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,2,6,7,4,5] => {{1,3},{2},{4,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,2,6,7,5,4] => {{1,3},{2},{4,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,2,7,4,5,6] => {{1,3},{2},{4,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,2,7,4,6,5] => {{1,3},{2},{4,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,2,7,5,4,6] => {{1,3},{2},{4,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,2,7,5,6,4] => {{1,3},{2},{4,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,2,7,6,4,5] => {{1,3},{2},{4,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,2,7,6,5,4] => {{1,3},{2},{4,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,4,2,5,6,7] => {{1,3,4},{2},{5},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,4,2,5,7,6] => {{1,3,4},{2},{5},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,4,2,6,5,7] => {{1,3,4},{2},{5,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,4,2,6,7,5] => {{1,3,4},{2},{5,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,4,2,7,5,6] => {{1,3,4},{2},{5,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,4,2,7,6,5] => {{1,3,4},{2},{5,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,4,5,2,6,7] => {{1,3,4,5},{2},{6},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,4,5,2,7,6] => {{1,3,4,5},{2},{6,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,4,5,6,2,7] => {{1,3,4,5,6},{2},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,4,5,6,7,2] => {{1,3,4,5,6,7},{2}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,1,4,5,7,2,6] => {{1,3,4,5,7},{2},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,4,5,7,6,2] => {{1,3,4,5,7},{2},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,4,6,2,5,7] => {{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,4,6,2,7,5] => {{1,3,4,6,7},{2},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,4,6,5,2,7] => {{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,4,6,5,7,2] => {{1,3,4,6,7},{2},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,4,6,7,2,5] => {{1,3,4,6},{2},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,4,6,7,5,2] => {{1,3,4,6},{2},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,4,7,2,5,6] => {{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,4,7,2,6,5] => {{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,4,7,5,2,6] => {{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,4,7,5,6,2] => {{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,4,7,6,2,5] => {{1,3,4,7},{2},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,4,7,6,5,2] => {{1,3,4,7},{2},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,5,2,4,6,7] => {{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,5,2,4,7,6] => {{1,3,5},{2},{4},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,2,6,4,7] => {{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,2,6,7,4] => {{1,3,5,6,7},{2},{4}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,5,2,7,4,6] => {{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,2,7,6,4] => {{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,4,2,6,7] => {{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,5,4,2,7,6] => {{1,3,5},{2},{4},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,4,6,2,7] => {{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,4,6,7,2] => {{1,3,5,6,7},{2},{4}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,5,4,7,2,6] => {{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,4,7,6,2] => {{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,6,2,4,7] => {{1,3,5},{2},{4,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,6,2,7,4] => {{1,3,5},{2},{4,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,5,6,4,2,7] => {{1,3,5},{2},{4,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,6,4,7,2] => {{1,3,5},{2},{4,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,5,6,7,2,4] => {{1,3,5,7},{2},{4,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,5,6,7,4,2] => {{1,3,5,7},{2},{4,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,5,7,2,4,6] => {{1,3,5},{2},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,7,2,6,4] => {{1,3,5},{2},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,7,4,2,6] => {{1,3,5},{2},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,7,4,6,2] => {{1,3,5},{2},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,5,7,6,2,4] => {{1,3,5,6},{2},{4,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,5,7,6,4,2] => {{1,3,5,6},{2},{4,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,6,2,4,5,7] => {{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,6,2,4,7,5] => {{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,2,5,4,7] => {{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,6,2,5,7,4] => {{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,2,7,4,5] => {{1,3,6},{2},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,2,7,5,4] => {{1,3,6},{2},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,4,2,5,7] => {{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,6,4,2,7,5] => {{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,4,5,2,7] => {{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,6,4,5,7,2] => {{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,4,7,2,5] => {{1,3,6},{2},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,4,7,5,2] => {{1,3,6},{2},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,5,2,4,7] => {{1,3,6},{2},{4,5},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,5,2,7,4] => {{1,3,6,7},{2},{4,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,6,5,4,2,7] => {{1,3,6},{2},{4,5},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,5,4,7,2] => {{1,3,6,7},{2},{4,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,6,5,7,2,4] => {{1,3,6},{2},{4,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,6,5,7,4,2] => {{1,3,6},{2},{4,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,6,7,2,4,5] => {{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,7,2,5,4] => {{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,7,4,2,5] => {{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,7,4,5,2] => {{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,7,5,2,4] => {{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,6,7,5,4,2] => {{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,2,4,5,6] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,7,2,4,6,5] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,7,2,5,4,6] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,7,2,5,6,4] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,7,2,6,4,5] => {{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,2,6,5,4] => {{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,4,2,5,6] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,7,4,2,6,5] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,7,4,5,2,6] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,7,4,5,6,2] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,1,7,4,6,2,5] => {{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,4,6,5,2] => {{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,5,2,4,6] => {{1,3,7},{2},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,5,2,6,4] => {{1,3,7},{2},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,5,4,2,6] => {{1,3,7},{2},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,5,4,6,2] => {{1,3,7},{2},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,5,6,2,4] => {{1,3,7},{2},{4,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,7,5,6,4,2] => {{1,3,7},{2},{4,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,1,7,6,2,4,5] => {{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,6,2,5,4] => {{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,6,4,2,5] => {{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,6,4,5,2] => {{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,6,5,2,4] => {{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,1,7,6,5,4,2] => {{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,1,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[3,2,1,4,5,7,6] => {{1,3},{2},{4},{5},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,1,4,6,5,7] => {{1,3},{2},{4},{5,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,1,4,6,7,5] => {{1,3},{2},{4},{5,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,1,4,7,5,6] => {{1,3},{2},{4},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,1,4,7,6,5] => {{1,3},{2},{4},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,1,5,4,6,7] => {{1,3},{2},{4,5},{6},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,1,5,4,7,6] => {{1,3},{2},{4,5},{6,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,1,5,6,4,7] => {{1,3},{2},{4,5,6},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,1,5,6,7,4] => {{1,3},{2},{4,5,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,1,5,7,4,6] => {{1,3},{2},{4,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,1,5,7,6,4] => {{1,3},{2},{4,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,1,6,4,5,7] => {{1,3},{2},{4,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,1,6,4,7,5] => {{1,3},{2},{4,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,1,6,5,4,7] => {{1,3},{2},{4,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,1,6,5,7,4] => {{1,3},{2},{4,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,1,6,7,4,5] => {{1,3},{2},{4,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,1,6,7,5,4] => {{1,3},{2},{4,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,1,7,4,5,6] => {{1,3},{2},{4,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,1,7,4,6,5] => {{1,3},{2},{4,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,1,7,5,4,6] => {{1,3},{2},{4,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,1,7,5,6,4] => {{1,3},{2},{4,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,1,7,6,4,5] => {{1,3},{2},{4,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,1,7,6,5,4] => {{1,3},{2},{4,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,4,1,5,6,7] => {{1,3,4},{2},{5},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,4,1,5,7,6] => {{1,3,4},{2},{5},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,4,1,6,5,7] => {{1,3,4},{2},{5,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,4,1,6,7,5] => {{1,3,4},{2},{5,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,4,1,7,5,6] => {{1,3,4},{2},{5,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,4,1,7,6,5] => {{1,3,4},{2},{5,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,4,5,1,6,7] => {{1,3,4,5},{2},{6},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,4,5,1,7,6] => {{1,3,4,5},{2},{6,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,4,5,6,1,7] => {{1,3,4,5,6},{2},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,4,5,6,7,1] => {{1,3,4,5,6,7},{2}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,2,4,5,7,1,6] => {{1,3,4,5,7},{2},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,4,5,7,6,1] => {{1,3,4,5,7},{2},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,4,6,1,5,7] => {{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,4,6,1,7,5] => {{1,3,4,6,7},{2},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,4,6,5,1,7] => {{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,4,6,5,7,1] => {{1,3,4,6,7},{2},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,4,6,7,1,5] => {{1,3,4,6},{2},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,4,6,7,5,1] => {{1,3,4,6},{2},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,4,7,1,5,6] => {{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,4,7,1,6,5] => {{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,4,7,5,1,6] => {{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,4,7,5,6,1] => {{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,4,7,6,1,5] => {{1,3,4,7},{2},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,4,7,6,5,1] => {{1,3,4,7},{2},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,5,1,4,6,7] => {{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,5,1,4,7,6] => {{1,3,5},{2},{4},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,1,6,4,7] => {{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,1,6,7,4] => {{1,3,5,6,7},{2},{4}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,5,1,7,4,6] => {{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,1,7,6,4] => {{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,4,1,6,7] => {{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,5,4,1,7,6] => {{1,3,5},{2},{4},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,4,6,1,7] => {{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,4,6,7,1] => {{1,3,5,6,7},{2},{4}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,5,4,7,1,6] => {{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,4,7,6,1] => {{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,6,1,4,7] => {{1,3,5},{2},{4,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,6,1,7,4] => {{1,3,5},{2},{4,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,5,6,4,1,7] => {{1,3,5},{2},{4,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,6,4,7,1] => {{1,3,5},{2},{4,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,5,6,7,1,4] => {{1,3,5,7},{2},{4,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,5,6,7,4,1] => {{1,3,5,7},{2},{4,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,5,7,1,4,6] => {{1,3,5},{2},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,7,1,6,4] => {{1,3,5},{2},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,7,4,1,6] => {{1,3,5},{2},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,7,4,6,1] => {{1,3,5},{2},{4,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,5,7,6,1,4] => {{1,3,5,6},{2},{4,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,5,7,6,4,1] => {{1,3,5,6},{2},{4,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,6,1,4,5,7] => {{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,6,1,4,7,5] => {{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,1,5,4,7] => {{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,6,1,5,7,4] => {{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,1,7,4,5] => {{1,3,6},{2},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,1,7,5,4] => {{1,3,6},{2},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,4,1,5,7] => {{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,6,4,1,7,5] => {{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,4,5,1,7] => {{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,6,4,5,7,1] => {{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,4,7,1,5] => {{1,3,6},{2},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,4,7,5,1] => {{1,3,6},{2},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,5,1,4,7] => {{1,3,6},{2},{4,5},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,5,1,7,4] => {{1,3,6,7},{2},{4,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,6,5,4,1,7] => {{1,3,6},{2},{4,5},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,5,4,7,1] => {{1,3,6,7},{2},{4,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,6,5,7,1,4] => {{1,3,6},{2},{4,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,6,5,7,4,1] => {{1,3,6},{2},{4,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,6,7,1,4,5] => {{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,7,1,5,4] => {{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,7,4,1,5] => {{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,7,4,5,1] => {{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,7,5,1,4] => {{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,6,7,5,4,1] => {{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,1,4,5,6] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,7,1,4,6,5] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,7,1,5,4,6] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,7,1,5,6,4] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,7,1,6,4,5] => {{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,1,6,5,4] => {{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,4,1,5,6] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,7,4,1,6,5] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,7,4,5,1,6] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,7,4,5,6,1] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,2,7,4,6,1,5] => {{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,4,6,5,1] => {{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,5,1,4,6] => {{1,3,7},{2},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,5,1,6,4] => {{1,3,7},{2},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,5,4,1,6] => {{1,3,7},{2},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,5,4,6,1] => {{1,3,7},{2},{4,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,5,6,1,4] => {{1,3,7},{2},{4,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,7,5,6,4,1] => {{1,3,7},{2},{4,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,2,7,6,1,4,5] => {{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,6,1,5,4] => {{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,6,4,1,5] => {{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,6,4,5,1] => {{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,6,5,1,4] => {{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,2,7,6,5,4,1] => {{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,1,2,5,6,7] => {{1,3},{2,4},{5},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,4,1,2,5,7,6] => {{1,3},{2,4},{5},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,1,2,6,5,7] => {{1,3},{2,4},{5,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,1,2,6,7,5] => {{1,3},{2,4},{5,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,1,2,7,5,6] => {{1,3},{2,4},{5,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,1,2,7,6,5] => {{1,3},{2,4},{5,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,1,5,2,6,7] => {{1,3},{2,4,5},{6},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,1,5,2,7,6] => {{1,3},{2,4,5},{6,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,1,5,6,2,7] => {{1,3},{2,4,5,6},{7}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,1,5,6,7,2] => {{1,3},{2,4,5,6,7}} => [2,5] => ([(4,6),(5,6)],7) => 2

[3,4,1,5,7,2,6] => {{1,3},{2,4,5,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,1,5,7,6,2] => {{1,3},{2,4,5,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,1,6,2,5,7] => {{1,3},{2,4,6},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,1,6,2,7,5] => {{1,3},{2,4,6,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,1,6,5,2,7] => {{1,3},{2,4,6},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,1,6,5,7,2] => {{1,3},{2,4,6,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,1,6,7,2,5] => {{1,3},{2,4,6},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,1,6,7,5,2] => {{1,3},{2,4,6},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,1,7,2,5,6] => {{1,3},{2,4,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,1,7,2,6,5] => {{1,3},{2,4,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,1,7,5,2,6] => {{1,3},{2,4,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,1,7,5,6,2] => {{1,3},{2,4,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,1,7,6,2,5] => {{1,3},{2,4,7},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,1,7,6,5,2] => {{1,3},{2,4,7},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,2,1,5,6,7] => {{1,3},{2,4},{5},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,4,2,1,5,7,6] => {{1,3},{2,4},{5},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,2,1,6,5,7] => {{1,3},{2,4},{5,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,2,1,6,7,5] => {{1,3},{2,4},{5,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,2,1,7,5,6] => {{1,3},{2,4},{5,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,2,1,7,6,5] => {{1,3},{2,4},{5,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,2,5,1,6,7] => {{1,3},{2,4,5},{6},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,2,5,1,7,6] => {{1,3},{2,4,5},{6,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,2,5,6,1,7] => {{1,3},{2,4,5,6},{7}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,2,5,6,7,1] => {{1,3},{2,4,5,6,7}} => [2,5] => ([(4,6),(5,6)],7) => 2

[3,4,2,5,7,1,6] => {{1,3},{2,4,5,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,2,5,7,6,1] => {{1,3},{2,4,5,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,2,6,1,5,7] => {{1,3},{2,4,6},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,2,6,1,7,5] => {{1,3},{2,4,6,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,2,6,5,1,7] => {{1,3},{2,4,6},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,2,6,5,7,1] => {{1,3},{2,4,6,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,2,6,7,1,5] => {{1,3},{2,4,6},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,2,6,7,5,1] => {{1,3},{2,4,6},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,2,7,1,5,6] => {{1,3},{2,4,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,2,7,1,6,5] => {{1,3},{2,4,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,2,7,5,1,6] => {{1,3},{2,4,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,2,7,5,6,1] => {{1,3},{2,4,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,2,7,6,1,5] => {{1,3},{2,4,7},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,2,7,6,5,1] => {{1,3},{2,4,7},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,1,2,6,7] => {{1,3,5},{2,4},{6},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,5,1,2,7,6] => {{1,3,5},{2,4},{6,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,1,6,2,7] => {{1,3,5,6},{2,4},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,1,6,7,2] => {{1,3,5,6,7},{2,4}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,4,5,1,7,2,6] => {{1,3,5,7},{2,4},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,1,7,6,2] => {{1,3,5,7},{2,4},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,2,1,6,7] => {{1,3,5},{2,4},{6},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,5,2,1,7,6] => {{1,3,5},{2,4},{6,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,2,6,1,7] => {{1,3,5,6},{2,4},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,2,6,7,1] => {{1,3,5,6,7},{2,4}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,4,5,2,7,1,6] => {{1,3,5,7},{2,4},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,2,7,6,1] => {{1,3,5,7},{2,4},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,6,1,2,7] => {{1,3,5},{2,4,6},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,6,1,7,2] => {{1,3,5},{2,4,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[3,4,5,6,2,1,7] => {{1,3,5},{2,4,6},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,6,2,7,1] => {{1,3,5},{2,4,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[3,4,5,6,7,1,2] => {{1,3,5,7},{2,4,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,4,5,6,7,2,1] => {{1,3,5,7},{2,4,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,4,5,7,1,2,6] => {{1,3,5},{2,4,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,7,1,6,2] => {{1,3,5},{2,4,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,7,2,1,6] => {{1,3,5},{2,4,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,7,2,6,1] => {{1,3,5},{2,4,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,5,7,6,1,2] => {{1,3,5,6},{2,4,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,4,5,7,6,2,1] => {{1,3,5,6},{2,4,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,4,6,1,2,5,7] => {{1,3,6},{2,4},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,6,1,2,7,5] => {{1,3,6,7},{2,4},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,1,5,2,7] => {{1,3,6},{2,4},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,6,1,5,7,2] => {{1,3,6,7},{2,4},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,1,7,2,5] => {{1,3,6},{2,4},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,1,7,5,2] => {{1,3,6},{2,4},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,2,1,5,7] => {{1,3,6},{2,4},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,6,2,1,7,5] => {{1,3,6,7},{2,4},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,2,5,1,7] => {{1,3,6},{2,4},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,6,2,5,7,1] => {{1,3,6,7},{2,4},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,2,7,1,5] => {{1,3,6},{2,4},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,2,7,5,1] => {{1,3,6},{2,4},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,5,1,2,7] => {{1,3,6},{2,4,5},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,5,1,7,2] => {{1,3,6,7},{2,4,5}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,4,6,5,2,1,7] => {{1,3,6},{2,4,5},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,5,2,7,1] => {{1,3,6,7},{2,4,5}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,4,6,5,7,1,2] => {{1,3,6},{2,4,5,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[3,4,6,5,7,2,1] => {{1,3,6},{2,4,5,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[3,4,6,7,1,2,5] => {{1,3,6},{2,4,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,7,1,5,2] => {{1,3,6},{2,4,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,7,2,1,5] => {{1,3,6},{2,4,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,7,2,5,1] => {{1,3,6},{2,4,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,7,5,1,2] => {{1,3,6},{2,4,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,6,7,5,2,1] => {{1,3,6},{2,4,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,1,2,5,6] => {{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,7,1,2,6,5] => {{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,7,1,5,2,6] => {{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,7,1,5,6,2] => {{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,7,1,6,2,5] => {{1,3,7},{2,4},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,1,6,5,2] => {{1,3,7},{2,4},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,2,1,5,6] => {{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,7,2,1,6,5] => {{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,7,2,5,1,6] => {{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,7,2,5,6,1] => {{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,4,7,2,6,1,5] => {{1,3,7},{2,4},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,2,6,5,1] => {{1,3,7},{2,4},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,5,1,2,6] => {{1,3,7},{2,4,5},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,5,1,6,2] => {{1,3,7},{2,4,5},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,5,2,1,6] => {{1,3,7},{2,4,5},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,5,2,6,1] => {{1,3,7},{2,4,5},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,5,6,1,2] => {{1,3,7},{2,4,5,6}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[3,4,7,5,6,2,1] => {{1,3,7},{2,4,5,6}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[3,4,7,6,1,2,5] => {{1,3,7},{2,4,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,6,1,5,2] => {{1,3,7},{2,4,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,6,2,1,5] => {{1,3,7},{2,4,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,6,2,5,1] => {{1,3,7},{2,4,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,6,5,1,2] => {{1,3,7},{2,4,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,4,7,6,5,2,1] => {{1,3,7},{2,4,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,1,2,4,6,7] => {{1,3},{2,5},{4},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,5,1,2,4,7,6] => {{1,3},{2,5},{4},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,2,6,4,7] => {{1,3},{2,5,6},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,2,6,7,4] => {{1,3},{2,5,6,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,1,2,7,4,6] => {{1,3},{2,5,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,2,7,6,4] => {{1,3},{2,5,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,4,2,6,7] => {{1,3},{2,5},{4},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,5,1,4,2,7,6] => {{1,3},{2,5},{4},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,4,6,2,7] => {{1,3},{2,5,6},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,4,6,7,2] => {{1,3},{2,5,6,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,1,4,7,2,6] => {{1,3},{2,5,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,4,7,6,2] => {{1,3},{2,5,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,6,2,4,7] => {{1,3},{2,5},{4,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,6,2,7,4] => {{1,3},{2,5},{4,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,1,6,4,2,7] => {{1,3},{2,5},{4,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,6,4,7,2] => {{1,3},{2,5},{4,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,1,6,7,2,4] => {{1,3},{2,5,7},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,1,6,7,4,2] => {{1,3},{2,5,7},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,1,7,2,4,6] => {{1,3},{2,5},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,7,2,6,4] => {{1,3},{2,5},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,7,4,2,6] => {{1,3},{2,5},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,7,4,6,2] => {{1,3},{2,5},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,1,7,6,2,4] => {{1,3},{2,5,6},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,1,7,6,4,2] => {{1,3},{2,5,6},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,2,1,4,6,7] => {{1,3},{2,5},{4},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,5,2,1,4,7,6] => {{1,3},{2,5},{4},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,1,6,4,7] => {{1,3},{2,5,6},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,1,6,7,4] => {{1,3},{2,5,6,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,2,1,7,4,6] => {{1,3},{2,5,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,1,7,6,4] => {{1,3},{2,5,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,4,1,6,7] => {{1,3},{2,5},{4},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,5,2,4,1,7,6] => {{1,3},{2,5},{4},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,4,6,1,7] => {{1,3},{2,5,6},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,4,6,7,1] => {{1,3},{2,5,6,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,2,4,7,1,6] => {{1,3},{2,5,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,4,7,6,1] => {{1,3},{2,5,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,6,1,4,7] => {{1,3},{2,5},{4,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,6,1,7,4] => {{1,3},{2,5},{4,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,2,6,4,1,7] => {{1,3},{2,5},{4,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,6,4,7,1] => {{1,3},{2,5},{4,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,2,6,7,1,4] => {{1,3},{2,5,7},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,2,6,7,4,1] => {{1,3},{2,5,7},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,2,7,1,4,6] => {{1,3},{2,5},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,7,1,6,4] => {{1,3},{2,5},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,7,4,1,6] => {{1,3},{2,5},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,7,4,6,1] => {{1,3},{2,5},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,2,7,6,1,4] => {{1,3},{2,5,6},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,2,7,6,4,1] => {{1,3},{2,5,6},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,1,2,6,7] => {{1,3,4},{2,5},{6},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,4,1,2,7,6] => {{1,3,4},{2,5},{6,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,1,6,2,7] => {{1,3,4},{2,5,6},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,1,6,7,2] => {{1,3,4},{2,5,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[3,5,4,1,7,2,6] => {{1,3,4},{2,5,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,1,7,6,2] => {{1,3,4},{2,5,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,2,1,6,7] => {{1,3,4},{2,5},{6},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,4,2,1,7,6] => {{1,3,4},{2,5},{6,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,2,6,1,7] => {{1,3,4},{2,5,6},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,2,6,7,1] => {{1,3,4},{2,5,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[3,5,4,2,7,1,6] => {{1,3,4},{2,5,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,2,7,6,1] => {{1,3,4},{2,5,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,6,1,2,7] => {{1,3,4,6},{2,5},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,6,1,7,2] => {{1,3,4,6,7},{2,5}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,5,4,6,2,1,7] => {{1,3,4,6},{2,5},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,6,2,7,1] => {{1,3,4,6,7},{2,5}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,5,4,6,7,1,2] => {{1,3,4,6},{2,5,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,5,4,6,7,2,1] => {{1,3,4,6},{2,5,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,5,4,7,1,2,6] => {{1,3,4,7},{2,5},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,7,1,6,2] => {{1,3,4,7},{2,5},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,7,2,1,6] => {{1,3,4,7},{2,5},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,7,2,6,1] => {{1,3,4,7},{2,5},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,4,7,6,1,2] => {{1,3,4,7},{2,5,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,5,4,7,6,2,1] => {{1,3,4,7},{2,5,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,5,6,1,2,4,7] => {{1,3,6},{2,5},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,6,1,2,7,4] => {{1,3,6,7},{2,5},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,1,4,2,7] => {{1,3,6},{2,5},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,6,1,4,7,2] => {{1,3,6,7},{2,5},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,1,7,2,4] => {{1,3,6},{2,5,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,1,7,4,2] => {{1,3,6},{2,5,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,2,1,4,7] => {{1,3,6},{2,5},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,6,2,1,7,4] => {{1,3,6,7},{2,5},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,2,4,1,7] => {{1,3,6},{2,5},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,6,2,4,7,1] => {{1,3,6,7},{2,5},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,2,7,1,4] => {{1,3,6},{2,5,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,2,7,4,1] => {{1,3,6},{2,5,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,4,1,2,7] => {{1,3,6},{2,5},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,6,4,1,7,2] => {{1,3,6,7},{2,5},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,4,2,1,7] => {{1,3,6},{2,5},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,6,4,2,7,1] => {{1,3,6,7},{2,5},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,4,7,1,2] => {{1,3,6},{2,5,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,4,7,2,1] => {{1,3,6},{2,5,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,7,1,2,4] => {{1,3,6},{2,5},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,7,1,4,2] => {{1,3,6},{2,5},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,7,2,1,4] => {{1,3,6},{2,5},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,7,2,4,1] => {{1,3,6},{2,5},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,7,4,1,2] => {{1,3,6},{2,5},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,6,7,4,2,1] => {{1,3,6},{2,5},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,7,1,2,4,6] => {{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,7,1,2,6,4] => {{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,7,1,4,2,6] => {{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,7,1,4,6,2] => {{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,7,1,6,2,4] => {{1,3,7},{2,5,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,7,1,6,4,2] => {{1,3,7},{2,5,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,7,2,1,4,6] => {{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,7,2,1,6,4] => {{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,7,2,4,1,6] => {{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,7,2,4,6,1] => {{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,7,2,6,1,4] => {{1,3,7},{2,5,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,7,2,6,4,1] => {{1,3,7},{2,5,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,7,4,1,2,6] => {{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,7,4,1,6,2] => {{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,7,4,2,1,6] => {{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,7,4,2,6,1] => {{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,5,7,4,6,1,2] => {{1,3,7},{2,5,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,7,4,6,2,1] => {{1,3,7},{2,5,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,7,6,1,2,4] => {{1,3,7},{2,5},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,7,6,1,4,2] => {{1,3,7},{2,5},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,7,6,2,1,4] => {{1,3,7},{2,5},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,7,6,2,4,1] => {{1,3,7},{2,5},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,7,6,4,1,2] => {{1,3,7},{2,5},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,5,7,6,4,2,1] => {{1,3,7},{2,5},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,1,2,4,5,7] => {{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,6,1,2,4,7,5] => {{1,3},{2,6,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,2,5,4,7] => {{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,6,1,2,5,7,4] => {{1,3},{2,6,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,2,7,4,5] => {{1,3},{2,6},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,2,7,5,4] => {{1,3},{2,6},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,4,2,5,7] => {{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,6,1,4,2,7,5] => {{1,3},{2,6,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,4,5,2,7] => {{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,6,1,4,5,7,2] => {{1,3},{2,6,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,4,7,2,5] => {{1,3},{2,6},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,4,7,5,2] => {{1,3},{2,6},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,5,2,4,7] => {{1,3},{2,6},{4,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,5,2,7,4] => {{1,3},{2,6,7},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,1,5,4,2,7] => {{1,3},{2,6},{4,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,5,4,7,2] => {{1,3},{2,6,7},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,1,5,7,2,4] => {{1,3},{2,6},{4,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,1,5,7,4,2] => {{1,3},{2,6},{4,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,1,7,2,4,5] => {{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,7,2,5,4] => {{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,7,4,2,5] => {{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,7,4,5,2] => {{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,7,5,2,4] => {{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,1,7,5,4,2] => {{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,1,4,5,7] => {{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,6,2,1,4,7,5] => {{1,3},{2,6,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,1,5,4,7] => {{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,6,2,1,5,7,4] => {{1,3},{2,6,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,1,7,4,5] => {{1,3},{2,6},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,1,7,5,4] => {{1,3},{2,6},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,4,1,5,7] => {{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,6,2,4,1,7,5] => {{1,3},{2,6,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,4,5,1,7] => {{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,6,2,4,5,7,1] => {{1,3},{2,6,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,4,7,1,5] => {{1,3},{2,6},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,4,7,5,1] => {{1,3},{2,6},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,5,1,4,7] => {{1,3},{2,6},{4,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,5,1,7,4] => {{1,3},{2,6,7},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,2,5,4,1,7] => {{1,3},{2,6},{4,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,5,4,7,1] => {{1,3},{2,6,7},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,2,5,7,1,4] => {{1,3},{2,6},{4,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,2,5,7,4,1] => {{1,3},{2,6},{4,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,2,7,1,4,5] => {{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,7,1,5,4] => {{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,7,4,1,5] => {{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,7,4,5,1] => {{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,7,5,1,4] => {{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,2,7,5,4,1] => {{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,4,1,2,5,7] => {{1,3,4},{2,6},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,4,1,2,7,5] => {{1,3,4},{2,6,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,1,5,2,7] => {{1,3,4},{2,6},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,4,1,5,7,2] => {{1,3,4},{2,6,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,1,7,2,5] => {{1,3,4},{2,6},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,1,7,5,2] => {{1,3,4},{2,6},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,2,1,5,7] => {{1,3,4},{2,6},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,4,2,1,7,5] => {{1,3,4},{2,6,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,2,5,1,7] => {{1,3,4},{2,6},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,4,2,5,7,1] => {{1,3,4},{2,6,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,2,7,1,5] => {{1,3,4},{2,6},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,2,7,5,1] => {{1,3,4},{2,6},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,5,1,2,7] => {{1,3,4,5},{2,6},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,5,1,7,2] => {{1,3,4,5},{2,6,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,6,4,5,2,1,7] => {{1,3,4,5},{2,6},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,5,2,7,1] => {{1,3,4,5},{2,6,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,6,4,5,7,1,2] => {{1,3,4,5,7},{2,6}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,6,4,5,7,2,1] => {{1,3,4,5,7},{2,6}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,6,4,7,1,2,5] => {{1,3,4,7},{2,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,7,1,5,2] => {{1,3,4,7},{2,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,7,2,1,5] => {{1,3,4,7},{2,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,7,2,5,1] => {{1,3,4,7},{2,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,7,5,1,2] => {{1,3,4,7},{2,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,4,7,5,2,1] => {{1,3,4,7},{2,6},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,1,2,4,7] => {{1,3,5},{2,6},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,5,1,2,7,4] => {{1,3,5},{2,6,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,1,4,2,7] => {{1,3,5},{2,6},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,5,1,4,7,2] => {{1,3,5},{2,6,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,1,7,2,4] => {{1,3,5,7},{2,6},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,1,7,4,2] => {{1,3,5,7},{2,6},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,2,1,4,7] => {{1,3,5},{2,6},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,5,2,1,7,4] => {{1,3,5},{2,6,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,2,4,1,7] => {{1,3,5},{2,6},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,5,2,4,7,1] => {{1,3,5},{2,6,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,2,7,1,4] => {{1,3,5,7},{2,6},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,2,7,4,1] => {{1,3,5,7},{2,6},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,4,1,2,7] => {{1,3,5},{2,6},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,5,4,1,7,2] => {{1,3,5},{2,6,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,4,2,1,7] => {{1,3,5},{2,6},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,5,4,2,7,1] => {{1,3,5},{2,6,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,4,7,1,2] => {{1,3,5,7},{2,6},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,4,7,2,1] => {{1,3,5,7},{2,6},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,7,1,2,4] => {{1,3,5},{2,6},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,7,1,4,2] => {{1,3,5},{2,6},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,7,2,1,4] => {{1,3,5},{2,6},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,7,2,4,1] => {{1,3,5},{2,6},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,7,4,1,2] => {{1,3,5},{2,6},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,5,7,4,2,1] => {{1,3,5},{2,6},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,7,1,2,4,5] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,1,2,5,4] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,1,4,2,5] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,1,4,5,2] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,1,5,2,4] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,1,5,4,2] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,2,1,4,5] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,2,1,5,4] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,2,4,1,5] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,2,4,5,1] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,2,5,1,4] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,2,5,4,1] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,4,1,2,5] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,4,1,5,2] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,4,2,1,5] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,4,2,5,1] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,4,5,1,2] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,4,5,2,1] => {{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,6,7,5,1,2,4] => {{1,3,7},{2,6},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,7,5,1,4,2] => {{1,3,7},{2,6},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,7,5,2,1,4] => {{1,3,7},{2,6},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,7,5,2,4,1] => {{1,3,7},{2,6},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,7,5,4,1,2] => {{1,3,7},{2,6},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,6,7,5,4,2,1] => {{1,3,7},{2,6},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,1,2,4,5,6] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,1,2,4,6,5] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,1,2,5,4,6] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,1,2,5,6,4] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,1,2,6,4,5] => {{1,3},{2,7},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,1,2,6,5,4] => {{1,3},{2,7},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,1,4,2,5,6] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,1,4,2,6,5] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,1,4,5,2,6] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,1,4,5,6,2] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,1,4,6,2,5] => {{1,3},{2,7},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,1,4,6,5,2] => {{1,3},{2,7},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,1,5,2,4,6] => {{1,3},{2,7},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,1,5,2,6,4] => {{1,3},{2,7},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,1,5,4,2,6] => {{1,3},{2,7},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,1,5,4,6,2] => {{1,3},{2,7},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,1,5,6,2,4] => {{1,3},{2,7},{4,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,1,5,6,4,2] => {{1,3},{2,7},{4,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,1,6,2,4,5] => {{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,1,6,2,5,4] => {{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,1,6,4,2,5] => {{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,1,6,4,5,2] => {{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,1,6,5,2,4] => {{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,1,6,5,4,2] => {{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,1,4,5,6] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,2,1,4,6,5] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,2,1,5,4,6] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,2,1,5,6,4] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,2,1,6,4,5] => {{1,3},{2,7},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,1,6,5,4] => {{1,3},{2,7},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,4,1,5,6] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,2,4,1,6,5] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,2,4,5,1,6] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,2,4,5,6,1] => {{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[3,7,2,4,6,1,5] => {{1,3},{2,7},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,4,6,5,1] => {{1,3},{2,7},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,5,1,4,6] => {{1,3},{2,7},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,5,1,6,4] => {{1,3},{2,7},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,5,4,1,6] => {{1,3},{2,7},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,5,4,6,1] => {{1,3},{2,7},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,5,6,1,4] => {{1,3},{2,7},{4,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,2,5,6,4,1] => {{1,3},{2,7},{4,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,2,6,1,4,5] => {{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,6,1,5,4] => {{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,6,4,1,5] => {{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,6,4,5,1] => {{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,6,5,1,4] => {{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,2,6,5,4,1] => {{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,4,1,2,5,6] => {{1,3,4},{2,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,4,1,2,6,5] => {{1,3,4},{2,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,4,1,5,2,6] => {{1,3,4},{2,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,4,1,5,6,2] => {{1,3,4},{2,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,4,1,6,2,5] => {{1,3,4},{2,7},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,4,1,6,5,2] => {{1,3,4},{2,7},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,4,2,1,5,6] => {{1,3,4},{2,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,4,2,1,6,5] => {{1,3,4},{2,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,4,2,5,1,6] => {{1,3,4},{2,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,4,2,5,6,1] => {{1,3,4},{2,7},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,4,2,6,1,5] => {{1,3,4},{2,7},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,4,2,6,5,1] => {{1,3,4},{2,7},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,4,5,1,2,6] => {{1,3,4,5},{2,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,4,5,1,6,2] => {{1,3,4,5},{2,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,4,5,2,1,6] => {{1,3,4,5},{2,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,4,5,2,6,1] => {{1,3,4,5},{2,7},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,4,5,6,1,2] => {{1,3,4,5,6},{2,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,7,4,5,6,2,1] => {{1,3,4,5,6},{2,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[3,7,4,6,1,2,5] => {{1,3,4,6},{2,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,4,6,1,5,2] => {{1,3,4,6},{2,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,4,6,2,1,5] => {{1,3,4,6},{2,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,4,6,2,5,1] => {{1,3,4,6},{2,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,4,6,5,1,2] => {{1,3,4,6},{2,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,4,6,5,2,1] => {{1,3,4,6},{2,7},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,5,1,2,4,6] => {{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,5,1,2,6,4] => {{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,5,1,4,2,6] => {{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,5,1,4,6,2] => {{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,5,1,6,2,4] => {{1,3,5,6},{2,7},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,5,1,6,4,2] => {{1,3,5,6},{2,7},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,5,2,1,4,6] => {{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,5,2,1,6,4] => {{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,5,2,4,1,6] => {{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,5,2,4,6,1] => {{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,5,2,6,1,4] => {{1,3,5,6},{2,7},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,5,2,6,4,1] => {{1,3,5,6},{2,7},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,5,4,1,2,6] => {{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,5,4,1,6,2] => {{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,5,4,2,1,6] => {{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,5,4,2,6,1] => {{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,5,4,6,1,2] => {{1,3,5,6},{2,7},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,5,4,6,2,1] => {{1,3,5,6},{2,7},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,5,6,1,2,4] => {{1,3,5},{2,7},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,5,6,1,4,2] => {{1,3,5},{2,7},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,5,6,2,1,4] => {{1,3,5},{2,7},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,5,6,2,4,1] => {{1,3,5},{2,7},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,5,6,4,1,2] => {{1,3,5},{2,7},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,5,6,4,2,1] => {{1,3,5},{2,7},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,6,1,2,4,5] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,1,2,5,4] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,1,4,2,5] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,1,4,5,2] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,1,5,2,4] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,1,5,4,2] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,2,1,4,5] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,2,1,5,4] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,2,4,1,5] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,2,4,5,1] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,2,5,1,4] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,2,5,4,1] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,4,1,2,5] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,4,1,5,2] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,4,2,1,5] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,4,2,5,1] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,4,5,1,2] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,4,5,2,1] => {{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[3,7,6,5,1,2,4] => {{1,3,6},{2,7},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,6,5,1,4,2] => {{1,3,6},{2,7},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,6,5,2,1,4] => {{1,3,6},{2,7},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,6,5,2,4,1] => {{1,3,6},{2,7},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,6,5,4,1,2] => {{1,3,6},{2,7},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[3,7,6,5,4,2,1] => {{1,3,6},{2,7},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,2,3,5,6,7] => {{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[4,1,2,3,5,7,6] => {{1,4},{2},{3},{5},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,2,3,6,5,7] => {{1,4},{2},{3},{5,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,2,3,6,7,5] => {{1,4},{2},{3},{5,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,2,3,7,5,6] => {{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,2,3,7,6,5] => {{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,2,5,3,6,7] => {{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,2,5,3,7,6] => {{1,4,5},{2},{3},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,2,5,6,3,7] => {{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,2,5,6,7,3] => {{1,4,5,6,7},{2},{3}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,2,5,7,3,6] => {{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,2,5,7,6,3] => {{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,2,6,3,5,7] => {{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,2,6,3,7,5] => {{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,2,6,5,3,7] => {{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,2,6,5,7,3] => {{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,2,6,7,3,5] => {{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,2,6,7,5,3] => {{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,2,7,3,5,6] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,2,7,3,6,5] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,2,7,5,3,6] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,2,7,5,6,3] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,2,7,6,3,5] => {{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,2,7,6,5,3] => {{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,3,2,5,6,7] => {{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[4,1,3,2,5,7,6] => {{1,4},{2},{3},{5},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,3,2,6,5,7] => {{1,4},{2},{3},{5,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,3,2,6,7,5] => {{1,4},{2},{3},{5,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,3,2,7,5,6] => {{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,3,2,7,6,5] => {{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,3,5,2,6,7] => {{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,3,5,2,7,6] => {{1,4,5},{2},{3},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,3,5,6,2,7] => {{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,3,5,6,7,2] => {{1,4,5,6,7},{2},{3}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,3,5,7,2,6] => {{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,3,5,7,6,2] => {{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,3,6,2,5,7] => {{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,3,6,2,7,5] => {{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,3,6,5,2,7] => {{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,3,6,5,7,2] => {{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,3,6,7,2,5] => {{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,3,6,7,5,2] => {{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,3,7,2,5,6] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,3,7,2,6,5] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,3,7,5,2,6] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,3,7,5,6,2] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,3,7,6,2,5] => {{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,3,7,6,5,2] => {{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,2,3,6,7] => {{1,4},{2},{3,5},{6},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,5,2,3,7,6] => {{1,4},{2},{3,5},{6,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,2,6,3,7] => {{1,4},{2},{3,5,6},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,2,6,7,3] => {{1,4},{2},{3,5,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,5,2,7,3,6] => {{1,4},{2},{3,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,2,7,6,3] => {{1,4},{2},{3,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,3,2,6,7] => {{1,4},{2},{3,5},{6},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,5,3,2,7,6] => {{1,4},{2},{3,5},{6,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,3,6,2,7] => {{1,4},{2},{3,5,6},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,3,6,7,2] => {{1,4},{2},{3,5,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,5,3,7,2,6] => {{1,4},{2},{3,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,3,7,6,2] => {{1,4},{2},{3,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,6,2,3,7] => {{1,4,6},{2},{3,5},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,6,2,7,3] => {{1,4,6,7},{2},{3,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,5,6,3,2,7] => {{1,4,6},{2},{3,5},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,6,3,7,2] => {{1,4,6,7},{2},{3,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,5,6,7,2,3] => {{1,4,6},{2},{3,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,5,6,7,3,2] => {{1,4,6},{2},{3,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,5,7,2,3,6] => {{1,4,7},{2},{3,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,7,2,6,3] => {{1,4,7},{2},{3,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,7,3,2,6] => {{1,4,7},{2},{3,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,7,3,6,2] => {{1,4,7},{2},{3,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,5,7,6,2,3] => {{1,4,7},{2},{3,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,5,7,6,3,2] => {{1,4,7},{2},{3,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,6,2,3,5,7] => {{1,4},{2},{3,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,6,2,3,7,5] => {{1,4},{2},{3,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,2,5,3,7] => {{1,4},{2},{3,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,6,2,5,7,3] => {{1,4},{2},{3,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,2,7,3,5] => {{1,4},{2},{3,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,2,7,5,3] => {{1,4},{2},{3,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,3,2,5,7] => {{1,4},{2},{3,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,6,3,2,7,5] => {{1,4},{2},{3,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,3,5,2,7] => {{1,4},{2},{3,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,6,3,5,7,2] => {{1,4},{2},{3,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,3,7,2,5] => {{1,4},{2},{3,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,3,7,5,2] => {{1,4},{2},{3,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,5,2,3,7] => {{1,4,5},{2},{3,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,5,2,7,3] => {{1,4,5},{2},{3,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,6,5,3,2,7] => {{1,4,5},{2},{3,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,5,3,7,2] => {{1,4,5},{2},{3,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,6,5,7,2,3] => {{1,4,5,7},{2},{3,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,6,5,7,3,2] => {{1,4,5,7},{2},{3,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,6,7,2,3,5] => {{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,7,2,5,3] => {{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,7,3,2,5] => {{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,7,3,5,2] => {{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,7,5,2,3] => {{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,6,7,5,3,2] => {{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,2,3,5,6] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,7,2,3,6,5] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,7,2,5,3,6] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,7,2,5,6,3] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,7,2,6,3,5] => {{1,4},{2},{3,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,2,6,5,3] => {{1,4},{2},{3,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,3,2,5,6] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,7,3,2,6,5] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,7,3,5,2,6] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,7,3,5,6,2] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,1,7,3,6,2,5] => {{1,4},{2},{3,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,3,6,5,2] => {{1,4},{2},{3,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,5,2,3,6] => {{1,4,5},{2},{3,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,5,2,6,3] => {{1,4,5},{2},{3,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,5,3,2,6] => {{1,4,5},{2},{3,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,5,3,6,2] => {{1,4,5},{2},{3,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,5,6,2,3] => {{1,4,5,6},{2},{3,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,7,5,6,3,2] => {{1,4,5,6},{2},{3,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,1,7,6,2,3,5] => {{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,6,2,5,3] => {{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,6,3,2,5] => {{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,6,3,5,2] => {{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,6,5,2,3] => {{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,1,7,6,5,3,2] => {{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,1,3,5,6,7] => {{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[4,2,1,3,5,7,6] => {{1,4},{2},{3},{5},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,1,3,6,5,7] => {{1,4},{2},{3},{5,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,1,3,6,7,5] => {{1,4},{2},{3},{5,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,1,3,7,5,6] => {{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,1,3,7,6,5] => {{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,1,5,3,6,7] => {{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,1,5,3,7,6] => {{1,4,5},{2},{3},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,1,5,6,3,7] => {{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,1,5,6,7,3] => {{1,4,5,6,7},{2},{3}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,1,5,7,3,6] => {{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,1,5,7,6,3] => {{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,1,6,3,5,7] => {{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,1,6,3,7,5] => {{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,1,6,5,3,7] => {{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,1,6,5,7,3] => {{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,1,6,7,3,5] => {{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,1,6,7,5,3] => {{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,1,7,3,5,6] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,1,7,3,6,5] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,1,7,5,3,6] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,1,7,5,6,3] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,1,7,6,3,5] => {{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,1,7,6,5,3] => {{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,3,1,5,6,7] => {{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[4,2,3,1,5,7,6] => {{1,4},{2},{3},{5},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,3,1,6,5,7] => {{1,4},{2},{3},{5,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,3,1,6,7,5] => {{1,4},{2},{3},{5,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,3,1,7,5,6] => {{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,3,1,7,6,5] => {{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,3,5,1,6,7] => {{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,3,5,1,7,6] => {{1,4,5},{2},{3},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,3,5,6,1,7] => {{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,3,5,6,7,1] => {{1,4,5,6,7},{2},{3}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,3,5,7,1,6] => {{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,3,5,7,6,1] => {{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,3,6,1,5,7] => {{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,3,6,1,7,5] => {{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,3,6,5,1,7] => {{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,3,6,5,7,1] => {{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,3,6,7,1,5] => {{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,3,6,7,5,1] => {{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,3,7,1,5,6] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,3,7,1,6,5] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,3,7,5,1,6] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,3,7,5,6,1] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,3,7,6,1,5] => {{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,3,7,6,5,1] => {{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,1,3,6,7] => {{1,4},{2},{3,5},{6},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,5,1,3,7,6] => {{1,4},{2},{3,5},{6,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,1,6,3,7] => {{1,4},{2},{3,5,6},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,1,6,7,3] => {{1,4},{2},{3,5,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,5,1,7,3,6] => {{1,4},{2},{3,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,1,7,6,3] => {{1,4},{2},{3,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,3,1,6,7] => {{1,4},{2},{3,5},{6},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,5,3,1,7,6] => {{1,4},{2},{3,5},{6,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,3,6,1,7] => {{1,4},{2},{3,5,6},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,3,6,7,1] => {{1,4},{2},{3,5,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,5,3,7,1,6] => {{1,4},{2},{3,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,3,7,6,1] => {{1,4},{2},{3,5,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,6,1,3,7] => {{1,4,6},{2},{3,5},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,6,1,7,3] => {{1,4,6,7},{2},{3,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,5,6,3,1,7] => {{1,4,6},{2},{3,5},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,6,3,7,1] => {{1,4,6,7},{2},{3,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,5,6,7,1,3] => {{1,4,6},{2},{3,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,5,6,7,3,1] => {{1,4,6},{2},{3,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,5,7,1,3,6] => {{1,4,7},{2},{3,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,7,1,6,3] => {{1,4,7},{2},{3,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,7,3,1,6] => {{1,4,7},{2},{3,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,7,3,6,1] => {{1,4,7},{2},{3,5},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,5,7,6,1,3] => {{1,4,7},{2},{3,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,5,7,6,3,1] => {{1,4,7},{2},{3,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,6,1,3,5,7] => {{1,4},{2},{3,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,6,1,3,7,5] => {{1,4},{2},{3,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,1,5,3,7] => {{1,4},{2},{3,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,6,1,5,7,3] => {{1,4},{2},{3,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,1,7,3,5] => {{1,4},{2},{3,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,1,7,5,3] => {{1,4},{2},{3,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,3,1,5,7] => {{1,4},{2},{3,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,6,3,1,7,5] => {{1,4},{2},{3,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,3,5,1,7] => {{1,4},{2},{3,6},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,6,3,5,7,1] => {{1,4},{2},{3,6,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,3,7,1,5] => {{1,4},{2},{3,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,3,7,5,1] => {{1,4},{2},{3,6},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,5,1,3,7] => {{1,4,5},{2},{3,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,5,1,7,3] => {{1,4,5},{2},{3,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,6,5,3,1,7] => {{1,4,5},{2},{3,6},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,5,3,7,1] => {{1,4,5},{2},{3,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,6,5,7,1,3] => {{1,4,5,7},{2},{3,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,6,5,7,3,1] => {{1,4,5,7},{2},{3,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,6,7,1,3,5] => {{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,7,1,5,3] => {{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,7,3,1,5] => {{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,7,3,5,1] => {{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,7,5,1,3] => {{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,6,7,5,3,1] => {{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,1,3,5,6] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,7,1,3,6,5] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,7,1,5,3,6] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,7,1,5,6,3] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,7,1,6,3,5] => {{1,4},{2},{3,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,1,6,5,3] => {{1,4},{2},{3,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,3,1,5,6] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,7,3,1,6,5] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,7,3,5,1,6] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,7,3,5,6,1] => {{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,2,7,3,6,1,5] => {{1,4},{2},{3,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,3,6,5,1] => {{1,4},{2},{3,7},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,5,1,3,6] => {{1,4,5},{2},{3,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,5,1,6,3] => {{1,4,5},{2},{3,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,5,3,1,6] => {{1,4,5},{2},{3,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,5,3,6,1] => {{1,4,5},{2},{3,7},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,5,6,1,3] => {{1,4,5,6},{2},{3,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,7,5,6,3,1] => {{1,4,5,6},{2},{3,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,2,7,6,1,3,5] => {{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,6,1,5,3] => {{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,6,3,1,5] => {{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,6,3,5,1] => {{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,6,5,1,3] => {{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,2,7,6,5,3,1] => {{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,1,2,5,6,7] => {{1,4},{2,3},{5},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,3,1,2,5,7,6] => {{1,4},{2,3},{5},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,1,2,6,5,7] => {{1,4},{2,3},{5,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,1,2,6,7,5] => {{1,4},{2,3},{5,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,1,2,7,5,6] => {{1,4},{2,3},{5,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,1,2,7,6,5] => {{1,4},{2,3},{5,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,1,5,2,6,7] => {{1,4,5},{2,3},{6},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,1,5,2,7,6] => {{1,4,5},{2,3},{6,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,1,5,6,2,7] => {{1,4,5,6},{2,3},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,1,5,6,7,2] => {{1,4,5,6,7},{2,3}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[4,3,1,5,7,2,6] => {{1,4,5,7},{2,3},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,1,5,7,6,2] => {{1,4,5,7},{2,3},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,1,6,2,5,7] => {{1,4,6},{2,3},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,1,6,2,7,5] => {{1,4,6,7},{2,3},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,1,6,5,2,7] => {{1,4,6},{2,3},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,1,6,5,7,2] => {{1,4,6,7},{2,3},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,1,6,7,2,5] => {{1,4,6},{2,3},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,1,6,7,5,2] => {{1,4,6},{2,3},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,1,7,2,5,6] => {{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,1,7,2,6,5] => {{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,1,7,5,2,6] => {{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,1,7,5,6,2] => {{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,1,7,6,2,5] => {{1,4,7},{2,3},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,1,7,6,5,2] => {{1,4,7},{2,3},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,2,1,5,6,7] => {{1,4},{2,3},{5},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,3,2,1,5,7,6] => {{1,4},{2,3},{5},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,2,1,6,5,7] => {{1,4},{2,3},{5,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,2,1,6,7,5] => {{1,4},{2,3},{5,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,2,1,7,5,6] => {{1,4},{2,3},{5,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,2,1,7,6,5] => {{1,4},{2,3},{5,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,2,5,1,6,7] => {{1,4,5},{2,3},{6},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,2,5,1,7,6] => {{1,4,5},{2,3},{6,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,2,5,6,1,7] => {{1,4,5,6},{2,3},{7}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,2,5,6,7,1] => {{1,4,5,6,7},{2,3}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[4,3,2,5,7,1,6] => {{1,4,5,7},{2,3},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,2,5,7,6,1] => {{1,4,5,7},{2,3},{6}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,2,6,1,5,7] => {{1,4,6},{2,3},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,2,6,1,7,5] => {{1,4,6,7},{2,3},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,2,6,5,1,7] => {{1,4,6},{2,3},{5},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,2,6,5,7,1] => {{1,4,6,7},{2,3},{5}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,2,6,7,1,5] => {{1,4,6},{2,3},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,2,6,7,5,1] => {{1,4,6},{2,3},{5,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,2,7,1,5,6] => {{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,2,7,1,6,5] => {{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,2,7,5,1,6] => {{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,2,7,5,6,1] => {{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,2,7,6,1,5] => {{1,4,7},{2,3},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,2,7,6,5,1] => {{1,4,7},{2,3},{5,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,1,2,6,7] => {{1,4},{2,3,5},{6},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,5,1,2,7,6] => {{1,4},{2,3,5},{6,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,1,6,2,7] => {{1,4},{2,3,5,6},{7}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,1,6,7,2] => {{1,4},{2,3,5,6,7}} => [2,5] => ([(4,6),(5,6)],7) => 2

[4,3,5,1,7,2,6] => {{1,4},{2,3,5,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,1,7,6,2] => {{1,4},{2,3,5,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,2,1,6,7] => {{1,4},{2,3,5},{6},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,5,2,1,7,6] => {{1,4},{2,3,5},{6,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,2,6,1,7] => {{1,4},{2,3,5,6},{7}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,2,6,7,1] => {{1,4},{2,3,5,6,7}} => [2,5] => ([(4,6),(5,6)],7) => 2

[4,3,5,2,7,1,6] => {{1,4},{2,3,5,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,2,7,6,1] => {{1,4},{2,3,5,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,6,1,2,7] => {{1,4,6},{2,3,5},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,6,1,7,2] => {{1,4,6,7},{2,3,5}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[4,3,5,6,2,1,7] => {{1,4,6},{2,3,5},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,6,2,7,1] => {{1,4,6,7},{2,3,5}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[4,3,5,6,7,1,2] => {{1,4,6},{2,3,5,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[4,3,5,6,7,2,1] => {{1,4,6},{2,3,5,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[4,3,5,7,1,2,6] => {{1,4,7},{2,3,5},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,7,1,6,2] => {{1,4,7},{2,3,5},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,7,2,1,6] => {{1,4,7},{2,3,5},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,7,2,6,1] => {{1,4,7},{2,3,5},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,5,7,6,1,2] => {{1,4,7},{2,3,5,6}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[4,3,5,7,6,2,1] => {{1,4,7},{2,3,5,6}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[4,3,6,1,2,5,7] => {{1,4},{2,3,6},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,6,1,2,7,5] => {{1,4},{2,3,6,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,1,5,2,7] => {{1,4},{2,3,6},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,6,1,5,7,2] => {{1,4},{2,3,6,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,1,7,2,5] => {{1,4},{2,3,6},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,1,7,5,2] => {{1,4},{2,3,6},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,2,1,5,7] => {{1,4},{2,3,6},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,6,2,1,7,5] => {{1,4},{2,3,6,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,2,5,1,7] => {{1,4},{2,3,6},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,6,2,5,7,1] => {{1,4},{2,3,6,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,2,7,1,5] => {{1,4},{2,3,6},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,2,7,5,1] => {{1,4},{2,3,6},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,5,1,2,7] => {{1,4,5},{2,3,6},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,5,1,7,2] => {{1,4,5},{2,3,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[4,3,6,5,2,1,7] => {{1,4,5},{2,3,6},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,5,2,7,1] => {{1,4,5},{2,3,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[4,3,6,5,7,1,2] => {{1,4,5,7},{2,3,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[4,3,6,5,7,2,1] => {{1,4,5,7},{2,3,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[4,3,6,7,1,2,5] => {{1,4,7},{2,3,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,7,1,5,2] => {{1,4,7},{2,3,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,7,2,1,5] => {{1,4,7},{2,3,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,7,2,5,1] => {{1,4,7},{2,3,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,7,5,1,2] => {{1,4,7},{2,3,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,6,7,5,2,1] => {{1,4,7},{2,3,6},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,1,2,5,6] => {{1,4},{2,3,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,7,1,2,6,5] => {{1,4},{2,3,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,7,1,5,2,6] => {{1,4},{2,3,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,7,1,5,6,2] => {{1,4},{2,3,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,7,1,6,2,5] => {{1,4},{2,3,7},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,1,6,5,2] => {{1,4},{2,3,7},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,2,1,5,6] => {{1,4},{2,3,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,7,2,1,6,5] => {{1,4},{2,3,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,7,2,5,1,6] => {{1,4},{2,3,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,7,2,5,6,1] => {{1,4},{2,3,7},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,3,7,2,6,1,5] => {{1,4},{2,3,7},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,2,6,5,1] => {{1,4},{2,3,7},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,5,1,2,6] => {{1,4,5},{2,3,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,5,1,6,2] => {{1,4,5},{2,3,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,5,2,1,6] => {{1,4,5},{2,3,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,5,2,6,1] => {{1,4,5},{2,3,7},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,5,6,1,2] => {{1,4,5,6},{2,3,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[4,3,7,5,6,2,1] => {{1,4,5,6},{2,3,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[4,3,7,6,1,2,5] => {{1,4,6},{2,3,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,6,1,5,2] => {{1,4,6},{2,3,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,6,2,1,5] => {{1,4,6},{2,3,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,6,2,5,1] => {{1,4,6},{2,3,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,6,5,1,2] => {{1,4,6},{2,3,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,3,7,6,5,2,1] => {{1,4,6},{2,3,7},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,1,2,3,6,7] => {{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,5,1,2,3,7,6] => {{1,4},{2,5},{3},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,2,6,3,7] => {{1,4},{2,5,6},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,2,6,7,3] => {{1,4},{2,5,6,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,1,2,7,3,6] => {{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,2,7,6,3] => {{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,3,2,6,7] => {{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,5,1,3,2,7,6] => {{1,4},{2,5},{3},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,3,6,2,7] => {{1,4},{2,5,6},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,3,6,7,2] => {{1,4},{2,5,6,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,1,3,7,2,6] => {{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,3,7,6,2] => {{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,6,2,3,7] => {{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,6,2,7,3] => {{1,4,6,7},{2,5},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,1,6,3,2,7] => {{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,6,3,7,2] => {{1,4,6,7},{2,5},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,1,6,7,2,3] => {{1,4,6},{2,5,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,1,6,7,3,2] => {{1,4,6},{2,5,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,1,7,2,3,6] => {{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,7,2,6,3] => {{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,7,3,2,6] => {{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,7,3,6,2] => {{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,1,7,6,2,3] => {{1,4,7},{2,5,6},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,1,7,6,3,2] => {{1,4,7},{2,5,6},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,2,1,3,6,7] => {{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,5,2,1,3,7,6] => {{1,4},{2,5},{3},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,1,6,3,7] => {{1,4},{2,5,6},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,1,6,7,3] => {{1,4},{2,5,6,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,2,1,7,3,6] => {{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,1,7,6,3] => {{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,3,1,6,7] => {{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,5,2,3,1,7,6] => {{1,4},{2,5},{3},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,3,6,1,7] => {{1,4},{2,5,6},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,3,6,7,1] => {{1,4},{2,5,6,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,2,3,7,1,6] => {{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,3,7,6,1] => {{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,6,1,3,7] => {{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,6,1,7,3] => {{1,4,6,7},{2,5},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,2,6,3,1,7] => {{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,6,3,7,1] => {{1,4,6,7},{2,5},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,2,6,7,1,3] => {{1,4,6},{2,5,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,2,6,7,3,1] => {{1,4,6},{2,5,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,2,7,1,3,6] => {{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,7,1,6,3] => {{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,7,3,1,6] => {{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,7,3,6,1] => {{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,2,7,6,1,3] => {{1,4,7},{2,5,6},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,2,7,6,3,1] => {{1,4,7},{2,5,6},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,3,1,2,6,7] => {{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,5,3,1,2,7,6] => {{1,4},{2,5},{3},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,1,6,2,7] => {{1,4},{2,5,6},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,1,6,7,2] => {{1,4},{2,5,6,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,3,1,7,2,6] => {{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,1,7,6,2] => {{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,2,1,6,7] => {{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,5,3,2,1,7,6] => {{1,4},{2,5},{3},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,2,6,1,7] => {{1,4},{2,5,6},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,2,6,7,1] => {{1,4},{2,5,6,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,3,2,7,1,6] => {{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,2,7,6,1] => {{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,6,1,2,7] => {{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,6,1,7,2] => {{1,4,6,7},{2,5},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,3,6,2,1,7] => {{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,6,2,7,1] => {{1,4,6,7},{2,5},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,3,6,7,1,2] => {{1,4,6},{2,5,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,3,6,7,2,1] => {{1,4,6},{2,5,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,3,7,1,2,6] => {{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,7,1,6,2] => {{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,7,2,1,6] => {{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,7,2,6,1] => {{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,3,7,6,1,2] => {{1,4,7},{2,5,6},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,3,7,6,2,1] => {{1,4,7},{2,5,6},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,1,2,3,7] => {{1,4},{2,5},{3,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,6,1,2,7,3] => {{1,4},{2,5},{3,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,1,3,2,7] => {{1,4},{2,5},{3,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,6,1,3,7,2] => {{1,4},{2,5},{3,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,1,7,2,3] => {{1,4},{2,5,7},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,1,7,3,2] => {{1,4},{2,5,7},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,2,1,3,7] => {{1,4},{2,5},{3,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,6,2,1,7,3] => {{1,4},{2,5},{3,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,2,3,1,7] => {{1,4},{2,5},{3,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,6,2,3,7,1] => {{1,4},{2,5},{3,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,2,7,1,3] => {{1,4},{2,5,7},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,2,7,3,1] => {{1,4},{2,5,7},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,3,1,2,7] => {{1,4},{2,5},{3,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,6,3,1,7,2] => {{1,4},{2,5},{3,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,3,2,1,7] => {{1,4},{2,5},{3,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,6,3,2,7,1] => {{1,4},{2,5},{3,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,3,7,1,2] => {{1,4},{2,5,7},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,3,7,2,1] => {{1,4},{2,5,7},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,7,1,2,3] => {{1,4,7},{2,5},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,7,1,3,2] => {{1,4,7},{2,5},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,7,2,1,3] => {{1,4,7},{2,5},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,7,2,3,1] => {{1,4,7},{2,5},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,7,3,1,2] => {{1,4,7},{2,5},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,6,7,3,2,1] => {{1,4,7},{2,5},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,7,1,2,3,6] => {{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,7,1,2,6,3] => {{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,7,1,3,2,6] => {{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,7,1,3,6,2] => {{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,7,1,6,2,3] => {{1,4},{2,5,6},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,7,1,6,3,2] => {{1,4},{2,5,6},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,7,2,1,3,6] => {{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,7,2,1,6,3] => {{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,7,2,3,1,6] => {{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,7,2,3,6,1] => {{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,7,2,6,1,3] => {{1,4},{2,5,6},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,7,2,6,3,1] => {{1,4},{2,5,6},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,7,3,1,2,6] => {{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,7,3,1,6,2] => {{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,7,3,2,1,6] => {{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,7,3,2,6,1] => {{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,5,7,3,6,1,2] => {{1,4},{2,5,6},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,7,3,6,2,1] => {{1,4},{2,5,6},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,7,6,1,2,3] => {{1,4,6},{2,5},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,7,6,1,3,2] => {{1,4,6},{2,5},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,7,6,2,1,3] => {{1,4,6},{2,5},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,7,6,2,3,1] => {{1,4,6},{2,5},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,7,6,3,1,2] => {{1,4,6},{2,5},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,5,7,6,3,2,1] => {{1,4,6},{2,5},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,1,2,3,5,7] => {{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,6,1,2,3,7,5] => {{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,2,5,3,7] => {{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,6,1,2,5,7,3] => {{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,2,7,3,5] => {{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,2,7,5,3] => {{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,3,2,5,7] => {{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,6,1,3,2,7,5] => {{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,3,5,2,7] => {{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,6,1,3,5,7,2] => {{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,3,7,2,5] => {{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,3,7,5,2] => {{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,5,2,3,7] => {{1,4,5},{2,6},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,5,2,7,3] => {{1,4,5},{2,6,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,1,5,3,2,7] => {{1,4,5},{2,6},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,5,3,7,2] => {{1,4,5},{2,6,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,1,5,7,2,3] => {{1,4,5,7},{2,6},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,1,5,7,3,2] => {{1,4,5,7},{2,6},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,1,7,2,3,5] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,7,2,5,3] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,7,3,2,5] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,7,3,5,2] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,7,5,2,3] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,1,7,5,3,2] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,1,3,5,7] => {{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,6,2,1,3,7,5] => {{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,1,5,3,7] => {{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,6,2,1,5,7,3] => {{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,1,7,3,5] => {{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,1,7,5,3] => {{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,3,1,5,7] => {{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,6,2,3,1,7,5] => {{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,3,5,1,7] => {{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,6,2,3,5,7,1] => {{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,3,7,1,5] => {{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,3,7,5,1] => {{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,5,1,3,7] => {{1,4,5},{2,6},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,5,1,7,3] => {{1,4,5},{2,6,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,2,5,3,1,7] => {{1,4,5},{2,6},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,5,3,7,1] => {{1,4,5},{2,6,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,2,5,7,1,3] => {{1,4,5,7},{2,6},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,2,5,7,3,1] => {{1,4,5,7},{2,6},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,2,7,1,3,5] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,7,1,5,3] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,7,3,1,5] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,7,3,5,1] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,7,5,1,3] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,2,7,5,3,1] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,1,2,5,7] => {{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,6,3,1,2,7,5] => {{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,1,5,2,7] => {{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,6,3,1,5,7,2] => {{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,1,7,2,5] => {{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,1,7,5,2] => {{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,2,1,5,7] => {{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,6,3,2,1,7,5] => {{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,2,5,1,7] => {{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,6,3,2,5,7,1] => {{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,2,7,1,5] => {{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,2,7,5,1] => {{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,5,1,2,7] => {{1,4,5},{2,6},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,5,1,7,2] => {{1,4,5},{2,6,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,3,5,2,1,7] => {{1,4,5},{2,6},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,5,2,7,1] => {{1,4,5},{2,6,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,3,5,7,1,2] => {{1,4,5,7},{2,6},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,3,5,7,2,1] => {{1,4,5,7},{2,6},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,3,7,1,2,5] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,7,1,5,2] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,7,2,1,5] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,7,2,5,1] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,7,5,1,2] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,3,7,5,2,1] => {{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,5,1,2,3,7] => {{1,4},{2,6},{3,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,5,1,2,7,3] => {{1,4},{2,6,7},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,1,3,2,7] => {{1,4},{2,6},{3,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,5,1,3,7,2] => {{1,4},{2,6,7},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,1,7,2,3] => {{1,4},{2,6},{3,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,1,7,3,2] => {{1,4},{2,6},{3,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,2,1,3,7] => {{1,4},{2,6},{3,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,5,2,1,7,3] => {{1,4},{2,6,7},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,2,3,1,7] => {{1,4},{2,6},{3,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,5,2,3,7,1] => {{1,4},{2,6,7},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,2,7,1,3] => {{1,4},{2,6},{3,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,2,7,3,1] => {{1,4},{2,6},{3,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,3,1,2,7] => {{1,4},{2,6},{3,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,5,3,1,7,2] => {{1,4},{2,6,7},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,3,2,1,7] => {{1,4},{2,6},{3,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,5,3,2,7,1] => {{1,4},{2,6,7},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,3,7,1,2] => {{1,4},{2,6},{3,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,3,7,2,1] => {{1,4},{2,6},{3,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,7,1,2,3] => {{1,4,7},{2,6},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,7,1,3,2] => {{1,4,7},{2,6},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,7,2,1,3] => {{1,4,7},{2,6},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,7,2,3,1] => {{1,4,7},{2,6},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,7,3,1,2] => {{1,4,7},{2,6},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,5,7,3,2,1] => {{1,4,7},{2,6},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,7,1,2,3,5] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,1,2,5,3] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,1,3,2,5] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,1,3,5,2] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,1,5,2,3] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,1,5,3,2] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,2,1,3,5] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,2,1,5,3] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,2,3,1,5] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,2,3,5,1] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,2,5,1,3] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,2,5,3,1] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,3,1,2,5] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,3,1,5,2] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,3,2,1,5] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,3,2,5,1] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,3,5,1,2] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,3,5,2,1] => {{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,6,7,5,1,2,3] => {{1,4,5},{2,6},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,7,5,1,3,2] => {{1,4,5},{2,6},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,7,5,2,1,3] => {{1,4,5},{2,6},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,7,5,2,3,1] => {{1,4,5},{2,6},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,7,5,3,1,2] => {{1,4,5},{2,6},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,6,7,5,3,2,1] => {{1,4,5},{2,6},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,1,2,3,5,6] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,1,2,3,6,5] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,1,2,5,3,6] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,1,2,5,6,3] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,1,2,6,3,5] => {{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,1,2,6,5,3] => {{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,1,3,2,5,6] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,1,3,2,6,5] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,1,3,5,2,6] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,1,3,5,6,2] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,1,3,6,2,5] => {{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,1,3,6,5,2] => {{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,1,5,2,3,6] => {{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,1,5,2,6,3] => {{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,1,5,3,2,6] => {{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,1,5,3,6,2] => {{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,1,5,6,2,3] => {{1,4,5,6},{2,7},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,1,5,6,3,2] => {{1,4,5,6},{2,7},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,1,6,2,3,5] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,1,6,2,5,3] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,1,6,3,2,5] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,1,6,3,5,2] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,1,6,5,2,3] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,1,6,5,3,2] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,1,3,5,6] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,2,1,3,6,5] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,2,1,5,3,6] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,2,1,5,6,3] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,2,1,6,3,5] => {{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,1,6,5,3] => {{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,3,1,5,6] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,2,3,1,6,5] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,2,3,5,1,6] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,2,3,5,6,1] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,2,3,6,1,5] => {{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,3,6,5,1] => {{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,5,1,3,6] => {{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,5,1,6,3] => {{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,5,3,1,6] => {{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,5,3,6,1] => {{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,5,6,1,3] => {{1,4,5,6},{2,7},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,2,5,6,3,1] => {{1,4,5,6},{2,7},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,2,6,1,3,5] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,6,1,5,3] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,6,3,1,5] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,6,3,5,1] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,6,5,1,3] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,2,6,5,3,1] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,1,2,5,6] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,3,1,2,6,5] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,3,1,5,2,6] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,3,1,5,6,2] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,3,1,6,2,5] => {{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,1,6,5,2] => {{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,2,1,5,6] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,3,2,1,6,5] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,3,2,5,1,6] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,3,2,5,6,1] => {{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[4,7,3,2,6,1,5] => {{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,2,6,5,1] => {{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,5,1,2,6] => {{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,5,1,6,2] => {{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,5,2,1,6] => {{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,5,2,6,1] => {{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,5,6,1,2] => {{1,4,5,6},{2,7},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,3,5,6,2,1] => {{1,4,5,6},{2,7},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,3,6,1,2,5] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,6,1,5,2] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,6,2,1,5] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,6,2,5,1] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,6,5,1,2] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,3,6,5,2,1] => {{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,5,1,2,3,6] => {{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,5,1,2,6,3] => {{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,5,1,3,2,6] => {{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,5,1,3,6,2] => {{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,5,1,6,2,3] => {{1,4},{2,7},{3,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,5,1,6,3,2] => {{1,4},{2,7},{3,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,5,2,1,3,6] => {{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,5,2,1,6,3] => {{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,5,2,3,1,6] => {{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,5,2,3,6,1] => {{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,5,2,6,1,3] => {{1,4},{2,7},{3,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,5,2,6,3,1] => {{1,4},{2,7},{3,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,5,3,1,2,6] => {{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,5,3,1,6,2] => {{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,5,3,2,1,6] => {{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,5,3,2,6,1] => {{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,5,3,6,1,2] => {{1,4},{2,7},{3,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,5,3,6,2,1] => {{1,4},{2,7},{3,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,5,6,1,2,3] => {{1,4,6},{2,7},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,5,6,1,3,2] => {{1,4,6},{2,7},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,5,6,2,1,3] => {{1,4,6},{2,7},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,5,6,2,3,1] => {{1,4,6},{2,7},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,5,6,3,1,2] => {{1,4,6},{2,7},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,5,6,3,2,1] => {{1,4,6},{2,7},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,6,1,2,3,5] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,1,2,5,3] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,1,3,2,5] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,1,3,5,2] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,1,5,2,3] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,1,5,3,2] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,2,1,3,5] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,2,1,5,3] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,2,3,1,5] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,2,3,5,1] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,2,5,1,3] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,2,5,3,1] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,3,1,2,5] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,3,1,5,2] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,3,2,1,5] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,3,2,5,1] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,3,5,1,2] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,3,5,2,1] => {{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[4,7,6,5,1,2,3] => {{1,4,5},{2,7},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,6,5,1,3,2] => {{1,4,5},{2,7},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,6,5,2,1,3] => {{1,4,5},{2,7},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,6,5,2,3,1] => {{1,4,5},{2,7},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,6,5,3,1,2] => {{1,4,5},{2,7},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[4,7,6,5,3,2,1] => {{1,4,5},{2,7},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,1,2,3,4,6,7] => {{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[5,1,2,3,4,7,6] => {{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,3,6,4,7] => {{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,3,6,7,4] => {{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,2,3,7,4,6] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,3,7,6,4] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,4,3,6,7] => {{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[5,1,2,4,3,7,6] => {{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,4,6,3,7] => {{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,4,6,7,3] => {{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,2,4,7,3,6] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,4,7,6,3] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,6,3,4,7] => {{1,5},{2},{3},{4,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,6,3,7,4] => {{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,2,6,4,3,7] => {{1,5},{2},{3},{4,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,6,4,7,3] => {{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,2,6,7,3,4] => {{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,2,6,7,4,3] => {{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,2,7,3,4,6] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,7,3,6,4] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,7,4,3,6] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,7,4,6,3] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,2,7,6,3,4] => {{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,2,7,6,4,3] => {{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,3,2,4,6,7] => {{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[5,1,3,2,4,7,6] => {{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,2,6,4,7] => {{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,2,6,7,4] => {{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,3,2,7,4,6] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,2,7,6,4] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,4,2,6,7] => {{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[5,1,3,4,2,7,6] => {{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,4,6,2,7] => {{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,4,6,7,2] => {{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,3,4,7,2,6] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,4,7,6,2] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,6,2,4,7] => {{1,5},{2},{3},{4,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,6,2,7,4] => {{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,3,6,4,2,7] => {{1,5},{2},{3},{4,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,6,4,7,2] => {{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,3,6,7,2,4] => {{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,3,6,7,4,2] => {{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,3,7,2,4,6] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,7,2,6,4] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,7,4,2,6] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,7,4,6,2] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,3,7,6,2,4] => {{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,3,7,6,4,2] => {{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,2,3,6,7] => {{1,5},{2},{3,4},{6},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,4,2,3,7,6] => {{1,5},{2},{3,4},{6,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,2,6,3,7] => {{1,5,6},{2},{3,4},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,2,6,7,3] => {{1,5,6,7},{2},{3,4}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,1,4,2,7,3,6] => {{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,2,7,6,3] => {{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,3,2,6,7] => {{1,5},{2},{3,4},{6},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,4,3,2,7,6] => {{1,5},{2},{3,4},{6,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,3,6,2,7] => {{1,5,6},{2},{3,4},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,3,6,7,2] => {{1,5,6,7},{2},{3,4}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,1,4,3,7,2,6] => {{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,3,7,6,2] => {{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,6,2,3,7] => {{1,5},{2},{3,4,6},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,6,2,7,3] => {{1,5},{2},{3,4,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,1,4,6,3,2,7] => {{1,5},{2},{3,4,6},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,6,3,7,2] => {{1,5},{2},{3,4,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,1,4,6,7,2,3] => {{1,5,7},{2},{3,4,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,1,4,6,7,3,2] => {{1,5,7},{2},{3,4,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,1,4,7,2,3,6] => {{1,5},{2},{3,4,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,7,2,6,3] => {{1,5},{2},{3,4,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,7,3,2,6] => {{1,5},{2},{3,4,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,7,3,6,2] => {{1,5},{2},{3,4,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,4,7,6,2,3] => {{1,5,6},{2},{3,4,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,1,4,7,6,3,2] => {{1,5,6},{2},{3,4,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,1,6,2,3,4,7] => {{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,6,2,3,7,4] => {{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,2,4,3,7] => {{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,6,2,4,7,3] => {{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,2,7,3,4] => {{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,2,7,4,3] => {{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,3,2,4,7] => {{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,6,3,2,7,4] => {{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,3,4,2,7] => {{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,6,3,4,7,2] => {{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,3,7,2,4] => {{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,3,7,4,2] => {{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,4,2,3,7] => {{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,6,4,2,7,3] => {{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,4,3,2,7] => {{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,6,4,3,7,2] => {{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,4,7,2,3] => {{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,4,7,3,2] => {{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,7,2,3,4] => {{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,7,2,4,3] => {{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,7,3,2,4] => {{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,7,3,4,2] => {{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,7,4,2,3] => {{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,6,7,4,3,2] => {{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,7,2,3,4,6] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,7,2,3,6,4] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,7,2,4,3,6] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,7,2,4,6,3] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,7,2,6,3,4] => {{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,7,2,6,4,3] => {{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,7,3,2,4,6] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,7,3,2,6,4] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,7,3,4,2,6] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,7,3,4,6,2] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,7,3,6,2,4] => {{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,7,3,6,4,2] => {{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,7,4,2,3,6] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,7,4,2,6,3] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,7,4,3,2,6] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,7,4,3,6,2] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,1,7,4,6,2,3] => {{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,7,4,6,3,2] => {{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,7,6,2,3,4] => {{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,7,6,2,4,3] => {{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,7,6,3,2,4] => {{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,7,6,3,4,2] => {{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,7,6,4,2,3] => {{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,1,7,6,4,3,2] => {{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,1,3,4,6,7] => {{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[5,2,1,3,4,7,6] => {{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,3,6,4,7] => {{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,3,6,7,4] => {{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,1,3,7,4,6] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,3,7,6,4] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,4,3,6,7] => {{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[5,2,1,4,3,7,6] => {{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,4,6,3,7] => {{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,4,6,7,3] => {{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,1,4,7,3,6] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,4,7,6,3] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,6,3,4,7] => {{1,5},{2},{3},{4,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,6,3,7,4] => {{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,1,6,4,3,7] => {{1,5},{2},{3},{4,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,6,4,7,3] => {{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,1,6,7,3,4] => {{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,1,6,7,4,3] => {{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,1,7,3,4,6] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,7,3,6,4] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,7,4,3,6] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,7,4,6,3] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,1,7,6,3,4] => {{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,1,7,6,4,3] => {{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,3,1,4,6,7] => {{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[5,2,3,1,4,7,6] => {{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,1,6,4,7] => {{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,1,6,7,4] => {{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,3,1,7,4,6] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,1,7,6,4] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,4,1,6,7] => {{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[5,2,3,4,1,7,6] => {{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,4,6,1,7] => {{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,4,6,7,1] => {{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,3,4,7,1,6] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,4,7,6,1] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,6,1,4,7] => {{1,5},{2},{3},{4,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,6,1,7,4] => {{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,3,6,4,1,7] => {{1,5},{2},{3},{4,6},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,6,4,7,1] => {{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,3,6,7,1,4] => {{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,3,6,7,4,1] => {{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,3,7,1,4,6] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,7,1,6,4] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,7,4,1,6] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,7,4,6,1] => {{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,3,7,6,1,4] => {{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,3,7,6,4,1] => {{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,1,3,6,7] => {{1,5},{2},{3,4},{6},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,4,1,3,7,6] => {{1,5},{2},{3,4},{6,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,1,6,3,7] => {{1,5,6},{2},{3,4},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,1,6,7,3] => {{1,5,6,7},{2},{3,4}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,2,4,1,7,3,6] => {{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,1,7,6,3] => {{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,3,1,6,7] => {{1,5},{2},{3,4},{6},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,4,3,1,7,6] => {{1,5},{2},{3,4},{6,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,3,6,1,7] => {{1,5,6},{2},{3,4},{7}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,3,6,7,1] => {{1,5,6,7},{2},{3,4}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,2,4,3,7,1,6] => {{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,3,7,6,1] => {{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,6,1,3,7] => {{1,5},{2},{3,4,6},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,6,1,7,3] => {{1,5},{2},{3,4,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,2,4,6,3,1,7] => {{1,5},{2},{3,4,6},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,6,3,7,1] => {{1,5},{2},{3,4,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,2,4,6,7,1,3] => {{1,5,7},{2},{3,4,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,2,4,6,7,3,1] => {{1,5,7},{2},{3,4,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,2,4,7,1,3,6] => {{1,5},{2},{3,4,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,7,1,6,3] => {{1,5},{2},{3,4,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,7,3,1,6] => {{1,5},{2},{3,4,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,7,3,6,1] => {{1,5},{2},{3,4,7},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,4,7,6,1,3] => {{1,5,6},{2},{3,4,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,2,4,7,6,3,1] => {{1,5,6},{2},{3,4,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,2,6,1,3,4,7] => {{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,6,1,3,7,4] => {{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,1,4,3,7] => {{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,6,1,4,7,3] => {{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,1,7,3,4] => {{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,1,7,4,3] => {{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,3,1,4,7] => {{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,6,3,1,7,4] => {{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,3,4,1,7] => {{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,6,3,4,7,1] => {{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,3,7,1,4] => {{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,3,7,4,1] => {{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,4,1,3,7] => {{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,6,4,1,7,3] => {{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,4,3,1,7] => {{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,6,4,3,7,1] => {{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,4,7,1,3] => {{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,4,7,3,1] => {{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,7,1,3,4] => {{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,7,1,4,3] => {{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,7,3,1,4] => {{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,7,3,4,1] => {{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,7,4,1,3] => {{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,6,7,4,3,1] => {{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,7,1,3,4,6] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,7,1,3,6,4] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,7,1,4,3,6] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,7,1,4,6,3] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,7,1,6,3,4] => {{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,7,1,6,4,3] => {{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,7,3,1,4,6] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,7,3,1,6,4] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,7,3,4,1,6] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,7,3,4,6,1] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,7,3,6,1,4] => {{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,7,3,6,4,1] => {{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,7,4,1,3,6] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,7,4,1,6,3] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,7,4,3,1,6] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,7,4,3,6,1] => {{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,2,7,4,6,1,3] => {{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,7,4,6,3,1] => {{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,7,6,1,3,4] => {{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,7,6,1,4,3] => {{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,7,6,3,1,4] => {{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,7,6,3,4,1] => {{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,7,6,4,1,3] => {{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,2,7,6,4,3,1] => {{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,2,4,6,7] => {{1,5},{2,3},{4},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,3,1,2,4,7,6] => {{1,5},{2,3},{4},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,2,6,4,7] => {{1,5,6},{2,3},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,2,6,7,4] => {{1,5,6,7},{2,3},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,1,2,7,4,6] => {{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,2,7,6,4] => {{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,4,2,6,7] => {{1,5},{2,3},{4},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,3,1,4,2,7,6] => {{1,5},{2,3},{4},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,4,6,2,7] => {{1,5,6},{2,3},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,4,6,7,2] => {{1,5,6,7},{2,3},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,1,4,7,2,6] => {{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,4,7,6,2] => {{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,6,2,4,7] => {{1,5},{2,3},{4,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,6,2,7,4] => {{1,5},{2,3},{4,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,1,6,4,2,7] => {{1,5},{2,3},{4,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,6,4,7,2] => {{1,5},{2,3},{4,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,1,6,7,2,4] => {{1,5,7},{2,3},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,1,6,7,4,2] => {{1,5,7},{2,3},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,1,7,2,4,6] => {{1,5},{2,3},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,7,2,6,4] => {{1,5},{2,3},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,7,4,2,6] => {{1,5},{2,3},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,7,4,6,2] => {{1,5},{2,3},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,1,7,6,2,4] => {{1,5,6},{2,3},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,1,7,6,4,2] => {{1,5,6},{2,3},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,2,1,4,6,7] => {{1,5},{2,3},{4},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,3,2,1,4,7,6] => {{1,5},{2,3},{4},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,1,6,4,7] => {{1,5,6},{2,3},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,1,6,7,4] => {{1,5,6,7},{2,3},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,2,1,7,4,6] => {{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,1,7,6,4] => {{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,4,1,6,7] => {{1,5},{2,3},{4},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,3,2,4,1,7,6] => {{1,5},{2,3},{4},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,4,6,1,7] => {{1,5,6},{2,3},{4},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,4,6,7,1] => {{1,5,6,7},{2,3},{4}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,2,4,7,1,6] => {{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,4,7,6,1] => {{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,6,1,4,7] => {{1,5},{2,3},{4,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,6,1,7,4] => {{1,5},{2,3},{4,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,2,6,4,1,7] => {{1,5},{2,3},{4,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,6,4,7,1] => {{1,5},{2,3},{4,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,2,6,7,1,4] => {{1,5,7},{2,3},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,2,6,7,4,1] => {{1,5,7},{2,3},{4,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,2,7,1,4,6] => {{1,5},{2,3},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,7,1,6,4] => {{1,5},{2,3},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,7,4,1,6] => {{1,5},{2,3},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,7,4,6,1] => {{1,5},{2,3},{4,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,2,7,6,1,4] => {{1,5,6},{2,3},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,2,7,6,4,1] => {{1,5,6},{2,3},{4,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,1,2,6,7] => {{1,5},{2,3,4},{6},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,4,1,2,7,6] => {{1,5},{2,3,4},{6,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,1,6,2,7] => {{1,5,6},{2,3,4},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,1,6,7,2] => {{1,5,6,7},{2,3,4}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[5,3,4,1,7,2,6] => {{1,5,7},{2,3,4},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,1,7,6,2] => {{1,5,7},{2,3,4},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,2,1,6,7] => {{1,5},{2,3,4},{6},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,4,2,1,7,6] => {{1,5},{2,3,4},{6,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,2,6,1,7] => {{1,5,6},{2,3,4},{7}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,2,6,7,1] => {{1,5,6,7},{2,3,4}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

[5,3,4,2,7,1,6] => {{1,5,7},{2,3,4},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,2,7,6,1] => {{1,5,7},{2,3,4},{6}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,6,1,2,7] => {{1,5},{2,3,4,6},{7}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,6,1,7,2] => {{1,5},{2,3,4,6,7}} => [2,5] => ([(4,6),(5,6)],7) => 2

[5,3,4,6,2,1,7] => {{1,5},{2,3,4,6},{7}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,6,2,7,1] => {{1,5},{2,3,4,6,7}} => [2,5] => ([(4,6),(5,6)],7) => 2

[5,3,4,6,7,1,2] => {{1,5,7},{2,3,4,6}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[5,3,4,6,7,2,1] => {{1,5,7},{2,3,4,6}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[5,3,4,7,1,2,6] => {{1,5},{2,3,4,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,7,1,6,2] => {{1,5},{2,3,4,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,7,2,1,6] => {{1,5},{2,3,4,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,7,2,6,1] => {{1,5},{2,3,4,7},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,4,7,6,1,2] => {{1,5,6},{2,3,4,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[5,3,4,7,6,2,1] => {{1,5,6},{2,3,4,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[5,3,6,1,2,4,7] => {{1,5},{2,3,6},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,6,1,2,7,4] => {{1,5},{2,3,6,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,1,4,2,7] => {{1,5},{2,3,6},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,6,1,4,7,2] => {{1,5},{2,3,6,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,1,7,2,4] => {{1,5,7},{2,3,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,1,7,4,2] => {{1,5,7},{2,3,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,2,1,4,7] => {{1,5},{2,3,6},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,6,2,1,7,4] => {{1,5},{2,3,6,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,2,4,1,7] => {{1,5},{2,3,6},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,6,2,4,7,1] => {{1,5},{2,3,6,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,2,7,1,4] => {{1,5,7},{2,3,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,2,7,4,1] => {{1,5,7},{2,3,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,4,1,2,7] => {{1,5},{2,3,6},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,6,4,1,7,2] => {{1,5},{2,3,6,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,4,2,1,7] => {{1,5},{2,3,6},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,6,4,2,7,1] => {{1,5},{2,3,6,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,4,7,1,2] => {{1,5,7},{2,3,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,4,7,2,1] => {{1,5,7},{2,3,6},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,7,1,2,4] => {{1,5},{2,3,6},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,7,1,4,2] => {{1,5},{2,3,6},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,7,2,1,4] => {{1,5},{2,3,6},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,7,2,4,1] => {{1,5},{2,3,6},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,7,4,1,2] => {{1,5},{2,3,6},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,6,7,4,2,1] => {{1,5},{2,3,6},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,7,1,2,4,6] => {{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,7,1,2,6,4] => {{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,7,1,4,2,6] => {{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,7,1,4,6,2] => {{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,7,1,6,2,4] => {{1,5,6},{2,3,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,7,1,6,4,2] => {{1,5,6},{2,3,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,7,2,1,4,6] => {{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,7,2,1,6,4] => {{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,7,2,4,1,6] => {{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,7,2,4,6,1] => {{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,7,2,6,1,4] => {{1,5,6},{2,3,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,7,2,6,4,1] => {{1,5,6},{2,3,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,7,4,1,2,6] => {{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,7,4,1,6,2] => {{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,7,4,2,1,6] => {{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,7,4,2,6,1] => {{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,3,7,4,6,1,2] => {{1,5,6},{2,3,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,7,4,6,2,1] => {{1,5,6},{2,3,7},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,7,6,1,2,4] => {{1,5},{2,3,7},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,7,6,1,4,2] => {{1,5},{2,3,7},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,7,6,2,1,4] => {{1,5},{2,3,7},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,7,6,2,4,1] => {{1,5},{2,3,7},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,7,6,4,1,2] => {{1,5},{2,3,7},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,3,7,6,4,2,1] => {{1,5},{2,3,7},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,1,2,3,6,7] => {{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,4,1,2,3,7,6] => {{1,5},{2,4},{3},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,2,6,3,7] => {{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,2,6,7,3] => {{1,5,6,7},{2,4},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,1,2,7,3,6] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,2,7,6,3] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,3,2,6,7] => {{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,4,1,3,2,7,6] => {{1,5},{2,4},{3},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,3,6,2,7] => {{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,3,6,7,2] => {{1,5,6,7},{2,4},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,1,3,7,2,6] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,3,7,6,2] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,6,2,3,7] => {{1,5},{2,4,6},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,6,2,7,3] => {{1,5},{2,4,6,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,1,6,3,2,7] => {{1,5},{2,4,6},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,6,3,7,2] => {{1,5},{2,4,6,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,1,6,7,2,3] => {{1,5,7},{2,4,6},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,1,6,7,3,2] => {{1,5,7},{2,4,6},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,1,7,2,3,6] => {{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,7,2,6,3] => {{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,7,3,2,6] => {{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,7,3,6,2] => {{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,1,7,6,2,3] => {{1,5,6},{2,4,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,1,7,6,3,2] => {{1,5,6},{2,4,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,2,1,3,6,7] => {{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,4,2,1,3,7,6] => {{1,5},{2,4},{3},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,1,6,3,7] => {{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,1,6,7,3] => {{1,5,6,7},{2,4},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,2,1,7,3,6] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,1,7,6,3] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,3,1,6,7] => {{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,4,2,3,1,7,6] => {{1,5},{2,4},{3},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,3,6,1,7] => {{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,3,6,7,1] => {{1,5,6,7},{2,4},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,2,3,7,1,6] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,3,7,6,1] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,6,1,3,7] => {{1,5},{2,4,6},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,6,1,7,3] => {{1,5},{2,4,6,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,2,6,3,1,7] => {{1,5},{2,4,6},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,6,3,7,1] => {{1,5},{2,4,6,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,2,6,7,1,3] => {{1,5,7},{2,4,6},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,2,6,7,3,1] => {{1,5,7},{2,4,6},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,2,7,1,3,6] => {{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,7,1,6,3] => {{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,7,3,1,6] => {{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,7,3,6,1] => {{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,2,7,6,1,3] => {{1,5,6},{2,4,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,2,7,6,3,1] => {{1,5,6},{2,4,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,3,1,2,6,7] => {{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,4,3,1,2,7,6] => {{1,5},{2,4},{3},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,1,6,2,7] => {{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,1,6,7,2] => {{1,5,6,7},{2,4},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,3,1,7,2,6] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,1,7,6,2] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,2,1,6,7] => {{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,4,3,2,1,7,6] => {{1,5},{2,4},{3},{6,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,2,6,1,7] => {{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,2,6,7,1] => {{1,5,6,7},{2,4},{3}} => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,3,2,7,1,6] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,2,7,6,1] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,6,1,2,7] => {{1,5},{2,4,6},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,6,1,7,2] => {{1,5},{2,4,6,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,3,6,2,1,7] => {{1,5},{2,4,6},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,6,2,7,1] => {{1,5},{2,4,6,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,3,6,7,1,2] => {{1,5,7},{2,4,6},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,3,6,7,2,1] => {{1,5,7},{2,4,6},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,3,7,1,2,6] => {{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,7,1,6,2] => {{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,7,2,1,6] => {{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,7,2,6,1] => {{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,3,7,6,1,2] => {{1,5,6},{2,4,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,3,7,6,2,1] => {{1,5,6},{2,4,7},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,1,2,3,7] => {{1,5},{2,4},{3,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,6,1,2,7,3] => {{1,5},{2,4},{3,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,1,3,2,7] => {{1,5},{2,4},{3,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,6,1,3,7,2] => {{1,5},{2,4},{3,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,1,7,2,3] => {{1,5,7},{2,4},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,1,7,3,2] => {{1,5,7},{2,4},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,2,1,3,7] => {{1,5},{2,4},{3,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,6,2,1,7,3] => {{1,5},{2,4},{3,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,2,3,1,7] => {{1,5},{2,4},{3,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,6,2,3,7,1] => {{1,5},{2,4},{3,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,2,7,1,3] => {{1,5,7},{2,4},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,2,7,3,1] => {{1,5,7},{2,4},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,3,1,2,7] => {{1,5},{2,4},{3,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,6,3,1,7,2] => {{1,5},{2,4},{3,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,3,2,1,7] => {{1,5},{2,4},{3,6},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,6,3,2,7,1] => {{1,5},{2,4},{3,6,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,3,7,1,2] => {{1,5,7},{2,4},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,3,7,2,1] => {{1,5,7},{2,4},{3,6}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,7,1,2,3] => {{1,5},{2,4,7},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,7,1,3,2] => {{1,5},{2,4,7},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,7,2,1,3] => {{1,5},{2,4,7},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,7,2,3,1] => {{1,5},{2,4,7},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,7,3,1,2] => {{1,5},{2,4,7},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,6,7,3,2,1] => {{1,5},{2,4,7},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,7,1,2,3,6] => {{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,7,1,2,6,3] => {{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,7,1,3,2,6] => {{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,7,1,3,6,2] => {{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,7,1,6,2,3] => {{1,5,6},{2,4},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,7,1,6,3,2] => {{1,5,6},{2,4},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,7,2,1,3,6] => {{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,7,2,1,6,3] => {{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,7,2,3,1,6] => {{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,7,2,3,6,1] => {{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,7,2,6,1,3] => {{1,5,6},{2,4},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,7,2,6,3,1] => {{1,5,6},{2,4},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,7,3,1,2,6] => {{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,7,3,1,6,2] => {{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,7,3,2,1,6] => {{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,7,3,2,6,1] => {{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,4,7,3,6,1,2] => {{1,5,6},{2,4},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,7,3,6,2,1] => {{1,5,6},{2,4},{3,7}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,7,6,1,2,3] => {{1,5},{2,4,6},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,7,6,1,3,2] => {{1,5},{2,4,6},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,7,6,2,1,3] => {{1,5},{2,4,6},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,7,6,2,3,1] => {{1,5},{2,4,6},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,7,6,3,1,2] => {{1,5},{2,4,6},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,4,7,6,3,2,1] => {{1,5},{2,4,6},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,1,2,3,4,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,1,2,3,7,4] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,2,4,3,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,1,2,4,7,3] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,2,7,3,4] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,2,7,4,3] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,3,2,4,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,1,3,2,7,4] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,3,4,2,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,1,3,4,7,2] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,3,7,2,4] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,3,7,4,2] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,4,2,3,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,1,4,2,7,3] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,4,3,2,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,1,4,3,7,2] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,4,7,2,3] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,4,7,3,2] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,7,2,3,4] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,7,2,4,3] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,7,3,2,4] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,7,3,4,2] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,7,4,2,3] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,1,7,4,3,2] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,1,3,4,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,2,1,3,7,4] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,1,4,3,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,2,1,4,7,3] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,1,7,3,4] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,1,7,4,3] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,3,1,4,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,2,3,1,7,4] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,3,4,1,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,2,3,4,7,1] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,3,7,1,4] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,3,7,4,1] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,4,1,3,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,2,4,1,7,3] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,4,3,1,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,2,4,3,7,1] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,4,7,1,3] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,4,7,3,1] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,7,1,3,4] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,7,1,4,3] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,7,3,1,4] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,7,3,4,1] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,7,4,1,3] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,2,7,4,3,1] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,1,2,4,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,3,1,2,7,4] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,1,4,2,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,3,1,4,7,2] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,1,7,2,4] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,1,7,4,2] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,2,1,4,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,3,2,1,7,4] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,2,4,1,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,3,2,4,7,1] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,2,7,1,4] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,2,7,4,1] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,4,1,2,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,3,4,1,7,2] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,4,2,1,7] => {{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,6,3,4,2,7,1] => {{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,4,7,1,2] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,4,7,2,1] => {{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,7,1,2,4] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,7,1,4,2] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,7,2,1,4] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,7,2,4,1] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,7,4,1,2] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,3,7,4,2,1] => {{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,4,1,2,3,7] => {{1,5},{2,6},{3,4},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,4,1,2,7,3] => {{1,5},{2,6,7},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,1,3,2,7] => {{1,5},{2,6},{3,4},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,4,1,3,7,2] => {{1,5},{2,6,7},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,1,7,2,3] => {{1,5,7},{2,6},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,1,7,3,2] => {{1,5,7},{2,6},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,2,1,3,7] => {{1,5},{2,6},{3,4},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,4,2,1,7,3] => {{1,5},{2,6,7},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,2,3,1,7] => {{1,5},{2,6},{3,4},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,4,2,3,7,1] => {{1,5},{2,6,7},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,2,7,1,3] => {{1,5,7},{2,6},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,2,7,3,1] => {{1,5,7},{2,6},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,3,1,2,7] => {{1,5},{2,6},{3,4},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,4,3,1,7,2] => {{1,5},{2,6,7},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,3,2,1,7] => {{1,5},{2,6},{3,4},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,4,3,2,7,1] => {{1,5},{2,6,7},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,3,7,1,2] => {{1,5,7},{2,6},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,3,7,2,1] => {{1,5,7},{2,6},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,7,1,2,3] => {{1,5},{2,6},{3,4,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,7,1,3,2] => {{1,5},{2,6},{3,4,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,7,2,1,3] => {{1,5},{2,6},{3,4,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,7,2,3,1] => {{1,5},{2,6},{3,4,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,7,3,1,2] => {{1,5},{2,6},{3,4,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,4,7,3,2,1] => {{1,5},{2,6},{3,4,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,6,7,1,2,3,4] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,1,2,4,3] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,1,3,2,4] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,1,3,4,2] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,1,4,2,3] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,1,4,3,2] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,2,1,3,4] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,2,1,4,3] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,2,3,1,4] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,2,3,4,1] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,2,4,1,3] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,2,4,3,1] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,3,1,2,4] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,3,1,4,2] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,3,2,1,4] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,3,2,4,1] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,3,4,1,2] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,3,4,2,1] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,4,1,2,3] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,4,1,3,2] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,4,2,1,3] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,4,2,3,1] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,4,3,1,2] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,6,7,4,3,2,1] => {{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,1,2,3,4,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,1,2,3,6,4] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,1,2,4,3,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,1,2,4,6,3] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,1,2,6,3,4] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,1,2,6,4,3] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,1,3,2,4,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,1,3,2,6,4] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,1,3,4,2,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,1,3,4,6,2] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,1,3,6,2,4] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,1,3,6,4,2] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,1,4,2,3,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,1,4,2,6,3] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,1,4,3,2,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,1,4,3,6,2] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,1,4,6,2,3] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,1,4,6,3,2] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,1,6,2,3,4] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,1,6,2,4,3] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,1,6,3,2,4] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,1,6,3,4,2] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,1,6,4,2,3] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,1,6,4,3,2] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,2,1,3,4,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,2,1,3,6,4] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,2,1,4,3,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,2,1,4,6,3] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,2,1,6,3,4] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,2,1,6,4,3] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,2,3,1,4,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,2,3,1,6,4] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,2,3,4,1,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,2,3,4,6,1] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,2,3,6,1,4] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,2,3,6,4,1] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,2,4,1,3,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,2,4,1,6,3] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,2,4,3,1,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,2,4,3,6,1] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,2,4,6,1,3] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,2,4,6,3,1] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,2,6,1,3,4] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,2,6,1,4,3] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,2,6,3,1,4] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,2,6,3,4,1] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,2,6,4,1,3] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,2,6,4,3,1] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,3,1,2,4,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,3,1,2,6,4] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,3,1,4,2,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,3,1,4,6,2] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,3,1,6,2,4] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,3,1,6,4,2] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,3,2,1,4,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,3,2,1,6,4] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,3,2,4,1,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,3,2,4,6,1] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,3,2,6,1,4] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,3,2,6,4,1] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,3,4,1,2,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,3,4,1,6,2] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,3,4,2,1,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,3,4,2,6,1] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[5,7,3,4,6,1,2] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,3,4,6,2,1] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,3,6,1,2,4] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,3,6,1,4,2] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,3,6,2,1,4] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,3,6,2,4,1] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,3,6,4,1,2] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,3,6,4,2,1] => {{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,4,1,2,3,6] => {{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,4,1,2,6,3] => {{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,4,1,3,2,6] => {{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,4,1,3,6,2] => {{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,4,1,6,2,3] => {{1,5,6},{2,7},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,7,4,1,6,3,2] => {{1,5,6},{2,7},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,7,4,2,1,3,6] => {{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,4,2,1,6,3] => {{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,4,2,3,1,6] => {{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,4,2,3,6,1] => {{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,4,2,6,1,3] => {{1,5,6},{2,7},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,7,4,2,6,3,1] => {{1,5,6},{2,7},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,7,4,3,1,2,6] => {{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,4,3,1,6,2] => {{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,4,3,2,1,6] => {{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,4,3,2,6,1] => {{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,4,3,6,1,2] => {{1,5,6},{2,7},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,7,4,3,6,2,1] => {{1,5,6},{2,7},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,7,4,6,1,2,3] => {{1,5},{2,7},{3,4,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,7,4,6,1,3,2] => {{1,5},{2,7},{3,4,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,7,4,6,2,1,3] => {{1,5},{2,7},{3,4,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,7,4,6,2,3,1] => {{1,5},{2,7},{3,4,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,7,4,6,3,1,2] => {{1,5},{2,7},{3,4,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,7,4,6,3,2,1] => {{1,5},{2,7},{3,4,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[5,7,6,1,2,3,4] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,1,2,4,3] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,1,3,2,4] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,1,3,4,2] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,1,4,2,3] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,1,4,3,2] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,2,1,3,4] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,2,1,4,3] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,2,3,1,4] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,2,3,4,1] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,2,4,1,3] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,2,4,3,1] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,3,1,2,4] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,3,1,4,2] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,3,2,1,4] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,3,2,4,1] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,3,4,1,2] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,3,4,2,1] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,4,1,2,3] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,4,1,3,2] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,4,2,1,3] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,4,2,3,1] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,4,3,1,2] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[5,7,6,4,3,2,1] => {{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,2,3,4,5,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,1,2,3,4,7,5] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,3,5,4,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,1,2,3,5,7,4] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,3,7,4,5] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,3,7,5,4] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,4,3,5,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,1,2,4,3,7,5] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,4,5,3,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,1,2,4,5,7,3] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,4,7,3,5] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,4,7,5,3] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,5,3,4,7] => {{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,5,3,7,4] => {{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,2,5,4,3,7] => {{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,5,4,7,3] => {{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,2,5,7,3,4] => {{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,2,5,7,4,3] => {{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,2,7,3,4,5] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,7,3,5,4] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,7,4,3,5] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,7,4,5,3] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,7,5,3,4] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,2,7,5,4,3] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,2,4,5,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,1,3,2,4,7,5] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,2,5,4,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,1,3,2,5,7,4] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,2,7,4,5] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,2,7,5,4] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,4,2,5,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,1,3,4,2,7,5] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,4,5,2,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,1,3,4,5,7,2] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,4,7,2,5] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,4,7,5,2] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,5,2,4,7] => {{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,5,2,7,4] => {{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,3,5,4,2,7] => {{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,5,4,7,2] => {{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,3,5,7,2,4] => {{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,3,5,7,4,2] => {{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,3,7,2,4,5] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,7,2,5,4] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,7,4,2,5] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,7,4,5,2] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,7,5,2,4] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,3,7,5,4,2] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,4,2,3,5,7] => {{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,4,2,3,7,5] => {{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,2,5,3,7] => {{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,4,2,5,7,3] => {{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,2,7,3,5] => {{1,6},{2},{3,4},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,2,7,5,3] => {{1,6},{2},{3,4},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,3,2,5,7] => {{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,4,3,2,7,5] => {{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,3,5,2,7] => {{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,4,3,5,7,2] => {{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,3,7,2,5] => {{1,6},{2},{3,4},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,3,7,5,2] => {{1,6},{2},{3,4},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,5,2,3,7] => {{1,6},{2},{3,4,5},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,5,2,7,3] => {{1,6,7},{2},{3,4,5}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,1,4,5,3,2,7] => {{1,6},{2},{3,4,5},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,5,3,7,2] => {{1,6,7},{2},{3,4,5}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,1,4,5,7,2,3] => {{1,6},{2},{3,4,5,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,1,4,5,7,3,2] => {{1,6},{2},{3,4,5,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,1,4,7,2,3,5] => {{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,7,2,5,3] => {{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,7,3,2,5] => {{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,7,3,5,2] => {{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,7,5,2,3] => {{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,4,7,5,3,2] => {{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,2,3,4,7] => {{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,5,2,3,7,4] => {{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,2,4,3,7] => {{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,5,2,4,7,3] => {{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,2,7,3,4] => {{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,2,7,4,3] => {{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,3,2,4,7] => {{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,5,3,2,7,4] => {{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,3,4,2,7] => {{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,5,3,4,7,2] => {{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,3,7,2,4] => {{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,3,7,4,2] => {{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,4,2,3,7] => {{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,5,4,2,7,3] => {{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,4,3,2,7] => {{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,5,4,3,7,2] => {{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,4,7,2,3] => {{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,4,7,3,2] => {{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,7,2,3,4] => {{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,7,2,4,3] => {{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,7,3,2,4] => {{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,7,3,4,2] => {{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,7,4,2,3] => {{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,5,7,4,3,2] => {{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,7,2,3,4,5] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,2,3,5,4] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,2,4,3,5] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,2,4,5,3] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,2,5,3,4] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,2,5,4,3] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,3,2,4,5] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,3,2,5,4] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,3,4,2,5] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,3,4,5,2] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,3,5,2,4] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,3,5,4,2] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,4,2,3,5] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,4,2,5,3] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,4,3,2,5] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,4,3,5,2] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,4,5,2,3] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,4,5,3,2] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,1,7,5,2,3,4] => {{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,7,5,2,4,3] => {{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,7,5,3,2,4] => {{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,7,5,3,4,2] => {{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,7,5,4,2,3] => {{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,1,7,5,4,3,2] => {{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,1,3,4,5,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,2,1,3,4,7,5] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,3,5,4,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,2,1,3,5,7,4] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,3,7,4,5] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,3,7,5,4] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,4,3,5,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,2,1,4,3,7,5] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,4,5,3,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,2,1,4,5,7,3] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,4,7,3,5] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,4,7,5,3] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,5,3,4,7] => {{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,5,3,7,4] => {{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,1,5,4,3,7] => {{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,5,4,7,3] => {{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,1,5,7,3,4] => {{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,1,5,7,4,3] => {{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,1,7,3,4,5] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,7,3,5,4] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,7,4,3,5] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,7,4,5,3] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,7,5,3,4] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,1,7,5,4,3] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,1,4,5,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,2,3,1,4,7,5] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,1,5,4,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,2,3,1,5,7,4] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,1,7,4,5] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,1,7,5,4] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,4,1,5,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,2,3,4,1,7,5] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,4,5,1,7] => {{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[6,2,3,4,5,7,1] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,4,7,1,5] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,4,7,5,1] => {{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,5,1,4,7] => {{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,5,1,7,4] => {{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,3,5,4,1,7] => {{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,5,4,7,1] => {{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,3,5,7,1,4] => {{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,3,5,7,4,1] => {{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,3,7,1,4,5] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,7,1,5,4] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,7,4,1,5] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,7,4,5,1] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,7,5,1,4] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,3,7,5,4,1] => {{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,4,1,3,5,7] => {{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,4,1,3,7,5] => {{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,1,5,3,7] => {{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,4,1,5,7,3] => {{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,1,7,3,5] => {{1,6},{2},{3,4},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,1,7,5,3] => {{1,6},{2},{3,4},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,3,1,5,7] => {{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,4,3,1,7,5] => {{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,3,5,1,7] => {{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,4,3,5,7,1] => {{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,3,7,1,5] => {{1,6},{2},{3,4},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,3,7,5,1] => {{1,6},{2},{3,4},{5,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,5,1,3,7] => {{1,6},{2},{3,4,5},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,5,1,7,3] => {{1,6,7},{2},{3,4,5}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,2,4,5,3,1,7] => {{1,6},{2},{3,4,5},{7}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,5,3,7,1] => {{1,6,7},{2},{3,4,5}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,2,4,5,7,1,3] => {{1,6},{2},{3,4,5,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,2,4,5,7,3,1] => {{1,6},{2},{3,4,5,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,2,4,7,1,3,5] => {{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,7,1,5,3] => {{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,7,3,1,5] => {{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,7,3,5,1] => {{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,7,5,1,3] => {{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,4,7,5,3,1] => {{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,1,3,4,7] => {{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,5,1,3,7,4] => {{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,1,4,3,7] => {{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,5,1,4,7,3] => {{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,1,7,3,4] => {{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,1,7,4,3] => {{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,3,1,4,7] => {{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,5,3,1,7,4] => {{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,3,4,1,7] => {{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,5,3,4,7,1] => {{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,3,7,1,4] => {{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,3,7,4,1] => {{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,4,1,3,7] => {{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,5,4,1,7,3] => {{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,4,3,1,7] => {{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,5,4,3,7,1] => {{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,4,7,1,3] => {{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,4,7,3,1] => {{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,7,1,3,4] => {{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,7,1,4,3] => {{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,7,3,1,4] => {{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,7,3,4,1] => {{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,7,4,1,3] => {{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,5,7,4,3,1] => {{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,7,1,3,4,5] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,1,3,5,4] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,1,4,3,5] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,1,4,5,3] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,1,5,3,4] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,1,5,4,3] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,3,1,4,5] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,3,1,5,4] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,3,4,1,5] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,3,4,5,1] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,3,5,1,4] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,3,5,4,1] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,4,1,3,5] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,4,1,5,3] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,4,3,1,5] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,4,3,5,1] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,4,5,1,3] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,4,5,3,1] => {{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,2,7,5,1,3,4] => {{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,7,5,1,4,3] => {{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,7,5,3,1,4] => {{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,7,5,3,4,1] => {{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,7,5,4,1,3] => {{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,2,7,5,4,3,1] => {{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,2,4,5,7] => {{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,3,1,2,4,7,5] => {{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,2,5,4,7] => {{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,3,1,2,5,7,4] => {{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,2,7,4,5] => {{1,6},{2,3},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,2,7,5,4] => {{1,6},{2,3},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,4,2,5,7] => {{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,3,1,4,2,7,5] => {{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,4,5,2,7] => {{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,3,1,4,5,7,2] => {{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,4,7,2,5] => {{1,6},{2,3},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,4,7,5,2] => {{1,6},{2,3},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,5,2,4,7] => {{1,6},{2,3},{4,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,5,2,7,4] => {{1,6,7},{2,3},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,1,5,4,2,7] => {{1,6},{2,3},{4,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,5,4,7,2] => {{1,6,7},{2,3},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,1,5,7,2,4] => {{1,6},{2,3},{4,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,1,5,7,4,2] => {{1,6},{2,3},{4,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,1,7,2,4,5] => {{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,7,2,5,4] => {{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,7,4,2,5] => {{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,7,4,5,2] => {{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,7,5,2,4] => {{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,1,7,5,4,2] => {{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,1,4,5,7] => {{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,3,2,1,4,7,5] => {{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,1,5,4,7] => {{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,3,2,1,5,7,4] => {{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,1,7,4,5] => {{1,6},{2,3},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,1,7,5,4] => {{1,6},{2,3},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,4,1,5,7] => {{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,3,2,4,1,7,5] => {{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,4,5,1,7] => {{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,3,2,4,5,7,1] => {{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,4,7,1,5] => {{1,6},{2,3},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,4,7,5,1] => {{1,6},{2,3},{4},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,5,1,4,7] => {{1,6},{2,3},{4,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,5,1,7,4] => {{1,6,7},{2,3},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,2,5,4,1,7] => {{1,6},{2,3},{4,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,5,4,7,1] => {{1,6,7},{2,3},{4,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,2,5,7,1,4] => {{1,6},{2,3},{4,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,2,5,7,4,1] => {{1,6},{2,3},{4,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,2,7,1,4,5] => {{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,7,1,5,4] => {{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,7,4,1,5] => {{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,7,4,5,1] => {{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,7,5,1,4] => {{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,2,7,5,4,1] => {{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,4,1,2,5,7] => {{1,6},{2,3,4},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,4,1,2,7,5] => {{1,6,7},{2,3,4},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,1,5,2,7] => {{1,6},{2,3,4},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,4,1,5,7,2] => {{1,6,7},{2,3,4},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,1,7,2,5] => {{1,6},{2,3,4},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,1,7,5,2] => {{1,6},{2,3,4},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,2,1,5,7] => {{1,6},{2,3,4},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,4,2,1,7,5] => {{1,6,7},{2,3,4},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,2,5,1,7] => {{1,6},{2,3,4},{5},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,4,2,5,7,1] => {{1,6,7},{2,3,4},{5}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,2,7,1,5] => {{1,6},{2,3,4},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,2,7,5,1] => {{1,6},{2,3,4},{5,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,5,1,2,7] => {{1,6},{2,3,4,5},{7}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,5,1,7,2] => {{1,6,7},{2,3,4,5}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[6,3,4,5,2,1,7] => {{1,6},{2,3,4,5},{7}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,5,2,7,1] => {{1,6,7},{2,3,4,5}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

[6,3,4,5,7,1,2] => {{1,6},{2,3,4,5,7}} => [2,5] => ([(4,6),(5,6)],7) => 2

[6,3,4,5,7,2,1] => {{1,6},{2,3,4,5,7}} => [2,5] => ([(4,6),(5,6)],7) => 2

[6,3,4,7,1,2,5] => {{1,6},{2,3,4,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,7,1,5,2] => {{1,6},{2,3,4,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,7,2,1,5] => {{1,6},{2,3,4,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,7,2,5,1] => {{1,6},{2,3,4,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,7,5,1,2] => {{1,6},{2,3,4,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,4,7,5,2,1] => {{1,6},{2,3,4,7},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,1,2,4,7] => {{1,6},{2,3,5},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,5,1,2,7,4] => {{1,6,7},{2,3,5},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,1,4,2,7] => {{1,6},{2,3,5},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,5,1,4,7,2] => {{1,6,7},{2,3,5},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,1,7,2,4] => {{1,6},{2,3,5,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,1,7,4,2] => {{1,6},{2,3,5,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,2,1,4,7] => {{1,6},{2,3,5},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,5,2,1,7,4] => {{1,6,7},{2,3,5},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,2,4,1,7] => {{1,6},{2,3,5},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,5,2,4,7,1] => {{1,6,7},{2,3,5},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,2,7,1,4] => {{1,6},{2,3,5,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,2,7,4,1] => {{1,6},{2,3,5,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,4,1,2,7] => {{1,6},{2,3,5},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,5,4,1,7,2] => {{1,6,7},{2,3,5},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,4,2,1,7] => {{1,6},{2,3,5},{4},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,5,4,2,7,1] => {{1,6,7},{2,3,5},{4}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,4,7,1,2] => {{1,6},{2,3,5,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,4,7,2,1] => {{1,6},{2,3,5,7},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,7,1,2,4] => {{1,6},{2,3,5},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,7,1,4,2] => {{1,6},{2,3,5},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,7,2,1,4] => {{1,6},{2,3,5},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,7,2,4,1] => {{1,6},{2,3,5},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,7,4,1,2] => {{1,6},{2,3,5},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,5,7,4,2,1] => {{1,6},{2,3,5},{4,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,7,1,2,4,5] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,1,2,5,4] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,1,4,2,5] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,1,4,5,2] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,1,5,2,4] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,1,5,4,2] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,2,1,4,5] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,2,1,5,4] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,2,4,1,5] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,2,4,5,1] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,2,5,1,4] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,2,5,4,1] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,4,1,2,5] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,4,1,5,2] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,4,2,1,5] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,4,2,5,1] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,4,5,1,2] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,4,5,2,1] => {{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,3,7,5,1,2,4] => {{1,6},{2,3,7},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,7,5,1,4,2] => {{1,6},{2,3,7},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,7,5,2,1,4] => {{1,6},{2,3,7},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,7,5,2,4,1] => {{1,6},{2,3,7},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,7,5,4,1,2] => {{1,6},{2,3,7},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,3,7,5,4,2,1] => {{1,6},{2,3,7},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,1,2,3,5,7] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,4,1,2,3,7,5] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,2,5,3,7] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,4,1,2,5,7,3] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,2,7,3,5] => {{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,2,7,5,3] => {{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,3,2,5,7] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,4,1,3,2,7,5] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,3,5,2,7] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,4,1,3,5,7,2] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,3,7,2,5] => {{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,3,7,5,2] => {{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,5,2,3,7] => {{1,6},{2,4,5},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,5,2,7,3] => {{1,6,7},{2,4,5},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,1,5,3,2,7] => {{1,6},{2,4,5},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,5,3,7,2] => {{1,6,7},{2,4,5},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,1,5,7,2,3] => {{1,6},{2,4,5,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,1,5,7,3,2] => {{1,6},{2,4,5,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,1,7,2,3,5] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,7,2,5,3] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,7,3,2,5] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,7,3,5,2] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,7,5,2,3] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,1,7,5,3,2] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,1,3,5,7] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,4,2,1,3,7,5] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,1,5,3,7] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,4,2,1,5,7,3] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,1,7,3,5] => {{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,1,7,5,3] => {{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,3,1,5,7] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,4,2,3,1,7,5] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,3,5,1,7] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,4,2,3,5,7,1] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,3,7,1,5] => {{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,3,7,5,1] => {{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,5,1,3,7] => {{1,6},{2,4,5},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,5,1,7,3] => {{1,6,7},{2,4,5},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,2,5,3,1,7] => {{1,6},{2,4,5},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,5,3,7,1] => {{1,6,7},{2,4,5},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,2,5,7,1,3] => {{1,6},{2,4,5,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,2,5,7,3,1] => {{1,6},{2,4,5,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,2,7,1,3,5] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,7,1,5,3] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,7,3,1,5] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,7,3,5,1] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,7,5,1,3] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,2,7,5,3,1] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,1,2,5,7] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,4,3,1,2,7,5] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,1,5,2,7] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,4,3,1,5,7,2] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,1,7,2,5] => {{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,1,7,5,2] => {{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,2,1,5,7] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,4,3,2,1,7,5] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,2,5,1,7] => {{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,4,3,2,5,7,1] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,2,7,1,5] => {{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,2,7,5,1] => {{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,5,1,2,7] => {{1,6},{2,4,5},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,5,1,7,2] => {{1,6,7},{2,4,5},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,3,5,2,1,7] => {{1,6},{2,4,5},{3},{7}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,5,2,7,1] => {{1,6,7},{2,4,5},{3}} => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,3,5,7,1,2] => {{1,6},{2,4,5,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,3,5,7,2,1] => {{1,6},{2,4,5,7},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,3,7,1,2,5] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,7,1,5,2] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,7,2,1,5] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,7,2,5,1] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,7,5,1,2] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,3,7,5,2,1] => {{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,5,1,2,3,7] => {{1,6},{2,4},{3,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,5,1,2,7,3] => {{1,6,7},{2,4},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,1,3,2,7] => {{1,6},{2,4},{3,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,5,1,3,7,2] => {{1,6,7},{2,4},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,1,7,2,3] => {{1,6},{2,4},{3,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,1,7,3,2] => {{1,6},{2,4},{3,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,2,1,3,7] => {{1,6},{2,4},{3,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,5,2,1,7,3] => {{1,6,7},{2,4},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,2,3,1,7] => {{1,6},{2,4},{3,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,5,2,3,7,1] => {{1,6,7},{2,4},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,2,7,1,3] => {{1,6},{2,4},{3,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,2,7,3,1] => {{1,6},{2,4},{3,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,3,1,2,7] => {{1,6},{2,4},{3,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,5,3,1,7,2] => {{1,6,7},{2,4},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,3,2,1,7] => {{1,6},{2,4},{3,5},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,5,3,2,7,1] => {{1,6,7},{2,4},{3,5}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,3,7,1,2] => {{1,6},{2,4},{3,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,3,7,2,1] => {{1,6},{2,4},{3,5,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,7,1,2,3] => {{1,6},{2,4,7},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,7,1,3,2] => {{1,6},{2,4,7},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,7,2,1,3] => {{1,6},{2,4,7},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,7,2,3,1] => {{1,6},{2,4,7},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,7,3,1,2] => {{1,6},{2,4,7},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,5,7,3,2,1] => {{1,6},{2,4,7},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,7,1,2,3,5] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,1,2,5,3] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,1,3,2,5] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,1,3,5,2] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,1,5,2,3] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,1,5,3,2] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,2,1,3,5] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,2,1,5,3] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,2,3,1,5] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,2,3,5,1] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,2,5,1,3] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,2,5,3,1] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,3,1,2,5] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,3,1,5,2] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,3,2,1,5] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,3,2,5,1] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,3,5,1,2] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,3,5,2,1] => {{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,4,7,5,1,2,3] => {{1,6},{2,4,5},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,7,5,1,3,2] => {{1,6},{2,4,5},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,7,5,2,1,3] => {{1,6},{2,4,5},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,7,5,2,3,1] => {{1,6},{2,4,5},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,7,5,3,1,2] => {{1,6},{2,4,5},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,4,7,5,3,2,1] => {{1,6},{2,4,5},{3,7}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,1,2,3,4,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,1,2,3,7,4] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,2,4,3,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,1,2,4,7,3] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,2,7,3,4] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,2,7,4,3] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,3,2,4,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,1,3,2,7,4] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,3,4,2,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,1,3,4,7,2] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,3,7,2,4] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,3,7,4,2] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,4,2,3,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,1,4,2,7,3] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,4,3,2,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,1,4,3,7,2] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,4,7,2,3] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,4,7,3,2] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,7,2,3,4] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,7,2,4,3] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,7,3,2,4] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,7,3,4,2] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,7,4,2,3] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,1,7,4,3,2] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,1,3,4,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,2,1,3,7,4] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,1,4,3,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,2,1,4,7,3] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,1,7,3,4] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,1,7,4,3] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,3,1,4,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,2,3,1,7,4] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,3,4,1,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,2,3,4,7,1] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,3,7,1,4] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,3,7,4,1] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,4,1,3,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,2,4,1,7,3] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,4,3,1,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,2,4,3,7,1] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,4,7,1,3] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,4,7,3,1] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,7,1,3,4] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,7,1,4,3] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,7,3,1,4] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,7,3,4,1] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,7,4,1,3] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,2,7,4,3,1] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,1,2,4,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,3,1,2,7,4] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,1,4,2,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,3,1,4,7,2] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,1,7,2,4] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,1,7,4,2] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,2,1,4,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,3,2,1,7,4] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,2,4,1,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,3,2,4,7,1] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,2,7,1,4] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,2,7,4,1] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,4,1,2,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,3,4,1,7,2] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,4,2,1,7] => {{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,5,3,4,2,7,1] => {{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,4,7,1,2] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,4,7,2,1] => {{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,7,1,2,4] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,7,1,4,2] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,7,2,1,4] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,7,2,4,1] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,7,4,1,2] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,3,7,4,2,1] => {{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,4,1,2,3,7] => {{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,4,1,2,7,3] => {{1,6,7},{2,5},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,1,3,2,7] => {{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,4,1,3,7,2] => {{1,6,7},{2,5},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,1,7,2,3] => {{1,6},{2,5,7},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,1,7,3,2] => {{1,6},{2,5,7},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,2,1,3,7] => {{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,4,2,1,7,3] => {{1,6,7},{2,5},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,2,3,1,7] => {{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,4,2,3,7,1] => {{1,6,7},{2,5},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,2,7,1,3] => {{1,6},{2,5,7},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,2,7,3,1] => {{1,6},{2,5,7},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,3,1,2,7] => {{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,4,3,1,7,2] => {{1,6,7},{2,5},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,3,2,1,7] => {{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,4,3,2,7,1] => {{1,6,7},{2,5},{3,4}} => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,3,7,1,2] => {{1,6},{2,5,7},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,3,7,2,1] => {{1,6},{2,5,7},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,7,1,2,3] => {{1,6},{2,5},{3,4,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,7,1,3,2] => {{1,6},{2,5},{3,4,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,7,2,1,3] => {{1,6},{2,5},{3,4,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,7,2,3,1] => {{1,6},{2,5},{3,4,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,7,3,1,2] => {{1,6},{2,5},{3,4,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,4,7,3,2,1] => {{1,6},{2,5},{3,4,7}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,5,7,1,2,3,4] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,1,2,4,3] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,1,3,2,4] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,1,3,4,2] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,1,4,2,3] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,1,4,3,2] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,2,1,3,4] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,2,1,4,3] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,2,3,1,4] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,2,3,4,1] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,2,4,1,3] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,2,4,3,1] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,3,1,2,4] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,3,1,4,2] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,3,2,1,4] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,3,2,4,1] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,3,4,1,2] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,3,4,2,1] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,4,1,2,3] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,4,1,3,2] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,4,2,1,3] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,4,2,3,1] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,4,3,1,2] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,5,7,4,3,2,1] => {{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,1,2,3,4,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,2,3,5,4] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,2,4,3,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,2,4,5,3] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,2,5,3,4] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,2,5,4,3] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,3,2,4,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,3,2,5,4] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,3,4,2,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,3,4,5,2] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,3,5,2,4] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,3,5,4,2] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,4,2,3,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,4,2,5,3] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,4,3,2,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,4,3,5,2] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,4,5,2,3] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,4,5,3,2] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,1,5,2,3,4] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,1,5,2,4,3] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,1,5,3,2,4] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,1,5,3,4,2] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,1,5,4,2,3] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,1,5,4,3,2] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,2,1,3,4,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,1,3,5,4] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,1,4,3,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,1,4,5,3] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,1,5,3,4] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,1,5,4,3] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,3,1,4,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,3,1,5,4] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,3,4,1,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,3,4,5,1] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,3,5,1,4] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,3,5,4,1] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,4,1,3,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,4,1,5,3] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,4,3,1,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,4,3,5,1] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,4,5,1,3] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,4,5,3,1] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,2,5,1,3,4] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,2,5,1,4,3] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,2,5,3,1,4] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,2,5,3,4,1] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,2,5,4,1,3] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,2,5,4,3,1] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,3,1,2,4,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,1,2,5,4] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,1,4,2,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,1,4,5,2] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,1,5,2,4] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,1,5,4,2] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,2,1,4,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,2,1,5,4] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,2,4,1,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,2,4,5,1] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,2,5,1,4] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,2,5,4,1] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,4,1,2,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,4,1,5,2] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,4,2,1,5] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,4,2,5,1] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,4,5,1,2] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,4,5,2,1] => {{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[6,7,3,5,1,2,4] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,3,5,1,4,2] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,3,5,2,1,4] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,3,5,2,4,1] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,3,5,4,1,2] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,3,5,4,2,1] => {{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,1,2,3,5] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,1,2,5,3] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,1,3,2,5] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,1,3,5,2] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,1,5,2,3] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,1,5,3,2] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,2,1,3,5] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,2,1,5,3] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,2,3,1,5] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,2,3,5,1] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,2,5,1,3] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,2,5,3,1] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,3,1,2,5] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,3,1,5,2] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,3,2,1,5] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,3,2,5,1] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,3,5,1,2] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,3,5,2,1] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,4,5,1,2,3] => {{1,6},{2,7},{3,4,5}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,7,4,5,1,3,2] => {{1,6},{2,7},{3,4,5}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,7,4,5,2,1,3] => {{1,6},{2,7},{3,4,5}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,7,4,5,2,3,1] => {{1,6},{2,7},{3,4,5}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,7,4,5,3,1,2] => {{1,6},{2,7},{3,4,5}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,7,4,5,3,2,1] => {{1,6},{2,7},{3,4,5}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[6,7,5,1,2,3,4] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,1,2,4,3] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,1,3,2,4] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,1,3,4,2] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,1,4,2,3] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,1,4,3,2] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,2,1,3,4] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,2,1,4,3] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,2,3,1,4] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,2,3,4,1] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,2,4,1,3] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,2,4,3,1] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,3,1,2,4] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,3,1,4,2] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,3,2,1,4] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,3,2,4,1] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,3,4,1,2] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,3,4,2,1] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,4,1,2,3] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,4,1,3,2] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,4,2,1,3] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,4,2,3,1] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,4,3,1,2] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[6,7,5,4,3,2,1] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,2,3,4,5,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,2,3,4,6,5] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,2,3,5,4,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,2,3,5,6,4] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,2,3,6,4,5] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,2,3,6,5,4] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,2,4,3,5,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,2,4,3,6,5] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,2,4,5,3,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,2,4,5,6,3] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,2,4,6,3,5] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,2,4,6,5,3] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,2,5,3,4,6] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,2,5,3,6,4] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,2,5,4,3,6] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,2,5,4,6,3] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,2,5,6,3,4] => {{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,2,5,6,4,3] => {{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,2,6,3,4,5] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,2,6,3,5,4] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,2,6,4,3,5] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,2,6,4,5,3] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,2,6,5,3,4] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,2,6,5,4,3] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,2,4,5,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,3,2,4,6,5] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,3,2,5,4,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,3,2,5,6,4] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,3,2,6,4,5] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,2,6,5,4] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,4,2,5,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,3,4,2,6,5] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,3,4,5,2,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,3,4,5,6,2] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,1,3,4,6,2,5] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,4,6,5,2] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,5,2,4,6] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,5,2,6,4] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,5,4,2,6] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,5,4,6,2] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,5,6,2,4] => {{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,3,5,6,4,2] => {{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,3,6,2,4,5] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,6,2,5,4] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,6,4,2,5] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,6,4,5,2] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,6,5,2,4] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,3,6,5,4,2] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,4,2,3,5,6] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,4,2,3,6,5] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,4,2,5,3,6] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,4,2,5,6,3] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,4,2,6,3,5] => {{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,4,2,6,5,3] => {{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,4,3,2,5,6] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,4,3,2,6,5] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,4,3,5,2,6] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,4,3,5,6,2] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,4,3,6,2,5] => {{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,4,3,6,5,2] => {{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,4,5,2,3,6] => {{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,4,5,2,6,3] => {{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,4,5,3,2,6] => {{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,4,5,3,6,2] => {{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,4,5,6,2,3] => {{1,7},{2},{3,4,5,6}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,1,4,5,6,3,2] => {{1,7},{2},{3,4,5,6}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,1,4,6,2,3,5] => {{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,4,6,2,5,3] => {{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,4,6,3,2,5] => {{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,4,6,3,5,2] => {{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,4,6,5,2,3] => {{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,4,6,5,3,2] => {{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,5,2,3,4,6] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,5,2,3,6,4] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,5,2,4,3,6] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,5,2,4,6,3] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,5,2,6,3,4] => {{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,5,2,6,4,3] => {{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,5,3,2,4,6] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,5,3,2,6,4] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,5,3,4,2,6] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,5,3,4,6,2] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,5,3,6,2,4] => {{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,5,3,6,4,2] => {{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,5,4,2,3,6] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,5,4,2,6,3] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,5,4,3,2,6] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,5,4,3,6,2] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,5,4,6,2,3] => {{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,5,4,6,3,2] => {{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,5,6,2,3,4] => {{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,5,6,2,4,3] => {{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,5,6,3,2,4] => {{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,5,6,3,4,2] => {{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,5,6,4,2,3] => {{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,5,6,4,3,2] => {{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,6,2,3,4,5] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,2,3,5,4] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,2,4,3,5] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,2,4,5,3] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,2,5,3,4] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,2,5,4,3] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,3,2,4,5] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,3,2,5,4] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,3,4,2,5] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,3,4,5,2] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,3,5,2,4] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,3,5,4,2] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,4,2,3,5] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,4,2,5,3] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,4,3,2,5] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,4,3,5,2] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,4,5,2,3] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,4,5,3,2] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,1,6,5,2,3,4] => {{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,6,5,2,4,3] => {{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,6,5,3,2,4] => {{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,6,5,3,4,2] => {{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,6,5,4,2,3] => {{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,1,6,5,4,3,2] => {{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,1,3,4,5,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,1,3,4,6,5] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,1,3,5,4,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,1,3,5,6,4] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,1,3,6,4,5] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,1,3,6,5,4] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,1,4,3,5,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,1,4,3,6,5] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,1,4,5,3,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,1,4,5,6,3] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,1,4,6,3,5] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,1,4,6,5,3] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,1,5,3,4,6] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,1,5,3,6,4] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,1,5,4,3,6] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,1,5,4,6,3] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,1,5,6,3,4] => {{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,1,5,6,4,3] => {{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,1,6,3,4,5] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,1,6,3,5,4] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,1,6,4,3,5] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,1,6,4,5,3] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,1,6,5,3,4] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,1,6,5,4,3] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,1,4,5,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,3,1,4,6,5] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,3,1,5,4,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,3,1,5,6,4] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,3,1,6,4,5] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,1,6,5,4] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,4,1,5,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,3,4,1,6,5] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,3,4,5,1,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,3,4,5,6,1] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6

[7,2,3,4,6,1,5] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,4,6,5,1] => {{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,5,1,4,6] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,5,1,6,4] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,5,4,1,6] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,5,4,6,1] => {{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,5,6,1,4] => {{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,3,5,6,4,1] => {{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,3,6,1,4,5] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,6,1,5,4] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,6,4,1,5] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,6,4,5,1] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,6,5,1,4] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,3,6,5,4,1] => {{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,4,1,3,5,6] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,4,1,3,6,5] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,4,1,5,3,6] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,4,1,5,6,3] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,4,1,6,3,5] => {{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,4,1,6,5,3] => {{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,4,3,1,5,6] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,4,3,1,6,5] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,4,3,5,1,6] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,4,3,5,6,1] => {{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,4,3,6,1,5] => {{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,4,3,6,5,1] => {{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,4,5,1,3,6] => {{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,4,5,1,6,3] => {{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,4,5,3,1,6] => {{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,4,5,3,6,1] => {{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,4,5,6,1,3] => {{1,7},{2},{3,4,5,6}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,2,4,5,6,3,1] => {{1,7},{2},{3,4,5,6}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,2,4,6,1,3,5] => {{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,4,6,1,5,3] => {{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,4,6,3,1,5] => {{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,4,6,3,5,1] => {{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,4,6,5,1,3] => {{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,4,6,5,3,1] => {{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,5,1,3,4,6] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,5,1,3,6,4] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,5,1,4,3,6] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,5,1,4,6,3] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,5,1,6,3,4] => {{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,5,1,6,4,3] => {{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,5,3,1,4,6] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,5,3,1,6,4] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,5,3,4,1,6] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,5,3,4,6,1] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,5,3,6,1,4] => {{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,5,3,6,4,1] => {{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,5,4,1,3,6] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,5,4,1,6,3] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,5,4,3,1,6] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,5,4,3,6,1] => {{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,5,4,6,1,3] => {{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,5,4,6,3,1] => {{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,5,6,1,3,4] => {{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,5,6,1,4,3] => {{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,5,6,3,1,4] => {{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,5,6,3,4,1] => {{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,5,6,4,1,3] => {{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,5,6,4,3,1] => {{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,6,1,3,4,5] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,1,3,5,4] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,1,4,3,5] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,1,4,5,3] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,1,5,3,4] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,1,5,4,3] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,3,1,4,5] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,3,1,5,4] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,3,4,1,5] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,3,4,5,1] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,3,5,1,4] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,3,5,4,1] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,4,1,3,5] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,4,1,5,3] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,4,3,1,5] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,4,3,5,1] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,4,5,1,3] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,4,5,3,1] => {{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,2,6,5,1,3,4] => {{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,6,5,1,4,3] => {{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,6,5,3,1,4] => {{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,6,5,3,4,1] => {{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,6,5,4,1,3] => {{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,2,6,5,4,3,1] => {{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,2,4,5,6] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,1,2,4,6,5] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,1,2,5,4,6] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,1,2,5,6,4] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,1,2,6,4,5] => {{1,7},{2,3},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,2,6,5,4] => {{1,7},{2,3},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,4,2,5,6] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,1,4,2,6,5] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,1,4,5,2,6] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,1,4,5,6,2] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,1,4,6,2,5] => {{1,7},{2,3},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,4,6,5,2] => {{1,7},{2,3},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,5,2,4,6] => {{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,5,2,6,4] => {{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,5,4,2,6] => {{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,5,4,6,2] => {{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,5,6,2,4] => {{1,7},{2,3},{4,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,1,5,6,4,2] => {{1,7},{2,3},{4,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,1,6,2,4,5] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,6,2,5,4] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,6,4,2,5] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,6,4,5,2] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,6,5,2,4] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,1,6,5,4,2] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,1,4,5,6] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,2,1,4,6,5] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,2,1,5,4,6] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,2,1,5,6,4] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,2,1,6,4,5] => {{1,7},{2,3},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,1,6,5,4] => {{1,7},{2,3},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,4,1,5,6] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,2,4,1,6,5] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,2,4,5,1,6] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,2,4,5,6,1] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,3,2,4,6,1,5] => {{1,7},{2,3},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,4,6,5,1] => {{1,7},{2,3},{4},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,5,1,4,6] => {{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,5,1,6,4] => {{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,5,4,1,6] => {{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,5,4,6,1] => {{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,5,6,1,4] => {{1,7},{2,3},{4,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,2,5,6,4,1] => {{1,7},{2,3},{4,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,2,6,1,4,5] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,6,1,5,4] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,6,4,1,5] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,6,4,5,1] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,6,5,1,4] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,2,6,5,4,1] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,4,1,2,5,6] => {{1,7},{2,3,4},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,4,1,2,6,5] => {{1,7},{2,3,4},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,4,1,5,2,6] => {{1,7},{2,3,4},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,4,1,5,6,2] => {{1,7},{2,3,4},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,4,1,6,2,5] => {{1,7},{2,3,4},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,4,1,6,5,2] => {{1,7},{2,3,4},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,4,2,1,5,6] => {{1,7},{2,3,4},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,4,2,1,6,5] => {{1,7},{2,3,4},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,4,2,5,1,6] => {{1,7},{2,3,4},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,4,2,5,6,1] => {{1,7},{2,3,4},{5},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,4,2,6,1,5] => {{1,7},{2,3,4},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,4,2,6,5,1] => {{1,7},{2,3,4},{5,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,4,5,1,2,6] => {{1,7},{2,3,4,5},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,4,5,1,6,2] => {{1,7},{2,3,4,5},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,4,5,2,1,6] => {{1,7},{2,3,4,5},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,4,5,2,6,1] => {{1,7},{2,3,4,5},{6}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,4,5,6,1,2] => {{1,7},{2,3,4,5,6}} => [2,5] => ([(4,6),(5,6)],7) => 2

[7,3,4,5,6,2,1] => {{1,7},{2,3,4,5,6}} => [2,5] => ([(4,6),(5,6)],7) => 2

[7,3,4,6,1,2,5] => {{1,7},{2,3,4,6},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,4,6,1,5,2] => {{1,7},{2,3,4,6},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,4,6,2,1,5] => {{1,7},{2,3,4,6},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,4,6,2,5,1] => {{1,7},{2,3,4,6},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,4,6,5,1,2] => {{1,7},{2,3,4,6},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,4,6,5,2,1] => {{1,7},{2,3,4,6},{5}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,5,1,2,4,6] => {{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,5,1,2,6,4] => {{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,5,1,4,2,6] => {{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,5,1,4,6,2] => {{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,5,1,6,2,4] => {{1,7},{2,3,5,6},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,5,1,6,4,2] => {{1,7},{2,3,5,6},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,5,2,1,4,6] => {{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,5,2,1,6,4] => {{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,5,2,4,1,6] => {{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,5,2,4,6,1] => {{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,5,2,6,1,4] => {{1,7},{2,3,5,6},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,5,2,6,4,1] => {{1,7},{2,3,5,6},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,5,4,1,2,6] => {{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,5,4,1,6,2] => {{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,5,4,2,1,6] => {{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,5,4,2,6,1] => {{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,5,4,6,1,2] => {{1,7},{2,3,5,6},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,5,4,6,2,1] => {{1,7},{2,3,5,6},{4}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,5,6,1,2,4] => {{1,7},{2,3,5},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,5,6,1,4,2] => {{1,7},{2,3,5},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,5,6,2,1,4] => {{1,7},{2,3,5},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,5,6,2,4,1] => {{1,7},{2,3,5},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,5,6,4,1,2] => {{1,7},{2,3,5},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,5,6,4,2,1] => {{1,7},{2,3,5},{4,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,6,1,2,4,5] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,1,2,5,4] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,1,4,2,5] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,1,4,5,2] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,1,5,2,4] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,1,5,4,2] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,2,1,4,5] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,2,1,5,4] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,2,4,1,5] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,2,4,5,1] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,2,5,1,4] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,2,5,4,1] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,4,1,2,5] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,4,1,5,2] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,4,2,1,5] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,4,2,5,1] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,4,5,1,2] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,4,5,2,1] => {{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,3,6,5,1,2,4] => {{1,7},{2,3,6},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,6,5,1,4,2] => {{1,7},{2,3,6},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,6,5,2,1,4] => {{1,7},{2,3,6},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,6,5,2,4,1] => {{1,7},{2,3,6},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,6,5,4,1,2] => {{1,7},{2,3,6},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,3,6,5,4,2,1] => {{1,7},{2,3,6},{4,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,1,2,3,5,6] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,1,2,3,6,5] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,1,2,5,3,6] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,1,2,5,6,3] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,1,2,6,3,5] => {{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,1,2,6,5,3] => {{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,1,3,2,5,6] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,1,3,2,6,5] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,1,3,5,2,6] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,1,3,5,6,2] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,1,3,6,2,5] => {{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,1,3,6,5,2] => {{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,1,5,2,3,6] => {{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,1,5,2,6,3] => {{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,1,5,3,2,6] => {{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,1,5,3,6,2] => {{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,1,5,6,2,3] => {{1,7},{2,4,5,6},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,1,5,6,3,2] => {{1,7},{2,4,5,6},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,1,6,2,3,5] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,1,6,2,5,3] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,1,6,3,2,5] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,1,6,3,5,2] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,1,6,5,2,3] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,1,6,5,3,2] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,1,3,5,6] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,2,1,3,6,5] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,2,1,5,3,6] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,2,1,5,6,3] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,2,1,6,3,5] => {{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,1,6,5,3] => {{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,3,1,5,6] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,2,3,1,6,5] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,2,3,5,1,6] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,2,3,5,6,1] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,2,3,6,1,5] => {{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,3,6,5,1] => {{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,5,1,3,6] => {{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,5,1,6,3] => {{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,5,3,1,6] => {{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,5,3,6,1] => {{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,5,6,1,3] => {{1,7},{2,4,5,6},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,2,5,6,3,1] => {{1,7},{2,4,5,6},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,2,6,1,3,5] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,6,1,5,3] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,6,3,1,5] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,6,3,5,1] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,6,5,1,3] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,2,6,5,3,1] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,1,2,5,6] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,3,1,2,6,5] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,3,1,5,2,6] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,3,1,5,6,2] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,3,1,6,2,5] => {{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,1,6,5,2] => {{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,2,1,5,6] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,3,2,1,6,5] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,3,2,5,1,6] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,3,2,5,6,1] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,4,3,2,6,1,5] => {{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,2,6,5,1] => {{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,5,1,2,6] => {{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,5,1,6,2] => {{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,5,2,1,6] => {{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,5,2,6,1] => {{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,5,6,1,2] => {{1,7},{2,4,5,6},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,3,5,6,2,1] => {{1,7},{2,4,5,6},{3}} => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,3,6,1,2,5] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,6,1,5,2] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,6,2,1,5] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,6,2,5,1] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,6,5,1,2] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,3,6,5,2,1] => {{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,5,1,2,3,6] => {{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,5,1,2,6,3] => {{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,5,1,3,2,6] => {{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,5,1,3,6,2] => {{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,5,1,6,2,3] => {{1,7},{2,4},{3,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,5,1,6,3,2] => {{1,7},{2,4},{3,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,5,2,1,3,6] => {{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,5,2,1,6,3] => {{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,5,2,3,1,6] => {{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,5,2,3,6,1] => {{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,5,2,6,1,3] => {{1,7},{2,4},{3,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,5,2,6,3,1] => {{1,7},{2,4},{3,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,5,3,1,2,6] => {{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,5,3,1,6,2] => {{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,5,3,2,1,6] => {{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,5,3,2,6,1] => {{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,5,3,6,1,2] => {{1,7},{2,4},{3,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,5,3,6,2,1] => {{1,7},{2,4},{3,5,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,5,6,1,2,3] => {{1,7},{2,4,6},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,5,6,1,3,2] => {{1,7},{2,4,6},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,5,6,2,1,3] => {{1,7},{2,4,6},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,5,6,2,3,1] => {{1,7},{2,4,6},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,5,6,3,1,2] => {{1,7},{2,4,6},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,5,6,3,2,1] => {{1,7},{2,4,6},{3,5}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,6,1,2,3,5] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,1,2,5,3] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,1,3,2,5] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,1,3,5,2] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,1,5,2,3] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,1,5,3,2] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,2,1,3,5] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,2,1,5,3] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,2,3,1,5] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,2,3,5,1] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,2,5,1,3] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,2,5,3,1] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,3,1,2,5] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,3,1,5,2] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,3,2,1,5] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,3,2,5,1] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,3,5,1,2] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,3,5,2,1] => {{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,4,6,5,1,2,3] => {{1,7},{2,4,5},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,6,5,1,3,2] => {{1,7},{2,4,5},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,6,5,2,1,3] => {{1,7},{2,4,5},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,6,5,2,3,1] => {{1,7},{2,4,5},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,6,5,3,1,2] => {{1,7},{2,4,5},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,4,6,5,3,2,1] => {{1,7},{2,4,5},{3,6}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,5,1,2,3,4,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,1,2,3,6,4] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,1,2,4,3,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,1,2,4,6,3] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,1,2,6,3,4] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,1,2,6,4,3] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,1,3,2,4,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,1,3,2,6,4] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,1,3,4,2,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,1,3,4,6,2] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,1,3,6,2,4] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,1,3,6,4,2] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,1,4,2,3,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,1,4,2,6,3] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,1,4,3,2,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,1,4,3,6,2] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,1,4,6,2,3] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,1,4,6,3,2] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,1,6,2,3,4] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,1,6,2,4,3] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,1,6,3,2,4] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,1,6,3,4,2] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,1,6,4,2,3] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,1,6,4,3,2] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,2,1,3,4,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,2,1,3,6,4] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,2,1,4,3,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,2,1,4,6,3] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,2,1,6,3,4] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,2,1,6,4,3] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,2,3,1,4,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,2,3,1,6,4] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,2,3,4,1,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,2,3,4,6,1] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,2,3,6,1,4] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,2,3,6,4,1] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,2,4,1,3,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,2,4,1,6,3] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,2,4,3,1,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,2,4,3,6,1] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,2,4,6,1,3] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,2,4,6,3,1] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,2,6,1,3,4] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,2,6,1,4,3] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,2,6,3,1,4] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,2,6,3,4,1] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,2,6,4,1,3] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,2,6,4,3,1] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,3,1,2,4,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,3,1,2,6,4] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,3,1,4,2,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,3,1,4,6,2] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,3,1,6,2,4] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,3,1,6,4,2] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,3,2,1,4,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,3,2,1,6,4] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,3,2,4,1,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,3,2,4,6,1] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,3,2,6,1,4] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,3,2,6,4,1] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,3,4,1,2,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,3,4,1,6,2] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,3,4,2,1,6] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,3,4,2,6,1] => {{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,5,3,4,6,1,2] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,3,4,6,2,1] => {{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,3,6,1,2,4] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,3,6,1,4,2] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,3,6,2,1,4] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,3,6,2,4,1] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,3,6,4,1,2] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,3,6,4,2,1] => {{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,4,1,2,3,6] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,4,1,2,6,3] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,4,1,3,2,6] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,4,1,3,6,2] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,4,1,6,2,3] => {{1,7},{2,5,6},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,5,4,1,6,3,2] => {{1,7},{2,5,6},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,5,4,2,1,3,6] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,4,2,1,6,3] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,4,2,3,1,6] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,4,2,3,6,1] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,4,2,6,1,3] => {{1,7},{2,5,6},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,5,4,2,6,3,1] => {{1,7},{2,5,6},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,5,4,3,1,2,6] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,4,3,1,6,2] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,4,3,2,1,6] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,4,3,2,6,1] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,4,3,6,1,2] => {{1,7},{2,5,6},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,5,4,3,6,2,1] => {{1,7},{2,5,6},{3,4}} => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,5,4,6,1,2,3] => {{1,7},{2,5},{3,4,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,5,4,6,1,3,2] => {{1,7},{2,5},{3,4,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,5,4,6,2,1,3] => {{1,7},{2,5},{3,4,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,5,4,6,2,3,1] => {{1,7},{2,5},{3,4,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,5,4,6,3,1,2] => {{1,7},{2,5},{3,4,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,5,4,6,3,2,1] => {{1,7},{2,5},{3,4,6}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,5,6,1,2,3,4] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,1,2,4,3] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,1,3,2,4] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,1,3,4,2] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,1,4,2,3] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,1,4,3,2] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,2,1,3,4] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,2,1,4,3] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,2,3,1,4] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,2,3,4,1] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,2,4,1,3] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,2,4,3,1] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,3,1,2,4] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,3,1,4,2] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,3,2,1,4] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,3,2,4,1] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,3,4,1,2] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,3,4,2,1] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,4,1,2,3] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,4,1,3,2] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,4,2,1,3] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,4,2,3,1] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,4,3,1,2] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,5,6,4,3,2,1] => {{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,1,2,3,4,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,2,3,5,4] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,2,4,3,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,2,4,5,3] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,2,5,3,4] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,2,5,4,3] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,3,2,4,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,3,2,5,4] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,3,4,2,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,3,4,5,2] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,3,5,2,4] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,3,5,4,2] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,4,2,3,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,4,2,5,3] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,4,3,2,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,4,3,5,2] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,4,5,2,3] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,4,5,3,2] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,1,5,2,3,4] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,1,5,2,4,3] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,1,5,3,2,4] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,1,5,3,4,2] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,1,5,4,2,3] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,1,5,4,3,2] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,2,1,3,4,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,1,3,5,4] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,1,4,3,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,1,4,5,3] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,1,5,3,4] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,1,5,4,3] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,3,1,4,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,3,1,5,4] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,3,4,1,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,3,4,5,1] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,3,5,1,4] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,3,5,4,1] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,4,1,3,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,4,1,5,3] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,4,3,1,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,4,3,5,1] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,4,5,1,3] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,4,5,3,1] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,2,5,1,3,4] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,2,5,1,4,3] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,2,5,3,1,4] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,2,5,3,4,1] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,2,5,4,1,3] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,2,5,4,3,1] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,3,1,2,4,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,1,2,5,4] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,1,4,2,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,1,4,5,2] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,1,5,2,4] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,1,5,4,2] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,2,1,4,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,2,1,5,4] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,2,4,1,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,2,4,5,1] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,2,5,1,4] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,2,5,4,1] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,4,1,2,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,4,1,5,2] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,4,2,1,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,4,2,5,1] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,4,5,1,2] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,4,5,2,1] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5

[7,6,3,5,1,2,4] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,3,5,1,4,2] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,3,5,2,1,4] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,3,5,2,4,1] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,3,5,4,1,2] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,3,5,4,2,1] => {{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,1,2,3,5] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,1,2,5,3] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,1,3,2,5] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,1,3,5,2] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,1,5,2,3] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,1,5,3,2] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,2,1,3,5] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,2,1,5,3] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,2,3,1,5] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,2,3,5,1] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,2,5,1,3] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,2,5,3,1] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,3,1,2,5] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,3,1,5,2] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,3,2,1,5] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,3,2,5,1] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,3,5,1,2] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,3,5,2,1] => {{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,4,5,1,2,3] => {{1,7},{2,6},{3,4,5}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,6,4,5,1,3,2] => {{1,7},{2,6},{3,4,5}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,6,4,5,2,1,3] => {{1,7},{2,6},{3,4,5}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,6,4,5,2,3,1] => {{1,7},{2,6},{3,4,5}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,6,4,5,3,1,2] => {{1,7},{2,6},{3,4,5}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,6,4,5,3,2,1] => {{1,7},{2,6},{3,4,5}} => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

[7,6,5,1,2,3,4] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,1,2,4,3] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,1,3,2,4] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,1,3,4,2] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,1,4,2,3] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,1,4,3,2] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,2,1,3,4] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,2,1,4,3] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,2,3,1,4] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,2,3,4,1] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,2,4,1,3] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,2,4,3,1] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,3,1,2,4] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,3,1,4,2] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,3,2,1,4] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,3,2,4,1] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,3,4,1,2] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,3,4,2,1] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,4,1,2,3] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,4,1,3,2] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,4,2,1,3] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,4,2,3,1] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,4,3,1,2] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[7,6,5,4,3,2,1] => {{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

[8,7,6,5,4,3,2,1] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,6,5,4,3,2,1] => {{1,7},{2,8},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,8,5,4,3,2,1] => {{1,7},{2,6},{3,8},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,8,5,4,3,2,1] => {{1,6},{2,7},{3,8},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,5,6,4,3,2,1] => {{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,8,4,3,2,1] => {{1,7},{2,6},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,6,8,4,3,2,1] => {{1,7},{2,5},{3,6},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,8,4,3,2,1] => {{1,6},{2,5},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,4,3,2,1] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,4,8,3,2,1] => {{1,7},{2,6},{3,5,8},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,4,8,3,2,1] => {{1,6},{2,5,8},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,4,5,8,3,2,1] => {{1,7},{2,6},{3,4,5,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,5,4,6,8,3,2,1] => {{1,7},{2,5,8},{3,4,6}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,6,7,8,3,2,1] => {{1,4,7},{2,5,8},{3,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,7,6,5,3,4,2,1] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,6,5,3,4,2,1] => {{1,7},{2,8},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,7,5,3,4,2,1] => {{1,8},{2,6},{3,7},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,5,6,3,4,2,1] => {{1,8},{2,7},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,3,4,2,1] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,4,3,8,2,1] => {{1,7},{2,6,8},{3,5},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,5,7,3,8,2,1] => {{1,6,8},{2,4,7},{3,5}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,6,7,3,8,2,1] => {{1,5},{2,4,7},{3,6,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,6,7,3,8,2,1] => {{1,4,7},{2,5},{3,6,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,6,5,3,4,8,2,1] => {{1,7},{2,6,8},{3,5},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,4,3,5,8,2,1] => {{1,7},{2,6,8},{3,4},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,4,5,7,8,2,1] => {{1,6,8},{2,3,4,5,7}} => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2

[4,3,5,6,7,8,2,1] => {{1,4,6,8},{2,3,5,7}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[8,7,6,5,4,2,3,1] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,6,5,4,2,3,1] => {{1,7},{2,8},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,7,5,4,2,3,1] => {{1,8},{2,6},{3,7},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,5,6,4,2,3,1] => {{1,8},{2,7},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,4,2,3,1] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,7,8,2,3,1] => {{1,4,7},{2,5,8},{3,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,7,6,5,3,2,4,1] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,5,7,3,2,4,1] => {{1,8},{2,6},{3,5},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,3,2,4,1] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,2,3,4,1] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,8,5,2,3,4,1] => {{1,6},{2,7},{3,8},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,6,7,2,3,4,1] => {{1,8},{2,5},{3,6},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,2,3,4,1] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,3,2,4,5,6,1] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,6,5,4,3,2,8,1] => {{1,7,8},{2,6},{3,5},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,5,4,3,2,8,1] => {{1,6},{2,7,8},{3,5},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,4,3,2,8,1] => {{1,6},{2,5},{3,7,8},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,5,7,3,2,8,1] => {{1,6},{2,4,7,8},{3,5}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,6,7,3,2,8,1] => {{1,4,7,8},{2,5},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,5,4,3,7,2,8,1] => {{1,6},{2,5,7,8},{3,4}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,6,3,7,2,8,1] => {{1,5,7,8},{2,4},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,5,3,4,7,2,8,1] => {{1,6},{2,5,7,8},{3},{4}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,4,2,3,8,1] => {{1,7,8},{2,6},{3,5},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,5,7,2,3,8,1] => {{1,6},{2,4,7,8},{3,5}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,6,7,2,3,8,1] => {{1,4,7,8},{2,5},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,6,5,3,2,4,8,1] => {{1,7,8},{2,6},{3,5},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,2,3,4,8,1] => {{1,7,8},{2,6},{3,5},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,2,6,7,8,1] => {{1,5,6,7,8},{2,4},{3}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,5,2,6,7,8,1] => {{1,3,5,6,7,8},{2,4}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[5,2,3,4,6,7,8,1] => {{1,5,6,7,8},{2},{3},{4}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,5,6,7,8,1] => {{1,4,5,6,7,8},{2,3}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[3,4,2,5,6,7,8,1] => {{1,3},{2,4,5,6,7,8}} => [2,6] => ([(5,7),(6,7)],8) => 2

[4,2,3,5,6,7,8,1] => {{1,4,5,6,7,8},{2},{3}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,2,4,5,6,7,8,1] => {{1,3,4,5,6,7,8},{2}} => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => [8] => ([],8) => 1

[8,7,6,5,4,3,1,2] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,6,5,4,3,1,2] => {{1,7},{2,8},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,7,5,4,3,1,2] => {{1,8},{2,6},{3,7},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,5,6,4,3,1,2] => {{1,8},{2,7},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,8,4,3,1,2] => {{1,6},{2,5},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,4,3,1,2] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,7,8,3,1,2] => {{1,4,7},{2,5,8},{3,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,7,6,5,3,4,1,2] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,5,6,3,4,1,2] => {{1,8},{2,7},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,5,6,3,4,1,2] => {{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,8,3,4,1,2] => {{1,7},{2,6},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,5,8,3,4,1,2] => {{1,6},{2,7},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,6,8,3,4,1,2] => {{1,7},{2,5},{3,6},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,8,3,4,1,2] => {{1,6},{2,5},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,3,4,1,2] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,5,3,6,1,2] => {{1,7},{2,8},{3,4,5},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,3,5,6,1,2] => {{1,7},{2,8},{3,4},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,3,4,5,6,1,2] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,4,3,5,6,7,1,2] => {{1,8},{2,4,5,6,7},{3}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,4,5,6,7,1,2] => {{1,8},{2,3,4,5,6,7}} => [2,6] => ([(5,7),(6,7)],8) => 2

[7,6,5,4,3,8,1,2] => {{1,7},{2,6,8},{3,5},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,4,3,8,1,2] => {{1,6,8},{2,5},{3,7},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,4,3,8,1,2] => {{1,5},{2,6,8},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,4,7,3,8,1,2] => {{1,5},{2,6,8},{3,4,7}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,6,7,3,8,1,2] => {{1,5},{2,4,7},{3,6,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,6,7,3,8,1,2] => {{1,4,7},{2,5},{3,6,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,6,3,4,7,8,1,2] => {{1,5,7},{2,6,8},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,4,5,7,8,1,2] => {{1,6,8},{2,3,4,5,7}} => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2

[5,4,3,6,7,8,1,2] => {{1,5,7},{2,4,6,8},{3}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,5,6,7,8,1,2] => {{1,4,6,8},{2,3,5,7}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[3,4,5,6,7,8,1,2] => {{1,3,5,7},{2,4,6,8}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[8,7,6,5,4,2,1,3] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,8,5,4,2,1,3] => {{1,7},{2,6},{3,8},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,4,2,1,3] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,7,8,2,1,3] => {{1,4,7},{2,5,8},{3,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,7,6,5,4,1,2,3] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,8,5,4,1,2,3] => {{1,6},{2,7},{3,8},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,6,7,4,1,2,3] => {{1,8},{2,5},{3,6},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,8,4,1,2,3] => {{1,6},{2,5},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,4,1,2,3] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,4,7,8,1,2,3] => {{1,6},{2,5,8},{3,4,7}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,6,7,8,1,2,3] => {{1,4,7},{2,5,8},{3,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,7,6,5,3,2,1,4] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,5,6,3,2,1,4] => {{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,8,3,2,1,4] => {{1,7},{2,6},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,3,2,1,4] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,2,3,1,4] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,5,6,2,3,1,4] => {{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,5,8,2,3,1,4] => {{1,6},{2,7},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,6,8,2,3,1,4] => {{1,7},{2,5},{3,6},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,2,3,1,4] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,3,1,2,4] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,5,6,3,1,2,4] => {{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,5,8,3,1,2,4] => {{1,6},{2,7},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,6,8,3,1,2,4] => {{1,7},{2,5},{3,6},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,3,1,2,4] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,2,1,3,4] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,6,5,2,1,3,4] => {{1,7},{2,8},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,8,5,2,1,3,4] => {{1,6},{2,7},{3,8},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,5,6,2,1,3,4] => {{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,8,2,1,3,4] => {{1,6},{2,5},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,2,1,3,4] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,1,2,3,4] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,6,5,1,2,3,4] => {{1,7},{2,8},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,7,5,1,2,3,4] => {{1,8},{2,6},{3,7},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,8,5,1,2,3,4] => {{1,7},{2,6},{3,8},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,8,5,1,2,3,4] => {{1,6},{2,7},{3,8},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,5,6,1,2,3,4] => {{1,8},{2,7},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,5,6,1,2,3,4] => {{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,5,7,1,2,3,4] => {{1,8},{2,6},{3,5},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,6,7,1,2,3,4] => {{1,8},{2,5},{3,6},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,8,1,2,3,4] => {{1,7},{2,6},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,5,8,1,2,3,4] => {{1,6},{2,7},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,6,8,1,2,3,4] => {{1,7},{2,5},{3,6},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,8,1,2,3,4] => {{1,6},{2,5},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,1,2,3,4] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,5,2,3,1,6] => {{1,7},{2,8},{3,4,5},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,3,4,2,5,1,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,4,5,1,2,3,6] => {{1,7},{2,8},{3,4,5},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,3,2,1,5,6] => {{1,8},{2,7},{3,4},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,4,3,2,1,5,6] => {{1,7},{2,8},{3,4},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,3,2,4,1,5,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,2,3,4,1,5,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,3,4,1,2,5,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,4,2,1,3,5,6] => {{1,7},{2,8},{3,4},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,7,4,1,2,3,5,6] => {{1,8},{2,7},{3,4},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,7,3,2,1,4,5,6] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,3,2,1,4,5,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,2,1,3,4,5,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,7,1,2,3,4,5,6] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,1,2,3,4,5,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,4,5,6,3,2,1,7] => {{1,8},{2,4,6},{3,5},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,3,5,6,1,2,7] => {{1,8},{2,4,5,6},{3},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,4,5,6,1,2,7] => {{1,8},{2,3,4,5,6},{7}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,6,4,5,1,2,3,7] => {{1,8},{2,6},{3,4,5},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,4,3,2,1,5,7] => {{1,8},{2,6},{3,4},{5},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,6,4,2,1,3,5,7] => {{1,8},{2,6},{3,4},{5},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,3,2,1,5,6,7] => {{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,2,3,4,1,5,6,7] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[8,4,1,2,3,5,6,7] => {{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,3,2,1,4,5,6,7] => {{1,8},{2,3},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,2,3,1,4,5,6,7] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[8,3,1,2,4,5,6,7] => {{1,8},{2,3},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,2,1,3,4,5,6,7] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[8,1,2,3,4,5,6,7] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[7,6,5,4,3,2,1,8] => {{1,7},{2,6},{3,5},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,6,7,4,3,2,1,8] => {{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,5,6,3,2,1,8] => {{1,7},{2,4,6},{3,5},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,4,7,3,2,1,8] => {{1,6},{2,5},{3,4,7},{8}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,7,3,2,1,8] => {{1,4,7},{2,5},{3,6},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,6,3,4,2,1,8] => {{1,7},{2,5},{3,6},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,6,7,3,4,2,1,8] => {{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,6,7,4,2,3,1,8] => {{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,6,4,5,2,3,1,8] => {{1,7},{2,6},{3,4,5},{8}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,5,2,3,1,8] => {{1,6},{2,7},{3,4,5},{8}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,5,6,2,3,1,8] => {{1,7},{2,4,6},{3,5},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,4,7,2,3,1,8] => {{1,5},{2,6},{3,4,7},{8}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,7,2,3,1,8] => {{1,4,7},{2,5},{3,6},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,3,2,4,1,8] => {{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,6,5,2,3,4,1,8] => {{1,7},{2,6},{3,5},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,5,6,2,3,4,1,8] => {{1,7},{2,5},{3,6},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,6,7,2,3,4,1,8] => {{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,5,3,6,2,7,1,8] => {{1,4,6,7},{2,5},{3},{8}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,2,6,7,1,8] => {{1,5,6,7},{2,4},{3},{8}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,4,5,6,7,1,8] => {{1,3,4,5,6,7},{2},{8}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[7,6,5,4,3,1,2,8] => {{1,7},{2,6},{3,5},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,5,6,4,3,1,2,8] => {{1,7},{2,5},{3,6},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,5,6,3,1,2,8] => {{1,7},{2,4,6},{3,5},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,7,3,1,2,8] => {{1,4,7},{2,5},{3,6},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,4,2,1,3,8] => {{1,7},{2,6},{3,5},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,5,4,6,2,1,3,8] => {{1,7},{2,5},{3,4,6},{8}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,5,6,2,1,3,8] => {{1,7},{2,4,6},{3,5},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,7,2,1,3,8] => {{1,4,7},{2,5},{3,6},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,4,1,2,3,8] => {{1,7},{2,6},{3,5},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,6,7,4,1,2,3,8] => {{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,5,6,1,2,3,8] => {{1,7},{2,4,6},{3,5},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,4,7,1,2,3,8] => {{1,5},{2,6},{3,4,7},{8}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,6,7,1,2,3,8] => {{1,5},{2,4,7},{3,6},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,7,1,2,3,8] => {{1,4,7},{2,5},{3,6},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,3,1,2,4,8] => {{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,6,7,2,1,3,4,8] => {{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,6,5,1,2,3,4,8] => {{1,7},{2,6},{3,5},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,5,6,1,2,3,4,8] => {{1,7},{2,5},{3,6},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,6,7,1,2,3,4,8] => {{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,6,4,3,2,1,5,8] => {{1,7},{2,6},{3,4},{5},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,6,4,3,1,2,5,8] => {{1,7},{2,6},{3,4},{5},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,5,3,1,2,4,6,8] => {{1,7},{2,5},{3},{4},{6},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,5,1,2,3,4,6,8] => {{1,7},{2,5},{3},{4},{6},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,4,3,2,1,5,6,8] => {{1,7},{2,4},{3},{5},{6},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,3,1,2,4,5,6,8] => {{1,7},{2,3},{4},{5},{6},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,2,1,3,4,5,6,8] => {{1,7},{2},{3},{4},{5},{6},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[7,1,2,3,4,5,6,8] => {{1,7},{2},{3},{4},{5},{6},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[4,2,3,5,6,1,7,8] => {{1,4,5,6},{2},{3},{7},{8}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,3,4,5,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,6,3,4,1,2,7,8] => {{1,5},{2,6},{3},{4},{7},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,5,6,1,2,3,7,8] => {{1,4},{2,5},{3,6},{7},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,6,3,2,1,4,7,8] => {{1,5},{2,6},{3},{4},{7},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,3,1,4,5,7,8] => {{1,6},{2},{3},{4},{5},{7},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[6,1,2,3,4,5,7,8] => {{1,6},{2},{3},{4},{5},{7},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[5,4,3,2,1,6,7,8] => {{1,5},{2,4},{3},{6},{7},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,5,2,3,1,6,7,8] => {{1,4},{2,5},{3},{6},{7},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,2,3,4,1,6,7,8] => {{1,5},{2},{3},{4},{6},{7},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[2,3,4,5,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,1,2,4,6,7,8] => {{1,5},{2,3},{4},{6},{7},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,2,3,4,6,7,8] => {{1,5},{2},{3},{4},{6},{7},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[4,3,2,1,5,6,7,8] => {{1,4},{2,3},{5},{6},{7},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,2,4,1,5,6,7,8] => {{1,3,4},{2},{5},{6},{7},{8}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,3,4,1,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,4,1,2,5,6,7,8] => {{1,3},{2,4},{5},{6},{7},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,1,2,3,5,6,7,8] => {{1,4},{2},{3},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[3,2,1,4,5,6,7,8] => {{1,3},{2},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[3,1,2,4,5,6,7,8] => {{1,3},{2},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[2,1,3,4,5,6,7,8] => {{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,2,3,4,5,6,7,8] => {{1},{2},{3},{4},{5},{6},{7},{8}} => [1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 8

[5,8,7,6,4,3,2,1] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,8,7,4,3,2,1] => {{1,6},{2,5},{3,8},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,6,5,3,2,1] => {{1,4,6},{2,8},{3,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,5,8,3,2,1] => {{1,4,5,8},{2,7},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,7,6,8,5,4,2,1] => {{1,3,6},{2,7},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,8,7,4,2,1] => {{1,3,6},{2,5,7},{4,8}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,6,7,8,4,2,1] => {{1,3,6},{2,5,8},{4,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,5,8,7,6,2,1] => {{1,3,5,7},{2,4,8},{6}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,6,5,8,7,2,1] => {{1,4,5,8},{2,3,6,7}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[5,7,6,4,3,8,2,1] => {{1,5},{2,7},{3,6,8},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,8,6,5,4,3,1] => {{1,2,7},{3,8},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,8,7,5,4,3,1] => {{1,2,6},{3,8},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,6,7,8,4,3,1] => {{1,2,5,8},{3,6},{4,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,7,6,5,4,8,3,1] => {{1,2,7},{3,6,8},{4,5}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,5,6,8,7,4,1] => {{1,2,3,5,8},{4,6,7}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,3,5,6,7,8,4,1] => {{1,2,3,5,7},{4,6,8}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[4,3,2,8,7,6,5,1] => {{1,4,8},{2,3},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,2,8,7,6,5,1] => {{1,3},{2,4,8},{5,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,8,7,6,5,1] => {{1,2,4,8},{3},{5,7},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,4,8,7,6,5,1] => {{1,3,4,8},{2},{5,7},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,8,7,6,5,1] => {{1,2,3,4,8},{5,7},{6}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,3,2,8,7,6,1] => {{1,5,8},{2,4},{3},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,2,7,8,6,1] => {{1,5,7},{2,4},{3},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,4,3,7,8,6,1] => {{1,2,5,7},{3,4},{6,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,5,3,7,8,6,1] => {{1,2,4},{3,5,7},{6,8}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,2,5,7,8,6,1] => {{1,3},{2,4,5,7},{6,8}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,2,6,5,4,8,7,1] => {{1,3,6,8},{2},{4,5},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,6,5,8,7,1] => {{1,2,4,6,8},{3},{5},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,2,6,8,7,1] => {{1,5,6,8},{2,4},{3},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,4,3,6,8,7,1] => {{1,2,5,6,8},{3,4},{7}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,3,5,6,8,7,1] => {{1,2,4,5,6,8},{3},{7}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,5,6,8,7,1] => {{1,2,3,4,5,6,8},{7}} => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[4,3,6,5,7,2,8,1] => {{1,4,5,7,8},{2,3,6}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,5,4,7,6,3,8,1] => {{1,2,5,6},{3,4,7,8}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,5,4,6,7,3,8,1] => {{1,2,5,7,8},{3,4,6}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[3,2,6,5,7,4,8,1] => {{1,3,6},{2},{4,5,7,8}} => [3,1,4] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,3,7,6,5,8,1] => {{1,2,4,7,8},{3},{5,6}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,7,6,5,8,1] => {{1,2,3,4,7,8},{5,6}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[5,4,3,2,7,6,8,1] => {{1,5,7,8},{2,4},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,5,2,7,6,8,1] => {{1,4},{2,3,5,7,8},{6}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,2,5,4,7,6,8,1] => {{1,3,5,7,8},{2},{4},{6}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,5,4,7,6,8,1] => {{1,2,3,5,7,8},{4},{6}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,2,4,5,7,6,8,1] => {{1,3,4,5,7,8},{2},{6}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,3,6,5,7,8,1] => {{1,2,4,6,7,8},{3},{5}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,5,4,3,6,7,8,1] => {{1,2,5,6,7,8},{3,4}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[1,8,7,6,5,4,3,2] => {{1},{2,8},{3,7},{4,6},{5}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,6,7,8,5,4,3,2] => {{1},{2,6},{3,7},{4,8},{5}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,8,7,6,4,3,2] => {{1},{2,5,6},{3,8},{4,7}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,6,5,8,4,3,2] => {{1},{2,7},{3,6},{4,5,8}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,6,7,8,4,3,2] => {{1},{2,5,8},{3,6},{4,7}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,8,7,6,5,3,2] => {{1},{2,4,7},{3,8},{5,6}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,7,8,6,5,3,2] => {{1},{2,4,8},{3,7},{5,6}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,5,7,8,6,4,2] => {{1},{2,3,5,8},{4,7},{6}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,5,6,7,8,4,2] => {{1},{2,3,5,7},{4,6,8}} => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,4,3,8,7,6,5,2] => {{1},{2,4,8},{3},{5,7},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,3,7,8,6,5,2] => {{1},{2,4,7},{3},{5,8},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,3,7,6,8,5,2] => {{1},{2,4,7},{3},{5,6,8}} => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,4,8,7,6,5,2] => {{1},{2,3,4,8},{5,7},{6}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,4,5,7,8,6,2] => {{1},{2,3,4,5,7},{6,8}} => [1,5,2] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,6,5,4,3,8,7,2] => {{1},{2,6,8},{3,5},{4},{7}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,6,4,3,8,7,2] => {{1},{2,5},{3,6,8},{4},{7}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,3,6,5,8,7,2] => {{1},{2,4,6,8},{3},{5},{7}} => [1,4,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,4,5,6,8,7,2] => {{1},{2,3,4,5,6,8},{7}} => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,5,4,3,6,7,8,2] => {{1},{2,5,6,7,8},{3,4}} => [1,5,2] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,4,5,3,6,7,8,2] => {{1},{2,4},{3,5,6,7,8}} => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,4,3,5,6,7,8,2] => {{1},{2,4,5,6,7,8},{3}} => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,3,4,5,6,7,8,2] => {{1},{2,3,4,5,6,7,8}} => [1,7] => ([(6,7)],8) => 2

[2,1,8,7,6,5,4,3] => {{1,2},{3,8},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,7,8,5,4,3] => {{1,2},{3,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,5,8,7,4,3] => {{1,2},{3,6,7},{4,5,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,1,7,6,5,8,4,3] => {{1,2},{3,7},{4,6,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,7,5,8,4,3] => {{1,2},{3,6,8},{4,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,5,7,8,4,3] => {{1,2},{3,6,8},{4,5,7}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,1,5,6,7,8,4,3] => {{1,2},{3,5,7},{4,6,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,1,4,8,7,6,5,3] => {{1,2},{3,4,8},{5,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,7,8,6,5,3] => {{1,2},{3,4,7},{5,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,5,8,7,6,3] => {{1,2},{3,4,5,8},{6,7}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,1,4,5,7,8,6,3] => {{1,2},{3,4,5,7},{6,8}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,1,4,6,5,8,7,3] => {{1,2},{3,4,6,8},{5},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,5,7,4,8,3] => {{1,2},{3,6},{4,5,7,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,1,5,4,7,6,8,3] => {{1,2},{3,5,7,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,5,6,7,8,3] => {{1,2},{3,4,5,6,7,8}} => [2,6] => ([(5,7),(6,7)],8) => 2

[1,2,5,6,7,8,4,3] => {{1},{2},{3,5,7},{4,6,8}} => [1,1,3,3] => ([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,4,6,7,8,5,3] => {{1},{2},{3,4,6,8},{5,7}} => [1,1,4,2] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,6,5,4,7,8,3] => {{1},{2},{3,6,7,8},{4,5}} => [1,1,4,2] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,5,6,4,7,8,3] => {{1},{2},{3,5},{4,6,7,8}} => [1,1,2,4] => ([(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,5,4,6,7,8,3] => {{1},{2},{3,5,6,7,8},{4}} => [1,1,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,4,5,6,7,8,3] => {{1},{2},{3,4,5,6,7,8}} => [1,1,6] => ([(5,6),(5,7),(6,7)],8) => 3

[3,2,1,8,7,6,5,4] => {{1,3},{2},{4,8},{5,7},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,1,7,8,6,5,4] => {{1,3},{2},{4,7},{5,8},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,1,6,8,7,5,4] => {{1,3},{2},{4,6,7},{5,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,7,6,8,5,4] => {{1,3},{2},{4,7},{5,6,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,6,7,8,5,4] => {{1,3},{2},{4,6,8},{5,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,5,8,7,6,4] => {{1,3},{2},{4,5,8},{6,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,5,7,8,6,4] => {{1,3},{2},{4,5,7},{6,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,6,5,8,7,4] => {{1,3},{2},{4,6,8},{5},{7}} => [2,1,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,1,5,6,8,7,4] => {{1,3},{2},{4,5,6,8},{7}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,7,6,5,8,4] => {{1,3},{2},{4,7,8},{5,6}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,6,7,5,8,4] => {{1,3},{2},{4,6},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,5,7,6,8,4] => {{1,3},{2},{4,5,7,8},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,6,5,7,8,4] => {{1,3},{2},{4,6,7,8},{5}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,5,6,7,8,4] => {{1,3},{2},{4,5,6,7,8}} => [2,1,5] => ([(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,1,8,7,6,5,4] => {{1,2,3},{4,8},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,2,8,7,6,5,4] => {{1},{2,3},{4,8},{5,7},{6}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,3,8,7,6,5,4] => {{1},{2},{3},{4,8},{5,7},{6}} => [1,1,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,3,7,8,6,5,4] => {{1},{2},{3},{4,7},{5,8},{6}} => [1,1,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,3,6,8,7,5,4] => {{1},{2},{3},{4,6,7},{5,8}} => [1,1,1,3,2] => ([(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,3,6,7,8,5,4] => {{1},{2},{3},{4,6,8},{5,7}} => [1,1,1,3,2] => ([(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,3,7,6,5,8,4] => {{1},{2},{3},{4,7,8},{5,6}} => [1,1,1,3,2] => ([(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,3,6,5,7,8,4] => {{1},{2},{3},{4,6,7,8},{5}} => [1,1,1,4,1] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,3,5,6,7,8,4] => {{1},{2},{3},{4,5,6,7,8}} => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,1,8,7,6,5] => {{1,4},{2,3},{5,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,1,7,8,6,5] => {{1,4},{2,3},{5,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,1,6,8,7,5] => {{1,4},{2,3},{5,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,1,7,6,8,5] => {{1,4},{2,3},{5,7,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,1,6,7,8,5] => {{1,4},{2,3},{5,6,7,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,2,1,8,7,6,5] => {{1,3},{2,4},{5,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,2,1,7,8,6,5] => {{1,3},{2,4},{5,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,2,1,6,8,7,5] => {{1,3},{2,4},{5,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,2,1,7,6,8,5] => {{1,3},{2,4},{5,7,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,2,1,6,7,8,5] => {{1,3},{2,4},{5,6,7,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,3,1,8,7,6,5] => {{1,2,4},{3},{5,8},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,1,7,8,6,5] => {{1,2,4},{3},{5,7},{6,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,1,6,8,7,5] => {{1,2,4},{3},{5,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,1,7,6,8,5] => {{1,2,4},{3},{5,7,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,1,6,7,8,5] => {{1,2,4},{3},{5,6,7,8}} => [3,1,4] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,2,4,1,8,7,6,5] => {{1,3,4},{2},{5,8},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,4,1,7,8,6,5] => {{1,3,4},{2},{5,7},{6,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,4,1,6,8,7,5] => {{1,3,4},{2},{5,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,4,1,7,6,8,5] => {{1,3,4},{2},{5,7,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,4,1,6,7,8,5] => {{1,3,4},{2},{5,6,7,8}} => [3,1,4] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,1,8,7,6,5] => {{1,2,3,4},{5,8},{6,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,1,7,8,6,5] => {{1,2,3,4},{5,7},{6,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,1,6,8,7,5] => {{1,2,3,4},{5,6,8},{7}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,1,7,6,8,5] => {{1,2,3,4},{5,7,8},{6}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,1,6,7,8,5] => {{1,2,3,4},{5,6,7,8}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[1,4,3,2,8,7,6,5] => {{1},{2,4},{3},{5,8},{6,7}} => [1,2,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,3,2,7,6,8,5] => {{1},{2,4},{3},{5,7,8},{6}} => [1,2,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,3,2,6,7,8,5] => {{1},{2,4},{3},{5,6,7,8}} => [1,2,1,4] => ([(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,4,2,8,7,6,5] => {{1},{2,3,4},{5,8},{6,7}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,3,8,7,6,5] => {{1,2},{3,4},{5,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,3,7,8,6,5] => {{1,2},{3,4},{5,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,3,6,8,7,5] => {{1,2},{3,4},{5,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,3,7,6,8,5] => {{1,2},{3,4},{5,7,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,3,6,7,8,5] => {{1,2},{3,4},{5,6,7,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,2,4,3,8,7,6,5] => {{1},{2},{3,4},{5,8},{6,7}} => [1,1,2,2,2] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,4,3,6,7,8,5] => {{1},{2},{3,4},{5,6,7,8}} => [1,1,2,4] => ([(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,4,8,7,6,5] => {{1,3},{2},{4},{5,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,1,4,7,6,8,5] => {{1,3},{2},{4},{5,7,8},{6}} => [2,1,1,3,1] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,1,4,6,7,8,5] => {{1,3},{2},{4},{5,6,7,8}} => [2,1,1,4] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,1,4,8,7,6,5] => {{1,2,3},{4},{5,8},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,2,4,8,7,6,5] => {{1},{2,3},{4},{5,8},{6,7}} => [1,2,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,2,4,6,7,8,5] => {{1},{2,3},{4},{5,6,7,8}} => [1,2,1,4] => ([(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,3,4,8,7,6,5] => {{1,2},{3},{4},{5,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,3,4,6,7,8,5] => {{1,2},{3},{4},{5,6,7,8}} => [2,1,1,4] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,3,4,8,7,6,5] => {{1},{2},{3},{4},{5,8},{6,7}} => [1,1,1,1,2,2] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,3,4,7,8,6,5] => {{1},{2},{3},{4},{5,7},{6,8}} => [1,1,1,1,2,2] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,3,4,7,6,8,5] => {{1},{2},{3},{4},{5,7,8},{6}} => [1,1,1,1,3,1] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,3,4,6,7,8,5] => {{1},{2},{3},{4},{5,6,7,8}} => [1,1,1,1,4] => ([(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,4,3,2,1,8,7,6] => {{1,5},{2,4},{3},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,4,3,2,1,7,8,6] => {{1,5},{2,4},{3},{6,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,3,2,1,8,7,6] => {{1,4},{2,5},{3},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,5,4,2,1,8,7,6] => {{1,3,4},{2,5},{6,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,5,2,1,8,7,6] => {{1,4},{2,3,5},{6,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,5,2,1,8,7,6] => {{1,3,5},{2,4},{6,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,4,3,1,8,7,6] => {{1,2,5},{3,4},{6,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,4,1,8,7,6] => {{1,3,5},{2},{4},{6,8},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,3,5,4,1,8,7,6] => {{1,2,3,5},{4},{6,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,5,1,8,7,6] => {{1,4,5},{2,3},{6,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,2,5,1,8,7,6] => {{1,3},{2,4,5},{6,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,4,5,1,8,7,6] => {{1,3,4,5},{2},{6,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,5,1,8,7,6] => {{1,2,3,4,5},{6,8},{7}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,2,1,5,8,7,6] => {{1,4},{2,3},{5},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,2,1,5,7,8,6] => {{1,4},{2,3},{5},{6,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,4,1,5,8,7,6] => {{1,3,4},{2},{5},{6,8},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,4,1,5,7,8,6] => {{1,3,4},{2},{5},{6,7,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,1,5,8,7,6] => {{1,2,3,4},{5},{6,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,4,5,8,7,6] => {{1,3},{2},{4},{5},{6,8},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,3,1,4,5,7,8,6] => {{1,2,3},{4},{5},{6,7,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,3,4,5,8,7,6] => {{1},{2},{3},{4},{5},{6,8},{7}} => [1,1,1,1,1,2,1] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,2,3,4,5,7,8,6] => {{1},{2},{3},{4},{5},{6,7,8}} => [1,1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,5,4,3,2,1,8,7] => {{1,6},{2,5},{3,4},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,4,3,2,1,8,7] => {{1,5},{2,6},{3,4},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,3,2,1,8,7] => {{1,4},{2,5},{3,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,5,4,2,1,8,7] => {{1,3,5},{2,6},{4},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,6,5,2,1,8,7] => {{1,4,5},{2,3,6},{7,8}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,3,6,2,1,8,7] => {{1,5},{2,4,6},{3},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,3,6,2,1,8,7] => {{1,4,6},{2,5},{3},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,5,6,2,1,8,7] => {{1,4,6},{2,3,5},{7,8}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,6,5,4,1,8,7] => {{1,2,3,6},{4,5},{7,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,3,6,5,1,8,7] => {{1,2,4,6},{3},{5},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,2,6,1,8,7] => {{1,5,6},{2,4},{3},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,3,2,6,1,8,7] => {{1,4},{2,5,6},{3},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,5,2,6,1,8,7] => {{1,4},{2,3,5,6},{7,8}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,2,5,4,6,1,8,7] => {{1,3,5,6},{2},{4},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,5,6,1,8,7] => {{1,4,5,6},{2,3},{7,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,5,6,1,8,7] => {{1,2,3,4,5,6},{7,8}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[1,5,6,4,3,2,8,7] => {{1},{2,5},{3,6},{4},{7,8}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,6,5,4,3,8,7] => {{1,2},{3,6},{4,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,6,4,3,8,7] => {{1,2},{3,5},{4,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,6,5,3,8,7] => {{1,2},{3,4,6},{5},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,4,6,3,8,7] => {{1,2},{3,5,6},{4},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,5,6,3,8,7] => {{1,2},{3,4,5,6},{7,8}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,2,1,6,5,8,7] => {{1,4},{2,3},{5,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,2,1,6,5,8,7] => {{1,3},{2,4},{5,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,1,6,5,8,7] => {{1,2,4},{3},{5,6},{7,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,4,1,6,5,8,7] => {{1,3,4},{2},{5,6},{7,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,1,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,2,1,6,8,7] => {{1,5},{2,4},{3},{6},{7,8}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,2,1,5,6,8,7] => {{1,4},{2,3},{5},{6},{7,8}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,4,1,5,6,8,7] => {{1,3,4},{2},{5},{6},{7,8}} => [3,1,1,1,2] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,3,4,5,6,8,7] => {{1,2},{3},{4},{5},{6},{7,8}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,3,4,5,6,8,7] => {{1},{2},{3},{4},{5},{6},{7,8}} => [1,1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[4,7,6,5,3,2,1,8] => {{1,4,5},{2,7},{3,6},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,7,6,5,2,1,8] => {{1,3,7},{2,4,6},{5},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,7,6,5,4,1,8] => {{1,3,7},{2},{4,6},{5},{8}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,6,7,5,4,1,8] => {{1,3,6},{2},{4,7},{5},{8}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,4,3,2,7,6,1,8] => {{1,5,7},{2,4},{3},{6},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,5,3,2,7,6,1,8] => {{1,4},{2,5,7},{3},{6},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,5,4,2,7,6,1,8] => {{1,3,4},{2,5,7},{6},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,4,7,6,1,8] => {{1,3,5,7},{2},{4},{6},{8}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,3,4,5,7,6,1,8] => {{1,2,3,4,5,7},{6},{8}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,3,4,6,7,5,2,8] => {{1},{2,3,4,6},{5,7},{8}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,4,5,7,6,2,8] => {{1},{2,3,4,5,7},{6},{8}} => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,1,5,6,7,4,8] => {{1,2,3},{4,5,6,7},{8}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,2,1,7,6,5,8] => {{1,4},{2,3},{5,7},{6},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,2,1,6,7,5,8] => {{1,4},{2,3},{5,6,7},{8}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,1,6,7,5,8] => {{1,2,3,4},{5,6,7},{8}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,4,3,2,7,6,5,8] => {{1},{2,4},{3},{5,7},{6},{8}} => [1,2,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,3,4,2,6,7,5,8] => {{1},{2,3,4},{5,6,7},{8}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,2,1,7,6,8] => {{1,5},{2,4},{3},{6,7},{8}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,1,5,4,7,6,8] => {{1,3},{2},{4,5},{6,7},{8}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,2,1,5,7,6,8] => {{1,4},{2,3},{5},{6,7},{8}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,3,4,1,5,7,6,8] => {{1,2,3,4},{5},{6,7},{8}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,2,4,5,7,6,8] => {{1},{2,3},{4},{5},{6,7},{8}} => [1,2,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,3,4,6,5,1,7,8] => {{1,2,3,4,6},{5},{7},{8}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,1,6,5,7,8] => {{1,4},{2,3},{5,6},{7},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,4,3,6,5,7,8] => {{1},{2},{3,4},{5,6},{7},{8}} => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,2,5,4,1,6,7,8] => {{1,3,5},{2},{4},{6},{7},{8}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,3,8,5,6,7,4] => {{1},{2},{3},{4,8},{5},{6},{7}} => [1,1,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,2,3,8,6,5,7,4] => {{1},{2},{3},{4,8},{5,6},{7}} => [1,1,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,3,8,6,7,5,4] => {{1},{2},{3},{4,8},{5,6,7}} => [1,1,1,2,3] => ([(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,4,5,8,6,7,3] => {{1},{2},{3,4,5,8},{6},{7}} => [1,1,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,8,5,4,6,7,3] => {{1},{2},{3,8},{4,5},{6},{7}} => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,3,2,8,6,5,7,4] => {{1},{2,3},{4,8},{5,6},{7}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,7,4,5,6,2,8] => {{1},{2,3,7},{4},{5},{6},{8}} => [1,3,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,3,8,5,4,6,7,2] => {{1},{2,3,8},{4,5},{6},{7}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,8,6,5,7,4,2] => {{1},{2,3,8},{4,6,7},{5}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,3,5,4,8,7,2] => {{1},{2,6,8},{3},{4,5},{7}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,4,3,5,6,7,2] => {{1},{2,8},{3,4},{5},{6},{7}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,8,5,4,3,6,7,2] => {{1},{2,8},{3,5},{4},{6},{7}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,8,5,4,7,6,3,2] => {{1},{2,8},{3,5,7},{4},{6}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,4,5,8,6,7,3] => {{1,2},{3,4,5,8},{6},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,4,6,5,8,3] => {{1,2},{3,7,8},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,5,4,7,6,3] => {{1,2},{3,8},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,1,8,6,7,5,4] => {{1,2,3},{4,8},{5,6,7}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,8,5,6,7,1] => {{1,2,3,4,8},{5},{6},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,8,5,7,6,1] => {{1,2,3,4,8},{5},{6,7}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,8,6,5,7,1] => {{1,2,3,4,8},{5,6},{7}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,8,6,7,5,1] => {{1,2,3,4,8},{5,6,7}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,3,6,4,5,1,8,7] => {{1,2,3,6},{4},{5},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,7,4,5,6,8,1] => {{1,2,3,7,8},{4},{5},{6}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,3,4,5,6,7,1] => {{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,8,3,5,4,7,6,1] => {{1,2,8},{3},{4,5},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,3,5,7,6,4,1] => {{1,2,8},{3},{4,5,7},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,4,3,8,6,7,1] => {{1,2,5,8},{3,4},{6},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,4,3,5,7,6,1] => {{1,2,8},{3,4},{5},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,8,5,7,6,4] => {{1,3},{2},{4,8},{5},{6,7}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,1,8,6,5,7,4] => {{1,3},{2},{4,8},{5,6},{7}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,1,8,6,7,5,4] => {{1,3},{2},{4,8},{5,6,7}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,7,4,6,5,8,1] => {{1,3,7,8},{2},{4},{5,6}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,7,5,4,6,1,8] => {{1,3,7},{2},{4,5},{6},{8}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,3,1,6,5,8,7] => {{1,4},{2},{3},{5,6},{7,8}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,3,1,6,7,8,5] => {{1,4},{2},{3},{5,6,7,8}} => [2,1,1,4] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,3,1,8,6,7,5] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,2,3,1,8,7,6,5] => {{1,4},{2},{3},{5,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,3,5,1,8,7,6] => {{1,4,5},{2},{3},{6,8},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,3,7,6,5,8,1] => {{1,4,7,8},{2},{3},{5,6}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,2,3,4,6,5,1,8] => {{1,7},{2},{3},{4},{5,6},{8}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,3,5,4,1,7,8] => {{1,6},{2},{3},{4,5},{7},{8}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,2,3,6,5,4,1,8] => {{1,7},{2},{3},{4,6},{5},{8}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,2,4,3,1,6,7,8] => {{1,5},{2},{3,4},{6},{7},{8}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,2,4,3,1,8,7,6] => {{1,5},{2},{3,4},{6,8},{7}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,2,4,3,6,1,8,7] => {{1,5,6},{2},{3,4},{7,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,4,3,7,6,8,1] => {{1,5,7,8},{2},{3,4},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,2,4,3,6,5,8,1] => {{1,7,8},{2},{3,4},{5,6}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,1,8,6,7,5] => {{1,4},{2,3},{5,8},{6},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,2,7,5,6,8,1] => {{1,4,7,8},{2,3},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,8,5,7,6,1] => {{1,4,8},{2,3},{5},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,4,1,8,7,6] => {{1,5},{2,3},{4},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,2,5,4,1,8,7] => {{1,6},{2,3},{4,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,5,4,7,6,1] => {{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,7,6,5,4,1] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,4,2,1,7,8,6] => {{1,5},{2,3,4},{6,7,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,4,2,1,8,7,6] => {{1,5},{2,3,4},{6,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,4,6,5,2,1] => {{1,8},{2,3,7},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,3,6,5,2,1,8] => {{1,7},{2,4,6},{3},{5},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,5,4,3,2,7,6,1] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,3,6,5,2,1] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,3,6,5,8,7] => {{1,2,4},{3},{5,6},{7,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,6,3,5,8,7] => {{1,2},{3,4,6},{5},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,6,3,5,8,7] => {{1,2,4,6},{3},{5},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,1,3,5,8,7] => {{1,2,4},{3,6},{5},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,3,6,8,5,7] => {{1,2},{3,4},{5,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,3,6,8,5,7] => {{1,2,4},{3},{5,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,6,3,8,5,7] => {{1,2},{3,4,6,8},{5},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,6,3,8,5,7] => {{1,2,4,6,8},{3},{5},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,1,3,8,5,7] => {{1,2,4},{3,6,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,6,8,3,5,7] => {{1,2},{3,4,6},{5,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,6,8,3,5,7] => {{1,2,4,6},{3},{5,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,1,8,3,5,7] => {{1,2,4},{3,6},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,8,1,3,5,7] => {{1,2,4,8},{3,6},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,3,6,7,8,5] => {{1,2,4},{3},{5,6,7,8}} => [3,1,4] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,1,6,3,7,8,5] => {{1,2,4,6,7,8},{3},{5}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,1,6,7,3,8,5] => {{1,2,4,6},{3},{5,7,8}} => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,6,1,7,3,8,5] => {{1,2,4},{3,6},{5,7,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,1,6,7,8,3,5] => {{1,2,4,6,8},{3},{5,7}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,6,7,1,8,3,5] => {{1,2,4,7},{3,6,8},{5}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,1,4,3,7,5,8,6] => {{1,2},{3,4},{5,7,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,3,7,5,8,6] => {{1,2,4},{3},{5,7,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,7,1,3,5,8,6] => {{1,2,4},{3,7,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,3,7,8,5,6] => {{1,2},{3,4},{5,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,3,7,8,5,6] => {{1,2,4},{3},{5,7},{6,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,7,1,3,8,5,6] => {{1,2,4},{3,7},{5},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,7,8,1,3,5,6] => {{1,2,4,8},{3,7},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,5,7,3,8,6] => {{1,2},{3,4,5,7,8},{6}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,1,4,5,8,3,6,7] => {{1,2},{3,4,5,8},{6},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,5,1,8,3,6,7] => {{1,2,4},{3,5,8},{6},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,5,6,3,8,7] => {{1,2,4,5,6},{3},{7,8}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,1,5,6,7,8,3] => {{1,2,4,5,6,7,8},{3}} => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,4,5,6,1,7,8,3] => {{1,2,4,6,7,8},{3,5}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,4,5,6,7,1,8,3] => {{1,2,4,6},{3,5,7,8}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,4,5,6,7,8,1,3] => {{1,2,4,6,8},{3,5,7}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,1,5,3,6,4,8,7] => {{1,2},{3,5,6},{4},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,6,3,4,8,7] => {{1,2},{3,5},{4,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,6,8,1,3,4,7] => {{1,2,5},{3,6},{4,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,1,6,7,3,8,4] => {{1,2,5,7,8},{3},{4,6}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,1,5,6,7,8,3,4] => {{1,2},{3,5,7},{4,6,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,5,1,6,7,8,3,4] => {{1,2,5,7},{3},{4,6,8}} => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,5,6,7,8,1,3,4] => {{1,2,5,8},{3,6},{4,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,1,5,3,7,4,8,6] => {{1,2},{3,5,7,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,1,7,3,4,8,6] => {{1,2,5},{3},{4,7,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,1,3,7,8,4,6] => {{1,2,5,7},{3},{4},{6,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,7,3,8,4,6] => {{1,2},{3,5},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,7,8,3,4,6] => {{1,2},{3,5,8},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,7,1,8,3,4,6] => {{1,2,5,8},{3,7},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,7,8,1,3,4,6] => {{1,2,5},{3,7},{4,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,5,1,7,4,8,6] => {{1,2,3,5,7,8},{4},{6}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,5,1,6,4,7,8] => {{1,2,3,5,6},{4},{7},{8}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,5,1,6,7,8,4] => {{1,2,3,5,6,7,8},{4}} => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,3,5,6,1,7,8,4] => {{1,2,3,5},{4,6,7,8}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,3,5,6,7,8,1,4] => {{1,2,3,5,7},{4,6,8}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,1,6,3,7,4,8,5] => {{1,2},{3,6},{4},{5,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,1,3,7,4,8,5] => {{1,2,6},{3},{4},{5,7,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,7,1,3,4,8,5] => {{1,2,6},{3,7,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,3,7,8,4,5] => {{1,2},{3,6,8},{4},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,1,7,3,8,4,5] => {{1,2,6,8},{3},{4,7},{5}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,7,8,3,4,5] => {{1,2},{3,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,7,8,1,3,4,5] => {{1,2,6},{3,7},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,1,6,4,7,5,8] => {{1,2,3},{4,6,7},{5},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,3,4,7,8,5] => {{1,2},{3,6,7,8},{4},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,3,6,7,8,4,5] => {{1,2},{3},{4,6,8},{5,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,1,6,4,8,5,7] => {{1,2,3},{4,6,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,1,6,8,4,5,7] => {{1,2,3},{4,6},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,6,1,8,4,5,7] => {{1,2,3,6},{4},{5,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,6,1,4,5,8,7] => {{1,2,3,6},{4},{5},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,1,6,8,5,7] => {{1,2,3,4},{5,6,8},{7}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,6,1,3,4,5,7,8] => {{1,2,6},{3},{4},{5},{7},{8}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,3,4,6,1,7,5,8] => {{1,2,3,4,6,7},{5},{8}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,6,7,8,1,5] => {{1,2,3,4,6,8},{5,7}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,3,1,7,4,8,5,6] => {{1,2,3},{4,7},{5},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,1,7,5,8,6] => {{1,2,3,4},{5,7,8},{6}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,1,7,8,5,6] => {{1,2,3,4},{5,7},{6,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,7,1,3,4,5,6,8] => {{1,2,7},{3},{4},{5},{6},{8}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,3,4,5,7,1,8,6] => {{1,2,3,4,5,7,8},{6}} => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,3,4,5,7,8,1,6] => {{1,2,3,4,5,7},{6,8}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,1,8,3,4,5,6,7] => {{1,2},{3,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,8,1,3,4,5,6,7] => {{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,1,3,8,4,5,6,7] => {{1,2},{3},{4,8},{5},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,1,3,4,8,5,6,7] => {{1,2},{3},{4},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,3,4,8,1,5,6,7] => {{1,2,3,4,8},{5},{6},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,1,5,8,6,7] => {{1,2,3,4},{5},{6,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,5,1,8,6,7] => {{1,2,3,4,5},{6,8},{7}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,5,8,1,6,7] => {{1,2,3,4,5,8},{6},{7}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,5,6,8,1,7] => {{1,2,3,4,5,6,8},{7}} => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[3,1,4,2,6,5,8,7] => {{1,3,4},{2},{5,6},{7,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,1,2,6,5,8,7] => {{1,3},{2,4},{5,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,4,2,6,8,5,7] => {{1,3,4},{2},{5,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,1,2,6,8,5,7] => {{1,3},{2,4},{5,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,4,6,8,2,5,7] => {{1,3,4,6},{2},{5,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,6,8,1,2,5,7] => {{1,3,6},{2,4,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,6,7,1,2,5,8] => {{1,3,6},{2,4,7},{5},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,4,2,6,7,8,5] => {{1,3,4},{2},{5,6,7,8}} => [3,1,4] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,1,2,6,7,8,5] => {{1,3},{2,4},{5,6,7,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,6,1,2,7,8,5] => {{1,3,6,7,8},{2,4},{5}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,6,1,7,2,8,5] => {{1,3,6},{2,4},{5,7,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,6,1,7,8,2,5] => {{1,3,6,8},{2,4},{5,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,1,4,2,7,5,8,6] => {{1,3,4},{2},{5,7,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,1,2,7,8,5,6] => {{1,3},{2,4},{5,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,7,1,8,2,5,6] => {{1,3,7},{2,4},{5,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,7,8,1,2,5,6] => {{1,3,7},{2,4,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,1,5,8,2,6,7] => {{1,3},{2,4,5,8},{6},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,5,8,1,2,6,7] => {{1,3,5},{2,4,8},{6},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,4,2,5,6,7,8] => {{1,3,4},{2},{5},{6},{7},{8}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,1,4,5,6,7,8,2] => {{1,3,4,5,6,7,8},{2}} => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[3,4,1,5,6,7,8,2] => {{1,3},{2,4,5,6,7,8}} => [2,6] => ([(5,7),(6,7)],8) => 2

[3,4,5,6,7,1,8,2] => {{1,3,5,7,8},{2,4,6}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[3,1,5,2,6,4,8,7] => {{1,3,5,6},{2},{4},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,6,2,4,8,7] => {{1,3},{2,5},{4,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,1,2,4,8,7] => {{1,3,6},{2,5},{4},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,2,6,8,4,7] => {{1,3},{2,5,6,8},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,5,6,2,8,4,7] => {{1,3,5},{2},{4,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,1,8,2,4,7] => {{1,3,6},{2,5,8},{4},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,8,1,2,4,7] => {{1,3,6},{2,5},{4,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,1,7,2,4,8] => {{1,3,6},{2,5,7},{4},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,1,7,8,2,4] => {{1,3,6,8},{2,5,7},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,6,7,8,1,2,4] => {{1,3,6},{2,5,8},{4,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,1,5,2,7,4,8,6] => {{1,3,5,7,8},{2},{4},{6}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,5,7,2,4,8,6] => {{1,3,5},{2},{4,7,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,5,7,2,8,4,6] => {{1,3,5},{2},{4,7},{6,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,7,2,8,4,6] => {{1,3},{2,5},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,7,8,2,4,6] => {{1,3},{2,5,8},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,7,8,1,2,4,6] => {{1,3,7},{2,5},{4,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,5,2,7,4,6,8] => {{1,3,5,7},{2},{4},{6},{8}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,5,2,7,4,8,6] => {{1},{2,3,5,7,8},{4},{6}} => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,5,2,8,4,6,7] => {{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,2,5,4,8,6,7] => {{1},{2,3},{4,5},{6,8},{7}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,2,5,8,4,6,7] => {{1},{2,3},{4,5,8},{6},{7}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,5,2,6,8,4,7] => {{1},{2,3,5,6,8},{4},{7}} => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,5,2,6,7,4,8] => {{1},{2,3,5,6,7},{4},{8}} => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,5,6,2,7,4,8] => {{1},{2,3,5},{4,6,7},{8}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,5,6,7,8,2,4] => {{1},{2,3,5,7},{4,6,8}} => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,1,6,2,7,4,8,5] => {{1,3,6},{2},{4},{5,7,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,7,2,4,8,5] => {{1,3},{2,6},{4,7,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,7,2,8,4,5] => {{1,3},{2,6,8},{4,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,1,2,8,4,5] => {{1,3,7},{2,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,7,8,2,4,5] => {{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,8,1,2,4,5] => {{1,3,7},{2,6},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,6,7,2,4,5,8] => {{1,3,6},{2},{4,7},{5},{8}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,2,6,4,7,5,8] => {{1},{2,3},{4,6,7},{5},{8}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,6,2,4,7,8,5] => {{1},{2,3,6,7,8},{4},{5}} => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,2,6,7,4,8,5] => {{1,3},{2},{4,6},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,6,2,7,8,4,5] => {{1},{2,3,6,8},{4},{5,7}} => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,6,2,8,4,5,7] => {{1,3,6},{2},{4},{5,8},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,2,6,4,8,5,7] => {{1},{2,3},{4,6,8},{5},{7}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,6,2,4,5,7,8] => {{1,3,6},{2},{4},{5},{7},{8}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,1,2,4,6,7,8,5] => {{1,3},{2},{4},{5,6,7,8}} => [2,1,1,4] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,4,6,7,2,8,5] => {{1},{2,3,4,6},{5,7,8}} => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,3,7,2,8,4,5,6] => {{1},{2,3,7},{4},{5,8},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,4,5,7,8,2,6] => {{1},{2,3,4,5,7},{6,8}} => [1,5,2] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,1,8,2,4,5,6,7] => {{1,3,8},{2},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,1,2,4,5,8,6,7] => {{1,3},{2},{4},{5},{6,8},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,3,2,4,5,8,6,7] => {{1},{2,3},{4},{5},{6,8},{7}} => [1,2,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,1,5,2,6,3,8,7] => {{1,4},{2},{3,5,6},{7,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,2,6,3,8,7] => {{1,4},{2,5,6},{3},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,1,2,3,8,7] => {{1,4},{2,5},{3,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,2,6,8,3,7] => {{1,4},{2},{3,5,6,8},{7}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,6,2,8,3,7] => {{1,4,6,8},{2,5},{3},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,1,2,8,3,7] => {{1,4},{2,5},{3,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,6,8,2,3,7] => {{1,4,6},{2},{3,5,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,8,1,2,3,7] => {{1,4,8},{2,5},{3,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,6,2,7,3,8] => {{1,4,6,7},{2,5},{3},{8}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,1,7,2,3,8] => {{1,4},{2,5,7},{3,6},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,7,1,2,8,3] => {{1,4,7,8},{2,5},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,1,5,6,7,8,2,3] => {{1,4,6,8},{2},{3,5,7}} => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,6,7,1,8,2,3] => {{1,4,7},{2,5},{3,6,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,1,5,2,7,3,8,6] => {{1,4},{2},{3,5,7,8},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,7,2,3,8,6] => {{1,4,7,8},{2,5},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,2,7,8,3,6] => {{1,4},{2},{3,5,7},{6,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,7,2,8,3,6] => {{1,4,7},{2},{3,5},{6,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,7,2,8,3,6] => {{1,4,7},{2,5},{3},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,1,2,8,3,6] => {{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,7,8,2,3,6] => {{1,4,7},{2,5,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,8,1,2,3,6] => {{1,4,8},{2,5},{3,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,2,7,3,6,8] => {{1,4},{2,5,7},{3},{6},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,2,5,3,7,6,8] => {{1},{2,4,5},{3},{6,7},{8}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,2,5,7,3,8,6] => {{1},{2,4,5,7,8},{3},{6}} => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,5,7,2,3,8,6] => {{1},{2,4,7,8},{3,5},{6}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,2,5,7,8,3,6] => {{1},{2,4,5,7},{3},{6,8}} => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,2,5,3,8,6,7] => {{1},{2,4,5},{3},{6,8},{7}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,2,5,6,3,8,7] => {{1,4,5,6},{2},{3},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,5,2,6,3,8,7] => {{1},{2,4},{3,5,6},{7,8}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,5,6,2,7,3,8] => {{1},{2,4,6,7},{3,5},{8}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,5,6,7,2,3,8] => {{1},{2,4,6},{3,5,7},{8}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,2,5,6,7,8,3] => {{1,4,5,6,7,8},{2},{3}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,4,2,5,6,7,8,3] => {{1},{2,4,5,6,7,8},{3}} => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,4,5,2,6,7,8,3] => {{1},{2,4},{3,5,6,7,8}} => [1,2,5] => ([(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,4,5,6,7,8,2,3] => {{1},{2,4,6,8},{3,5,7}} => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,1,6,2,7,3,8,5] => {{1,4},{2},{3,6},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,1,2,7,8,3,5] => {{1,4},{2,6,8},{3},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,1,8,2,3,5] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,8,1,2,3,5] => {{1,4,8},{2,6},{3,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,1,7,2,3,5,8] => {{1,4,7},{2,6},{3},{5},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,2,6,3,7,5,8] => {{1},{2,4,6,7},{3},{5},{8}} => [1,4,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,6,2,3,7,8,5] => {{1,4},{2},{3,6,7,8},{5}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,2,6,7,3,8,5] => {{1,4,6},{2},{3},{5,7,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,6,2,7,3,8,5] => {{1},{2,4},{3,6},{5,7,8}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,2,6,7,8,3,5] => {{1},{2,4,6,8},{3},{5,7}} => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,6,2,7,8,3,5] => {{1},{2,4},{3,6,8},{5,7}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,6,7,2,8,3,5] => {{1},{2,4,7},{3,6,8},{5}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,2,6,3,8,5,7] => {{1,4,6,8},{2},{3},{5},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,2,6,3,8,5,7] => {{1},{2,4,6,8},{3},{5},{7}} => [1,4,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,2,3,6,5,8,7] => {{1,4},{2},{3},{5,6},{7,8}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,2,3,6,7,8,5] => {{1,4},{2},{3},{5,6,7,8}} => [2,1,1,4] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,2,3,6,7,8,5] => {{1},{2,4},{3},{5,6,7,8}} => [1,2,1,4] => ([(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,4,6,7,8,3,5] => {{1},{2},{3,4,6,8},{5,7}} => [1,1,4,2] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,2,7,8,3,5,6] => {{1},{2,4,7},{3},{5,8},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,2,3,7,5,6,8] => {{1},{2,4},{3},{5,7},{6},{8}} => [1,2,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,1,2,3,5,7,8,6] => {{1,4},{2},{3},{5},{6,7,8}} => [2,1,1,1,3] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,8,1,2,3,5,6,7] => {{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,1,2,3,8,5,6,7] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,4,3,8,5,6,7] => {{1},{2},{3,4},{5,8},{6},{7}} => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,1,2,3,5,8,6,7] => {{1,4},{2},{3},{5},{6,8},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,4,2,3,5,8,6,7] => {{1},{2,4},{3},{5},{6,8},{7}} => [1,2,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,6,2,7,3,8,4] => {{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,1,2,7,8,3,4] => {{1,5,7},{2,6,8},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,2,6,3,7,4,8] => {{1},{2,5},{3},{4,6,7},{8}} => [1,2,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,6,1,2,3,7,8,4] => {{1,5},{2,6,7,8},{3},{4}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,6,7,8,2,3,4] => {{1},{2,5,8},{3,6},{4,7}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,2,6,3,8,4,7] => {{1},{2,5},{3},{4,6,8},{7}} => [1,2,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,6,2,3,8,4,7] => {{1},{2,5},{3,6,8},{4},{7}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,5,6,3,4,7,8] => {{1},{2},{3,5},{4,6},{7},{8}} => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,2,3,6,7,8,4] => {{1,5,6,7,8},{2},{3},{4}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,2,3,6,7,8,4] => {{1},{2,5,6,7,8},{3},{4}} => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,5,3,6,7,8,4] => {{1},{2},{3,5,6,7,8},{4}} => [1,1,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,5,6,3,7,8,4] => {{1},{2},{3,5},{4,6,7,8}} => [1,1,2,4] => ([(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,5,6,7,3,8,4] => {{1},{2},{3,5,7,8},{4,6}} => [1,1,4,2] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,5,6,7,8,3,4] => {{1},{2},{3,5,7},{4,6,8}} => [1,1,3,3] => ([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,2,7,3,8,4,6] => {{1},{2,5},{3},{4,7},{6,8}} => [1,2,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,7,2,8,3,4,6] => {{1},{2,5,8},{3,7},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,2,7,3,4,6,8] => {{1},{2,5},{3},{4,7},{6},{8}} => [1,2,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,2,8,3,4,6,7] => {{1,5},{2},{3},{4,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,5,8,2,3,4,6,7] => {{1},{2,5},{3,8},{4},{6},{7}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,2,3,8,4,6,7] => {{1,5,8},{2},{3},{4},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,5,2,3,4,8,6,7] => {{1},{2,5},{3},{4},{6,8},{7}} => [1,2,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,2,3,4,6,8,7] => {{1,5},{2},{3},{4},{6},{7,8}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,6,2,7,3,8,4,5] => {{1},{2,6,8},{3},{4,7},{5}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,6,7,8,2,3,4,5] => {{1},{2,6},{3,7},{4,8},{5}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,1,2,7,3,4,5,8] => {{1,6},{2},{3},{4,7},{5},{8}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,6,7,2,3,4,5,8] => {{1},{2,6},{3,7},{4},{5},{8}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,1,2,3,4,7,8,5] => {{1,6,7,8},{2},{3},{4},{5}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,3,6,4,7,8,5] => {{1},{2},{3},{4,6,7,8},{5}} => [1,1,1,4,1] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,1,8,2,3,4,5,7] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,6,2,8,3,4,5,7] => {{1},{2,6},{3},{4,8},{5},{7}} => [1,2,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,1,2,3,4,5,8,7] => {{1,6},{2},{3},{4},{5},{7,8}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,7,8,2,3,4,5,6] => {{1},{2,7},{3,8},{4},{5},{6}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,1,2,3,4,8,5,6] => {{1,7},{2},{3},{4},{5},{6,8}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,1,2,3,4,5,8,6] => {{1,7,8},{2},{3},{4},{5},{6}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,7,2,3,4,5,8,6] => {{1},{2,7,8},{3},{4},{5},{6}} => [1,3,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,7,3,4,5,8,6] => {{1},{2},{3,7,8},{4},{5},{6}} => [1,1,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,3,4,7,5,8,6] => {{1},{2},{3},{4},{5,7,8},{6}} => [1,1,1,1,3,1] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,3,4,7,8,5,6] => {{1},{2},{3},{4},{5,7},{6,8}} => [1,1,1,1,2,2] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,8,2,3,4,5,6,7] => {{1},{2,8},{3},{4},{5},{6},{7}} => [1,2,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,2,3,8,4,5,6,7] => {{1},{2},{3},{4,8},{5},{6},{7}} => [1,1,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,2,3,4,8,5,6,7] => {{1},{2},{3},{4},{5,8},{6},{7}} => [1,1,1,1,2,1,1] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,2,3,4,5,8,6,7] => {{1},{2},{3},{4},{5},{6,8},{7}} => [1,1,1,1,1,2,1] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[5,3,2,6,1,4,8,7] => {{1,5},{2,3},{4,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,2,5,4,8,1,6] => {{1,7},{2,3},{4,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,5,2,3,7,6,1] => {{1,8},{2,4},{3,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,5,2,3,8,1,6] => {{1,7},{2,4},{3,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,5,2,3,1,8,7] => {{1,6},{2,4},{3,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,6,2,1,3,8,7] => {{1,5},{2,4},{3,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,5,4,2,8,7] => {{1,3},{2,6},{4,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,5,1,3,2,8,7] => {{1,4},{2,6},{3,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,4,3,1,2,8,7] => {{1,5},{2,6},{3,4},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,4,3,2,8,1,6] => {{1,7},{2,5},{3,4},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,4,3,7,2,5,1] => {{1,8},{2,6},{3,4},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,4,3,8,2,1,5] => {{1,7},{2,6},{3,4},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,3,8,1,2,5] => {{1,6},{2,7},{3,4},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,4,3,1,8,2,6] => {{1,5},{2,7},{3,4},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,5,1,3,8,2,6] => {{1,4},{2,7},{3,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,1,5,4,8,2,6] => {{1,3},{2,7},{4,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,5,4,8,3,6] => {{1,2},{3,7},{4,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,1,5,4,7,6,2] => {{1,3},{2,8},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,5,1,3,7,6,2] => {{1,4},{2,8},{3,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,3,1,7,6,2] => {{1,5},{2,8},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,3,7,1,5,2] => {{1,6},{2,8},{3,4},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,3,6,5,1,2] => {{1,7},{2,8},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,5,7,3,1,4,2] => {{1,6},{2,8},{3,5},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,6,7,1,3,4,2] => {{1,5},{2,8},{3,6},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,6,1,7,3,5,2] => {{1,4},{2,8},{3,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,1,6,7,4,5,2] => {{1,3},{2,8},{4,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,6,7,4,5,3] => {{1,2},{3,8},{4,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,6,8,4,3,5] => {{1,2},{3,7},{4,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,1,6,8,4,2,5] => {{1,3},{2,7},{4,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,1,8,3,2,5] => {{1,4},{2,7},{3,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,6,8,1,3,2,4] => {{1,5},{2,7},{3,6},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,7,2,1,8,3,6] => {{1,5},{2,4},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,2,8,1,3,5] => {{1,6},{2,4},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,6,2,8,3,1,5] => {{1,7},{2,4},{3,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,6,2,7,3,5,1] => {{1,8},{2,4},{3,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,6,7,4,5,1] => {{1,8},{2,3},{4,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,2,6,8,4,1,5] => {{1,7},{2,3},{4,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,2,7,8,1,4,5] => {{1,6},{2,3},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,7,1,8,4,6] => {{1,5},{2,3},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,1,7,8,5,6] => {{1,4},{2,3},{5,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,1,2,8,7,6,5] => {{1,3},{2,4},{5,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,8,1,7,6,4] => {{1,5},{2,3},{4,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,2,8,7,1,5,4] => {{1,6},{2,3},{4,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,2,8,6,5,1,4] => {{1,7},{2,3},{4,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,7,2,6,5,3,1] => {{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,8,2,6,5,1,3] => {{1,7},{2,4},{3,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,2,7,1,5,3] => {{1,6},{2,4},{3,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,8,2,1,7,6,3] => {{1,5},{2,4},{3,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,8,1,2,7,6,3] => {{1,4},{2,5},{3,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,8,2,7,6,4] => {{1,3},{2,5},{4,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,8,3,7,6,4] => {{1,2},{3,5},{4,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,8,7,3,5,4] => {{1,2},{3,6},{4,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,8,7,2,5,4] => {{1,3},{2,6},{4,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,8,1,7,2,5,3] => {{1,4},{2,6},{3,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,8,7,1,2,4,3] => {{1,5},{2,6},{3,8},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,8,7,2,1,4,3] => {{1,6},{2,5},{3,8},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,8,6,2,4,1,3] => {{1,7},{2,5},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,7,6,2,4,3,1] => {{1,8},{2,5},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,8,6,1,4,2,3] => {{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,8,1,6,5,2,3] => {{1,4},{2,7},{3,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,1,8,6,5,2,4] => {{1,3},{2,7},{4,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,8,6,5,3,4] => {{1,2},{3,7},{4,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,1,7,6,5,4,2] => {{1,3},{2,8},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,1,6,5,3,2] => {{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,1,4,3,2] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,7,5,4,1,3,2] => {{1,6},{2,8},{3,7},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,6,1,4,5,7,8] => {{1,3,6},{2},{4},{5},{7},{8}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,8,1,3,4,5,7] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,3,5,1,2,4,6,7] => {{1,8},{2,3,5},{4},{6},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,3,7,1,2,4,5,6] => {{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,6,7,1,2,4,8] => {{1,5},{2,3,6},{4,7},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,7,1,2,4,8] => {{1,6},{2,3,5},{4,7},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,8,1,3,5,7] => {{1,4,8},{2},{3,6},{5},{7}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,6,8,1,2,5,7] => {{1,4,8},{2,3,6},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,8,1,2,4,7] => {{1,6},{2,3,5},{4,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,4,8,1,2,5,6] => {{1,7},{2,3,4,8},{5},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,5,7,1,2,4,6] => {{1,8},{2,3,5},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,4,1,3,7,8] => {{1,5},{2,6},{3},{4},{7},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,7,3,6,1,2,5,8] => {{1,4,6},{2,7},{3},{5},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,8,2,4,1,3,5,7] => {{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,8,4,7,1,2,3,6] => {{1,5},{2,8},{3,4,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,5,7,1,2,3,4] => {{1,6},{2,8},{3,5},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,2,4,1,3,5,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,4,6,1,2,3,5] => {{1,7},{2,8},{3,4,6},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,6,1,4,7,8] => {{1,5},{2,3},{4,6},{7},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,2,7,1,4,6,8] => {{1,5},{2,3},{4,7},{6},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,2,5,1,3,6,8] => {{1,7},{2,4,5},{3},{6},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,2,6,1,3,5,8] => {{1,7},{2,4,6},{3},{5},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,2,8,1,5,6,7] => {{1,4,8},{2,3},{5},{6},{7}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,2,8,1,4,6,7] => {{1,5},{2,3},{4,8},{6},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,4,2,8,1,3,5,7] => {{1,6},{2,4,8},{3},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,5,4,8,1,2,3,7] => {{1,6},{2,5},{3,4,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,2,7,1,3,5,6] => {{1,8},{2,4,7},{3},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,5,4,7,1,2,3,6] => {{1,8},{2,5},{3,4,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,2,4,1,3,5,6] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,7,4,6,1,2,3,5] => {{1,8},{2,7},{3,4,6},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,3,5,8,1,2,6] => {{1,4,5,8},{2,7},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,3,6,8,1,2,5] => {{1,4,6},{2,7},{3},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,3,5,7,1,2,6] => {{1,4,5,7},{2,8},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,6,7,1,2,3] => {{1,5,7},{2,8},{3,4,6}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,8,2,5,7,1,3,4] => {{1,6},{2,8},{3},{4,5,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,2,4,6,1,3,5] => {{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,2,6,8,1,5,7] => {{1,4,6},{2,3},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,2,6,8,1,3,7] => {{1,5,8},{2,4,6},{3},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,2,5,8,1,4,7] => {{1,6},{2,3},{4,5,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,3,5,8,1,2,7] => {{1,6},{2,4,5,8},{3},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,7,8,1,5,6] => {{1,4,7},{2,3},{5,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,2,7,8,1,3,6] => {{1,5,8},{2,4,7},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,7,2,6,1,5,8] => {{1,4},{2,3,7},{5,6},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,2,5,1,3,8] => {{1,6},{2,4},{3,7},{5},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,8,2,6,1,5,7] => {{1,4},{2,3,8},{5,6},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,2,5,1,3,7] => {{1,6},{2,4},{3,8},{5},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,8,2,7,1,5,6] => {{1,4},{2,3,8},{5,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,2,7,1,3,5] => {{1,6},{2,4},{3,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,8,2,7,1,3,4] => {{1,6},{2,5,7},{3,8},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,8,2,6,1,3,4] => {{1,7},{2,5,6},{3,8},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,8,4,6,1,2,3] => {{1,7},{2,5,6},{3,8},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,2,6,1,4,5] => {{1,8},{2,3,7},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,7,2,6,1,3,5] => {{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,7,3,6,1,2,5] => {{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,7,2,6,1,3,4] => {{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,2,7,1,6,8] => {{1,5,7},{2,4},{3},{6},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,4,3,2,7,1,5,8] => {{1,6},{2,4},{3},{5,7},{8}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,6,5,3,8,1,2,4] => {{1,7},{2,6},{3,5,8},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,3,2,7,1,4,6] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,6,5,3,7,1,2,4] => {{1,8},{2,6},{3,5,7},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,2,6,1,3,5] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,3,6,1,2,5] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,5,2,6,1,3,4] => {{1,8},{2,7},{3,5,6},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,5,3,6,1,2,4] => {{1,8},{2,7},{3,5,6},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,7,2,6,1,3] => {{1,5},{2,8},{3,4,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,7,3,6,1,2] => {{1,5},{2,8},{3,4,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,7,2,5,1,3] => {{1,6},{2,8},{3,4,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,7,3,5,1,2] => {{1,6},{2,8},{3,4,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,5,7,2,4,1,3] => {{1,6},{2,8},{3,5},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,5,7,3,4,1,2] => {{1,6},{2,8},{3,5},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,6,2,5,1,3] => {{1,7},{2,8},{3,4,6},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,6,3,5,1,2] => {{1,7},{2,8},{3,4,6},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,5,6,2,4,1,3] => {{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,3,8,2,7,1,5] => {{1,6,7},{2,4,8},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,8,2,7,1,4] => {{1,6,7},{2,5},{3},{4,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,3,8,2,6,1,4] => {{1,7},{2,5},{3},{4,8},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,6,4,8,2,5,1,3] => {{1,7},{2,6},{3,4,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,7,2,6,1,3] => {{1,8},{2,5},{3,4,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,7,3,6,1,2] => {{1,8},{2,5},{3,4,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,4,7,2,5,1,3] => {{1,8},{2,6},{3,4,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,5,6,2,4,1,3] => {{1,8},{2,7},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,4,3,2,8,1,7] => {{1,6,8},{2,5},{3,4},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,3,2,7,1,6] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,2,4,1,3] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,2,3,4,7,5,6] => {{1,8},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,2,3,7,4,5,6] => {{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,2,3,6,7,4,5] => {{1,8},{2},{3},{4},{5,6,7}} => [2,1,1,1,3] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,2,7,6,3,8,5] => {{1,4,7,8},{2},{3},{5,6}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,2,5,8,7,3,6] => {{1,4,5,8},{2},{3},{6,7}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,7,2,6,4,8,5] => {{1,3,7,8},{2},{4},{5,6}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,8,2,6,7,4,5] => {{1,3,8},{2},{4},{5,6,7}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,5,2,3,8,4,7] => {{1,6,8},{2},{3,5},{4},{7}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,1,4,2,7,3,8,6] => {{1,5,7,8},{2},{3,4},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,4,2,6,3,8,5] => {{1,7,8},{2},{3,4},{5,6}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,5,2,6,3,8,4] => {{1,7,8},{2},{3,5,6},{4}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,4,2,8,7,3,6] => {{1,5,8},{2},{3,4},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,8,6,2,7,4,5] => {{1,3,8},{2},{4,6,7},{5}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,4,5,2,3,6,7] => {{1,8},{2},{3,4,5},{6},{7}} => [2,1,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,1,4,5,2,7,3,6] => {{1,8},{2},{3,4,5},{6,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,6,5,2,7,3,4] => {{1,8},{2},{3,6,7},{4,5}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,4,8,7,2,5,6] => {{1,3,4,8},{2},{5,7},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,4,5,7,2,3,6] => {{1,8},{2},{3,4,5,7},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,4,7,6,2,3,5] => {{1,8},{2},{3,4,7},{5,6}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,4,5,6,2,8,3] => {{1,7,8},{2},{3,4,5,6}} => [3,1,4] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,1,4,5,8,7,2,6] => {{1,3,4,5,8},{2},{6,7}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,1,4,5,6,7,2,3] => {{1,8},{2},{3,4,5,6,7}} => [2,1,5] => ([(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,1,8,6,3,5,7] => {{1,2,4,8},{3},{5,6},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,1,2,3,4,8,5] => {{1,7,8},{2,6},{3},{4},{5}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,1,2,7,3,5,6] => {{1,8},{2,4},{3},{5,7},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,1,2,6,3,8,5] => {{1,7,8},{2,4},{3},{5,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,1,2,6,3,8,4] => {{1,5,6},{2,7,8},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,1,2,8,7,3,6] => {{1,5,8},{2,4},{3},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,2,6,7,3,5] => {{1,8},{2,4},{3},{5,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,1,2,6,7,3,4] => {{1,5,6,7},{2,8},{3},{4}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,1,2,6,7,8,3] => {{1,5,6,7,8},{2,4},{3}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,1,6,2,8,5,7] => {{1,4,6,8},{2,3},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,1,6,2,7,8,5] => {{1,4,6,7,8},{2,3},{5}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,3,1,8,2,4,5,6] => {{1,7},{2,3},{4,8},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,3,1,6,2,4,8,5] => {{1,7,8},{2,3},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,5,2,7,4,6] => {{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,6,2,7,4,5] => {{1,8},{2,3},{4,6,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,1,5,2,7,8,4] => {{1,6,7,8},{2,3},{4,5}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,4,1,5,2,3,8,6] => {{1,7,8},{2,4,5},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,1,6,2,3,8,5] => {{1,7,8},{2,4,6},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,1,5,2,3,8,4] => {{1,6},{2,7,8},{3},{4,5}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,1,5,2,8,3,7] => {{1,6,8},{2,4,5},{3},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,5,2,7,3,6] => {{1,8},{2,4,5},{3},{6,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,6,2,7,3,5] => {{1,8},{2,4,6,7},{3},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,1,5,2,7,3,4] => {{1,6,7},{2,8},{3},{4,5}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,1,8,7,2,5,6] => {{1,4,8},{2,3},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,5,7,2,4,6] => {{1,8},{2,3},{4,5,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,7,6,2,4,5] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,5,7,2,3,6] => {{1,8},{2,4,5,7},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,7,6,2,3,5] => {{1,8},{2,4,7},{3},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,1,5,6,2,3,4] => {{1,7},{2,8},{3},{4,5,6}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,1,5,6,2,8,3] => {{1,7,8},{2,4,5,6},{3}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,1,5,6,8,2,7] => {{1,4,5,6,8},{2,3},{7}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,1,5,8,7,2,6] => {{1,4,5,8},{2,3},{6,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,1,8,6,7,2,5] => {{1,4,8},{2,3},{5,6,7}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,4,1,5,6,7,2,3] => {{1,8},{2,4,5,6,7},{3}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,1,5,6,7,8,2] => {{1,4,5,6,7,8},{2,3}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,3,8,1,6,7,4,5] => {{1,2,3,8},{4},{5,6,7}} => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,6,4,1,3,8,5,7] => {{1,2,6,8},{3,4},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,5,1,3,4,8,6] => {{1,2,7,8},{3,5},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,5,1,3,7,4,6] => {{1,2,8},{3,5},{4},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,8,1,3,7,4,5] => {{1,2,6,7},{3,8},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,5,1,3,7,8,4] => {{1,2,6,7,8},{3,5},{4}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,8,4,1,6,3,5,7] => {{1,2,8},{3,4},{5,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,4,1,7,3,5,6] => {{1,2,8},{3,4},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,5,1,7,3,4,6] => {{1,2,8},{3,5,7},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,8,1,6,3,4,5] => {{1,2,7},{3,8},{4},{5,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,4,1,6,7,8,3] => {{1,2,5,6,7,8},{3,4}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[7,3,5,1,2,4,8,6] => {{1,7,8},{2,3,5},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,1,2,4,8,5] => {{1,6},{2,3,7,8},{4},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,5,1,2,7,4,6] => {{1,8},{2,3,5},{4},{6,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,8,1,2,7,4,5] => {{1,6,7},{2,3,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,1,2,7,8,4] => {{1,6,7,8},{2,3,5},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,5,4,1,2,3,8,6] => {{1,7,8},{2,5},{3,4},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,1,2,3,8,5] => {{1,6},{2,7,8},{3,4},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,5,1,2,3,8,4] => {{1,6},{2,7,8},{3,5},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,1,2,7,3,6] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,1,2,7,3,5] => {{1,6,7},{2,8},{3,4},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,5,1,2,7,3,4] => {{1,6,7},{2,8},{3,5},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,4,1,2,7,8,3] => {{1,6,7,8},{2,5},{3,4}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,4,1,7,2,5,6] => {{1,8},{2,3,4},{5,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,5,1,6,2,4,7] => {{1,8},{2,3,5,6},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,5,1,7,2,4,6] => {{1,8},{2,3,5,7},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,8,1,6,2,4,5] => {{1,7},{2,3,8},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,1,6,2,3,7] => {{1,8},{2,5,6},{3,4},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,1,7,2,3,6] => {{1,8},{2,5,7},{3,4},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,1,6,2,3,5] => {{1,7},{2,8},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,5,1,6,2,3,4] => {{1,7},{2,8},{3,5,6},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,4,1,6,2,8,3] => {{1,7,8},{2,5,6},{3,4}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,4,1,6,8,2,7] => {{1,5,6,8},{2,3,4},{7}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,4,1,8,7,2,6] => {{1,5,8},{2,3,4},{6,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,5,1,6,7,2,4] => {{1,8},{2,3,5,6,7},{4}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,4,1,6,7,8,2] => {{1,5,6,7,8},{2,3,4}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,3,4,8,1,7,5,6] => {{1,2,3,4,8},{5},{6,7}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,7,6,1,4,8,5] => {{1,2,3,7,8},{4,6},{5}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,8,5,1,7,4,6] => {{1,2,3,8},{4,5},{6,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,6,5,1,7,8,4] => {{1,2,3,6,7,8},{4,5}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,8,4,6,1,3,5,7] => {{1,2,8},{3,4,6},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,4,8,1,3,5,6] => {{1,2,7},{3,4,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,4,6,1,3,8,5] => {{1,2,7,8},{3,4,6},{5}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,8,6,5,1,3,4,7] => {{1,2,8},{3,6},{4,5},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,8,5,1,3,4,6] => {{1,2,7},{3,8},{4,5},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,8,6,1,3,4,5] => {{1,2,7},{3,8},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,4,5,1,7,3,6] => {{1,2,8},{3,4,5},{6,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,8,4,6,1,7,3,5] => {{1,2,8},{3,4,6,7},{5}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,6,4,5,1,7,8,3] => {{1,2,6,7,8},{3,4,5}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[7,3,4,6,1,2,8,5] => {{1,7,8},{2,3,4,6},{5}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,6,5,1,2,4,7] => {{1,8},{2,3,6},{4,5},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,8,5,1,2,4,6] => {{1,7},{2,3,8},{4,5},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,8,6,1,2,4,5] => {{1,7},{2,3,8},{4,6},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,6,5,1,2,8,4] => {{1,7,8},{2,3,6},{4,5}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,6,4,5,1,2,8,3] => {{1,7,8},{2,6},{3,4,5}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,3,4,5,1,8,2,7] => {{1,6,8},{2,3,4,5},{7}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,4,6,1,7,2,5] => {{1,8},{2,3,4,6,7},{5}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,6,5,1,7,2,4] => {{1,8},{2,3,6,7},{4,5}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,3,4,5,1,7,8,2] => {{1,6,7,8},{2,3,4,5}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,3,4,8,6,1,5,7] => {{1,2,3,4,8},{5,6},{7}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,8,7,1,5,6] => {{1,2,3,4,8},{5,7},{6}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,7,6,1,8,5] => {{1,2,3,4,7,8},{5,6}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,3,8,5,6,1,4,7] => {{1,2,3,8},{4,5,6},{7}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,8,5,7,1,4,6] => {{1,2,3,8},{4,5,7},{6}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,8,7,6,1,4,5] => {{1,2,3,8},{4,7},{5,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,7,5,6,1,8,4] => {{1,2,3,7,8},{4,5,6}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,8,4,5,7,1,3,6] => {{1,2,8},{3,4,5,7},{6}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,8,4,7,6,1,3,5] => {{1,2,8},{3,4,7},{5,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,8,7,5,6,1,3,4] => {{1,2,8},{3,7},{4,5,6}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,7,4,5,6,1,8,3] => {{1,2,7,8},{3,4,5,6}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[8,3,4,5,7,1,2,6] => {{1,8},{2,3,4,5,7},{6}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,4,7,6,1,2,5] => {{1,8},{2,3,4,7},{5,6}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,7,5,6,1,2,4] => {{1,8},{2,3,7},{4,5,6}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,3,4,5,6,1,8,2] => {{1,7,8},{2,3,4,5,6}} => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2

[2,3,4,5,8,7,1,6] => {{1,2,3,4,5,8},{6,7}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,3,4,8,6,7,1,5] => {{1,2,3,4,8},{5,6,7}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,3,8,5,6,7,1,4] => {{1,2,3,8},{4,5,6,7}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,8,4,5,6,7,1,3] => {{1,2,8},{3,4,5,6,7}} => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2

[9,1,2,3,4,5,6,7,8] => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 8

[3,5,2,6,1,4,8,7] => {{1,3},{2,5},{4,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,2,6,4,1,8,7] => {{1,3},{2,5},{4,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,2,7,4,8,1,6] => {{1,3},{2,5},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,2,7,4,8,6,1] => {{1,3},{2,5},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,2,3,8,6,1] => {{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,2,3,8,1,6] => {{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,2,3,1,8,7] => {{1,4},{2,5},{3,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,2,1,3,8,7] => {{1,4},{2,5},{3,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,6,4,2,8,7] => {{1,3},{2,5},{4,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,1,3,2,8,7] => {{1,4},{2,5},{3,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,3,1,2,8,7] => {{1,4},{2,5},{3,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,3,2,8,1,6] => {{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,3,2,8,6,1] => {{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,3,8,2,5,1] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,3,8,2,1,5] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,3,8,1,2,5] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,3,1,8,2,6] => {{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,1,3,8,2,6] => {{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,7,4,8,2,6] => {{1,3},{2,5},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,7,4,8,3,6] => {{1,2},{3,5},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,7,4,8,6,3] => {{1,2},{3,5},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,7,4,8,6,2] => {{1,3},{2,5},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,1,3,8,6,2] => {{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,3,1,8,6,2] => {{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,3,8,1,5,2] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,3,8,5,1,2] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,3,8,5,2,1] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,3,1,4,2] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,1,3,4,2] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,1,8,3,5,2] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,7,8,4,5,2] => {{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,7,8,4,5,3] => {{1,2},{3,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,7,8,4,3,5] => {{1,2},{3,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,7,8,4,2,5] => {{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,1,8,3,2,5] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,1,3,2,4] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,2,1,8,3,6] => {{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,2,8,1,3,5] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,2,8,3,1,5] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,2,8,3,5,1] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,8,4,5,1] => {{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,8,4,1,5] => {{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,8,1,4,5] => {{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,2,7,1,8,4,6] => {{1,3},{2,5},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,2,1,7,8,5,6] => {{1,3},{2,4},{5,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,1,2,7,8,6,5] => {{1,3},{2,4},{5,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,2,7,1,8,6,4] => {{1,3},{2,5},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,8,1,5,4] => {{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,8,5,1,4] => {{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,8,5,4,1] => {{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,2,8,5,3,1] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,2,8,5,1,3] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,2,8,1,5,3] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,2,1,8,6,3] => {{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,1,2,8,6,3] => {{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,7,2,8,6,4] => {{1,3},{2,5},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,7,3,8,6,4] => {{1,2},{3,5},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,7,8,3,5,4] => {{1,2},{3,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,7,8,2,5,4] => {{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,1,8,2,5,3] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,1,2,4,3] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,2,1,4,3] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,2,4,1,3] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,2,4,3,1] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,1,4,2,3] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,1,8,5,2,3] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,7,8,5,2,4] => {{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,7,8,5,3,4] => {{1,2},{3,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,7,8,5,4,2] => {{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,1,8,5,3,2] => {{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,1,4,3,2] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,8,4,1,3,2] => {{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,8,7,3,4,1,2] => {{1,6},{2,5},{3,8},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,4,5,8,1,2] => {{1,3,7},{2,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,7,4,5,1,8,3] => {{1,2,6},{3,7,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,7,4,5,2,3,8] => {{1},{2,6},{3,7},{4},{5},{8}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,5,4,7,6,2,3,8] => {{1},{2,5,6},{3,4,7},{8}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,4,7,6,1,8,3] => {{1,2,5,6},{3,4,7,8}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[3,5,4,7,6,8,1,2] => {{1,3,4,7},{2,5,6,8}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[4,5,3,7,8,6,1,2] => {{1,4,7},{2,5,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,8,7,6,1,2] => {{1,5,7},{2,4,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,3,7,5,1,2] => {{1,6},{2,4},{3,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,8,4,5,7,1,2] => {{1,6,7},{2,3,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,4,8,6,7,1,2] => {{1,5,6,7},{2,3,4,8}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[4,3,5,6,8,7,1,2] => {{1,4,6,7},{2,3,5,8}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[3,2,5,6,1,8,7,4] => {{1,3,5},{2},{4,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,6,8,1,7,3] => {{1,4,6},{2},{3,5,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,4,8,6,1,7,3] => {{1,5,6},{2},{3,4,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,8,4,5,1,7,3] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,2,4,5,1,6,3] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,1,4,5,2,3,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,1,8,4,5,2,3,7] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,4,8,6,2,3,7] => {{1,5,6},{2},{3,4,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,3,2,8,6,5,7] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,3,8,2,6,4,7] => {{1,5},{2},{3},{4,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,1,8,3,2,5,4,7] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,1,3,2,5,4,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,2,3,1,5,6,4] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,8,3,1,5,7,4] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,2,3,8,1,6,7,4] => {{1,5},{2},{3},{4,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,3,8,2,1,7,5,4] => {{1,6,7},{2,3,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,3,2,1,6,5,4] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,4,2,6,1,5,3] => {{1,7},{2,8},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,2,8,7,1,6,3] => {{1,5,7},{2,4,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,2,7,8,1,6,3] => {{1,4,7},{2,5,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,3,7,1,6,8,4] => {{1,2,5},{3},{4,7,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,3,7,2,6,4,8] => {{1},{2,5},{3},{4,7},{6},{8}} => [1,2,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,6,7,3,2,5,4,8] => {{1},{2,6},{3,7},{4},{5},{8}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,6,7,3,1,5,8,4] => {{1,2,6},{3,7,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,2,1,8,5,4] => {{1,3,7},{2,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,5,6,2,1,4,3] => {{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,8,7,1,2,3,4] => {{1,6},{2,5},{3,8},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,1,8,7,2,3,6] => {{1,5,7},{2,4,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,1,7,2,3,5] => {{1,6},{2,4},{3,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,3,1,2,6,4,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,3,1,8,2,7,4,6] => {{1,5},{2,3},{4,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,1,2,8,7,5,6] => {{1,4},{2,3},{5,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,1,3,8,5,7,6] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,2,1,8,3,4,7,6] => {{1,5},{2},{3},{4,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,8,1,3,4,7,5] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,2,1,3,4,6,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,3,1,2,6,5,8,7] => {{1,4},{2,3},{5,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,1,6,2,4,8,7] => {{1,5},{2,3},{4,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,1,5,2,4,8,7] => {{1,6},{2,3},{4,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,1,5,2,8,4,6] => {{1,7},{2,3},{4,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,5,1,2,7,3,6] => {{1,8},{2,4},{3,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,5,1,2,8,3,6] => {{1,7},{2,4},{3,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,5,1,2,3,8,7] => {{1,6},{2,4},{3,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,6,1,2,3,8,7] => {{1,5},{2,4},{3,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,5,3,4,8,7] => {{1,2},{3,6},{4,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,5,2,4,8,7] => {{1,3},{2,6},{4,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,5,1,2,3,8,7] => {{1,4},{2,6},{3,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,4,1,2,3,8,7] => {{1,5},{2,6},{3,4},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,4,1,2,3,8,7] => {{1,6},{2,5},{3,4},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,4,1,2,8,3,6] => {{1,7},{2,5},{3,4},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,4,1,7,2,3,5] => {{1,8},{2,6},{3,4},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,4,1,8,2,3,5] => {{1,7},{2,6},{3,4},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,1,8,2,3,5] => {{1,6},{2,7},{3,4},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,4,1,2,8,3,6] => {{1,5},{2,7},{3,4},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,5,1,2,8,3,6] => {{1,4},{2,7},{3,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,1,5,2,8,4,6] => {{1,3},{2,7},{4,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,5,3,8,4,6] => {{1,2},{3,7},{4,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,5,3,7,4,6] => {{1,2},{3,8},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,1,5,2,7,4,6] => {{1,3},{2,8},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,5,1,2,7,3,6] => {{1,4},{2,8},{3,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,1,2,7,3,6] => {{1,5},{2,8},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,1,7,2,3,5] => {{1,6},{2,8},{3,4},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,1,6,2,3,5] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,6,7,1,2,3,4] => {{1,5},{2,8},{3,6},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,6,1,7,2,3,5] => {{1,4},{2,8},{3,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,1,6,7,2,4,5] => {{1,3},{2,8},{4,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,6,7,3,4,5] => {{1,2},{3,8},{4,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,6,8,3,4,5] => {{1,2},{3,7},{4,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,1,6,8,2,4,5] => {{1,3},{2,7},{4,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,1,8,2,3,5] => {{1,4},{2,7},{3,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,6,8,1,2,3,4] => {{1,5},{2,7},{3,6},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,7,1,2,8,3,6] => {{1,5},{2,4},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,1,8,2,3,5] => {{1,6},{2,4},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,6,1,8,2,3,5] => {{1,7},{2,4},{3,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,6,1,7,2,3,5] => {{1,8},{2,4},{3,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,6,7,2,4,5] => {{1,8},{2,3},{4,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,1,6,8,2,4,5] => {{1,7},{2,3},{4,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,1,7,8,2,4,5] => {{1,6},{2,3},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,1,7,2,8,4,6] => {{1,5},{2,3},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,1,2,7,8,5,6] => {{1,4},{2,3},{5,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,3,8,7,5,6] => {{1,2},{3,4},{5,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,1,2,8,7,5,6] => {{1,3},{2,4},{5,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,1,8,7,2,4,5] => {{1,6},{2,3},{4,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,1,8,6,2,4,5] => {{1,7},{2,3},{4,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,7,1,6,2,3,5] => {{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,8,1,6,2,3,5] => {{1,7},{2,4},{3,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,8,1,2,7,3,6] => {{1,5},{2,4},{3,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,8,1,2,7,3,6] => {{1,4},{2,5},{3,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,8,2,7,4,6] => {{1,3},{2,5},{4,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,8,3,7,4,6] => {{1,2},{3,5},{4,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,8,7,3,4,5] => {{1,2},{3,6},{4,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,8,7,2,4,5] => {{1,3},{2,6},{4,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,8,1,7,2,3,5] => {{1,4},{2,6},{3,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,8,7,1,2,3,4] => {{1,5},{2,6},{3,8},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,8,6,1,2,3,4] => {{1,7},{2,5},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,7,6,1,2,3,4] => {{1,8},{2,5},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,8,6,1,2,3,4] => {{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,8,1,6,2,3,5] => {{1,4},{2,7},{3,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,1,8,6,2,4,5] => {{1,3},{2,7},{4,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,8,6,3,4,5] => {{1,2},{3,7},{4,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,7,6,3,4,5] => {{1,2},{3,8},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,1,7,6,2,4,5] => {{1,3},{2,8},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,1,6,2,3,5] => {{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,1,2,3,4] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,7,5,1,2,3,4] => {{1,6},{2,8},{3,7},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,3,8,5,1,2] => {{1,6},{2,4},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,3,5,8,1,2] => {{1,6,8},{2,4},{3,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,2,5,1,8,3] => {{1,6},{2,4},{3,7,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,2,7,6,1,3,8] => {{1,5,6},{2,4,7},{3},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,7,6,8,1,2] => {{1,5,6,8},{2,4,7},{3}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,3,7,8,6,1,2] => {{1,5,8},{2,4,7},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,3,5,7,1,2] => {{1,6,7},{2,4},{3,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,8,6,7,1,2] => {{1,5,6,7},{2,4,8},{3}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,2,6,7,1,3,8] => {{1,5,7},{2,4,6},{3},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,6,1,7,4,8] => {{1,5},{2,3},{4,6,7},{8}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,6,1,7,8,4] => {{1,5},{2,3},{4,6,7,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,2,6,1,8,7,4] => {{1,5},{2,3},{4,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,2,6,8,1,7,3] => {{1,5,8},{2,4,6},{3},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,2,8,6,1,7,3] => {{1,5,6},{2,4,8},{3},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,2,5,1,7,3] => {{1,6},{2,4},{3,8},{5},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,4,2,5,1,6,3] => {{1,7},{2,8},{3,4},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,4,2,5,1,3,6] => {{1,7},{2,8},{3,4},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,4,2,8,6,1,3,7] => {{1,5,6},{2,4,8},{3},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,6,1,8,4,7] => {{1,5},{2,3},{4,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,1,6,8,5,7] => {{1,4},{2,3},{5,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,1,8,6,5,7] => {{1,4},{2,3},{5,8},{6},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,2,8,1,6,4,7] => {{1,5},{2,3},{4,8},{6},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,8,2,1,5,4,7] => {{1,6},{2,3,8},{4},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,3,2,1,5,4,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,3,2,1,5,6,4] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,3,8,2,1,5,7,4] => {{1,6},{2,3,8},{4},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,2,8,1,6,7,4] => {{1,5},{2,3},{4,8},{6},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,4,2,7,8,1,6,3] => {{1,5,8},{2,4,7},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,7,1,8,6,4] => {{1,5},{2,3},{4,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,7,1,6,8,4] => {{1,5},{2,3},{4,7,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,7,1,6,4,8] => {{1,5},{2,3},{4,7},{6},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,7,2,1,5,8,4] => {{1,6},{2,3,7,8},{4},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,2,1,8,5,4] => {{1,6,8},{2,3,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,2,8,1,5,3] => {{1,6},{2,4},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,8,2,1,4,3] => {{1,6},{2,5},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,8,7,2,1,3,4] => {{1,6},{2,5},{3,8},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,2,1,8,4,5] => {{1,6,8},{2,3,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,2,1,4,8,5] => {{1,6},{2,3,7,8},{4},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,7,1,4,8,6] => {{1,5},{2,3},{4,7,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,2,8,7,1,3,6] => {{1,5,7},{2,4,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,2,6,1,3,5] => {{1,7},{2,8},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,3,2,1,6,4,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,3,8,2,1,7,4,5] => {{1,6,7},{2,3,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,8,1,7,4,6] => {{1,5},{2,3},{4,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,1,8,7,5,6] => {{1,4},{2,3},{5,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,1,7,5,8,6] => {{1,4},{2,3},{5,7,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,1,7,5,6,8] => {{1,4},{2,3},{5,7},{6},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,2,1,8,5,7,6] => {{1,4},{2,3},{5,8},{6},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,2,8,1,4,7,6] => {{1,5},{2,3},{4,8},{6},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,8,2,1,4,7,5] => {{1,6},{2,3,8},{4},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,3,2,1,4,6,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,3,8,2,1,4,5,7] => {{1,6},{2,3,8},{4},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,2,1,8,5,6,7] => {{1,4},{2,3},{5,8},{6},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,2,1,5,8,6,7] => {{1,4},{2,3},{5},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,5,6,1,2,4,3] => {{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,1,6,2,5,3] => {{1,7},{2,8},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,1,4,6,2,5,3] => {{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,1,8,4,7,2,5,3] => {{1,6},{2},{3,8},{4},{5,7}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,6,8,4,7,2,5,3] => {{1},{2,6},{3,8},{4},{5,7}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,1,3,2,6,5,4] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,3,1,2,6,5,4] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,3,4,6,5,1,2] => {{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,2,4,6,1,5,3] => {{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,2,3,1,6,5,4] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,2,1,3,6,5,4] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,1,2,3,6,5,4] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,5,2,8,3,7,6,4] => {{1},{2,5},{3},{4,8},{6,7}} => [1,2,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,1,2,8,3,7,6,4] => {{1,5},{2},{3},{4,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,2,1,8,3,7,6,4] => {{1,5},{2},{3},{4,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,2,8,4,7,1,5,3] => {{1,6},{2},{3,8},{4},{5,7}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,8,4,7,5,1,2] => {{1,6},{2,3,8},{4},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,8,4,7,5,1,2] => {{1,3,8},{2,6},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,8,4,7,1,5,3] => {{1,2,6},{3,8},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,8,3,1,7,5,4] => {{1,2,6,7},{3,8},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,8,1,3,7,5,4] => {{1,2,6,7},{3,8},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,1,8,3,7,6,4] => {{1,2,5},{3},{4,8},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,5,8,3,7,6,4] => {{1},{2},{3,5},{4,8},{6,7}} => [1,1,2,2,2] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,4,1,3,8,7,6,5] => {{1,2,4},{3},{5,8},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,3,8,1,7,6,4] => {{1,2,5},{3},{4,8},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,4,8,7,1,6,3] => {{1,2,5,7},{3,4,8},{6}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,4,8,7,6,1,2] => {{1,3,4,8},{2,5,7},{6}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,4,8,7,6,1,2] => {{1,5,7},{2,3,4,8},{6}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,2,4,8,7,1,6,3] => {{1,5,7},{2},{3,4,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,3,8,1,7,6,4] => {{1,5},{2},{3},{4,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,1,3,8,7,6,5] => {{1,4},{2},{3},{5,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,2,3,8,7,6,5] => {{1,4},{2},{3},{5,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,2,3,8,7,6,5] => {{1},{2,4},{3},{5,8},{6,7}} => [1,2,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,3,2,8,7,6,5] => {{1,4},{2},{3},{5,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,1,2,8,7,6,5] => {{1,4},{2,3},{5,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,8,1,2,7,5,4] => {{1,6,7},{2,3,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,1,8,2,7,6,4] => {{1,5},{2,3},{4,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,3,8,2,7,6,4] => {{1,5},{2},{3},{4,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,3,8,2,7,6,4] => {{1},{2,5},{3},{4,8},{6,7}} => [1,2,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,4,8,7,2,6,3] => {{1},{2,5,7},{3,4,8},{6}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,4,8,7,2,6,3] => {{1,5,7},{2},{3,4,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,1,8,7,2,6,3] => {{1,5,7},{2,4,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,1,7,2,5,3] => {{1,6},{2,4},{3,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,8,7,1,2,4,3] => {{1,6},{2,5},{3,8},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,8,7,3,4,1,2] => {{1,5},{2,6},{3,8},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,8,7,2,1,4,3] => {{1,5},{2,6},{3,8},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,8,7,2,6,3] => {{1,4,8},{2,5,7},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,8,7,2,6,3] => {{1,4,8},{2},{3,5,7},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,5,8,7,2,6,3] => {{1},{2,4,8},{3,5,7},{6}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,5,8,2,7,6,4] => {{1},{2,3,5},{4,8},{6,7}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,5,8,2,7,6,4] => {{1,3,5},{2},{4,8},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,8,1,2,7,5,4] => {{1,3,8},{2,6,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,8,2,1,7,5,4] => {{1,3,8},{2,6,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,8,2,7,1,5,3] => {{1,4},{2,6},{3,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,8,3,7,5,1,2] => {{1,4},{2,6},{3,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,3,8,7,6,1,2] => {{1,4,8},{2,5,7},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,2,8,7,1,6,3] => {{1,4,8},{2,5,7},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,2,8,1,7,6,4] => {{1,3},{2,5},{4,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,4,2,8,7,6,5] => {{1,3,4},{2},{5,8},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,2,4,8,7,6,5] => {{1,3},{2},{4},{5,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,5,8,1,7,6,4] => {{1,3,5},{2},{4,8},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,8,7,1,6,3] => {{1,4,8},{2},{3,5,7},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,5,8,7,6,1,2] => {{1,4,8},{2,3,5,7},{6}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,5,8,7,6,1,2] => {{1,3,5,7},{2,4,8},{6}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,5,8,1,7,6,4] => {{1,2,3,5},{4,8},{6,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,1,3,2,6,5,8,7] => {{1,4},{2},{3},{5,6},{7,8}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,1,3,2,5,4,8,7] => {{1,6},{2},{3},{4},{5},{7,8}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,1,3,2,5,4,8,6] => {{1,7,8},{2},{3},{4},{5},{6}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,3,2,5,4,7,6] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[8,1,4,2,5,3,7,6] => {{1,8},{2},{3,4},{5},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,4,2,6,3,8,7] => {{1,5,6},{2},{3,4},{7,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,5,1,4,3,8,7] => {{1,6},{2},{3,5},{4},{7,8}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,2,8,1,4,3,7,5] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,1,7,2,5,4,8,6] => {{1,3,7,8},{2},{4},{5},{6}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,8,3,5,4,7,6] => {{1,2},{3,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,1,8,2,5,4,7,6] => {{1,3,8},{2},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,2,5,1,4,3,7,6] => {{1,8},{2},{3,5},{4},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,8,2,6,3,7,4] => {{1,5,6},{2},{3,8},{4},{7}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,7,3,6,4,8,5] => {{1,2},{3,7,8},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,7,2,6,3,8,5] => {{1,4},{2},{3,7,8},{5,6}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,7,2,6,3,8,4] => {{1,5,6},{2},{3,7,8},{4}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,8,1,5,3,7,4] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,1,5,2,7,3,8,4] => {{1,6},{2},{3,5,7,8},{4}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,4,2,7,3,8,5] => {{1,6},{2},{3,4},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,3,2,6,4,7,5] => {{1,8},{2},{3},{4},{5,6},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,3,2,7,4,8,6] => {{1,5,7,8},{2},{3},{4},{6}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,3,2,8,5,7,6] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,3,2,8,4,7,6] => {{1,5,8},{2},{3},{4},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,1,3,2,8,4,7,5] => {{1,6},{2},{3},{4},{5,8},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,4,8,1,3,2,6,5] => {{1,7},{2,4},{3,8},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,3,7,1,4,2,6,5] => {{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,5,2,8,4,7,6] => {{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,6,2,8,4,7,5] => {{1,3,6},{2},{4},{5,8},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,3,7,1,5,2,6,4] => {{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,2,8,3,7,1,5,4] => {{1,6},{2},{3,8},{4},{5,7}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,3,7,2,6,1,5,4] => {{1,8},{2,3,7},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,8,2,6,1,5,4] => {{1,7},{2,3,8},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,2,6,8,1,5,7] => {{1,3},{2,4,6},{5,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,6,2,8,1,4,7] => {{1,5,8},{2,3,6},{4},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,6,2,4,8,1,7] => {{1,5},{2,3,6,8},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,2,5,8,3,6,1] => {{1,7},{2,4,5,8},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,2,5,8,3,1,6] => {{1,7},{2,4,5,8},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,2,6,3,8,1,7] => {{1,4,6,8},{2,5},{3},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,2,1,6,8,3,7] => {{1,4},{2,5,6,8},{3},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,1,6,8,2,4,7] => {{1,5,8},{2,3},{4,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,8,1,3,4,7] => {{1,5},{2,6},{3},{4,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,5,6,1,4,8,2,7] => {{1,3,6,8},{2,5},{4},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,6,3,8,2,7] => {{1,4,6,8},{2},{3,5},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,6,3,8,2,7] => {{1,4,6,8},{2,5},{3},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,3,2,8,1,7] => {{1,4},{2,5},{3,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,5,3,8,2,1,6] => {{1,7},{2,4},{3,5,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,5,3,8,2,6,1] => {{1,7},{2,4},{3,5,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,8,3,2,5,1] => {{1,6},{2,7},{3,4,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,8,3,2,1,5] => {{1,6},{2,7},{3,4,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,1,8,3,2,5] => {{1,6},{2,7},{3,4},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,5,3,1,8,2,6] => {{1,7},{2,4},{3,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,1,5,8,3,2,6] => {{1,4,5,8},{2,7},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,7,8,1,4,2,6] => {{1,5},{2,3,7},{4,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,8,1,4,6,2] => {{1,7},{2,3,5},{4,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,7,8,3,6,2] => {{1,4,7},{2,5,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,1,5,8,3,6,2] => {{1,7},{2,4,5,8},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,3,8,1,5,2] => {{1,6},{2,7},{3,4},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,8,3,1,5,2] => {{1,6},{2,7},{3,4,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,8,3,5,2,1] => {{1,6},{2,7},{3,4,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,3,8,4,2,1] => {{1,5,8},{2,6},{3,7},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,3,1,8,4,2] => {{1,5},{2,6,8},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,1,7,3,8,4,2] => {{1,5},{2,6,8},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,6,7,3,8,4,2] => {{1,5},{2},{3,6,8},{4,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,1,8,3,5,2] => {{1,6},{2,4},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,6,7,3,2,8,4] => {{1,5},{2},{3,6},{4,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,1,7,3,2,8,4] => {{1,5},{2,6},{3},{4,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,3,2,1,8,4] => {{1,5},{2,6},{3,7,8},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,3,2,8,4,1] => {{1,5},{2,6,8},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,7,3,8,4,1] => {{1,5},{2,6,8},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,7,3,1,8,4] => {{1,5},{2,6},{3},{4,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,1,7,3,8,4] => {{1,5,7,8},{2,6},{3},{4}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,1,5,2,8,3,6] => {{1,4,5},{2,7},{3},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,2,5,1,8,3,6] => {{1,7},{2,4,5},{3},{6,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,2,1,8,3,5] => {{1,6,8},{2,7},{3,4},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,2,8,3,1,5] => {{1,6},{2,7},{3,4},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,2,8,3,5,1] => {{1,6},{2,7},{3,4},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,2,8,4,5,1] => {{1,3,7},{2,6},{4},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,2,8,4,1,5] => {{1,3,7},{2,6},{4},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,2,1,8,4,5] => {{1,3,7},{2,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,7,8,2,1,5,6] => {{1,3,7},{2,4,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,7,8,2,6,1,5] => {{1,3,7},{2,4,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,2,8,5,1,4] => {{1,3,7},{2,6},{4},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,8,5,2,1,4] => {{1,3,7},{2,6},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,8,5,2,4,1] => {{1,3,7},{2,6},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,8,2,5,3,1] => {{1,6},{2,4,8},{3,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,8,2,1,5,3] => {{1,6},{2,4,8},{3,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,7,8,2,6,3] => {{1,4,7},{2},{3,5,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,7,8,1,6,2,4] => {{1,5},{2,3,7},{4,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,1,7,8,2,5,3] => {{1,6},{2,4,7},{3},{5,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,6,2,7,8,4,3] => {{1,5,7},{2},{3,6,8},{4}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,1,7,8,4,3] => {{1,5,7},{2,6,8},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,7,1,8,4,3] => {{1,5},{2,6,8},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,7,8,4,3,1] => {{1,5,8},{2,6},{3},{4,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,2,8,4,3,1] => {{1,5,8},{2,6},{3,7},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,2,1,8,4,3] => {{1,5},{2,6,8},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,1,7,2,8,4,3] => {{1,5},{2,6,8},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,6,7,2,8,4,3] => {{1,5},{2},{3,6,8},{4,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,1,8,2,5,3] => {{1,6},{2,4},{3,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,1,8,5,2,4] => {{1,3,7},{2,6},{4},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,8,5,2,4,1,3] => {{1,6},{2,7},{3,8},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,8,1,5,3,2] => {{1,4,8},{2,6},{3,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,6,7,8,4,3,2] => {{1,5,8},{2},{3,6},{4,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,1,7,8,4,3,2] => {{1,5,8},{2,6},{3},{4,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,1,8,4,3,2] => {{1,5,8},{2,6},{3,7},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,5,1,6,4,7] => {{1,8},{2,3},{4,5},{6},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,2,7,4,1,8,6] => {{1,5},{2,3},{4,7,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,3,8,2,4,6,1] => {{1,7},{2,5},{3},{4,8},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,2,4,5,8,3,6,1] => {{1,7},{2},{3,4,5,8},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,5,3,7,1,8,6] => {{1,2,4},{3,5,7,8},{6}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,2,4,5,6,3,1,7] => {{1,8},{2},{3,4,5,6},{7}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,2,4,5,6,1,3,7] => {{1,8},{2},{3,4,5,6},{7}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,2,4,5,6,3,7] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[8,2,5,1,3,6,4,7] => {{1,8},{2},{3,5},{4},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,4,1,5,6,3,2,7] => {{1,8},{2,4,5,6},{3},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,4,5,6,3,2,7] => {{1,8},{2},{3,4,5,6},{7}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,3,7,2,1,8,6] => {{1,4,7,8},{2,5},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,5,8,3,2,6,1] => {{1,7},{2,4,8},{3,5},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,3,6,7,2,8,5] => {{1},{2,4,6},{3},{5,7,8}} => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,3,7,1,8,2,6] => {{1,4,7},{2,5},{3},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,3,7,2,8,6] => {{1,4},{2},{3,5,7,8},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,3,8,4,1,6,2] => {{1,7},{2,5},{3},{4,8},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,5,8,3,6,1,2] => {{1,7},{2,4,8},{3,5},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,4,7,8,3,5,2] => {{1},{2,6},{3,4,7},{5,8}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,8,3,5,2,1] => {{1,6},{2,4,8},{3,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,7,8,4,1,2] => {{1,3,6},{2,5,8},{4,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,1,5,6,7,8,4,2] => {{1,3,5,7},{2},{4,6,8}} => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,6,1,7,8,3,5,2] => {{1,4,7},{2,6},{3},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,1,4,8,5,2] => {{1,3,7},{2,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,4,1,7,8,5,3] => {{1,6,8},{2},{3,4},{5,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,7,1,4,8,3,5] => {{1,2,6,8},{3,7},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,3,6,7,8,2,4] => {{1},{2,5,7},{3},{4,6,8}} => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,7,8,2,1,4] => {{1,3,6},{2,5,8},{4,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,6,7,8,2,4,1] => {{1,3,6},{2,5,8},{4,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,2,7,1,3,8,4,6] => {{1,5},{2},{3,7},{4},{6,8}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,1,7,8,2,4,6] => {{1,5,8},{2,3},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,2,7,8,1,3,6] => {{1,4,7},{2,5,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,7,8,3,1,5] => {{1,4,7},{2},{3,6},{5,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,7,8,3,5,1] => {{1,4,7},{2},{3,6},{5,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,4,8,5,1] => {{1,3},{2,6,8},{4,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,4,8,1,5] => {{1,3},{2,6,8},{4,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,6,4,7,8,5] => {{1,3},{2},{4,6,7,8},{5}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,4,2,1,5,8,6] => {{1,3,4},{2,7,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,3,4,2,5,8,6] => {{1},{2,7,8},{3},{4},{5},{6}} => [1,3,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,4,2,1,3,6,5] => {{1,7},{2,8},{3,4},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,1,3,4,2,6,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,3,4,2,1,6,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,3,2,7,1,8,5,4] => {{1,6,8},{2,3},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,1,8,5,4] => {{1,3},{2,6,8},{4,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,8,5,2,3,1] => {{1,6},{2,4,8},{3,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,2,7,8,1,5,3] => {{1,4,7},{2,6},{3},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,1,5,8,6,2,3] => {{1,7},{2,4,5,8},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,3,8,6,1,2,4] => {{1,7},{2,5,6},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,1,7,8,2,5,4] => {{1,6},{2,3},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,1,7,8,5,2,3] => {{1,4,7},{2,6},{3},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,6,7,8,4,1,3] => {{1,5,8},{2},{3,6},{4,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,6,7,8,4,3,1] => {{1,5,8},{2},{3,6},{4,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,6,7,8,4,1,3] => {{1,2,5,8},{3,6},{4,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,5,2,6,7,8,4,3] => {{1},{2,5,7},{3},{4,6,8}} => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,4,7,8,5,2,3] => {{1},{2,6},{3,4,7},{5,8}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,7,1,3,8,5,4] => {{1,2,6,8},{3,7},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,8,5,3,1,2] => {{1,6},{2,4,8},{3,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,2,3,7,6,1,8] => {{1,4},{2,5,7},{3},{6},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,6,3,4,8,7,2] => {{1},{2,5},{3,6,8},{4},{7}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,6,2,7,3,5,1,8] => {{1,4,7},{2,6},{3},{5},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,6,7,4,5,1,8] => {{1,3,6},{2},{4,7},{5},{8}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,7,2,6,5,3,1,8] => {{1,4,6},{2,7},{3},{5},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,2,6,5,8,7,3] => {{1,4,6,8},{2},{3},{5},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,1,5,4,2,8,7,3] => {{1,6,8},{2},{3,5},{4},{7}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,1,7,8,5,6,4] => {{1,3},{2},{4,7},{5,8},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,6,7,8,3,4,5,2] => {{1},{2,6},{3,7},{4,8},{5}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,7,3,8,4,6,2] => {{1},{2,5,8},{3,7},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,3,7,8,5,6,2] => {{1},{2,4,7},{3},{5,8},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,3,7,1,5,2,6] => {{1,8},{2,4,7},{3},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,4,3,8,2,1,5,7] => {{1,6},{2,4,8},{3},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,5,4,8,1,6,7] => {{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,5,2,3,1,8,7,6] => {{1,4},{2,5},{3},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,3,1,7,6,2,5] => {{1,8},{2,4},{3},{5,7},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,8,3,7,6,4,2] => {{1},{2,5,7},{3,8},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,5,1,3,7,6,2,4] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,2,6,5,8,7,4] => {{1,3},{2},{4,6,8},{5},{7}} => [2,1,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,5,2,4,8,7,6] => {{1,3,5},{2},{4},{6,8},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,5,1,2,3,8,7,6] => {{1,4},{2,5},{3},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,6,5,3,4,8,7,2] => {{1},{2,6,8},{3,5},{4},{7}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,1,5,2,4,8,7,3] => {{1,6,8},{2},{3,5},{4},{7}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,4,1,2,3,8,7,6] => {{1,5},{2,4},{3},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,4,1,2,7,3,6,8] => {{1,5,7},{2,4},{3},{6},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,4,1,8,2,3,5,7] => {{1,6},{2,4,8},{3},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,5,3,7,4,6,2] => {{1},{2,8},{3,5,7},{4},{6}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,5,1,2,7,3,6,4] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,1,2,7,3,6,5] => {{1,8},{2,4},{3},{5,7},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,1,7,2,3,5,6] => {{1,8},{2,4,7},{3},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,1,6,2,3,5,8] => {{1,7},{2,4,6},{3},{5},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,2,7,8,5,6,4] => {{1,3},{2},{4,7},{5,8},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,3,8,7,5,6,2] => {{1},{2,4,8},{3},{5,7},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,2,8,7,5,6,4] => {{1,3},{2},{4,8},{5,7},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,7,6,2,4,5,8] => {{1,3,7},{2},{4,6},{5},{8}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,7,1,6,2,3,5,8] => {{1,4,6},{2,7},{3},{5},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,8,3,7,4,6,2] => {{1},{2,5,7},{3,8},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,7,6,3,4,5,2] => {{1},{2,8},{3,7},{4,6},{5}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,5,1,6,4,8,7] => {{1,3,5,6},{2},{4},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,4,7,1,8,6] => {{1,3,5,7,8},{2},{4},{6}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,3,7,6,8,1] => {{1,4},{2},{3,5,7,8},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,3,7,1,8,6] => {{1,4},{2},{3,5,7,8},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,3,6,1,8,7] => {{1,4},{2},{3,5,6},{7,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,1,6,3,8,7] => {{1,4},{2},{3,5,6},{7,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,5,4,6,2,8,7] => {{1,3,5,6},{2},{4},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,3,6,2,8,7] => {{1,4},{2},{3,5,6},{7,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,5,1,6,2,8,7] => {{1,4},{2,3,5,6},{7,8}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,5,2,7,1,8,6] => {{1,4},{2,3,5,7,8},{6}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,6,2,7,5,8,1] => {{1,4},{2,3,6},{5,7,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,6,2,7,1,8,5] => {{1,4},{2,3,6},{5,7,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,6,1,7,2,8,5] => {{1,4},{2,3,6},{5,7,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,5,1,7,2,8,6] => {{1,4},{2,3,5,7,8},{6}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,1,5,4,7,2,8,6] => {{1,3,5,7,8},{2},{4},{6}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,4,7,3,8,6] => {{1,2},{3,5,7,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,5,4,7,6,8,2] => {{1,3,5,7,8},{2},{4},{6}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,3,7,6,8,2] => {{1,4},{2},{3,5,7,8},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,5,1,7,6,8,2] => {{1,4},{2,3,5,7,8},{6}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,6,1,7,5,8,2] => {{1,4},{2,3,6},{5,7,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,6,5,7,1,8,2] => {{1,4,5,7,8},{2,3,6}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[5,3,6,4,7,2,8,1] => {{1,5,7,8},{2,3,6},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,6,4,7,1,8,2] => {{1,5,7,8},{2,3,6},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,6,1,7,4,8,2] => {{1,5,7,8},{2,3,6},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,1,6,3,7,4,8,2] => {{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,6,3,7,5,8,2] => {{1,4},{2},{3,6},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,6,4,7,5,8,2] => {{1,3,6},{2},{4},{5,7,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,4,7,5,8,3] => {{1,2},{3,6},{4},{5,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,4,7,3,8,5] => {{1,2},{3,6},{4},{5,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,6,4,7,2,8,5] => {{1,3,6},{2},{4},{5,7,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,6,3,7,2,8,5] => {{1,4},{2},{3,6},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,6,3,7,2,8,4] => {{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,6,1,7,2,8,4] => {{1,5,7,8},{2,3,6},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,6,2,7,1,8,4] => {{1,5,7,8},{2,3,6},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,6,2,7,4,8,1] => {{1,5,7,8},{2,3,6},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,2,6,3,7,4,8,1] => {{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,6,3,7,1,8,4] => {{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,6,1,7,3,8,4] => {{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,1,7,3,8,6] => {{1,4},{2},{3,5,7,8},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,1,7,3,8,5] => {{1,4},{2},{3,6},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,3,7,1,8,5] => {{1,4},{2},{3,6},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,3,7,5,8,1] => {{1,4},{2},{3,6},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,6,4,7,5,8,1] => {{1,3,6},{2},{4},{5,7,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,6,4,7,1,8,5] => {{1,3,6},{2},{4},{5,7,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,6,1,7,4,8,5] => {{1,3,6},{2},{4},{5,7,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,1,7,4,8,6] => {{1,3,5,7,8},{2},{4},{6}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,4,1,7,5,8,6] => {{1,3,4},{2},{5,7,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,4,2,7,6,8,5] => {{1,3,4},{2},{5,7,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,1,7,6,8,4] => {{1,3,5,7,8},{2},{4},{6}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,6,1,7,5,8,4] => {{1,3,6},{2},{4},{5,7,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,6,5,7,1,8,4] => {{1,3,6},{2},{4,5,7,8}} => [3,1,4] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,2,6,5,7,3,8,1] => {{1,4,5,7,8},{2},{3,6}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,2,6,5,7,1,8,3] => {{1,4,5,7,8},{2},{3,6}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,2,6,1,7,5,8,3] => {{1,4},{2},{3,6},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,1,7,6,8,3] => {{1,4},{2},{3,5,7,8},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,2,7,6,8,3] => {{1,4},{2},{3,5,7,8},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,5,2,7,6,8,4] => {{1,3,5,7,8},{2},{4},{6}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,3,7,6,8,4] => {{1,2},{3,5,7,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,3,7,5,8,4] => {{1,2},{3,6},{4},{5,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,6,2,7,5,8,4] => {{1,3,6},{2},{4},{5,7,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,6,2,7,5,8,3] => {{1,4},{2},{3,6},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,6,2,7,4,8,3] => {{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,6,1,7,4,8,3] => {{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,6,4,7,1,8,3] => {{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,6,4,7,3,8,1] => {{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,6,2,7,3,8,1] => {{1,5,7,8},{2,4},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,6,2,7,1,8,3] => {{1,5,7,8},{2,4},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,6,1,7,2,8,3] => {{1,5,7,8},{2,4},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,1,6,4,7,2,8,3] => {{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,6,5,7,2,8,3] => {{1,4,5,7,8},{2},{3,6}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,1,6,5,7,2,8,4] => {{1,3,6},{2},{4,5,7,8}} => [3,1,4] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,1,6,5,7,3,8,4] => {{1,2},{3,6},{4,5,7,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,1,6,5,7,4,8,2] => {{1,3,6},{2},{4,5,7,8}} => [3,1,4] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,1,6,5,7,3,8,2] => {{1,4,5,7,8},{2},{3,6}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,1,6,4,7,3,8,2] => {{1,5,7,8},{2},{3,6},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,6,1,7,3,8,2] => {{1,5,7,8},{2,4},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,6,3,7,1,8,2] => {{1,5,7,8},{2,4},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,5,2,1,6,4,7] => {{1,8},{2,3,5},{4},{6},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,7,5,2,4,1,8,6] => {{1,3,5},{2,7,8},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,5,2,4,6,1] => {{1,8},{2,3,7},{4,5},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,2,4,5,7,3,6,1] => {{1,8},{2},{3,4,5,7},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,4,3,2,1,8,6] => {{1,5},{2,7,8},{3,4},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,8,3,2,7,5,1] => {{1,4},{2,6,7},{3,8},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,3,2,8,1,5] => {{1,4},{2,7},{3,6,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,6,7,3,2,8,5] => {{1},{2,4,7,8},{3,6},{5}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,7,3,1,8,2,6] => {{1,5},{2,4},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,5,1,4,2,8,6] => {{1,3,5},{2,7,8},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,4,2,1,3,8,6] => {{1,5},{2,7,8},{3,4},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,5,1,4,6,2] => {{1,8},{2,3,7},{4,5},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,7,5,3,6,2] => {{1,8},{2,4,7},{3},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,6,3,8,7,1,5,2] => {{1,4,8},{2,6},{3},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,4,8,6,3,5,2] => {{1},{2,7},{3,4,8},{5,6}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,7,6,3,5,2,1] => {{1,8},{2,4,6},{3,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,5,8,7,4,1,2] => {{1,3,5,7},{2,6},{4,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,8,1,6,7,3,5,2] => {{1,4,6},{2,8},{3},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,8,1,4,3,5] => {{1,2,7},{3,6},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,1,6,4,8,2,5] => {{1,3},{2,7},{4,6,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,3,5,6,8,2,4] => {{1},{2,7},{3},{4,5,6,8}} => [1,2,1,4] => ([(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,6,7,5,8,2,4] => {{1},{2,3,6,8},{4,7},{5}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,6,5,8,2,1,4] => {{1,3,6},{2,7},{4,5,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,6,8,5,7,2,4,1] => {{1,3,8},{2,6},{4,5,7}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,5,7,6,8,1,4] => {{1,2,3,5,6,8},{4,7}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,1,6,5,7,8,3,4] => {{1,2},{3,6,8},{4,5,7}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,2,7,6,8,3,1,5] => {{1,4,6},{2},{3,7},{5,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,8,7,3,5,1] => {{1,4,8},{2},{3,6},{5,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,2,4,6,7,5,1] => {{1,3},{2,8},{4},{5,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,2,6,4,8,1,5] => {{1,3},{2,7},{4,6,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,7,2,1,8,4,6] => {{1,5},{2,3,7},{4},{6,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,6,7,2,1,5,4] => {{1,8},{2,3,6},{4,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,8,6,2,1,5,4] => {{1,3,8},{2,7},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,4,8,1,6,5,3] => {{1,2,7},{3,4,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,8,2,1,7,5,3] => {{1,4},{2,6,7},{3,8},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,5,7,2,6,3] => {{1,8},{2,4,5,7},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,6,1,7,5,2,4] => {{1,8},{2,3,6},{4},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,1,8,7,2,5,3] => {{1,4,8},{2,6},{3},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,2,6,5,7,4,1,3] => {{1,8},{2},{3,6},{4,5,7}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,2,5,7,6,4,3,1] => {{1,8},{2},{3,5,6},{4,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,8,5,4,1,3] => {{1,2,7},{3,6},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,8,1,6,5,2,4] => {{1,3,8},{2,7},{4},{5,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,8,6,1,3,5,4] => {{1,2,7},{3,8},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,7,6,5,1,3,2] => {{1,8},{2,4,6},{3,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,1,5,6,4,3,2] => {{1,8},{2,7},{3},{4,5,6}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,1,2,4,8,7] => {{1,6},{2,5},{3},{4},{7,8}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,6,3,5,1,2,8,7] => {{1,4,5},{2,6},{3},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,1,4,5,7,3,2] => {{1,6,7},{2,8},{3},{4},{5}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,7,2,4,5,1,3,6] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,6,1,4,5,3,8,7] => {{1,2,6},{3},{4},{5},{7,8}} => [3,1,1,1,2] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,1,2,4,5,3,8,7] => {{1,6},{2},{3},{4},{5},{7,8}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,4,3,6,1,2,8,7] => {{1,5},{2,4,6},{3},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,1,4,5,2,8,7] => {{1,6},{2,3},{4},{5},{7,8}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,3,7,4,5,1,2,6] => {{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,6,8,5,7,3,4] => {{1,2},{3,6,7},{4,8},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,3,8,1,7,2,4] => {{1,5},{2,6,7},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,6,4,5,8,2,1] => {{1,3,6,8},{2,7},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,4,7,6,1,3] => {{1,2,5,7},{3,8},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,4,2,5,6,7,1] => {{1,3,4},{2,8},{5},{6},{7}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,1,3,5,6,7,2] => {{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,1,4,8,3,6,7,5] => {{1,2},{3,4,8},{5},{6},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,4,3,8,2,1,7,5] => {{1,6},{2,4,8},{3},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,3,1,2,5,6,7,4] => {{1,8},{2,3},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,1,8,2,5,6,7,4] => {{1,3,8},{2},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,3,8,1,5,6,7,4] => {{1,2,3,8},{4},{5},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,8,2,3,5,6,7,1] => {{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,8,2,1,5,6,7,4] => {{1,3},{2,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,8,1,3,5,6,7,4] => {{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,2,3,5,6,7,4] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[7,8,2,4,3,6,1,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,8,3,2,4,1,7,5] => {{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,1,8,3,4,6,7,5] => {{1,2},{3,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,7,1,4,3,6,2,5] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,6,3,8,4,2,7,1] => {{1,5},{2,6},{3},{4,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,5,3,8,2,4,1,6] => {{1,7},{2,5},{3},{4,8},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,5,3,6,2,8,1,4] => {{1,7},{2,5},{3},{4,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,3,8,6,2,7,1] => {{1,4,8},{2,5,6},{3},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,8,4,7,6,2,1] => {{1,3,8},{2,5,7},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,4,5,8,1,3] => {{1,2,7},{3,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,3,6,1,8,2,4] => {{1,5},{2,7},{3},{4,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,6,5,8,3,4] => {{1,2},{3,7},{4,6,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,5,3,6,7,4] => {{1,2},{3,8},{4,5},{6},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,1,4,2,5,6,7,3] => {{1,8},{2},{3,4},{5},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,8,4,1,5,6,7,3] => {{1,2,8},{3,4},{5},{6},{7}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,8,1,2,5,6,7,3] => {{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,4,8,1,5,6,7,2] => {{1,3,8},{2,4},{5},{6},{7}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,4,1,8,5,6,7,3] => {{1,2,4,8},{3},{5},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,2,1,5,6,7,3] => {{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,4,3,5,8,1,7,2] => {{1,6},{2,4,5,8},{3},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,4,8,6,1,2] => {{1,7},{2,3,5,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,4,1,5,6,7,2] => {{1,8},{2,3,4},{5},{6},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,1,8,5,6,7,2] => {{1,4,8},{2,3},{5},{6},{7}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,4,8,5,6,7,2] => {{1,3,4,8},{2},{5},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,5,3,7,2,8,4,1] => {{1,6,8},{2,5},{3},{4,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,4,5,8,2,1] => {{1,6,8},{2,3,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,7,4,8,6,3,1] => {{1,2,5,8},{3,7},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,3,7,1,8,4,2] => {{1,5},{2,6,8},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,5,4,8,6,2,1] => {{1,3,5,8},{2,7},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,3,5,8,2,7,1] => {{1,4,5,8},{2,6},{3},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,1,6,8,4,7] => {{1,3,5,6,8},{2},{4},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,5,4,8,1,7] => {{1,3},{2,6,8},{4,5},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,2,4,7,1,8,6] => {{1,3},{2,5,7,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,8,2,4,7,6,1] => {{1,3,8},{2,5},{4},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,8,3,7,6,1] => {{1,4,8},{2},{3,5},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,5,3,8,1,7] => {{1,4,5},{2},{3,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,2,1,6,8,3,7] => {{1,5,6,8},{2,4},{3},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,1,4,8,2,7] => {{1,6,8},{2,3,5},{4},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,1,5,3,8,2,7] => {{1,4,5},{2,6,8},{3},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,2,7,1,8,6] => {{1,5,7,8},{2,4},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,8,2,7,6,1] => {{1,5},{2,4,8},{3},{6,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,6,2,8,7,5,1] => {{1,4},{2,3,6,7},{5,8}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,7,6,2,1,8,5] => {{1,4,6},{2,3,7,8},{5}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,4,3,1,7,2,8,5] => {{1,6},{2,4},{3},{5,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,4,3,1,8,2,6] => {{1,7},{2,5},{3,4},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,7,5,8,3,2,6] => {{1},{2,4,5,8},{3,7},{6}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,5,7,4,6,1,3] => {{1,2,8},{3,5},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,8,7,1,4,6,2] => {{1,3,8},{2,5},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,5,8,7,3,6,2] => {{1},{2,4,8},{3,5,7},{6}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,4,8,7,3,6,2] => {{1},{2,5,7},{3,4,8},{6}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,3,8,1,7,5,2] => {{1,6,7},{2,4,8},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,7,1,8,6,5,2] => {{1,4},{2,3,7},{5,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,3,7,6,5,2,1] => {{1,4,7},{2,8},{3},{5,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,6,5,3,7,4,2] => {{1},{2,8},{3,6,7},{4,5}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,8,6,3,7,4,2] => {{1},{2,5},{3,8},{4,6,7}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,1,8,7,3,5,2] => {{1,4,8},{2,6},{3},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,1,6,8,4,2,5] => {{1,7},{2,3},{4,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,6,4,8,3,2,5] => {{1},{2,7},{3,6},{4},{5,8}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,7,1,6,3,2,8,4] => {{1,5},{2,7,8},{3},{4,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,7,5,3,2,8,4] => {{1,6},{2},{3,7,8},{4,5}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,3,2,1,8,4] => {{1,7,8},{2,6},{3,5},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,2,8,7,4,1] => {{1,6,7},{2,5,8},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,6,3,8,7,4,1] => {{1,5,8},{2},{3,6,7},{4}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,7,6,3,1,8,4] => {{1,5},{2},{3,7,8},{4,6}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,2,1,7,3,8,4] => {{1,6},{2,5,7,8},{3},{4}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,7,4,1,8,3,6] => {{1,5},{2},{3,7},{4},{6,8}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,7,2,6,3,1,8,5] => {{1,4,6},{2,7,8},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,6,3,7,5,1] => {{1,2,4,6,7},{3,8},{5}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,8,6,2,4,7,5,1] => {{1,3,6,7},{2,8},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,6,2,4,1,8,5] => {{1,7,8},{2,3,6},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,2,1,4,8,5] => {{1,3,7,8},{2,6},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,7,8,2,1,5,6] => {{1,4,8},{2,3,7},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,1,4,6,2,5] => {{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,8,2,5,7,1,6,4] => {{1,3},{2,8},{4,5,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,6,2,7,1,5,4] => {{1,8},{2,3,6},{4},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,8,1,7,5,3] => {{1,4,8},{2},{3,6,7},{5}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,8,2,7,1,6,3] => {{1,5,7},{2,4},{3,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,1,5,7,2,6,3] => {{1,4,5,7},{2,8},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,2,6,1,3,4] => {{1,5,6},{2,8},{3,7},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,8,1,7,5,2,4] => {{1,3,8},{2,6},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,6,8,2,7,4,3] => {{1,5},{2},{3,6,7},{4,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,2,8,1,7,4,3] => {{1,6,7},{2,5},{3},{4,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,2,7,6,4,3,1] => {{1,5,6},{2,8},{3},{4,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,1,8,2,6,4,3] => {{1,7},{2,5},{3},{4,8},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,7,1,8,6,2,5,3] => {{1,4,8},{2,7},{3},{5,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,3,1,6,5,2,4] => {{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,7,4,6,1,5,3,2] => {{1,8},{2,7},{3,4,6},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,7,1,6,4,3,2] => {{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,2,3,7,6,1,8] => {{1,5,7},{2,4},{3},{6},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,2,6,3,5,1,8] => {{1,7},{2,4,6},{3},{5},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,7,6,4,5,1,8] => {{1,3,7},{2},{4,6},{5},{8}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,7,2,6,3,5,1,8] => {{1,4,6},{2,7},{3},{5},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,6,5,2,3,8,4,7] => {{1},{2,6,8},{3,5},{4},{7}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,1,6,4,8,5,7] => {{1,3},{2},{4,6,8},{5},{7}} => [2,1,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,5,2,7,3,4,6] => {{1},{2,8},{3,5,7},{4},{6}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,1,7,8,4,5,6] => {{1,3},{2},{4,7},{5,8},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,4,2,8,3,1,5,7] => {{1,6},{2,4,8},{3},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,5,4,1,8,6,7] => {{1,3,5},{2},{4},{6,8},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,5,2,3,1,8,6,7] => {{1,4},{2,5},{3},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,4,2,3,1,8,6,7] => {{1,5},{2,4},{3},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,2,1,7,3,5,6] => {{1,8},{2,4},{3},{5,7},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,2,8,7,3,5,6] => {{1},{2,4,8},{3},{5,7},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,8,2,7,3,4,6] => {{1},{2,5,7},{3,8},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,5,1,2,7,3,4,6] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,1,8,7,4,5,6] => {{1,3},{2},{4,8},{5,7},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,7,6,2,3,4,5] => {{1},{2,8},{3,7},{4,6},{5}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,5,1,2,4,8,7] => {{1,6},{2,3,5},{4},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,5,6,1,2,8,7] => {{1,4,6},{2,3,5},{7,8}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,7,5,2,1,4,6] => {{1,8},{2,3,7},{4,5},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,2,7,1,8,3,4] => {{1,6,8},{2,5},{3},{4,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,1,5,4,3,8,7] => {{1,2,6},{3},{4,5},{7,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,3,5,1,2,8,7] => {{1,6},{2,4,5},{3},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,1,4,6,2,8,7] => {{1,5,6},{2,3},{4},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,4,6,5,2,8,7] => {{1,3,4,6},{2},{5},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,4,6,2,8,3,1] => {{1,5},{2,7},{3,4,6,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,7,8,5,2,1,6] => {{1,3,7},{2,4,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,5,7,3,4,6] => {{1,2},{3,8},{4,5,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,3,5,1,7,4,2] => {{1,8},{2,6,7},{3},{4,5}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,2,4,6,7,3,1] => {{1,5,6,7},{2,8},{3},{4}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,8,6,5,7,1,2] => {{1,3,8},{2,4,6,7},{5}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,5,4,8,1,6,3,2] => {{1,7},{2,5},{3,4,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,4,6,8,2,7,3] => {{1,5,8},{2},{3,4,6},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,4,6,7,1,8,3] => {{1,2,5,7,8},{3,4,6}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[2,4,6,3,7,5,8,1] => {{1,2,4},{3,6},{5,7,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,7,4,2,8,6,5,1] => {{1,3,4},{2,7},{5,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,8,4,1,7,3,2] => {{1,6,7},{2,5},{3,8},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,8,3,7,6,5] => {{1,2},{3,4,8},{5},{6,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,4,1,8,2,5] => {{1,6,8},{2,3,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,8,1,6,7,5,4] => {{1,2,3,8},{4},{5,6,7}} => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,7,8,5,4,3,1,6] => {{1,2,7},{3,8},{4,5},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,6,7,2,4,1,5] => {{1,3,6},{2,8},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,8,7,4,2,6,1] => {{1,5},{2,3,8},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,8,7,2,1,6,5] => {{1,4,7},{2,3,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,6,1,4,2,7,5] => {{1,8},{2,3,6},{4},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,3,5,8,2,4,1,6] => {{1,7},{2,3,5},{4,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,3,2,6,7,8,5] => {{1,4},{2},{3},{5,6,7,8}} => [2,1,1,4] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,8,7,4,1,3] => {{1,5,7},{2,6},{3},{4,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,5,6,1,4,2,3] => {{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,3,6,1,7,2,4] => {{1,5},{2,8},{3},{4,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,6,5,7,3,4] => {{1,2},{3,8},{4,6,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,5,3,6,8,4] => {{1,2},{3,7,8},{4,5},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,3,5,2,1,8,4] => {{1,6},{2,7,8},{3},{4,5}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,1,2,8,7,3,5] => {{1,4},{2,6,7},{3},{5,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,5,8,7,6,3] => {{1,2,4,5,8},{3},{6,7}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,1,2,5,8,6,7,3] => {{1,4,5,8},{2},{3},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,5,3,2,6,8,1,4] => {{1,7},{2,5,6,8},{3},{4}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,3,6,8,7,4] => {{1,2},{3,5,6,8},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,1,5,7,6,8,2] => {{1,4,5,7,8},{2,3},{6}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,1,4,5,6,8,7,2] => {{1,3,4,5,6,8},{2},{7}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,2,6,3,1,8,7] => {{1,4,6},{2,5},{3},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,2,1,4,3,8,7] => {{1,6},{2,5},{3},{4},{7,8}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,5,2,7,4,8,3,1] => {{1,6,8},{2,5},{3},{4,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,5,2,1,6,4] => {{1,8},{2,3,7},{4,5},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,6,5,4,2,8,7] => {{1,3,6},{2},{4,5},{7,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,1,3,5,4,8,7] => {{1,2,6},{3},{4},{5},{7,8}} => [3,1,1,1,2] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,7,2,3,4,1,6,5] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,5,7,3,8,6,4,1] => {{1,2,5,8},{3,7},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,4,1,8,5,2] => {{1,3,7},{2,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,3,7,4,8,1,2] => {{1,5},{2,6,8},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,7,4,8,5,3] => {{1,2},{3,6,8},{4,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,1,3,5,2,6,4] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,8,4,1,6,3,7,5] => {{1,2,8},{3,4},{5,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,4,2,5,7,1,6] => {{1,3,4},{2,8},{5},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,3,5,2,7,4,1] => {{1,6,7},{2,8},{3},{4,5}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,3,8,7,6,4] => {{1,2},{3,5,8},{4},{6,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,2,8,7,1,4] => {{1,6,7},{2,5,8},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,2,8,5,7,6,1] => {{1,3},{2,4,8},{5},{6,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,8,7,6,5,3] => {{1,2,4,8},{3},{5,7},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,2,1,7,5,3,6] => {{1,8},{2,4},{3},{5,7},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,1,8,6,7,5,2] => {{1,4,8},{2,3},{5,6,7}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,1,4,8,6,5,7,2] => {{1,3,4,8},{2},{5,6},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,6,5,4,8,2,3] => {{1,7},{2},{3,6,8},{4,5}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,5,6,8,4,2,1] => {{1,3,5,8},{2,7},{4,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,7,1,6,8,2,4,3] => {{1,5,8},{2,7},{3},{4,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,2,5,1,7,4,3] => {{1,8},{2,6,7},{3},{4,5}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,1,8,7,3,4] => {{1,5,8},{2,6,7},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,2,5,8,3,7,1] => {{1,4,5,8},{2,6},{3},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,2,6,3,8,1,4] => {{1,7},{2,5},{3},{4,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,2,8,3,4,6,1] => {{1,7},{2,5},{3},{4,8},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,6,2,8,4,3,1,7] => {{1,5},{2,6},{3},{4,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,7,2,1,4,5,6,3] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,6,8,7,1,5,4,2] => {{1,3,8},{2,6},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,8,6,3,4,1,2] => {{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,8,1,7,2,5,6] => {{1,3,8},{2,4},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,3,7,2,6,5] => {{1,8},{2,4},{3},{5,7},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,3,8,1,4,6,7,5] => {{1,2,3,8},{4},{5},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,8,4,2,5,7,1] => {{1,6},{2,3,8},{4},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,4,8,3,5,7,6] => {{1,2},{3,4,8},{5},{6},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,8,2,4,3,5,1,7] => {{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,8,2,3,5,1,6,7] => {{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,8,2,1,4,6,5,7] => {{1,3},{2,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,8,1,3,4,5,7,6] => {{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,8,4,1,6,5,3,7] => {{1,2,8},{3,4},{5,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,4,1,6,5,7,3] => {{1,2,8},{3,4},{5,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,7,6,1,4,3,5] => {{1,2,8},{3,7},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,8,6,1,4,2,3] => {{1,7},{2,5},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,7,6,1,4,2,8] => {{1,3,7},{2,5},{4,6},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,5,3,4,7,6,1] => {{1,2,8},{3,5},{4},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,7,6,1,4,5,3] => {{1,2,8},{3,7},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,5,3,6,1,7,4] => {{1,2,8},{3,5,6},{4},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,5,3,4,7,1,6] => {{1,2,8},{3,5},{4},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,8,6,1,4,3,2] => {{1,7},{2,5},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,2,1,8,7,4] => {{1,3,6,8},{2,5},{4},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,7,2,4,1,8,6] => {{1,3,7,8},{2,5},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,7,2,4,6,8,1] => {{1,3,7,8},{2,5},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,2,7,3,1,8,4] => {{1,6},{2,5},{3},{4,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,2,7,3,4,8,1] => {{1,6},{2,5},{3},{4,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,6,7,4,3,8,2] => {{1,5},{2},{3,6},{4,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,6,8,7,3,4,2] => {{1,5,7},{2},{3,6},{4,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,2,8,3,7,4,1] => {{1,6,7},{2,5},{3},{4,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,2,3,8,7,5,6] => {{1,4},{2},{3},{5,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,2,3,8,6,5,7] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,1,2,3,8,6,7,5] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,1,2,3,8,5,7,6] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,5,2,8,3,4,1,6] => {{1,7},{2,5},{3},{4,8},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,5,2,8,3,7,1,4] => {{1,6,7},{2,5},{3},{4,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,6,8,7,3,2,4] => {{1,5,7},{2},{3,6},{4,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,8,6,3,4,2,1] => {{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,4,8,6,2,7,5] => {{1,3,4,8},{2},{5,6},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,4,8,6,5,2,7] => {{1,3,4,8},{2},{5,6},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,6,5,8,3,2,4] => {{1,7},{2},{3,6},{4,5,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,6,7,8,3,2,5] => {{1,4,7},{2},{3,6},{5,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,6,5,7,3,2,8] => {{1,4,5,7},{2},{3,6},{8}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,2,6,3,7,1,8] => {{1,4,6,7},{2,5},{3},{8}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,2,7,3,8,1,6] => {{1,4,7},{2,5},{3},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,2,4,8,7,1] => {{1,3,6,8},{2,5},{4},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,2,4,8,1,7] => {{1,3,6,8},{2,5},{4},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,5,6,8,4,1,2] => {{1,3,5,8},{2,7},{4,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,6,5,2,8,1,7,4] => {{1,3,5,8},{2,6},{4},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,6,5,8,3,4,2] => {{1,7},{2},{3,6},{4,5,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,2,6,3,8,4,1] => {{1,7},{2,5},{3},{4,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,2,3,5,8,7,6] => {{1,4},{2},{3},{5},{6,8},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,5,2,7,3,8,6,1] => {{1,4,7},{2,5},{3},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,6,7,8,3,5,2] => {{1,4,7},{2},{3,6},{5,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,2,5,6,8,7,3] => {{1,4,5,6,8},{2},{3},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,2,6,3,7,8,1] => {{1,4,6,7,8},{2,5},{3}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,8,5,6,1,4,3,2] => {{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,2,1,5,3,6] => {{1,7},{2,8},{3,4},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,2,1,6,5,3,4] => {{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,4,8,1,5,7,3,6] => {{1,2,4},{3,8},{5},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,8,1,7,2,5,6] => {{1,4},{2,3,8},{5,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,3,4,5,1,6,2] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,4,1,2,3,6,5] => {{1,7},{2,8},{3,4},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,2,1,5,3,4,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,2,5,6,4,1,3] => {{1,7},{2,8},{3},{4,5,6}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,1,7,5,4,3,8] => {{1,6},{2},{3},{4,7},{5},{8}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,3,6,2,7,4,1,8] => {{1,5,7},{2,3,6},{4},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,3,7,5,8,1,2] => {{1,6,8},{2,4,7},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,8,7,5,6,1,2] => {{1,4,7},{2,3,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,7,6,4,2,8,5] => {{1},{2,3,7,8},{4,6},{5}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,5,6,8,4,3] => {{1,2},{3,7},{4,5,6,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,7,2,8,6,4,1,5] => {{1,3},{2,7},{4,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,1,7,6,4,5,2] => {{1,3},{2,8},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,5,7,3,6,4,2] => {{1},{2,8},{3,5},{4,7},{6}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,7,5,8,3,6,1,4] => {{1,2,7},{3,5},{4,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,8,5,3,1,4,7] => {{1,2,6},{3,8},{4,5},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,3,8,4,1,2] => {{1,5,8},{2,6},{3,7},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,5,2,1,3,8] => {{1,4,5},{2,6},{3,7},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,7,2,8,1,3] => {{1,4,7},{2,5},{3,6,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,5,8,6,2,7,3,4] => {{1},{2,5},{3,8},{4,6,7}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,5,8,3,2,7,4] => {{1},{2,6},{3,5},{4,8},{7}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,6,5,7,1,2,8,3] => {{1,4,7,8},{2,6},{3,5}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,7,6,4,3,8,1,2] => {{1,5},{2,7},{3,6,8},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,4,5,8,7,1,2] => {{1,6,7},{2,3,4,5,8}} => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2

[6,1,3,4,5,8,7,2] => {{1,6,8},{2},{3},{4},{5},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,4,2,7,6,8,3] => {{1,5,7,8},{2},{3,4},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,5,8,1,4,3,2] => {{1,6},{2,7},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,3,4,1,2] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,2,3,1,4] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,2,1,5,6,3,7] => {{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,1,8,7,6,5,3,4] => {{1,2},{3,8},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,4,7,8,2,6,5] => {{1,3,4,7},{2},{5,8},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,7,4,5,6,8,2] => {{1,3,7,8},{2},{4},{5},{6}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,7,1,6,3,8,5] => {{1,4},{2},{3,7,8},{5,6}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,7,5,6,8,1,2] => {{1,4,5,6,8},{2,3,7}} => [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[4,8,6,3,5,7,1,2] => {{1,4},{2,8},{3,6,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,1,2,5,3,7,6] => {{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,8,6,5,2,4,1,7] => {{1,3,6},{2,8},{4,5},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,5,6,1,4,7,2] => {{1,3,5},{2,8},{4,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,7,8,2,1,6,4] => {{1,5},{2,3,7},{4,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,8,5,1,4,2] => {{1,3,7},{2,6},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,6,8,5,2,1,4] => {{1,3,6},{2,7},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,8,5,1,2,4,6] => {{1,3,8},{2,7},{4,5},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,1,6,4,2,5,8] => {{1,3},{2,7},{4,6},{5},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,7,8,6,3,5,1,2] => {{1,4,6},{2,7},{3,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,7,6,5,4,1,2] => {{1,3,7},{2,8},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,7,5,1,4,3,6] => {{1,2,8},{3,7},{4,5},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,6,7,5,1,3,4] => {{1,2,8},{3,6},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,8,6,5,4,1,3] => {{1,2,7},{3,8},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,1,2,7,4,8,5] => {{1,6},{2,3},{4},{5,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,2,7,1,3,8,5] => {{1,6},{2,4,7,8},{3},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,2,5,1,3,8,6] => {{1,7,8},{2,4,5},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,3,6,1,8,2,4] => {{1,7},{2,5},{3},{4,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,3,6,1,7,2,4] => {{1,8},{2,5},{3},{4,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,6,2,4,7,1,5] => {{1,8},{2,3,6,7},{4},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,6,2,4,8,1,5] => {{1,7},{2,3,6,8},{4},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,7,1,2,5,8,6] => {{1,4},{2,3,7,8},{5},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,1,4,8,5] => {{1,3},{2,6},{4,7,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,6,7,1,2,8,4] => {{1,5},{2,3,6},{4,7,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,3,7,4,1,2,8,5] => {{1,6},{2,3,7,8},{4},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,1,5,2,3,8,6] => {{1,4,5},{2,7,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,5,1,2,4,8,6] => {{1,3,5},{2,7,8},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,4,2,3,8,1,5] => {{1,7},{2,6,8},{3,4},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,4,2,3,7,1,5] => {{1,8},{2,6,7},{3,4},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,3,8,1,2,5] => {{1,4},{2,7},{3,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,4,2,3,8,1,6] => {{1,5},{2,7},{3,4},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,6,1,4,8,2,5] => {{1,3,6,8},{2,7},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,2,6,1,8,3,4] => {{1,5},{2,7},{3},{4,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,8,5,2,6,1,3] => {{1,7},{2,4,5},{3,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,2,6,3,7,1,4] => {{1,5},{2,8},{3},{4,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,6,1,2,7,4,5] => {{1,3,6,7},{2,8},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,6,2,4,7,1,5] => {{1,3,6,7},{2,8},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,3,7,1,2,5] => {{1,6},{2,8},{3,4},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,5,3,7,1,2,4] => {{1,6},{2,8},{3,5,7},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,5,7,1,2,4,6] => {{1,3,5},{2,8},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,5,7,1,3,4,6] => {{1,2,8},{3,5},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,6,2,7,1,3,5] => {{1,4},{2,8},{3,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,5,8,1,2,4] => {{1,6},{2,3,7},{4,5,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,7,6,4,8,1,3,5] => {{1,2,7},{3,6},{4},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,5,8,1,3,4,7] => {{1,2,6},{3,5},{4,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,5,8,1,2,4,7] => {{1,3,5},{2,6},{4,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,7,4,8,1,3,6] => {{1,2,5,8},{3,7},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,6,7,2,8,1,3] => {{1,5},{2,4,7},{3,6,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,6,3,7,1,8,2,5] => {{1,4,7},{2,6,8},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,7,1,4,8,2,6] => {{1,3,7},{2,5},{4},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,7,2,4,8,1,6] => {{1,5},{2,3,7},{4},{6,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,7,3,8,1,2,6] => {{1,5,8},{2,4},{3,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,6,3,8,1,2,5] => {{1,7},{2,4},{3,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,6,3,7,1,2,5] => {{1,8},{2,4},{3,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,6,7,2,3,5] => {{1,8},{2,4,6},{3},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,1,6,8,2,3,5] => {{1,7},{2,4,6},{3},{5,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,1,7,8,2,3,6] => {{1,5,8},{2,4,7},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,7,1,8,2,4] => {{1,6,8},{2,5},{3},{4,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,1,2,7,8,3,4] => {{1,6,8},{2,5,7},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,6,4,7,8,1,2] => {{1,5,7},{2,3,6,8},{4}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,3,7,4,8,5,1,2] => {{1,6},{2,3,7},{4},{5,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,1,5,8,6,2,3] => {{1,4,5,8},{2,7},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,3,8,1,6,2,4] => {{1,7},{2,5},{3},{4,8},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,1,8,6,2,3,5] => {{1,7},{2,4,8},{3},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,8,2,5,1,3] => {{1,6},{2,4,8},{3,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,8,5,1,2,4] => {{1,6},{2,3,7},{4,8},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,8,2,7,1,4,5] => {{1,3,8},{2,6},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,7,1,3,5,6] => {{1,2,4,7},{3,8},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,8,7,1,2,5,6] => {{1,4,7},{2,3,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,8,7,1,2,4,6] => {{1,5},{2,3,8},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,6,1,2,4,5] => {{1,8},{2,3,7},{4,6},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,7,6,1,2,3,5] => {{1,8},{2,4,6},{3,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,8,7,1,2,3,6] => {{1,5},{2,4,7},{3,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,8,7,1,2,4,6] => {{1,3,8},{2,5},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,7,1,3,4,6] => {{1,2,5},{3,8},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,8,2,7,1,3,5] => {{1,4},{2,6},{3,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,1,8,6,2,3,5] => {{1,4,8},{2,7},{3},{5,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,8,6,4,1,2,3] => {{1,7},{2,5},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,7,5,1,2,3] => {{1,6},{2,8},{3,4,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,1,6,2,3,4] => {{1,5,6},{2,8},{3,7},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,7,6,1,3,4,5] => {{1,2,8},{3,7},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,7,6,1,2,4,5] => {{1,3,7},{2,8},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,6,1,2,3,5] => {{1,4,6},{2,8},{3,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,3,8,2,1,6,4] => {{1,7},{2,5},{3},{4,8},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,7,1,4,5,3,2,6] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,4,3,8,1,5,7,2] => {{1,6},{2,4,8},{3},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,7,1,4,2,6,5,3] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,6,4,5,7,2,8,1] => {{1,3,4,5,7,8},{2,6}} => [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[5,3,2,7,4,6,8,1] => {{1,5},{2,3},{4,7,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,3,6,2,4,8,1] => {{1,7,8},{2,5},{3},{4,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,2,5,1,8,4,7] => {{1,6,8},{2,3},{4,5},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,3,6,2,7,1,4] => {{1,8},{2,5},{3},{4,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,4,5,8,1] => {{1,3},{2,6},{4,7,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,7,3,6,8,1] => {{1,4,7,8},{2},{3,5},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,3,5,2,4,8,1] => {{1,6},{2,7,8},{3},{4,5}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,6,2,4,5,8,1] => {{1,3,6},{2,7,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,3,4,5,8,1] => {{1,2,7,8},{3,6},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,5,2,3,7,1,4] => {{1,8},{2,6,7},{3,5},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,2,1,7,3,4,6] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,6,5,1,8,3,7] => {{1,4,5},{2},{3,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,3,5,2,7,1,4] => {{1,6,7},{2,8},{3},{4,5}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,6,3,7,2,4,5] => {{1},{2,8},{3,6},{4},{5,7}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,8,6,1,7,2,4,5] => {{1,3,6},{2,8},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,1,5,7,2,3,6] => {{1,4,5,7},{2,8},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,7,5,8,2,3,6] => {{1,4,5,8},{2},{3,7},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,7,1,8,3,6] => {{1,4,7},{2},{3,5},{6,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,1,8,4,5] => {{1,3},{2,6,8},{4,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,1,2,8,4,5] => {{1,6,8},{2,3,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,1,5,8,2,4,6] => {{1,7},{2,3},{4,5,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,1,3,6,8,2,7] => {{1,5,6,8},{2,4},{3},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,3,4,6,8,2,7] => {{1},{2,5,6,8},{3},{4},{7}} => [1,4,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,5,1,6,8,2,7] => {{1,4},{2,3,5,6,8},{7}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,5,3,4,8,7,1,2] => {{1,6,7},{2,5,8},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,8,7,1,4,6] => {{1,5,7},{2,3},{4,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,1,8,7,2,4,6] => {{1,5,7},{2,3},{4,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,3,7,6,1,2,4] => {{1,8},{2,5,6},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,8,3,7,2,4,5] => {{1,6},{2},{3,8},{4},{5,7}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,8,1,7,2,4,5] => {{1,6},{2,3,8},{4},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,7,8,2,6,1,3] => {{1,5},{2,4,8},{3,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,8,7,1,3,6] => {{1,4,8},{2},{3,5,7},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,8,7,1,4,5] => {{1,3},{2,6},{4,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,8,1,6,2,4,5] => {{1,3,8},{2,7},{4},{5,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,8,7,1,4,5,6] => {{1,2,3,8},{4,7},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,8,7,3,4,5,6] => {{1},{2},{3,8},{4,7},{5},{6}} => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,1,5,8,7,2,3,6] => {{1,4,8},{2},{3,5,7},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,8,7,6,1,2,3] => {{1,5,6},{2,4,7},{3,8}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,5,8,3,6,2,4,1] => {{1,7},{2,5,6},{3,8},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,8,3,2,6,5,1] => {{1,7},{2,4},{3,8},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,1,3,2,6,5,8] => {{1,7},{2,4},{3},{5},{6},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,4,3,2,6,5,7] => {{1,8},{2},{3,4},{5},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,4,3,2,6,7,5] => {{1,8},{2},{3,4},{5},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,4,3,2,5,7,6] => {{1,8},{2},{3,4},{5},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,4,3,2,5,6,7] => {{1,8},{2},{3,4},{5},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,4,1,3,2,5,6,8] => {{1,7},{2,4},{3},{5},{6},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,4,8,3,2,5,6,1] => {{1,7},{2,4},{3,8},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,4,3,8,2,5,7,1] => {{1,6},{2,4,8},{3},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,5,1,3,6,2,8,4] => {{1,7,8},{2,5,6},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,1,4,6,8,2,3] => {{1,7},{2,5,6,8},{3},{4}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,8,3,6,2,1,4] => {{1,7},{2,5,6},{3,8},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,8,3,2,6,1,5] => {{1,7},{2,4},{3,8},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,8,3,2,5,1,6] => {{1,7},{2,4},{3,8},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,4,3,8,2,5,1,7] => {{1,6},{2,4,8},{3},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,4,3,7,2,5,8,1] => {{1,6},{2,4,7,8},{3},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,2,8,7,1,6] => {{1,5,8},{2,4},{3},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,8,7,2,1,4] => {{1,6},{2,5,7},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,4,8,7,1,2,3] => {{1,6},{2,5,7},{3,4,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,5,4,1,7,8,2,3] => {{1,6,8},{2,5,7},{3,4}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,5,3,1,7,2,8,4] => {{1,6},{2,5,7,8},{3},{4}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,3,1,2,7,8,5] => {{1,6,7,8},{2,4},{3},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,2,1,8,6,7] => {{1,5},{2,4},{3},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,5,4,1,8,7,2,3] => {{1,6,7},{2,5,8},{3,4}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,4,3,8,2,7,5,1] => {{1,6,7},{2,4,8},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,8,7,2,4,1] => {{1,6},{2,5,7},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,7,8,2,4,1] => {{1,6},{2,5,8},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,3,7,2,8,5,1] => {{1,6,8},{2,4,7},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,8,3,2,1,5,6] => {{1,7},{2,4},{3,8},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,8,3,2,1,6,5] => {{1,7},{2,4},{3,8},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,4,3,7,2,1,8,5] => {{1,6},{2,4,7,8},{3},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,7,1,2,8,4] => {{1,6},{2,5},{3},{4,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,7,8,2,1,4] => {{1,6},{2,5,8},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,3,7,2,8,1,5] => {{1,6,8},{2,4,7},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,2,7,8,1,6] => {{1,5,7},{2,4},{3},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,2,6,8,1,7] => {{1,5,6,8},{2,4},{3},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,7,8,2,1,4,6] => {{1,5},{2,3,7},{4,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,4,1,5,6,2] => {{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,1,2,5,4,6,3] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,1,8,3,2,4,5,7] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,4,1,3,7,6,2,5] => {{1,8},{2,4},{3},{5,7},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,5,1,6,8,3,4,2] => {{1,7},{2,5,8},{3},{4,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,2,1,8,7,4,3] => {{1,6,7},{2,5,8},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,8,6,1,2,5,4] => {{1,7},{2,3,8},{4,6},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,7,1,8,2,6,5] => {{1,3,7},{2,4},{5,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,2,4,3,5,6,7] => {{1},{2,8},{3},{4},{5},{6},{7}} => [1,2,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,6,2,8,3,5,4,7] => {{1},{2,6},{3},{4,8},{5},{7}} => [1,2,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,3,8,4,6,5,7] => {{1},{2},{3},{4,8},{5},{6},{7}} => [1,1,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,5,2,7,3,6,4,8] => {{1},{2,5},{3},{4,7},{6},{8}} => [1,2,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,8,2,4,3,6,5,7] => {{1},{2,8},{3},{4},{5},{6},{7}} => [1,2,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,8,2,3,4,6,5,7] => {{1},{2,8},{3},{4},{5},{6},{7}} => [1,2,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,5,2,4,3,8,6,7] => {{1},{2,5},{3},{4},{6,8},{7}} => [1,2,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,6,2,5,3,8,4,7] => {{1},{2,6,8},{3},{4,5},{7}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,2,6,3,7,4,5] => {{1},{2,8},{3},{4,6,7},{5}} => [1,2,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,2,8,3,7,5,6] => {{1},{2,4,8},{3},{5},{6,7}} => [1,3,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,2,8,3,7,4,6] => {{1},{2,5},{3},{4,8},{6,7}} => [1,2,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,6,3,7,2,5,1,8] => {{1,4,7},{2,6},{3},{5},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,6,3,7,5,2,1,8] => {{1,4,7},{2,6},{3},{5},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,6,2,7,5,3,1,8] => {{1,4,7},{2,6},{3},{5},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,6,7,2,4,3,1,8] => {{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,5,4,8,1,7,6] => {{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,8,6,5,7,3,1,4] => {{1,2,8},{3,6},{4,5,7}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,8,4,5,3,7,1,6] => {{1,2,8},{3,4,5},{6,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,8,4,3,5,6,1,7] => {{1,2,8},{3,4},{5},{6},{7}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,8,2,5,6,3,1] => {{1,7},{2,4},{3,8},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,8,5,2,1,3,6] => {{1,7},{2,4,5},{3,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,5,1,3,7,2] => {{1,6},{2,4,5},{3,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,7,5,1,2,8,6] => {{1,4,5},{2,3,7,8},{6}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,7,1,5,6,8,2] => {{1,4},{2,3,7,8},{5},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,7,5,2,8,4] => {{1,3},{2,6},{4,7,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,1,2,7,6,8,5] => {{1,3},{2,4},{5,7,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,2,1,7,5,8,6] => {{1,3},{2,4},{5,7,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,5,7,1,4,8,2] => {{1,3,5},{2,6},{4,7,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,5,2,7,4,1,8,3] => {{1,6},{2,5},{3},{4,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,2,6,4,8,7,1] => {{1,3},{2,5},{4,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,1,8,6,4,7,2] => {{1,5,6},{2,3},{4,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,1,8,7,2,4,3] => {{1,5,7},{2,6},{3},{4,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,5,8,3,7,1,4] => {{1,6,7},{2},{3,5},{4,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,2,7,4,6,3,8] => {{1},{2,5},{3},{4,7},{6},{8}} => [1,2,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,3,4,8,6,1,7,5] => {{1,2,3,4,8},{5,6},{7}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,8,6,5,1,7] => {{1,2,3,4,8},{5,6},{7}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,7,3,5,8,6,1,4] => {{1,2,7},{3},{4,5,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,4,7,8,6,1,5] => {{1,3,4,7},{2},{5,8},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,4,6,2,7,3,8] => {{1},{2,5},{3,4,6,7},{8}} => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,4,7,1,8,3,6] => {{1,5},{2},{3,4,7},{6,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,6,4,1,8,7,2] => {{1,5},{2,3,6,8},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,6,1,4,8,2,7] => {{1,5},{2,3,6,8},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,6,8,4,2,1] => {{1,7},{2,3,5,8},{4,6}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,3,5,1,8,2,7,4] => {{1,6},{2,3,5,8},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,1,5,8,4,7,3] => {{1,2,6},{3},{4,5,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,1,6,3,8,4,2] => {{1,5},{2,7},{3},{4,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,4,1,7,8,5,6] => {{1,3,4},{2},{5,7},{6,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,4,2,7,8,6,5] => {{1,3,4},{2},{5,7},{6,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,4,7,2,8,6,3] => {{1,5},{2},{3,4,7},{6,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,4,7,8,2,5,1] => {{1,3,4,7},{2,6},{5,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,1,4,6,8,5,7,2] => {{1,3,4,6},{2},{5,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,4,5,7,1,8,2] => {{1,6},{2,3,4,5,7,8}} => [2,6] => ([(5,7),(6,7)],8) => 2

[2,5,4,6,1,7,8,3] => {{1,2,5},{3,4,6,7,8}} => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2

[7,2,1,4,3,6,5,8] => {{1,7},{2},{3},{4},{5},{6},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[7,3,4,1,2,6,5,8] => {{1,7},{2,3,4},{5},{6},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,3,2,1,6,5,8] => {{1,7},{2,4},{3},{5},{6},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,8,3,2,5,4,7,6] => {{1},{2,8},{3},{4},{5},{6},{7}} => [1,2,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,8,4,5,2,3,7,6] => {{1},{2,8},{3,4,5},{6},{7}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,3,5,1,6,2,4,8] => {{1,7},{2,3,5,6},{4},{8}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,2,1,5,6,3,4,8] => {{1,7},{2},{3},{4,5,6},{8}} => [2,1,1,3,1] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,2,1,6,5,4,3,8] => {{1,7},{2},{3},{4,6},{5},{8}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,4,6,5,1,3,2,8] => {{1,7},{2,4,5},{3,6},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,5,4,3,2,7,6] => {{1},{2,8},{3,5},{4},{6},{7}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,5,7,4,3,1,8,2] => {{1,6},{2,5},{3,7,8},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,1,5,4,8,2] => {{1,6},{2,3,7,8},{4},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,8,1,5,4,7,6] => {{1,2,3,8},{4},{5},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,4,8,5,1,3,7,6] => {{1,2,4,5},{3,8},{6},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,8,4,3,7,1,5] => {{1,2,6,7},{3,8},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,7,4,3,6,5,2] => {{1},{2,8},{3,7},{4},{5},{6}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,8,7,5,6,3,4,2] => {{1},{2,8},{3,7},{4,5,6}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,8,5,7,3,1,4] => {{1,2,6},{3,8},{4,5,7}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,5,8,6,7,1,3,4] => {{1,2,5,7},{3,8},{4,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,8,6,1,7,3,5] => {{1,2,4,6,7},{3,8},{5}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,2,1,8,6,7,4,5] => {{1,3},{2},{4,8},{5,6,7}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,1,7,6,8,4,3] => {{1,5,6,8},{2},{3},{4,7}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,7,1,6,8,4,2] => {{1,5,6,8},{2,3,7},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,7,6,1,8,3,2] => {{1,5},{2,4,6,8},{3,7}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,7,6,8,1,3,2] => {{1,4,6},{2,5,8},{3,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,6,7,5,8,3,1,2] => {{1,4,5,8},{2,6},{3,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,8,6,5,7,3,2,4] => {{1},{2,8},{3,6},{4,5,7}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,5,6,7,2,3,4] => {{1},{2,8},{3,5,7},{4,6}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,5,7,8,2,1,3] => {{1,4,7},{2,6},{3,5,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,6,7,1,8,2,3] => {{1,5},{2,4,7},{3,6,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,6,1,7,8,2,4] => {{1,5,7},{2,3,6,8},{4}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,2,1,5,7,3,8,4] => {{1,6},{2},{3},{4,5,7,8}} => [2,1,1,4] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,1,7,2,8,4] => {{1,6},{2,3,5,7,8},{4}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,4,5,7,1,2,8,3] => {{1,6},{2,4,7,8},{3,5}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,5,4,7,2,1,8,3] => {{1,6},{2,5},{3,4,7,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,6,4,7,2,8,1,3] => {{1,5},{2,6,8},{3,4,7}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,8,4,6,2,7,3,5] => {{1},{2,8},{3,4,6,7},{5}} => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,3,2,6,7,4,5] => {{1},{2,8},{3},{4},{5,6,7}} => [1,2,1,1,3] => ([(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,7,3,2,6,8,4,1] => {{1,5,6,8},{2,7},{3},{4}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,3,2,7,8,1,4] => {{1,5,7},{2,6,8},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,2,7,1,8,4] => {{1,6},{2,5,7,8},{3},{4}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,3,2,1,7,8,5] => {{1,6,7,8},{2,4},{3},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,1,4,3,7,8,5] => {{1,6,7,8},{2},{3},{4},{5}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,4,1,2,8,7,6] => {{1,5},{2,3,4},{6,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,3,2,8,7,1,5] => {{1,4},{2,6,7},{3},{5,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,4,7,2,6,5,3] => {{1},{2,8},{3,4,7},{5},{6}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,7,4,8,2,6,5,1] => {{1,3,4,8},{2,7},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,4,8,2,1,7,6] => {{1,3,4,8},{2,5},{6},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,5,8,1,2,7,6] => {{1,3,5},{2,4,8},{6},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,5,1,8,2,7,6] => {{1,4},{2,3,5,8},{6},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,1,5,8,3,7,6] => {{1,4,5,8},{2},{3},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,1,6,8,7,3,5] => {{1,4,6,7},{2},{3},{5,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,6,1,8,7,2,5] => {{1,4},{2,3,6,7},{5,8}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,6,8,1,7,2,5] => {{1,3,6,7},{2,4,8},{5}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,6,8,7,1,2,4] => {{1,3,6},{2,5,7},{4,8}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,6,5,8,7,2,1,4] => {{1,3,5,7},{2,6},{4,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,8,5,7,6,2,4,3] => {{1},{2,8},{3,5,6},{4,7}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,8,5,4,1,2] => {{1,3,7},{2,6},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,7,8,1,6,5,2] => {{1,3,7},{2,4,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,8,1,7,6,5,4] => {{1,2,3,8},{4},{5,7},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,7,1,6,5,3] => {{1,2,4,7},{3,8},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,7,6,1,4,3] => {{1,2,5,6},{3,8},{4,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,6,8,7,5,4,1,3] => {{1,2,6},{3,8},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,6,1,8,3,5,2] => {{1,7},{2,4},{3,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,5,1,7,4,6,2] => {{1,8},{2,3,5,7},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,4,1,7,5,6,2] => {{1,8},{2,3,4},{5,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,2,1,7,5,8,3] => {{1,4},{2,6},{3},{5,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,6,2,7,5,8,3] => {{1},{2,4},{3,6},{5,7,8}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,5,2,6,8,4,3] => {{1},{2,7},{3,5,6,8},{4}} => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,2,1,6,8,4,3] => {{1,7},{2,5,6,8},{3},{4}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,3,1,7,5,2] => {{1,6,7},{2,8},{3,4},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,8,4,1,7,5,2] => {{1,3,8},{2,6,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,5,1,8,4,2] => {{1,3,7},{2,6,8},{4,5}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,5,6,1,8,3,4,2] => {{1,7},{2,5,8},{3,6},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,6,5,7,1,8,2] => {{1,3,6},{2,4,5,7,8}} => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2

[6,7,5,1,8,4,3,2] => {{1,6},{2,7},{3,5,8},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,1,7,5,3,2] => {{1,6},{2,8},{3,4},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,5,3,1,8,4,2] => {{1,6,8},{2,7},{3,5},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,2,1,6,7,5,3] => {{1,8},{2,4},{3},{5,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,4,2,6,7,5,3] => {{1},{2,8},{3,4},{5,6,7}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,1,7,6,8,4] => {{1,5,7,8},{2,3},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,3,1,7,6,8,4] => {{1,2,5,7,8},{3},{4},{6}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,1,7,5,8,3] => {{1,2,4},{3,6},{5,7,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,7,1,6,5,8,2,3] => {{1,4,6,8},{2,7},{3},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,2,6,5,7,1,3] => {{1,4,6,7},{2,8},{3},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,1,2,7,5,8,3] => {{1,4},{2,6},{3},{5,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,1,2,6,8,4,3] => {{1,7},{2,5,6,8},{3},{4}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,2,6,7,5,3] => {{1,8},{2,4},{3},{5,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,1,2,7,6,8,4] => {{1,5,7,8},{2,3},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,5,3,7,6,8,4] => {{1},{2},{3,5,7,8},{4},{6}} => [1,1,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,1,2,7,6,8,5] => {{1,4},{2,3},{5,7,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,2,7,6,8,4] => {{1,3},{2,5,7,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,1,5,8,2,3,4] => {{1,6},{2,7},{3},{4,5,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,1,5,8,3,4] => {{1,2,7},{3,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,5,1,7,6,8,4] => {{1,2,3,5,7,8},{4},{6}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,6,1,5,8,3,2,4] => {{1,7},{2,6},{3},{4,5,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,1,5,8,2,4] => {{1,3,7},{2,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,6,5,8,2,4,3] => {{1,7},{2},{3,6},{4,5,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,1,6,8,4,2,3] => {{1,7},{2,5,8},{3},{4,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,6,7,5,2,3] => {{1,8},{2,4,6},{3},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,3,1,7,6,8,4] => {{1,5,7,8},{2},{3},{4},{6}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,5,2,1,7,6,8,4] => {{1,3},{2,5,7,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,5,2,7,6,8,4] => {{1},{2,3,5,7,8},{4},{6}} => [1,5,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,5,7,6,2,4] => {{1,8},{2,3},{4,5,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,4,1,7,5,8,3] => {{1,6},{2},{3,4},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,5,1,7,4,8,3] => {{1,6},{2},{3,5,7,8},{4}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,5,2,7,4,8,3] => {{1,6},{2},{3,5,7,8},{4}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,2,5,8,3,1,4] => {{1,7},{2,6},{3},{4,5,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,1,3,7,6,8,4] => {{1,5,7,8},{2},{3},{4},{6}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,5,2,6,8,4,1,3] => {{1,7},{2,5,8},{3},{4,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,2,6,7,5,1,3] => {{1,8},{2,4,6},{3},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,4,2,7,5,8,3] => {{1,6},{2},{3,4},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,2,6,5,7,1,4,3] => {{1,8},{2},{3,6},{4,5,7}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,8,2,5,7,1,4] => {{1,3,8},{2,6,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,5,7,6,1,4] => {{1,8},{2,3},{4,5,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,3,2,7,6,8,4] => {{1,5,7,8},{2},{3},{4},{6}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,2,3,7,6,8,5] => {{1},{2,4},{3},{5,7,8},{6}} => [1,2,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,4,1,3,7,6,8,5] => {{1,2,4},{3},{5,7,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,1,3,7,6,8,4] => {{1,2,5,7,8},{3},{4},{6}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,3,5,7,6,1,4] => {{1,2,8},{3},{4,5,7},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,2,3,5,7,1,4] => {{1,6,7},{2,8},{3},{4},{5}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,1,2,3,7,6,8,4] => {{1,5,7,8},{2},{3},{4},{6}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,2,4,7,6,8,5] => {{1,3},{2},{4},{5,7,8},{6}} => [2,1,1,3,1] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,1,2,4,3,6,5,7] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[8,1,3,4,2,6,7,5] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[8,1,3,2,4,5,7,6] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[6,3,2,1,4,5,8,7] => {{1,6},{2,3},{4},{5},{7,8}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,1,5,6,8,2,3] => {{1,7},{2,4,5,6,8},{3}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,4,2,8,7,1,6] => {{1,3,4},{2,5,8},{6,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,6,5,8,7,1,2,3] => {{1,4,8},{2,6},{3,5,7}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,4,5,1,7,8,2,3] => {{1,6,8},{2,4},{3,5,7}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,5,6,7,8,3,4,1] => {{1,2,5,8},{3,6},{4,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,6,7,3,8,5,1] => {{1,2,4,7},{3,6,8},{5}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,2,6,7,3,1,5,8] => {{1,4,7},{2},{3,6},{5},{8}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,6,3,8,1,2,7,4] => {{1,5},{2,6},{3},{4,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,6,7,2,1,8,5] => {{1,4,7,8},{2,3,6},{5}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,2,5,6,8,1,7] => {{1,3},{2,4,5,6,8},{7}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,2,7,8,6,4,1,3] => {{1,5,6},{2},{3,7},{4,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,1,8,6,5,2,3] => {{1,4,8},{2,7},{3},{5,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,8,1,2,7,5,3] => {{1,4},{2,6,7},{3,8},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,1,3,6,5,2,4] => {{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,7,2,8,6,1,5,3] => {{1,4,8},{2,7},{3},{5,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,2,3,6,5,1,4] => {{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,5,7,1,6,2,3,4] => {{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,4,8,7,1,5,3] => {{1,6},{2},{3,4,8},{5,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,8,3,7,4,5,2] => {{1},{2,6},{3,8},{4},{5,7}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,2,4,8,1,7,5,3] => {{1,6,7},{2},{3,4,8},{5}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,2,7,1,6,3] => {{1,5,7},{2,8},{3,4},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,7,5,3,4,6,2] => {{1},{2,8},{3,7},{4,5},{6}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,7,3,5,4,6,2] => {{1},{2,8},{3,7},{4},{5},{6}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,8,4,7,2,1,6,3] => {{1,5},{2,8},{3,4,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,7,5,4,3,6,2] => {{1},{2,8},{3,7},{4,5},{6}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,8,4,7,1,2,6,3] => {{1,5},{2,8},{3,4,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,1,7,2,6,3] => {{1,5,7},{2,8},{3,4},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,7,1,6,2,3] => {{1,5},{2,8},{3,4,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,2,5,6,7,4,1,3] => {{1,8},{2},{3,5,7},{4,6}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,5,7,1,6,2,3] => {{1,4,7},{2,8},{3,5},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,5,7,1,2,6,3] => {{1,4,7},{2,8},{3,5},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,5,1,7,2,6,3] => {{1,4},{2,8},{3,5,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,3,1,7,2,6,4] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,6,2,8,1,7,5,3] => {{1,4,8},{2,6,7},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,4,8,3,7,5,2] => {{1},{2,6,7},{3,4,8},{5}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,7,4,5,3,6,2] => {{1},{2,8},{3,7},{4},{5},{6}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,8,5,7,2,1,6,3] => {{1,4,7},{2,8},{3,5},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,3,2,7,1,6,4] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,8,5,2,7,1,6,3] => {{1,4},{2,8},{3,5,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,7,4,3,5,6,2] => {{1},{2,8},{3,7},{4},{5},{6}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,8,7,3,4,5,6,2] => {{1},{2,8},{3,7},{4},{5},{6}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,2,4,5,7,1,6,3] => {{1,8},{2},{3,4,5,7},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,2,3,7,1,6,4] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,1,5,4,2,8,7] => {{1,6},{2,3},{4,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,5,2,7,6,4] => {{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,2,1,7,3,6] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,2,1,7,6,3] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,4,2,1,3,8,7] => {{1,6},{2,5},{3,4},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,4,2,3,1,8,7] => {{1,6},{2,5},{3,4},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,2,5,1,4,8,7] => {{1,6},{2,3},{4,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,4,3,1,2,8,7] => {{1,6},{2,5},{3,4},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,4,1,3,2,8,7] => {{1,6},{2,5},{3,4},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,1,2,7,6,3] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,1,6,3,2,5] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,1,6,3,5,2] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,1,6,5,3,2] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,1,3,7,6,2] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,3,1,7,6,2] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,5,1,7,6,4] => {{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,5,3,7,6,4] => {{1,2},{3,8},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,5,1,7,4,6] => {{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,3,1,7,2,6] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,1,3,7,2,6] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,1,6,5,2,3] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,1,6,2,5,3] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,2,1,4,3] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,3,6,2,1,5] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,7,6,4,1,5] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,7,6,4,3,5] => {{1,2},{3,8},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,7,6,4,5,3] => {{1,2},{3,8},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,7,6,4,5,1] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,3,6,2,5,1] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,2,4,3,1] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,2,3,7,6,1] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,2,6,5,3,1] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,2,6,3,5,1] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,2,6,3,1,5] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,7,6,4,2,5] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,7,6,4,5,2] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,7,6,5,4,2] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,5,4,7,6,2] => {{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,5,4,7,2,6] => {{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,7,6,5,2,4] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,7,6,2,5,4] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,2,6,1,5,3] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,2,6,5,1,3] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,2,3,7,1,6] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,5,4,7,1,6] => {{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,5,4,7,3,6] => {{1,2},{3,8},{4,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,7,6,5,1,4] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,3,6,5,1,2] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,3,1,4,2] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,1,3,2,4] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,1,3,4,2] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,1,4,3,2] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,4,1,3,2] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,4,3,6,1,5,2] => {{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,7,6,1,5,4] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,7,6,3,5,4] => {{1,2},{3,8},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,7,6,1,4,5] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,1,4,2,3] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,6,5,1,2,4,3] => {{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,1,8,4,6,2] => {{1,7},{2,3,5,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,4,1,8,5,6,2] => {{1,7},{2,3,4},{5,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,2,1,8,7,3] => {{1,4},{2,5},{3,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,1,8,4,3,2] => {{1,7},{2,6},{3,5,8},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,4,1,8,5,3,2] => {{1,7},{2,6},{3,4},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,2,1,8,7,5,3] => {{1,6,7},{2,4},{3},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,2,1,8,7,6,4] => {{1,5,8},{2,3},{4},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,3,1,7,8,6,4] => {{1,2,5,7},{3},{4},{6,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,5,1,7,8,4,3] => {{1,2,6,8},{3,5,7},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,7,1,6,8,2,3] => {{1,4},{2,5,6,8},{3,7}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,1,2,8,6,5,7] => {{1,4},{2,3},{5,8},{6},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,1,5,6,8,2,3,4] => {{1,7},{2},{3,5,8},{4,6}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,1,5,7,8,3,4] => {{1,2,6,8},{3},{4,5,7}} => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,4,1,6,8,5,2,3] => {{1,7},{2,4,6},{3},{5,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,3,1,8,6,7,4] => {{1,5,8},{2},{3},{4},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,5,2,1,6,8,7,4] => {{1,3},{2,5,6,8},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,1,5,8,6,2,4] => {{1,7},{2,3},{4,5,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,1,4,8,2,5] => {{1,3,7},{2,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,1,3,8,7,5,6] => {{1,4},{2},{3},{5,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,6,1,4,7,8,3,5] => {{1,2,6,8},{3},{4},{5,7}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,4,6,8,2,3,5] => {{1,7},{2},{3,4,6},{5,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,2,4,8,3,5,7] => {{1,6},{2},{3},{4},{5,8},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,4,5,2,3,1,8,6] => {{1,7,8},{2,4},{3,5},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,2,4,1,8,6] => {{1,7,8},{2,3,5},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,2,4,1,8,7] => {{1,6},{2,3,5},{4},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,4,1,6,3,8,7] => {{1,5,6},{2},{3,4},{7,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,4,1,5,2,8,7] => {{1,6},{2,3,4},{5},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,8,6,7,3,4,1] => {{1,5,7},{2},{3,8},{4,6}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,8,5,7,3,4,1] => {{1,6},{2},{3,8},{4,5,7}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,7,4,5,2,8,6] => {{1,3,7,8},{2},{4},{5},{6}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,8,6,7,4,5,2] => {{1,3,8},{2},{4,6},{5,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,8,6,7,3,5,2] => {{1,4,6},{2},{3,8},{5,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,6,2,7,3,4,1] => {{1,8},{2,5,7},{3,6},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,8,5,7,3,6,2] => {{1,4,5,7},{2},{3,8},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,8,5,7,4,6,2] => {{1,3,8},{2},{4,5,7},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,5,7,4,6,3] => {{1,2},{3,8},{4,5,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,4,6,3,8,5] => {{1,2},{3,7,8},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,7,4,6,2,8,5] => {{1,3,7,8},{2},{4},{5,6}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,7,3,6,2,8,5] => {{1,4},{2},{3,7,8},{5,6}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,7,3,6,2,8,4] => {{1,5,6},{2},{3,7,8},{4}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,8,4,7,3,5,1] => {{1,6},{2},{3,8},{4},{5,7}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,7,3,6,2,5,1] => {{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,6,2,5,1,8,4] => {{1,7,8},{2,3,6},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,5,1,7,3,8,4] => {{1,6},{2},{3,5,7,8},{4}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,4,1,7,3,8,6] => {{1,5,7,8},{2},{3,4},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,4,1,7,3,8,5] => {{1,6},{2},{3,4},{5,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,7,3,6,2,4,1] => {{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,7,4,6,2,3,1] => {{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,6,2,3,1,8,5] => {{1,7,8},{2,4},{3,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,3,1,7,4,8,6] => {{1,5,7,8},{2},{3},{4},{6}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,2,3,1,8,5,7,4] => {{1,6},{2},{3},{4},{5,8},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,1,5,2,8,6,7,4] => {{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,6,2,8,5,7,4] => {{1,3,6},{2},{4},{5,8},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,3,8,4,6,2,5,1] => {{1,7},{2,3,8},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,5,1,6,2,7,3] => {{1,8},{2,4},{3,5,6},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,8,4,6,2,7,3] => {{1,5,6},{2},{3,8},{4},{7}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,8,5,6,2,7,3] => {{1,4,5,6},{2},{3,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,8,5,6,2,7,4] => {{1,3,8},{2},{4,5,6},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,5,6,3,7,4] => {{1,2},{3,8},{4,5,6},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,5,1,7,3,6,2] => {{1,8},{2,4},{3,5,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,6,2,8,4,5,1] => {{1,7},{2,3,6},{4},{5,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,5,6,1,3,4,2] => {{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,1,3,6,2,5,4] => {{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,2,4,5,6,1,3] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,2,1,6,3,4,5] => {{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,3,5,6,4,1,2] => {{1,7},{2,8},{3},{4,5,6}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,1,4,2,3,6,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,4,5,3,1,6,2] => {{1,7},{2,8},{3,4,5},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,8,4,3,2,7,6] => {{1},{2,5},{3,8},{4},{6},{7}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,6,1,4,3,2,7,8] => {{1,5},{2,6},{3},{4},{7},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,4,6,8,3,7,5,2] => {{1},{2,4,8},{3,6,7},{5}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,5,3,1,6,7] => {{1,2,4,5},{3,8},{6},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,1,4,7,6,3] => {{1,2,5},{3,8},{4},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,8,4,7,6,1,2] => {{1,3,8},{2,5,7},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,1,4,7,8,3] => {{1,5},{2,6,7,8},{3},{4}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,2,5,3,1,8,7] => {{1,4,5},{2,6},{3},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,5,1,3,6,8,2] => {{1,4},{2,7,8},{3,5},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,3,6,2,4,1,8] => {{1,7},{2,5},{3},{4,6},{8}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,7,3,6,1,4,8,2] => {{1,5},{2,7,8},{3},{4,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,6,7,2,1,8,4] => {{1,5},{2,3,6},{4,7,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,1,7,5,2,4,8,3] => {{1,6},{2},{3,7,8},{4,5}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,1,2,4,5,8,7] => {{1,6},{2,3},{4},{5},{7,8}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,7,2,5,3,8,6] => {{1},{2,4},{3,7,8},{5},{6}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,6,7,8,3,5,1,2] => {{1,4,8},{2,6},{3,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,7,5,8,2,4,3] => {{1},{2,6},{3,7},{4,5,8}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,7,8,1,4,2] => {{1,3,6},{2,5,8},{4,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,6,5,7,8,2,1,4] => {{1,3,5,8},{2,6},{4,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,2,7,6,1,4,3,8] => {{1,5},{2},{3,7},{4,6},{8}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,7,6,8,5,4,1,2] => {{1,3,6},{2,7},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,8,4,5,6,1,7] => {{1,3,8},{2},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,4,2,8,6,1,7,5] => {{1,3},{2,4,8},{5,6},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,7,1,5,2,6,8] => {{1,3,7},{2,4},{5},{6},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,7,8,1,2,6,5] => {{1,4,8},{2,3,7},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,8,6,3,2,1,4] => {{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,8,6,1,3,4,2] => {{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,8,1,3,4,2] => {{1,7},{2,6},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,5,1,7,8,6,3] => {{1,2,4},{3,5,7},{6,8}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,6,4,1,8,3,7,5] => {{1,2,6},{3,4},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,6,4,8,5,1,2] => {{1,7},{2,3,6},{4},{5,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,6,5,3,8,4,2] => {{1,7},{2},{3,6,8},{4,5}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,2,5,6,3,8,1,4] => {{1,7},{2},{3,5},{4,6,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,2,7,1,8,4,3] => {{1,6,8},{2,5},{3},{4,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,7,4,2,8,1,3] => {{1,5},{2,6,8},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,6,4,1,8,3,2] => {{1,5},{2,7},{3,6,8},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,1,5,2,8,3,4] => {{1,6,8},{2,7},{3},{4,5}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,5,2,4,8,3,6] => {{1},{2,7},{3,5},{4},{6,8}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,7,5,3,8,4,1,2] => {{1,6},{2,7},{3,5,8},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,5,4,2,3,8,7] => {{1},{2,6},{3,5},{4},{7,8}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,6,1,5,3,2,8,4] => {{1,7,8},{2,6},{3},{4,5}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,6,4,1,2,8,3] => {{1,7,8},{2,5},{3,6},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,5,4,3,1,8,2] => {{1,6},{2,7,8},{3,5},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,2,4,3,1,6,8] => {{1,7},{2,5},{3},{4},{6},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,4,6,1,2,5,3,8] => {{1,7},{2,4},{3,6},{5},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,8,1,4,2,5,7,3] => {{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,6,4,2,5,7,3,8] => {{1},{2,6,7},{3,4},{5},{8}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,1,3,5,6,4,2,8] => {{1,7},{2},{3},{4,5,6},{8}} => [2,1,1,3,1] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,3,1,6,4,5,2,8] => {{1,7},{2,3},{4,6},{5},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,2,6,5,1,3,8] => {{1,7},{2,4,6},{3},{5},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,6,3,1,5,2,8] => {{1,7},{2,4},{3,6},{5},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,8,1,2,3,4,7,5] => {{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,8,2,3,5,4,7,1] => {{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,8,2,4,1,5,7,3] => {{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,8,3,1,2,4,7,5] => {{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,6,3,5,7,1,4,8] => {{1,2,6},{3},{4,5,7},{8}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,1,7,8,3,6,4] => {{1,2,5,8},{3},{4,7},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,3,6,8,4,7,1] => {{1,2,5,8},{3},{4,6},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,7,8,5,6,3] => {{1,2},{3,4,7},{5,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,7,6,8,5,1,3] => {{1,2,4,6},{3,7},{5,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,5,7,8,1,4,6,3] => {{1,2,5},{3,7},{4,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,4,1,8,6,7,2] => {{1,5,8},{2,3,4},{6},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,8,4,6,1,7,3] => {{1,5,6},{2},{3,8},{4},{7}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,8,5,7,6,3,1] => {{1,4,5,7},{2},{3,8},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,8,6,7,5,3,2] => {{1,4,6},{2},{3,8},{5,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,7,6,2,1,3] => {{1,5,6},{2,8},{3,4,7}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,4,8,3,1,7,2,5] => {{1,6,7},{2,4},{3,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,2,8,7,1,3,5] => {{1,6},{2,4,8},{3},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,8,7,2,5,1,4] => {{1,6},{2,3,8},{4,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,3,8,6,7,2,4] => {{1,5,6,7},{2},{3},{4,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,7,6,4,2,8,3] => {{1},{2,5},{3,7,8},{4,6}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,1,2,7,3,5] => {{1,6,7},{2,4},{3,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,2,7,6,3,8] => {{1,4},{2,5,7},{3},{6},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,5,1,2,6,8,7,3] => {{1,4},{2,5,6,8},{3},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,1,8,4,7,2] => {{1,3,6},{2,5,8},{4},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,7,1,2,8,6,4] => {{1,3,7},{2,5},{4},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,5,1,4,8] => {{1,3},{2,6},{4,7},{5},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,5,3,1,7,6,2,8] => {{1,4},{2,5,7},{3},{6},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,5,2,7,8,1,6,4] => {{1,3},{2,5,8},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,6,5,8,7,1,2] => {{1,3,6,7},{2,4,5,8}} => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => 2

[3,1,4,5,8,6,7,2] => {{1,3,4,5,8},{2},{6},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,6,8,5,2,7,1] => {{1,3,6},{2,4,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,2,8,4,7,1] => {{1,3,6},{2,5,8},{4},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,6,1,8,7,3] => {{1,4,6,8},{2},{3,5},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,3,1,6,8,7,2] => {{1,4},{2,5,6,8},{3},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,5,8,6,4,3] => {{1,2},{3,7},{4,5,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,3,7,5,2,4,8] => {{1,6},{2},{3},{4,7},{5},{8}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,1,2,6,8,5,4,7] => {{1,3},{2},{4,6},{5,8},{7}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,4,1,7,8,6,5,3] => {{1,2,4,7},{3},{5,8},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,4,1,5,8,6,3] => {{1,2,7},{3,4},{5},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,4,8,5,1,7,2] => {{1,3,4,8},{2,6},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,4,5,1,8,2] => {{1,6},{2,3,7,8},{4},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,3,7,5,8,1,4] => {{1,2,6,8},{3},{4,7},{5}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,2,3,6,8,1,5] => {{1,4},{2,7},{3},{5,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,7,3,6,8,1,4] => {{1,5,6,8},{2},{3,7},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,4,6,2,8,1,3] => {{1,5},{2,7},{3,4,6,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,7,3,4,6,1,8,2] => {{1,5,6},{2,7,8},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,8,4,6,1,7,2] => {{1,5,6},{2,3,8},{4},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,2,4,1,6,7,3] => {{1,8},{2,5},{3},{4},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,2,3,5,1,6,7,4] => {{1,8},{2},{3},{4,5},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,2,8,3,6,7,1,5] => {{1,4},{2},{3,8},{5,6,7}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,1,7,3,5,6] => {{1,2,4},{3,8},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,7,3,1,6,2] => {{1,5},{2,8},{3,4,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,8,3,1,7,5,2] => {{1,4},{2,6,7},{3,8},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,8,2,7,1,5,4] => {{1,6},{2,3,8},{4},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,8,1,2,6,4,7] => {{1,5},{2,3,8},{4},{6},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,7,4,1,6,2,3,8] => {{1,5,6},{2,7},{3,4},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,2,8,5,3,7,4] => {{1},{2,6},{3},{4,8},{5},{7}} => [1,2,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,8,5,3,1,7,4,2] => {{1,6,7},{2,8},{3,5},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,3,7,2,8,4,5] => {{1},{2,6,8},{3},{4,7},{5}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,2,7,8,5,1,4] => {{1,6},{2,3},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,7,8,3,1,6,2] => {{1,4,8},{2,5},{3,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,2,5,8,1,6,3] => {{1,4,5,8},{2,7},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,3,4,6,2,5,7] => {{1,8},{2},{3},{4},{5,6},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,8,2,4,6,7,1,5] => {{1,3},{2,8},{4},{5,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,3,5,6,1,7,2] => {{1,4,5,6},{2,8},{3},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,3,7,8,1,4] => {{1,5,7},{2,6,8},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,7,1,5,3,2] => {{1,6},{2,8},{3,4,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,7,2,5,3,1] => {{1,6},{2,8},{3,4,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,8,7,2,6,3,1] => {{1,5},{2,4,7},{3,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,8,7,1,6,3,2] => {{1,5},{2,4,7},{3,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,8,7,6,1,2,5] => {{1,4,7},{2,3,8},{5,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,4,6,5,1,2,7] => {{1,8},{2,3,4,6},{5},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,4,7,5,1,2,6] => {{1,3,4,7},{2,8},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,8,7,1,6,3,2] => {{1,4,7},{2,5},{3,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,8,7,2,6,3,1] => {{1,4,7},{2,5},{3,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,8,2,7,6,4,1] => {{1,3,8},{2,5,7},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,8,1,7,6,4,2] => {{1,3,8},{2,5,7},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,1,7,6,4,3] => {{1,2,5,7},{3,8},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,7,1,6,3,4] => {{1,2,5},{3,8},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,7,1,6,3,5] => {{1,2,4,7},{3,8},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,4,7,1,5,3,6] => {{1,2,8},{3,4,7},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,4,7,2,5,3,6] => {{1},{2,8},{3,4,7},{5},{6}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,8,7,2,6,3,5] => {{1},{2,4,7},{3,8},{5},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,8,2,7,6,4,3] => {{1},{2,5,7},{3,8},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,5,8,3,7,6,4,1] => {{1,2,5,7},{3,8},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,2,8,7,6,5,3] => {{1},{2,4,8},{3},{5,7},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,1,3,2,6,5,4,7] => {{1,8},{2},{3},{4},{5,6},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,2,3,1,6,5,4,7] => {{1,8},{2},{3},{4},{5,6},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,3,8,1,7,6,4,5] => {{1,2,3,8},{4},{5,7},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,1,8,7,6,5,2] => {{1,3},{2,4,8},{5,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,1,8,7,6,5,2] => {{1,4,8},{2,3},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,8,1,7,6,4,2] => {{1,5,7},{2,3,8},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,8,2,7,6,4,1] => {{1,5,7},{2,3,8},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,2,8,7,6,5,4] => {{1,3},{2},{4,8},{5,7},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,4,8,7,6,5,2] => {{1,3,4,8},{2},{5,7},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,2,1,3,6,5,4,7] => {{1,8},{2},{3},{4},{5,6},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,2,3,6,5,4,7] => {{1,8},{2},{3},{4},{5,6},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,4,5,2,8,3,7,6] => {{1},{2,4},{3,5,8},{6},{7}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,2,6,5,8,3,7] => {{1},{2,4,6,8},{3},{5},{7}} => [1,4,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,6,5,8,2,4,7] => {{1,3,6},{2},{4,5,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,4,2,5,8,3,7] => {{1},{2,6,8},{3,4},{5},{7}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,2,6,4,8,3,7] => {{1},{2,5},{3},{4,6,8},{7}} => [1,2,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,5,4,7,3,8,6] => {{1},{2},{3,5,7,8},{4},{6}} => [1,1,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,2,6,3,8,7,5] => {{1,4,6,8},{2},{3},{5},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,7,5,2,8,3,6] => {{1},{2,4,5},{3,7},{6,8}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,5,2,8,7,3,6] => {{1},{2,4},{3,5,8},{6,7}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,2,8,3,7,6,5] => {{1},{2,4,8},{3},{5},{6,7}} => [1,3,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,5,3,8,7,6,4] => {{1},{2},{3,5,8},{4},{6,7}} => [1,1,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,8,6,5,3,7,4] => {{1},{2},{3,8},{4,6},{5},{7}} => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,6,4,2,8,7,3,5] => {{1},{2,6,7},{3,4},{5,8}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,1,6,2,8,4,5] => {{1,7},{2,3},{4,6,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,5,2,6,3,8,4] => {{1},{2,7,8},{3,5,6},{4}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,7,6,5,3,8,4] => {{1},{2},{3,7,8},{4,6},{5}} => [1,1,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,2,6,3,8,7,4] => {{1},{2,5},{3},{4,6,8},{7}} => [1,2,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,2,7,6,3,8,4] => {{1},{2,5,6},{3},{4,7,8}} => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,5,2,7,3,8,4] => {{1},{2,6},{3,5,7,8},{4}} => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,2,8,6,3,7,5] => {{1,4,8},{2},{3},{5,6},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,7,1,8,2,5,6] => {{1,4},{2,3,7},{5,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,7,3,2,4,6,5] => {{1},{2,8},{3,7},{4},{5},{6}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,4,2,8,7,3,6,5] => {{1},{2,4,8},{3},{5,7},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,8,5,2,7,3,6] => {{1},{2,4,5},{3,8},{6,7}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,3,1,7,2,4,6] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,5,2,6,3,7,4] => {{1},{2,8},{3,5,6},{4},{7}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,2,7,3,8,6,4] => {{1},{2,5},{3},{4,7},{6,8}} => [1,2,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,6,2,7,3,8,5,4] => {{1},{2,6,8},{3},{4,7},{5}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,7,3,2,6,4,5] => {{1},{2,8},{3,7},{4},{5},{6}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,4,2,8,7,6,3,5] => {{1},{2,4,8},{3},{5,7},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,8,7,5,3,6,4] => {{1},{2},{3,8},{4,7},{5},{6}} => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,8,6,3,7,5,4] => {{1},{2},{3,8},{4,6,7},{5}} => [1,1,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,7,3,6,5,8,2] => {{1,4},{2},{3,7,8},{5,6}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,8,7,6,2,4,3] => {{1,5,6},{2},{3,8},{4,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,8,6,2,4,1,3] => {{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,1,5,2,7,3,8] => {{1,6,7},{2,4,5},{3},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,4,5,3,7,6,2] => {{1,8},{2},{3,4,5},{6,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,4,5,3,8,7,2] => {{1,6,8},{2},{3,4,5},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,7,8,6,2,4,3] => {{1,5,6},{2},{3,7},{4,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,4,5,3,8,6,2] => {{1,7},{2},{3,4,5},{6,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,4,5,3,6,8,2] => {{1,7,8},{2},{3,4,5},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,4,5,3,6,7,2] => {{1,8},{2},{3,4,5},{6},{7}} => [2,1,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,1,5,2,6,3,8] => {{1,7},{2,4,5},{3},{6},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,5,7,2,1,4,8] => {{1,6},{2,3,5},{4,7},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,8,2,1,7,4] => {{1,6},{2,3,5},{4,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,7,2,1,8,4] => {{1,6},{2,3,5},{4,7,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,4,5,7,3,6,1,2] => {{1,8},{2,4,7},{3,5},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,2,4,1,3] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,8,6,3,1,7,2] => {{1,5},{2,4,6},{3,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,8,2,1,4,7] => {{1,6},{2,3,5},{4,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,5,6,2,1,4,7] => {{1,8},{2,3,5},{4,6},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,8,5,1,4,7,6] => {{1,2,3,8},{4,5},{6},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,8,6,1,5,7,4] => {{1,2,3,8},{4,6},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,6,7,1,3,5,4] => {{1,2,8},{3,6},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,5,7,2,1,6,4] => {{1,8},{2,3,5},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,8,5,6,1,7,4] => {{1,2,3,8},{4,5,6},{7}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,4,5,6,3,1,8,2] => {{1,7,8},{2,4,6},{3,5}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,4,5,6,3,1,7,2] => {{1,8},{2,4,6},{3,5},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,6,2,8,1,4] => {{1,7},{2,3,5},{4,6,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,3,5,8,2,1,6,4] => {{1,7},{2,3,5},{4,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,6,2,1,4,8] => {{1,7},{2,3,5},{4,6},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,5,1,3,4,8] => {{1,2,7},{3,6},{4,5},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,8,1,3,5,4] => {{1,2,7},{3,6},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,5,6,1,4,2,3] => {{1,8},{2,7},{3,5},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,4,1,8,5,7,3] => {{1,2,6},{3,4},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,1,3,6,5,8,4] => {{1,2,7,8},{3},{4},{5,6}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,8,4,3,1,5] => {{1,2,7},{3,6},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,1,8,3,4,5] => {{1,2,7},{3,6},{4},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,1,2,8,4,6] => {{1,7},{2,3,5},{4},{6,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,1,8,3,2,7,5] => {{1,6},{2,4,8},{3},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,3,8,6,4,1,7,5] => {{1,2,3,8},{4,6},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,6,7,4,3,1,5] => {{1,2,8},{3,6},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,5,7,2,4,1,6] => {{1,8},{2,3,5},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,1,8,7,5,6] => {{1,2,3,4},{5,8},{6,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,8,6,1,7,3,4,5] => {{1,2,8},{3,6},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,8,1,6,4,7,5] => {{1,2,3,8},{4},{5,6},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,8,1,4,5,7,6] => {{1,2,3,8},{4},{5},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,3,4,5,6,7,8,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 8

[2,1,3,4,5,6,7,8,9,10] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 9

[1,7,6,5,4,2,3,8] => {{1},{2,7},{3,6},{4,5},{8}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,6,5,2,7,3,4] => {{1},{2,8},{3,6,7},{4,5}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,7,6,4,5,8] => {{1,3},{2},{4,7},{5,6},{8}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,1,6,5,2,4,3,8] => {{1,7},{2},{3,6},{4,5},{8}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,1,8,4,7,5,6] => {{1,3},{2},{4,8},{5},{6,7}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,7,2,6,5,3,4] => {{1},{2,8},{3,7},{4},{5,6}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,7,8,2,5,6,3,4] => {{1},{2,7},{3,8},{4},{5},{6}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,5,4,8,2,7,3,6] => {{1},{2,5},{3,4,8},{6,7}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,3,7,1,6,5,2] => {{1,8},{2,4,7},{3},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,4,3,1,2,6,5,8] => {{1,7},{2,4},{3},{5},{6},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,4,3,1,2,5,7,6] => {{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,5,1,4,2,3,7,6] => {{1,8},{2,5},{3},{4},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,5,1,4,2,6,3,8] => {{1,7},{2,5},{3},{4},{6},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,5,1,4,3,2,7,8] => {{1,6},{2,5},{3},{4},{7},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,6,1,3,4,2,7,8] => {{1,5},{2,6},{3},{4},{7},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,2,6,1,5,4,7,8] => {{1,3,6},{2},{4},{5},{7},{8}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,2,7,1,4,6,5,8] => {{1,3,7},{2},{4},{5},{6},{8}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,7,1,2,3,6,5,4] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,1,2,3,5,6,4] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,8,1,2,4,3,7,5] => {{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,8,2,1,3,5,7,6] => {{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,2,8,1,4,5,7,6] => {{1,3,8},{2},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,1,3,2,5,6,7,8] => {{1,4},{2},{3},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[5,1,2,4,3,6,7,8] => {{1,5},{2},{3},{4},{6},{7},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[6,1,2,3,5,4,7,8] => {{1,6},{2},{3},{4},{5},{7},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[7,1,2,3,4,6,5,8] => {{1,7},{2},{3},{4},{5},{6},{8}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[8,1,2,3,4,5,7,6] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[5,4,7,6,8,1,2,3] => {{1,5,8},{2,4,6},{3,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,8,4,5,7,1,2,6] => {{1,3,4,5,7},{2,8},{6}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,6,7,1,8,3,2] => {{1,4,7},{2,5},{3,6,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,6,1,7,8,4,2] => {{1,3,6,8},{2,5,7},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,5,6,1,8,7,4,3] => {{1,2,5,8},{3,6,7},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,2,4,5,1,6,3,7] => {{1,8},{2},{3,4,5},{6},{7}} => [2,1,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,6,2,8,4,7,3] => {{1},{2,5,8},{3,6},{4},{7}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,1,3,2,5,4,6,7] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[8,2,3,1,5,6,4,7] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[2,4,1,6,8,7,5,3] => {{1,2,4,6,7},{3},{5,8}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,1,7,6,8,5,2] => {{1,4,7},{2,3},{5,6,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,2,7,8,1,6,3,4] => {{1,5},{2},{3,7},{4,8},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,1,7,3,4,8,6,2] => {{1,5},{2},{3,7},{4},{6,8}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,1,7,8,2,3,6,4] => {{1,5},{2},{3,7},{4,8},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,4,5,7,8,6,2] => {{1,3,4,5,7},{2},{6,8}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,2,1,3,4,6,5,7] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,8,2,3,4,5,7,6] => {{1},{2,8},{3},{4},{5},{6},{7}} => [1,2,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,2,8,3,4,6,7,5] => {{1},{2},{3,8},{4},{5},{6},{7}} => [1,1,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[4,2,1,6,5,8,7,3] => {{1,4,6,8},{2},{3},{5},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,7,4,8,3,6,2] => {{1},{2,5,8},{3,7},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,7,4,8,6,3,2] => {{1},{2,5,8},{3,7},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,6,7,8,4,5,3,2] => {{1},{2,6},{3,7},{4,8},{5}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,6,7,8,4,3,5,2] => {{1},{2,6},{3,7},{4,8},{5}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,7,3,8,6,4,2] => {{1},{2,5,8},{3,7},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,6,7,8,3,5,4,2] => {{1},{2,6},{3,7},{4,8},{5}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,6,7,8,5,3,4,2] => {{1},{2,6},{3,7},{4,8},{5}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,5,2,8,4,7,3,1] => {{1,6,7},{2,5},{3},{4,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,4,5,8,7,2,1] => {{1,6,7},{2,3,4,5,8}} => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2

[3,8,4,7,5,2,1,6] => {{1,3,4,7},{2,8},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,1,4,8,7,3,2] => {{1,5,8},{2,6,7},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,4,8,6,3,7,2] => {{1,5,6},{2},{3,4,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,7,1,8,6,5,2] => {{1,3,7},{2,4},{5,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,8,4,2,7,1,5] => {{1,6,7},{2,3,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,8,7,1,4,2,5] => {{1,3,8},{2,6},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,7,1,6,8,2,4] => {{1,5,6,8},{2,3,7},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,8,1,7,6,2,4,3] => {{1,5,6},{2,8},{3},{4,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,1,2,7,8,5,3] => {{1,4},{2,6,8},{3},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,2,7,3,6,8,1] => {{1,5},{2,4,7,8},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,3,6,4,2,8,1] => {{1,7,8},{2,5},{3},{4,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,1,5,3,8,2,7] => {{1,6,8},{2,4,5},{3},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,2,6,4,7,3,1] => {{1,8},{2,5},{3},{4,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,3,6,4,2,8,1] => {{1,5},{2,7,8},{3},{4,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,6,4,5,2,8,1] => {{1,3,6},{2,7,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,4,3,1,8,2,7] => {{1,6,8},{2,5},{3,4},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,5,4,2,7,3,1] => {{1,8},{2,6,7},{3,5},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,1,7,2,6,3] => {{1,8},{2,5,7},{3,4},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,4,1,8,3,2,6] => {{1,7},{2,5,8},{3,4},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,4,2,1,8,3,6] => {{1,5},{2,7},{3,4},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,5,3,4,8,2,7] => {{1},{2,6,8},{3,5},{4},{7}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,4,6,3,1,8,2,7] => {{1,5},{2,4},{3,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,8,4,2,7,3,1] => {{1,6,7},{2,5},{3,8},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,2,6,4,7,3,1] => {{1,5},{2,8},{3},{4,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,6,2,5,7,4,1] => {{1,3,6,7},{2,8},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,6,3,7,5,2,4] => {{1},{2,8},{3,6},{4},{5,7}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,7,5,2,6,4,3,1] => {{1,8},{2,7},{3,5,6},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,6,1,7,4,5,2] => {{1,3,6},{2,8},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,8,5,7,3,6,1] => {{1,4,5,7},{2},{3,8},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,7,6,8,3,2,4] => {{1,5,8},{2},{3,7},{4,6}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,1,5,8,4,2,6] => {{1,3},{2,7},{4,5,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,1,5,8,4,2,6] => {{1,7},{2,3},{4,5,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,1,5,8,3,6,7] => {{1,4,5,8},{2},{3},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,4,2,7,1,8,3,6] => {{1,5},{2,4,7},{3},{6,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,3,1,6,8,2,7] => {{1,5,6,8},{2,4},{3},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,2,8,7,3,4,1] => {{1,6},{2,5,7},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,1,8,7,4,2,3] => {{1,6},{2,5,7},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,4,7,5,3,2,1] => {{1,8},{2,6},{3,4,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,8,1,7,2,6,3] => {{1,5,7},{2,4},{3,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,8,2,4,7,5,1] => {{1,3,8},{2,6,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,6,8,7,3,4,1] => {{1,5,7},{2},{3,6},{4,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,2,8,6,3,5,1] => {{1,4,8},{2,7},{3},{5,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,8,1,7,2,5,4] => {{1,3,8},{2,6},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,8,7,4,5,6,1] => {{1,2,3,8},{4,7},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,8,7,6,3,4,5] => {{1},{2},{3,8},{4,7},{5,6}} => [1,1,2,2,2] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,8,3,7,6,2,4] => {{1},{2,5,7},{3,8},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,1,6,8,7,4,2,3] => {{1,5,7},{2},{3,6},{4,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,7,5,3,2,1] => {{1,6},{2,8},{3,4,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,7,6,4,5,2,1] => {{1,3,7},{2,8},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,7,6,5,3,4,1] => {{1,2,8},{3,7},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,7,6,5,4,2,3] => {{1},{2,8},{3,7},{4,6},{5}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,8,6,7,3,4,1,2] => {{1,5},{2,8},{3,6},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,6,7,3,5,1,2] => {{1,4,7},{2,8},{3,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,6,7,4,5,1,2] => {{1,3,6},{2,8},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,6,7,4,5,1,3] => {{1,2,8},{3,6},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,5,7,4,6,2,3] => {{1},{2,8},{3,5},{4,7},{6}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,8,5,7,4,6,1,2] => {{1,3,5},{2,8},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,5,7,3,6,1,2] => {{1,4,7},{2,8},{3,5},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,4,8,5,6,1,2] => {{1,3,4,8},{2,7},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,4,8,5,6,1,3] => {{1,2,7},{3,4,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,5,6,2,7,3,4] => {{1},{2,8},{3,5},{4,6,7}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,4,7,3,6,2,5] => {{1},{2,8},{3,4,7},{5},{6}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,8,4,7,3,6,1,5] => {{1,2,8},{3,4,7},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,4,7,2,6,1,5] => {{1,3,4,7},{2,8},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,5,7,2,6,1,3] => {{1,4,7},{2,8},{3,5},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,5,7,2,6,1,4] => {{1,3,5},{2,8},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,5,7,3,6,1,4] => {{1,2,8},{3,5},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,5,7,3,6,2,4] => {{1},{2,8},{3,5},{4,7},{6}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,8,6,7,3,5,1,4] => {{1,2,8},{3,6},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,6,7,2,5,1,4] => {{1,3,6},{2,8},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,6,7,2,5,1,3] => {{1,4,7},{2,8},{3,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,6,7,2,4,1,3] => {{1,5},{2,8},{3,6},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,5,7,1,4,2,3] => {{1,6},{2,8},{3,5},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,6,7,1,4,2,3] => {{1,5},{2,8},{3,6},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,6,7,1,5,2,3] => {{1,4,7},{2,8},{3,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,6,7,1,5,2,4] => {{1,3,6},{2,8},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,2,8,6,7,3,4] => {{1},{2,5,6,7},{3},{4,8}} => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,1,8,6,7,3,4] => {{1,2,5,6,7},{3},{4,8}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,6,1,8,5,7,3,4] => {{1,2,6,7},{3},{4,8},{5}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,5,7,1,6,2,4] => {{1,3,5},{2,8},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,7,1,5,2,3] => {{1,6},{2,8},{3,4,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,6,1,5,2,3] => {{1,7},{2,8},{3,4,6},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,4,7,1,6,2,5] => {{1,3,4,7},{2,8},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,1,8,4,7,3,5] => {{1,2,6,7},{3},{4,8},{5}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,2,6,1,8,4,5] => {{1,3},{2,7},{4,6,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,1,6,2,8,4,5] => {{1,3},{2,7},{4,6,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,1,6,2,7,3,5] => {{1,4,6,7},{2,8},{3},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,1,6,2,7,3,4] => {{1,5},{2,8},{3},{4,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,2,5,1,7,3,4] => {{1,6,7},{2,8},{3},{4,5}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,2,6,1,7,3,4] => {{1,5},{2,8},{3},{4,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,2,6,1,7,3,5] => {{1,4,6,7},{2,8},{3},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,3,6,1,8,4,5] => {{1,2,7},{3},{4,6,8},{5}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,3,4,5,6,7,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}} => [1,1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 9

[1,2,3,4,5,6,7,8,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [1,1,1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 10

[6,7,4,8,3,5,1,2] => {{1,6},{2,7},{3,4,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,4,6,2,3,1,8] => {{1,5},{2,7},{3,4,6},{8}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,4,6,3,8,1,2] => {{1,5},{2,7},{3,4,6,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,7,4,8,3,6,1,2] => {{1,5},{2,7},{3,4,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,3,7,2,8,1,4] => {{1,5},{2,6,8},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,3,8,2,7,1,4] => {{1,5},{2,6,7},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,5,2,6,1,3] => {{1,7},{2,8},{3,4,5},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,5,2,3,1,7] => {{1,6},{2,8},{3,4,5},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,6,2,3,1,7] => {{1,5},{2,8},{3,4,6},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,4,8,2,3,1,7] => {{1,5},{2,6},{3,4,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,3,8,2,4,1,7] => {{1,5},{2,6},{3},{4,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,6,3,5,2,8,1,7] => {{1,4,5},{2,6,8},{3},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,3,6,2,7,1,4] => {{1,5},{2,8},{3},{4,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,3,6,2,7,1,5] => {{1,4,6,7},{2,8},{3},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,3,8,2,7,1,5] => {{1,4,8},{2,6,7},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,3,7,2,8,1,5] => {{1,4,7},{2,6,8},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,3,6,2,5,1,8] => {{1,4,6},{2,7},{3},{5},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,7,3,6,2,8,1,5] => {{1,4,6,8},{2,7},{3},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,4,8,2,6,1,3] => {{1,5},{2,7},{3,4,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,3,6,2,8,1,4] => {{1,5},{2,7},{3},{4,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,3,5,2,8,1,4] => {{1,6,8},{2,7},{3},{4,5}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,8,2,5,1,3] => {{1,6},{2,7},{3,4,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,5,8,2,4,1,3] => {{1,6},{2,7},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,5,7,2,3,1,4] => {{1,6},{2,8},{3,5},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,8,2,3,1,5] => {{1,6},{2,7},{3,4,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,4,8,2,3,1,6] => {{1,5},{2,7},{3,4,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,7,2,3,1,6] => {{1,5},{2,8},{3,4,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,7,2,3,1,5] => {{1,6},{2,8},{3,4,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,6,2,3,1,5] => {{1,7},{2,8},{3,4,6},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,3,5,2,8,1,6] => {{1,4,5},{2,7},{3},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,3,7,2,6,1,8] => {{1,4,7},{2,5},{3},{6},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,5,3,7,2,8,1,6] => {{1,4,7},{2,5},{3},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,3,8,2,7,1,6] => {{1,4,8},{2,5},{3},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,3,5,2,7,1,6] => {{1,4,5},{2,8},{3},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,3,4,2,7,1,5] => {{1,6,7},{2,8},{3},{4},{5}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,3,4,2,6,1,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,8,3,4,2,5,1,7] => {{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,5,3,6,2,8,1,7] => {{1,4,6,8},{2,5},{3},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,5,2,1,8,3,6] => {{1,4},{2,7},{3,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,5,2,1,7,6,3] => {{1,4},{2,8},{3,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,5,2,1,3,8,7] => {{1,4},{2,6},{3,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,4,2,3,1,8,7] => {{1,5},{2,6},{3,4},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,5,3,1,2,8,7] => {{1,6},{2,4},{3,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,6,1,3,2,8,7] => {{1,5},{2,4},{3,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,8,1,7,3,2,5] => {{1,4},{2,6},{3,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,8,1,6,3,5,2] => {{1,4},{2,7},{3,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,8,1,6,5,3,2] => {{1,7},{2,4},{3,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,8,1,3,7,6,2] => {{1,5},{2,4},{3,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,5,3,1,7,6,2] => {{1,8},{2,4},{3,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,7,1,3,8,2,6] => {{1,5},{2,4},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,1,7,5,2,3] => {{1,6},{2,4},{3,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,8,7,2,1,3,4] => {{1,5},{2,6},{3,8},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,7,6,4,2,1,3] => {{1,8},{2,5},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,6,3,7,2,1,5] => {{1,8},{2,4},{3,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,2,8,7,4,1,5] => {{1,6},{2,3},{4,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,8,7,4,3,5] => {{1,2},{3,6},{4,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,8,6,4,5,3] => {{1,2},{3,7},{4,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,2,8,6,4,5,1] => {{1,7},{2,3},{4,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,8,5,2,4,3,1] => {{1,7},{2,6},{3,8},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,8,6,2,3,1,4] => {{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,3,2,1,4] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,7,5,3,2,4,1] => {{1,6},{2,8},{3,7},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,2,3,7,6,1] => {{1,5},{2,8},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,2,6,5,3,1] => {{1,7},{2,8},{3,4},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,2,6,3,5,1] => {{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,6,2,7,3,1,5] => {{1,4},{2,8},{3,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,8,7,4,2,5] => {{1,3},{2,6},{4,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,1,8,6,4,5,2] => {{1,3},{2,7},{4,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,1,6,7,5,2,4] => {{1,3},{2,8},{4,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,1,6,8,2,5,4] => {{1,3},{2,7},{4,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,2,8,1,3,5] => {{1,4},{2,7},{3,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,4,2,8,1,5,3] => {{1,6},{2,7},{3,4},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,2,7,5,1,3] => {{1,6},{2,8},{3,4},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,6,7,5,3,4] => {{1,2},{3,8},{4,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,6,7,5,1,4] => {{1,8},{2,3},{4,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,4,3,7,5,1,2] => {{1,8},{2,6},{3,4},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,6,7,3,1,2,4] => {{1,5},{2,8},{3,6},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,5,8,1,3,4,2] => {{1,6},{2,7},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,8,1,4,3,2] => {{1,7},{2,6},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,5,7,4,1,3,2] => {{1,8},{2,6},{3,5},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,4,3,8,1,5,2] => {{1,7},{2,6},{3,4},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,2,6,8,1,5,4] => {{1,7},{2,3},{4,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,6,8,3,5,4] => {{1,2},{3,7},{4,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,6,8,1,4,2,3] => {{1,7},{2,5},{3,6},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,8,1,2,4,3] => {{1,6},{2,5},{3,7},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,7,5,4,8,3,1] => {{1,6,8},{2},{3,7},{4,5}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,5,4,3,8,7,2] => {{1,6,8},{2},{3,5},{4},{7}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,1,8,3,4,5,7,2] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,3,4,5,6,7,2] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[6,3,2,7,5,1,8,4] => {{1,6},{2,3},{4,7,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,8,2,4,7,3,1] => {{1,6,7},{2,5},{3,8},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,2,1,4,3,7,6] => {{1,8},{2,5},{3},{4},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,3,1,2,6,8,5,7] => {{1,4},{2,3},{5,6,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,1,5,2,4,7,6] => {{1,8},{2,3},{4,5},{6},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,8,6,7,2,1,5,4] => {{1,3,6},{2,8},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,2,3,8,5,7,4] => {{1,6},{2},{3},{4},{5,8},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,2,7,3,1,8,4,6] => {{1,5},{2},{3,7},{4},{6,8}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,5,8,7,2,4,1,6] => {{1,3,8},{2,5},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,3,8,7,5,6] => {{1,2,4},{3},{5,8},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,3,1,7,4,6] => {{1,2,5},{3,8},{4},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,2,3,4,1,5,7] => {{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,4,2,7,8,6,3,5] => {{1},{2,4,7},{3},{5,8},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,5,7,8,6,1,3] => {{1,4,7},{2},{3,5,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,8,3,5,1,7,4] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,4,8,5,7,1,3] => {{1,6,7},{2},{3,4,8},{5}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,6,4,8,5,7,2] => {{1},{2,3,6},{4},{5,8},{7}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,6,4,7,5,8,2] => {{1},{2,3,6},{4},{5,7,8}} => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,4,7,5,8,1,3] => {{1,6,8},{2},{3,4,7},{5}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,2,1,4,3,5,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,6,4,2,3,1,8,5] => {{1,7,8},{2,6},{3,4},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,4,2,6,8,1,3] => {{1,7},{2,5,6,8},{3,4}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,2,8,4,3,5,6,7] => {{1},{2},{3,8},{4},{5},{6},{7}} => [1,1,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,8,7,4,3,2,5,6] => {{1},{2,8},{3,7},{4},{5},{6}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,6,3,8,2,4,7,5] => {{1},{2,6},{3},{4,8},{5},{7}} => [1,2,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,3,8,1,2,7,4,6] => {{1,5},{2,3,8},{4},{6,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,5,4,2,6,3,8] => {{1},{2,7},{3,5},{4},{6},{8}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,5,8,2,4,6,3,7] => {{1},{2,5},{3,8},{4},{6},{7}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,4,6,2,8,3,7,5] => {{1},{2,4},{3,6},{5,8},{7}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,1,6,7,2,4,8] => {{1,5,7},{2,3},{4,6},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,6,1,2,8,4,7] => {{1,5},{2,3,6,8},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,4,5,3,8,6,2] => {{1},{2,7},{3,4,5},{6,8}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,4,1,2,5,8,7] => {{1,6},{2,3,4},{5},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,3,2,4,5,6,7] => {{1},{2,8},{3},{4},{5},{6},{7}} => [1,2,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[8,5,3,2,6,7,1,4] => {{1,8},{2,5,6,7},{3},{4}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,2,6,8,1,7,3] => {{1,4,6},{2,5,8},{3},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,6,7,8,1,3] => {{1,4,6,8},{2},{3,5,7}} => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,2,3,6,7,1,8,4] => {{1,5,7,8},{2},{3},{4,6}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,3,4,1,7,8,5] => {{1,6,7,8},{2},{3},{4},{5}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,2,3,1,4,5,8,6] => {{1,7,8},{2},{3},{4},{5},{6}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,7,5,1,8,2,4,6] => {{1,3,5,8},{2,7},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,2,8,7,3,6] => {{1,4},{2},{3,5,8},{6,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,2,4,6,5,3,7] => {{1,8},{2},{3},{4},{5,6},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,2,5,4,6,3,7] => {{1,8},{2},{3},{4,5},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,7,5,4,2,8,3,6] => {{1},{2,7},{3,5},{4},{6,8}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,1,4,8,2,7,3,6] => {{1,5},{2},{3,4,8},{6,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,6,8,2,7,3,5] => {{1},{2,4,8},{3,6,7},{5}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,7,6,2,8,3,5] => {{1},{2,4,6,8},{3,7},{5}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,4,7,2,8,3,6] => {{1,5},{2},{3,4,7},{6,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,4,5,2,8,3,6] => {{1},{2,7},{3,4,5},{6,8}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,5,1,2,8,4,6] => {{1,3,5},{2,7},{4},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,8,2,7,3,6] => {{1,4,8},{2},{3,5},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,6,2,8,7,3,5] => {{1},{2,4},{3,6,7},{5,8}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,2,8,6,7,3,5] => {{1},{2,4,8},{3},{5,6,7}} => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,2,6,4,8,7,5] => {{1,3},{2},{4,6,8},{5},{7}} => [2,1,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,7,6,3,4,8,5] => {{1,2},{3,7,8},{4,6},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,7,2,6,8,3,5] => {{1},{2,4},{3,7},{5,6,8}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,3,6,8,5,7,4] => {{1},{2},{3},{4,6},{5,8},{7}} => [1,1,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,4,2,7,8,3,6] => {{1,5,7},{2},{3,4},{6,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,2,7,6,8,3,5] => {{1},{2,4,7},{3},{5,6,8}} => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,2,6,8,7,3,5] => {{1},{2,4,6,7},{3},{5,8}} => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,2,7,6,4,8,5] => {{1,3},{2},{4,7,8},{5,6}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,7,1,8,2,4,6] => {{1,5,8},{2,3,7},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,7,3,4,2,5,6] => {{1},{2,8},{3,7},{4},{5},{6}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,4,2,7,8,3,6,5] => {{1},{2,4,7},{3},{5,8},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,3,7,8,5,6,4] => {{1},{2},{3},{4,7},{5,8},{6}} => [1,1,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,3,8,7,5,6,4] => {{1},{2},{3},{4,8},{5,7},{6}} => [1,1,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[10,1,2,3,4,5,6,7,8,9] => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 9

[5,6,3,8,2,1,4,7] => {{1,5},{2,6},{3},{4,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,6,4,8,2,5,1,7] => {{1,3,4,8},{2,6},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,4,8,3,5,7,1] => {{1,2,6},{3,4,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,4,7,2,5,1,8] => {{1,3,4,7},{2,6},{5},{8}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,3,7,2,1,5,8] => {{1,4,7},{2,6},{3},{5},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,3,2,1,6,5,7] => {{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,5,3,2,7,1,6,8] => {{1,4},{2,5,7},{3},{6},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,5,4,2,8,6,1,7] => {{1,3,4},{2,5,8},{6},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,3,2,1,7,5,6] => {{1,8},{2,4},{3},{5},{6,7}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,3,2,1,7,6,5] => {{1,8},{2,4},{3},{5},{6,7}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,6,3,8,2,1,7,4] => {{1,5},{2,6},{3},{4,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,5,4,2,7,6,1,3] => {{1,8},{2,5,7},{3,4},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,4,2,8,6,1,3] => {{1,7},{2,5,8},{3,4},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,4,2,8,7,1,3] => {{1,6,7},{2,5,8},{3,4}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,6,5,8,7,2,1,3] => {{1,4,8},{2,6},{3,5,7}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,5,4,2,7,8,1,3] => {{1,6,8},{2,5,7},{3,4}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,5,3,2,6,1,8,4] => {{1,7,8},{2,5,6},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,3,7,2,1,8,4] => {{1,5},{2,6},{3},{4,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,3,7,2,1,8,5] => {{1,4,7,8},{2,6},{3},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,4,7,2,8,1,5] => {{1,3,4,7},{2,6,8},{5}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,3,2,7,1,8,6] => {{1,4},{2,5,7,8},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,3,2,1,6,7,5] => {{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,4,3,2,1,5,7,6] => {{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,2,6,4,8,5,1,7] => {{1,3,6},{2},{4},{5,8},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,5,2,3,7,1,6,8] => {{1,4},{2,5,7},{3},{6},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,5,4,2,8,6,7] => {{1,3,5},{2},{4},{6,8},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,8,5,2,1,6,7] => {{1,4,5},{2,3,8},{6},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,7,3,2,6,8] => {{1,4,7},{2,5},{3},{6},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,5,1,3,7,2,6,8] => {{1,4},{2,5,7},{3},{6},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,2,1,4,3,7,8,6] => {{1,5},{2},{3},{4},{6,7,8}} => [2,1,1,1,3] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,1,4,2,7,6,8] => {{1,5},{2,3},{4},{6,7},{8}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,1,5,7,2,6,8] => {{1,4,5,7},{2,3},{6},{8}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,6,1,7,2,5,8] => {{1,4},{2,3,6},{5,7},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,4,1,3,7,8,5] => {{1,6,7,8},{2},{3,4},{5}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,4,1,2,7,5,8] => {{1,3,4},{2,6,7},{5},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,2,7,3,1,6,8] => {{1,4,7},{2,5},{3},{6},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,5,2,7,4,6,1,8] => {{1,3},{2,5},{4,7},{6},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,3,1,4,6,8,2,5] => {{1,7},{2,3},{4},{5,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,1,5,3,7,8] => {{1,4},{2},{3,6},{5},{7},{8}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,4,1,5,6,2,3,8] => {{1,7},{2,4,5,6},{3},{8}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,1,5,2,6,4,8] => {{1,7},{2,3},{4,5},{6},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,2,5,1,3,7,8,4] => {{1,6,7,8},{2},{3,5},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,1,2,7,4,8] => {{1,6,7},{2,3,5},{4},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,5,1,7,2,3,8] => {{1,6},{2,4},{3,5,7},{8}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,5,1,7,2,3,8] => {{1,4},{2,6},{3,5,7},{8}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,5,1,2,7,4,8] => {{1,3,5},{2,6,7},{4},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,2,1,4,7,8,3] => {{1,6,7,8},{2,5},{3},{4}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,5,1,2,8,7,6] => {{1,3,5},{2,4},{6,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,4,5,3,2,7,6] => {{1},{2,8},{3,4,5},{6},{7}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,4,8,5,3,1,7,6] => {{1,2,4,5},{3,8},{6},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,5,8,2,1,7,6] => {{1,3,5},{2,4,8},{6},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,6,2,1,7,8,5] => {{1,3,6,7,8},{2,4},{5}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,6,2,7,1,4,8] => {{1,3,6},{2,5,7},{4},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,2,7,8,1,4] => {{1,3,6,8},{2,5,7},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,6,2,8,7,1,5] => {{1,3,6,7},{2,4},{5,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,6,8,2,7,1,5] => {{1,3,6,7},{2,4,8},{5}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,8,6,3,7,1,5] => {{1,2,4,6,7},{3,8},{5}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,8,4,6,3,7,2,5] => {{1},{2,8},{3,4,6,7},{5}} => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,4,6,3,7,5,2] => {{1},{2,8},{3,4,6,7},{5}} => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,6,8,2,7,5,1] => {{1,3,6,7},{2,4,8},{5}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,6,2,8,7,5,1] => {{1,3,6,7},{2,4},{5,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,6,2,7,8,4,1] => {{1,3,6,8},{2,5,7},{4}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,6,2,7,4,1,8] => {{1,3,6},{2,5,7},{4},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,7,2,8,3,1] => {{1,4,7},{2,5},{3,6,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,6,8,7,2,4,1] => {{1,3,6},{2,5,7},{4,8}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,5,8,6,7,3,4,1] => {{1,2,5,7},{3,8},{4,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,8,5,6,7,3,4,2] => {{1},{2,8},{3,5,7},{4,6}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,5,6,7,3,2,4] => {{1},{2,8},{3,5,7},{4,6}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,6,7,3,1,4] => {{1,2,5,7},{3,8},{4,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,6,8,7,2,1,4] => {{1,3,6},{2,5,7},{4,8}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,6,7,2,1,8,3] => {{1,4,7,8},{2,5},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,6,1,8,7,2,5] => {{1,3,6,7},{2,4},{5,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,1,6,8,7,3,5] => {{1,2,4,6,7},{3},{5,8}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,1,8,6,7,4,5] => {{1,2,3},{4,8},{5,6,7}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,8,3,2,6,7,5,4] => {{1},{2,8},{3},{4},{5,6,7}} => [1,2,1,1,3] => ([(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,5,1,6,7,8,4,3] => {{1,2,5,7},{3},{4,6,8}} => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,5,1,6,7,4,8,3] => {{1,2,5,7,8},{3},{4,6}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,6,1,7,4,2,8] => {{1,3,6},{2,5,7},{4},{8}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,6,1,8,7,5,2] => {{1,3,6,7},{2,4},{5,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,6,8,1,7,5,2] => {{1,3,6,7},{2,4,8},{5}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,8,6,1,7,5,3] => {{1,2,4,6,7},{3,8},{5}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,8,4,6,2,7,5,3] => {{1},{2,8},{3,4,6,7},{5}} => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,5,6,7,2,4,3] => {{1},{2,8},{3,5,7},{4,6}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,6,7,1,4,3] => {{1,2,5,7},{3,8},{4,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,6,8,7,1,4,2] => {{1,3,6},{2,5,7},{4,8}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,6,7,8,1,3,2] => {{1,4,7},{2,5,8},{3,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,6,7,1,3,8,2] => {{1,4,7,8},{2,5},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,5,6,7,1,3,2,8] => {{1,4,7},{2,5},{3,6},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,6,7,3,1,8,2] => {{1,4,7,8},{2,5},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,6,8,7,4,1,2] => {{1,3,6},{2,5,7},{4,8}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,5,8,6,7,4,1,3] => {{1,2,5,7},{3,8},{4,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,8,5,6,7,4,2,3] => {{1},{2,8},{3,5,7},{4,6}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,5,6,7,4,3,2] => {{1},{2,8},{3,5,7},{4,6}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,6,7,4,3,1] => {{1,2,5,7},{3,8},{4,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,2,5,6,1,8,3,7] => {{1,4,6,8},{2},{3,5},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,6,1,7,3,8] => {{1,4,6,7},{2},{3,5},{8}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,8,2,4,7,1,5] => {{1,3,8},{2,6,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,5,6,7,1,8,2] => {{1,4,6},{2,3,5,7,8}} => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2

[3,7,1,5,6,8,2,4] => {{1,3},{2,7},{4,5,6,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,7,1,5,8,2,4,6] => {{1,3},{2,7},{4,5,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,2,4,6,1,5,8] => {{1,7},{2,3},{4},{5,6},{8}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,5,1,7,4,6,8] => {{1,3,5,7},{2},{4},{6},{8}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,5,1,8,4,6,7] => {{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,5,1,7,8,4,6] => {{1,3,5,7},{2},{4},{6,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,3,2,4,6,1,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,1,5,7,8,3,2,4] => {{1,6},{2},{3,5,8},{4,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,6,1,7,8,3] => {{1,4,6,7,8},{2},{3,5}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,7,6,1,8,3,4,2] => {{1,5,8},{2,7},{3,6},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,6,1,7,3,4,2] => {{1,5,7},{2,8},{3,6},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,5,8,7,3,2,4] => {{1,6},{2},{3,5,7},{4,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,3,2,4,6,1,5] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,2,5,1,8,7,4,6] => {{1,3,5,8},{2},{4},{6,7}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,4,1,8,7,5,6] => {{1,3,4},{2},{5,8},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,1,6,8,7,4] => {{1,3,5,6,8},{2},{4},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,6,5,1,7,4,2] => {{1,3,6,7},{2,8},{4,5}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,7,6,5,1,8,4,2] => {{1,3,6,8},{2,7},{4,5}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,5,1,7,8,4,2,3] => {{1,6},{2,5,8},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,1,6,7,8,4] => {{1,3,5,6,7,8},{2},{4}} => [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,2,4,1,6,8,5,7] => {{1,3,4},{2},{5,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,1,8,4,7,6] => {{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,2,3,7,5,1,6] => {{1,8},{2,4},{3},{5,7},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,6,1,7,3,5,2] => {{1,8},{2,4},{3,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,1,6,4,2,3,8] => {{1,7},{2,5},{3},{4,6},{8}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,5,1,7,6,4,8] => {{1,3,5,7},{2},{4},{6},{8}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,5,1,8,6,4,7] => {{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,6,1,5,7,3,2,4] => {{1,8},{2,6},{3},{4,5,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,6,1,7,3,4,2] => {{1,8},{2,5,7},{3,6},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,1,6,7,4,2,3] => {{1,8},{2,5,7},{3},{4,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,1,8,6,7,4] => {{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,4,1,5,8,6,7] => {{1,3,4},{2},{5},{6,8},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,5,1,7,8,6,4] => {{1,3,5,7},{2},{4},{6,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,5,1,6,4,2,3] => {{1,7},{2,8},{3,5,6},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,5,1,7,6,4,2] => {{1,3,5,7},{2,8},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,5,1,8,6,4,2] => {{1,3,5,8},{2,7},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,5,1,6,4,2,3] => {{1,8},{2,7},{3,5,6},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,1,8,7,6,4] => {{1,3,5,8},{2},{4},{6,7}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,3,1,8,4,2] => {{1,6,8},{2,5},{3,7},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,3,7,1,8,5,2] => {{1,4,7},{2,6,8},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,3,7,5,1,8,2] => {{1,4,7,8},{2,6},{3},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,7,4,1,6,8,3] => {{1,2,5},{3,7,8},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,7,3,6,1,8,2] => {{1,5,6},{2,4},{3,7,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,7,8,3,1,6,2] => {{1,5},{2,4,8},{3,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,3,8,5,1,7,2] => {{1,6},{2,4,8},{3},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,8,4,3,6,1,7,2] => {{1,5,6},{2,8},{3,4},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,8,3,6,1,7,2] => {{1,5,6},{2,4},{3,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,4,6,8,1,7,3] => {{1,2,5,8},{3,4,6},{7}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,6,2,1,8,5,7,3] => {{1,4},{2,6},{3},{5,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,4,1,7,5,8,6,3] => {{1,2,4,7},{3},{5},{6,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,7,5,3,8,6] => {{1,2,4,7,8},{3},{5},{6}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,4,1,8,5,3,7] => {{1,2,6},{3,4},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,6,1,8,4,7] => {{1,3,5},{2},{4,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,6,8,5,4,7] => {{1,3},{2},{4,6},{5,8},{7}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,7,1,5,4,8,6] => {{1,3,7,8},{2},{4},{5},{6}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,7,1,5,8,6,4] => {{1,3,7},{2},{4},{5},{6,8}} => [3,1,1,1,2] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,8,3,2,6,7,1,5] => {{1,4},{2,8},{3},{5,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,6,7,1,5,8] => {{1,4,6},{2,3},{5,7},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,7,8,2,6,1,5] => {{1,4,8},{2,3,7},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,7,4,8,1,6,3] => {{1,2,5,8},{3,7},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,7,8,1,6,4] => {{1,3,5,8},{2},{4,7},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,7,1,6,8,4] => {{1,3,5},{2},{4,7,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,2,7,1,5,4,8] => {{1,6},{2,3},{4,7},{5},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,2,7,1,5,8,4] => {{1,6},{2,3},{4,7,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,2,7,8,1,5,4] => {{1,6},{2,3},{4,7},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,1,7,8,5,3] => {{1,4},{2},{3,6,8},{5,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,2,1,7,8,4,3] => {{1,6,8},{2,5,7},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,5,3,8,6,4] => {{1,2},{3,7},{4,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,2,7,1,4,8,5] => {{1,6},{2,3},{4,7,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,2,1,7,8,4,6] => {{1,3},{2,5,7},{4},{6,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,2,1,7,3,6] => {{1,5},{2,8},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,2,1,8,3,7,5] => {{1,4},{2,6},{3},{5,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,4,1,7,3,8,6,5] => {{1,2,4,7},{3},{5},{6,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,7,1,4,8,6,5] => {{1,3,7},{2},{4},{5},{6,8}} => [3,1,1,1,2] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,5,8,2,1,7,4,6] => {{1,3,8},{2,5},{4},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,7,2,8,1,5,6] => {{1,4},{2,3,7},{5,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,2,8,1,7,4,6] => {{1,3},{2,5},{4,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,4,7,5,8,6] => {{1,3},{2},{4},{5,7,8},{6}} => [2,1,1,3,1] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,8,3,2,1,5,6,7] => {{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,3,1,5,4,8,7] => {{1,6},{2},{3},{4},{5},{7,8}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,2,5,3,4,1,7,6] => {{1,8},{2},{3,5},{4},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,5,3,4,1,8,7] => {{1,6},{2},{3,5},{4},{7,8}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,1,5,2,4,3,8,7] => {{1,6},{2},{3,5},{4},{7,8}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,4,5,1,3,2,8,7] => {{1,6},{2,4},{3,5},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,5,3,4,2,8,7] => {{1,6},{2},{3,5},{4},{7,8}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,5,1,4,2,8,7] => {{1,6},{2,3,5},{4},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,5,2,4,1,7,6] => {{1,8},{2,3,5},{4},{6},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,3,7,5,6,2,4,1] => {{1,8},{2,3,7},{4,5,6}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,7,2,4,1,6,5] => {{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,3,5,1,4,2,7,6] => {{1,8},{2,3,5},{4},{6},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,1,5,3,4,2,7,6] => {{1,8},{2},{3,5},{4},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,1,8,4,5,3,7,6] => {{1,2},{3,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,3,7,5,6,1,4,2] => {{1,8},{2,3,7},{4,5,6}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,5,7,3,6,1,4,2] => {{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,4,6,2,5,1] => {{1,8},{2,3,7},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,4,6,1,5,2] => {{1,8},{2,3,7},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,1,6,4,5,2] => {{1,8},{2,3,7},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,1,6,2,5,4] => {{1,8},{2,3,7},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,2,6,4,5,1] => {{1,8},{2,3,7},{4},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,3,2,7,4,6,5] => {{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,5,2,4,3,7,6] => {{1,8},{2},{3,5},{4},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,2,3,1,7,4,6,5] => {{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,2,3,1,5,4,7,6] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[4,2,3,1,8,5,7,6] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,1,3,2,8,6,7,5] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,2,3,1,7,5,6,4] => {{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,5,7,2,6,3,4,1] => {{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,7,2,6,1,4,3] => {{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,6,7,3,5,4] => {{1,2},{3,8},{4,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,3,2,7,5,6,4] => {{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,4,7,2,6,3,5,1] => {{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,7,2,6,1,5,3] => {{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,7,1,6,2,5,3] => {{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,7,1,6,2,4,3] => {{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,8,5,7,3,6,4] => {{1,2},{3,8},{4,5,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,7,4,6,1,3,2] => {{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,7,1,6,3,4,2] => {{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,7,1,6,3,5,2] => {{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,7,3,6,1,5,2] => {{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,3,6,1,7,5] => {{1,2,4},{3,8},{5,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,8,6,3,2,7,1] => {{1,4,6},{2,5},{3,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,8,7,3,1,2,4] => {{1,6},{2,5},{3,8},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,4,6,1,5,7,3] => {{1,2,8},{3,4,6},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,6,8,4,5,7,1] => {{1,2,3,6},{4,8},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,8,4,1,5,2] => {{1,6},{2,3,7},{4,8},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,7,8,4,6,5,2] => {{1},{2,3,7},{4,8},{5},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,1,7,8,2,4,6,3] => {{1,5},{2},{3,7},{4,8},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,6,7,8,4,2,5,1] => {{1,3,7},{2,6},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,8,7,3,2,1,4] => {{1,5},{2,6},{3,8},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,7,8,1,4,6,3] => {{1,5},{2},{3,7},{4,8},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,7,8,5,4,6,3] => {{1},{2},{3,7},{4,8},{5},{6}} => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,2,1,3,8,5,6,7] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,4,8,5,2,3,1,7] => {{1,6},{2,4,5},{3,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,8,2,4,6,1] => {{1,7},{2,3,5},{4,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,1,2,8,5,6,7] => {{1,4},{2,3},{5,8},{6},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,7,6,8,4,3,5,1] => {{1,2,7},{3,6},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,5,8,1,4,6,2] => {{1,3,5},{2,7},{4,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,8,5,1,3,2,7] => {{1,4,5},{2,6},{3,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,8,6,3,4,2,1] => {{1,7},{2,5},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,3,6,5,1,7] => {{1,2,4},{3,8},{5,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,4,1,5,6,3,7] => {{1,2,8},{3,4},{5},{6},{7}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,3,2,8,5,6,7] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,3,2,8,5,4,6,1] => {{1,7},{2,3},{4,8},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,4,8,2,5,3,1,7] => {{1,6},{2,4},{3,8},{5},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,8,4,3,5,1,6,7] => {{1,2,8},{3,4},{5},{6},{7}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,8,3,4,5,1,6,7] => {{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,8,4,5,3,1,7] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,2,3,1,8,5,6,7] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,8,4,5,3,7,6] => {{1},{2},{3,8},{4},{5},{6},{7}} => [1,1,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[1,8,4,2,5,3,6,7] => {{1},{2,8},{3,4},{5},{6},{7}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,5,3,2,4,6,7] => {{1,8},{2},{3,5},{4},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,8,5,4,3,6,7] => {{1},{2},{3,8},{4,5},{6},{7}} => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,2,7,4,8,3,6] => {{1,5},{2},{3},{4,7},{6,8}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,3,5,1,4,7,2,6] => {{1,8},{2,3,5},{4},{6,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,1,5,4,7,3,6] => {{1,2,8},{3},{4,5},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,1,2,8,7,3,5] => {{1,6,7},{2,4},{3},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,1,4,8,2,5] => {{1,6,8},{2,3,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,2,7,8,5,3,6] => {{1},{2,4,7},{3},{5,8},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,6,1,3,2,4,8,5] => {{1,7,8},{2,6},{3},{4},{5}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,5,8,3,7,4,6] => {{1},{2},{3,5},{4,8},{6,7}} => [1,1,2,2,2] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,2,8,7,4,5,3,6] => {{1},{2},{3,8},{4,7},{5},{6}} => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,3,7,1,5,2,4,6] => {{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,8,6,1,4,7,2,5] => {{1,3,6,7},{2,8},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,4,8,1,6,2,5] => {{1,3,4,8},{2,7},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,8,7,1,6,2,5] => {{1,3,8},{2,4,7},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,1,7,6,4,3,5] => {{1,2,8},{3},{4,7},{5,6}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,3,4,1,5,2,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,3,4,1,6,2,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,8,3,4,1,7,2,5] => {{1,6,7},{2,8},{3},{4},{5}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,8,3,4,1,5,2,7] => {{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,6,2,8,3,4,1,7] => {{1,5},{2,6},{3},{4,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,8,3,5,1,7,2,6] => {{1,4,5},{2,8},{3},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,3,5,1,8,2,6] => {{1,4,5},{2,7},{3},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,2,5,1,8,3,7] => {{1,4,5},{2,6,8},{3},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,8,3,7,2,6] => {{1,4,8},{2,5},{3},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,7,3,8,2,6] => {{1,4,7},{2,5},{3},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,2,7,3,8,1,5] => {{1,4,7},{2,6,8},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,7,3,8,1,4] => {{1,5},{2,6,8},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,7,4,8,1,3] => {{1,5},{2,6,8},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,3,8,4,7,1,2] => {{1,5},{2,6,7},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,8,4,7,1,3] => {{1,5},{2,6,7},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,8,3,7,1,4] => {{1,5},{2,6,7},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,2,8,3,7,1,5] => {{1,4,8},{2,6,7},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,7,3,6,2,8] => {{1,4,7},{2,5},{3},{6},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[9,2,1,3,4,5,6,7,8] => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 8

[10,2,1,3,4,5,6,7,8,9] => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 9

[9,2,3,1,4,5,6,7,8] => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 8

[6,5,3,2,1,4,8,7] => {{1,6},{2,5},{3},{4},{7,8}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,6,3,5,2,1,8,7] => {{1,4,5},{2,6},{3},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,2,4,5,7,3,1] => {{1,6,7},{2,8},{3},{4},{5}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,7,2,4,5,3,1,6] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,3,7,4,5,2,1,6] => {{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,8,4,5,7,2,1] => {{1,6,7},{2,3,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,8,5,7,4,3] => {{1,2},{3,6,7},{4,8},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,3,5,1,7,4,2] => {{1,6,7},{2,8},{3},{4,5}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,4,7,6,3,1] => {{1,2,5,7},{3,8},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,1,3,5,6,7,2] => {{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,8,1,2,5,6,7,4] => {{1,3},{2,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,7,1,4,2,6,3,5] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,7,2,4,1,6,3,5] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,6,8,4,5,7,1,3] => {{1,2,6,7},{3,8},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,3,5,1,7,2,4] => {{1,6,7},{2,8},{3},{4,5}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,2,1,5,6,7,3] => {{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,4,8,2,5,6,7,1] => {{1,3,8},{2,4},{5},{6},{7}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,5,3,8,6,1,7,2] => {{1,4,8},{2,5,6},{3},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,7,3,6,8,4,2] => {{1},{2,5,6,8},{3,7},{4}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,3,7,6,1,5,2] => {{1,8},{2,4,7},{3},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,7,3,6,4,8,1] => {{1,5,6},{2},{3,7,8},{4}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,4,7,6,1,5,2] => {{1,8},{2,3,4,7},{5,6}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,1,3,7,6,8,5,2] => {{1,4,7},{2},{3},{5,6,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,7,3,6,8,4,2] => {{1,5,6,8},{2},{3,7},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,3,6,1,4,2] => {{1,5,6},{2,8},{3,7},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,3,7,6,1,5,2] => {{1,4,7},{2,8},{3},{5,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,4,7,1,6,5,3] => {{1,2,8},{3,4,7},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,3,2,7,6,5,4] => {{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,2,3,1,7,6,5,4] => {{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,4,2,7,8,6,5,3] => {{1},{2,4,7},{3},{5,8},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,2,7,1,6,5,3] => {{1,8},{2,4,7},{3},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,7,2,8,6,4,3] => {{1},{2,5,8},{3,7},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,5,7,1,8,6,4,3] => {{1,2,5,8},{3,7},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,7,6,8,1,3,2] => {{1,5,8},{2,4,6},{3,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,5,7,8,1,6,4,3] => {{1,2,5},{3,7},{4,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,7,2,6,5,3] => {{1,8},{2,4,7},{3},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,8,7,2,6,5,3] => {{1},{2,4,7},{3,8},{5},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,8,7,6,1,5,2] => {{1,4,7},{2,3,8},{5,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,2,7,8,1,6,4,3] => {{1,5},{2},{3,7},{4,8},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,2,1,3,7,6,5,4] => {{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,7,8,2,6,4,3] => {{1,5},{2},{3,7},{4,8},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,1,2,3,7,6,5,4] => {{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,7,1,5,8,2,6,4] => {{1,3},{2,7},{4,5,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,1,5,8,3,6,4] => {{1,2,7},{3},{4,5,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,5,1,8,3,7,4] => {{1,2,6},{3,5,8},{4},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,5,1,8,2,7,4] => {{1,3,5,8},{2,6},{4},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,4,5,7,6,2,3] => {{1,8},{2},{3,4,5,7},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,1,8,2,7,4] => {{1,3,6},{2,5,8},{4},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,6,1,8,3,7,4] => {{1,2,5,8},{3,6},{4},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,1,3,8,7,5] => {{1,2,4},{3,6,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,6,1,2,8,7,5] => {{1,3,6,8},{2,4},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,6,1,2,8,7,5] => {{1,4},{2,3,6,8},{5},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,6,1,8,2,7,4] => {{1,5,8},{2,3,6},{4},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,1,5,8,2,6,4] => {{1,7},{2,3},{4,5,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,6,1,4,8,7,5] => {{1,2,3,6,8},{4},{5},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,3,1,8,7,6] => {{1,4},{2},{3,5},{6,8},{7}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,2,1,4,3,8,6,5] => {{1,7},{2},{3},{4},{5},{6,8}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,2,4,3,7,6,5] => {{1,8},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,3,4,2,7,6,5] => {{1,8},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,3,4,1,2,8,7,5] => {{1,6,8},{2,3,4},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,4,1,2,8,7,5] => {{1,3,4},{2,6,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,4,1,3,8,7,5] => {{1,2,6,8},{3,4},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,2,3,1,8,7,6] => {{1,5},{2,4},{3},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,5,2,4,1,8,7,6] => {{1,3},{2,5},{4},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,2,1,4,8,7,5] => {{1,6,8},{2,3},{4},{5},{7}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,1,3,2,4,7,6,5] => {{1,8},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,2,3,4,7,6,5] => {{1,8},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,2,1,3,4,8,6,5] => {{1,7},{2},{3},{4},{5},{6,8}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,3,1,4,8,7,5] => {{1,6,8},{2},{3},{4},{5},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,4,3,6,1,5,8,7] => {{1,2,4,6},{3},{5},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,6,5,8,1,7] => {{1,2,4,6,8},{3},{5},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,3,5,8,7,1] => {{1,2,4},{3,6,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,3,5,8,1,7] => {{1,2,4},{3,6,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,3,5,1,8,7] => {{1,2,4},{3,6},{5},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,3,1,5,8,7] => {{1,2,4},{3,6},{5},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,6,5,3,8,7] => {{1,2,4,6},{3},{5},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,1,5,3,8,7] => {{1,2,4},{3,6},{5},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,5,3,1,8,7] => {{1,4,5},{2},{3,6},{7,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,5,1,3,8,7] => {{1,4,5},{2},{3,6},{7,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,5,1,8,7,3] => {{1,4,5},{2},{3,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,5,8,1,7,3] => {{1,4,5,8},{2},{3,6},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,5,8,1,3,7] => {{1,4,5,8},{2},{3,6},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,5,8,3,1,7] => {{1,4,5,8},{2},{3,6},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,1,5,8,3,7] => {{1,2,4},{3,6,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,6,5,8,3,7] => {{1,2,4,6,8},{3},{5},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,6,5,8,3,7] => {{1,2},{3,4,6,8},{5},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,6,5,8,7,3] => {{1,2,4,6,8},{3},{5},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,1,5,8,7,3] => {{1,2,4},{3,6,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,5,3,8,7,1] => {{1,4,5},{2},{3,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,5,8,3,7,1] => {{1,4,5,8},{2},{3,6},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,4,3,8,7,1,5] => {{1,2,6,7},{3,4},{5,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,6,4,3,8,7,5,1] => {{1,2,6,7},{3,4},{5,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,2,6,8,5,3,7,1] => {{1,4,8},{2},{3,6},{5},{7}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,4,6,8,1,5,7,3] => {{1,2,4,8},{3,6},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,1,8,5,7,3] => {{1,2,4},{3,6},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,6,8,5,7,3] => {{1,2,4,6},{3},{5,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,6,8,5,7,3] => {{1,2},{3,4,6},{5,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,6,8,5,3,7] => {{1,2},{3,4,6},{5,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,6,8,5,3,7] => {{1,2,4,6},{3},{5,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,1,8,5,3,7] => {{1,2,4},{3,6},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,8,1,5,3,7] => {{1,2,4,8},{3,6},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,8,5,3,1,7] => {{1,4,8},{2},{3,6},{5},{7}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,6,8,5,1,3,7] => {{1,4,8},{2},{3,6},{5},{7}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,6,8,5,1,7,3] => {{1,4,8},{2},{3,6},{5},{7}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,4,6,8,3,5,7,1] => {{1,2,4,8},{3,6},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,8,3,5,1,7] => {{1,2,4,8},{3,6},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,8,3,1,5,7] => {{1,2,4,8},{3,6},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,3,1,8,5,7] => {{1,2,4},{3,6,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,3,8,1,5,7] => {{1,2,4},{3,6},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,3,8,5,1,7] => {{1,2,4},{3,6},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,3,8,5,7,1] => {{1,2,4},{3,6},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,6,8,5,7,1] => {{1,2,4,6},{3},{5,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,6,8,5,1,7] => {{1,2,4,6},{3},{5,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,6,8,1,5,7] => {{1,2,4,6},{3},{5,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,6,1,8,5,7] => {{1,2,4,6,8},{3},{5},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,1,6,8,5,7] => {{1,2,4},{3},{5,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,3,6,8,7,5] => {{1,2,4},{3},{5,6,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,6,1,8,7,5] => {{1,2,4,6,8},{3},{5},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,3,6,8,1,7,5] => {{1,2,4,6},{3},{5,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,3,8,1,7,5] => {{1,2,4},{3,6},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,3,1,8,7,5] => {{1,2,4},{3,6,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,6,3,8,7,5] => {{1,2,4,6,8},{3},{5},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,6,3,8,7,5] => {{1,2},{3,4,6,8},{5},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,6,8,3,7,5] => {{1,2},{3,4,6},{5,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,6,8,3,7,5] => {{1,2,4,6},{3},{5,8},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,1,8,3,7,5] => {{1,2,4},{3,6},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,8,1,3,7,5] => {{1,2,4,8},{3,6},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,8,3,1,7,5] => {{1,2,4,8},{3,6},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,2,8,5,7,3,1] => {{1,4,8},{2,6,7},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,2,8,5,7,1,3] => {{1,4,8},{2,6,7},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,4,8,7,1,3,5] => {{1,6},{2},{3,4,8},{5,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,2,8,7,5,3,1] => {{1,6},{2,4,8},{3},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,4,1,8,7,5,3] => {{1,2,6,7},{3,4},{5,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,6,1,4,8,7,5,3] => {{1,2,6,7},{3},{4},{5,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,4,8,7,5,3] => {{1,2},{3,6,7},{4},{5,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,4,8,7,3,5] => {{1,2},{3,6,7},{4},{5,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,1,4,8,7,3,5] => {{1,2,6,7},{3},{4},{5,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,4,1,8,7,3,5] => {{1,2,6,7},{3,4},{5,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,4,2,8,7,5,1,3] => {{1,6},{2,4,8},{3},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,4,8,7,3,5,1] => {{1,6},{2},{3,4,8},{5,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,4,8,7,3,1,5] => {{1,6},{2},{3,4,8},{5,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,4,7,3,8,2,5] => {{1},{2,6,8},{3,4,7},{5}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,4,7,3,6,8,1] => {{1,5},{2},{3,4,7,8},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,4,7,3,8,2,6] => {{1,5},{2},{3,4,7},{6,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,1,7,5,8,2,6] => {{1,4,7},{2,3},{5},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,6,3,7,1,4,5] => {{1,2,8},{3,6},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,2,4,8,3,6,7] => {{1,5,8},{2},{3},{4},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,3,6,1,5,8,2,7] => {{1,4},{2,3,6,8},{5},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,1,3,7,2,4,6] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,3,2,8,4,6,7] => {{1},{2,5,8},{3},{4},{6},{7}} => [1,3,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,3,5,2,1,8,6,7] => {{1,4},{2,3,5},{6,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,4,8,7,1,3,5] => {{1,2,6},{3,4,8},{5,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,6,4,8,7,2,3,5] => {{1},{2,6},{3,4,8},{5,7}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,8,3,6,1,4,5] => {{1,2,7},{3,8},{4},{5,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,2,8,7,1,5,6] => {{1,4,8},{2,3},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,4,8,7,1,3,6] => {{1,5,7},{2},{3,4,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,8,3,7,1,4,5] => {{1,6},{2},{3,8},{4},{5,7}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,1,4,8,7,2,3,6] => {{1,5,7},{2},{3,4,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,2,5,1,3,8,6] => {{1,4,5},{2,7,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,2,1,5,4,7,6] => {{1,3},{2,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,3,2,1,5,4,6,7] => {{1,8},{2,3},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,3,2,1,5,6,4,7] => {{1,8},{2,3},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,3,2,1,4,6,5,7] => {{1,8},{2,3},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,8,2,1,4,5,7,6] => {{1,3},{2,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,2,7,1,4,6,8,5] => {{1,3,7,8},{2},{4},{5},{6}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,8,1,4,6,7,5] => {{1,3,8},{2},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,8,2,5,1,7,3,6] => {{1,4,5},{2,8},{3},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,2,5,1,8,3,6] => {{1,4,5},{2,7},{3},{6,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,7,5,8,6,4] => {{1,3},{2},{4,7},{5},{6,8}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,7,1,6,8,4,5] => {{1,3,7},{2},{4},{5,6,8}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,7,6,1,8,3,5] => {{1,4,6,8},{2},{3,7},{5}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,8,6,7,1,2,5] => {{1,4,6},{2,3,8},{5,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,2,8,6,1,7,3,5] => {{1,4,6,7},{2},{3,8},{5}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,8,1,6,7,4,5] => {{1,3,8},{2},{4},{5,6,7}} => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,8,7,5,6,4] => {{1,3},{2},{4,8},{5,7},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,7,1,6,4,8,5] => {{1,3,7,8},{2},{4},{5,6}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,7,6,1,3,8,5] => {{1,4,6},{2},{3,7,8},{5}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,8,1,3,7,5] => {{1,4,8},{2},{3,6},{5},{7}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,6,7,1,3,8,5] => {{1,4,7,8},{2},{3,6},{5}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,6,1,8,4,7,5] => {{1,3,6},{2},{4},{5,8},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,7,8,6,1,2,5] => {{1,4,8},{2,3,7},{5,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,2,1,6,8,5,7,4] => {{1,3},{2},{4,6},{5,8},{7}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,6,1,8,7,4,5] => {{1,3,6,7},{2},{4},{5,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,8,1,7,3,5] => {{1,4,8},{2},{3,6,7},{5}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,7,1,8,3,5] => {{1,4,7},{2},{3,6,8},{5}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,6,1,7,8,4,5] => {{1,3,6,8},{2},{4},{5,7}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,6,2,7,8,5,3] => {{1},{2,4},{3,6,8},{5,7}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,8,5,4,6,1,2] => {{1,7},{2,3,8},{4,5},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,7,5,4,6,1,2] => {{1,3,7},{2,8},{4,5},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,3,5,4,7,1,2] => {{1,6,7},{2,8},{3},{4,5}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,3,5,4,8,1,2] => {{1,7},{2,6,8},{3},{4,5}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,2,5,4,8,7,3] => {{1},{2,6,8},{3},{4,5},{7}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,6,2,8,7,5,3] => {{1,4},{2},{3,6,7},{5,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,1,2,4,6,5,3] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,3,1,4,2,6,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,3,6,1,8,2,7,5] => {{1,4},{2,3,6},{5,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,8,5,4,1,6,7] => {{1,2,3,8},{4,5},{6},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,1,6,4,3,2,8] => {{1,7},{2,5},{3},{4,6},{8}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,4,6,1,5,8,2,7] => {{1,3,6,8},{2,4},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,1,5,3,2,6] => {{1,7},{2,8},{3,4},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,5,1,6,3,2,4] => {{1,7},{2,8},{3,5,6},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,7,6,4,3,2,8] => {{1,5},{2},{3,7},{4,6},{8}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,7,6,4,3,2,5] => {{1},{2,8},{3,7},{4,6},{5}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,6,7,5,8,2,4] => {{1,3,6,8},{2},{4,7},{5}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,2,1,4,5,6,3] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,2,8,5,6,3,7,4] => {{1},{2},{3,8},{4,5,6},{7}} => [1,1,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,1,2,5,7,3,8,4] => {{1,6},{2},{3},{4,5,7,8}} => [2,1,1,4] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,1,5,6,3,7,8] => {{1,4,5,6},{2},{3},{7},{8}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,6,1,5,7,2,8] => {{1,4},{2,3,6,7},{5},{8}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,6,3,7,8,2,4] => {{1,5,7},{2},{3,6,8},{4}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,6,8,5,7,2,4] => {{1},{2,3,6,7},{4,8},{5}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,3,7,1,8,5] => {{1,2,4},{3,6},{5,7,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,3,6,4,8,7,2,5] => {{1},{2,3,6,7},{4},{5,8}} => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,6,7,3,8,2,5] => {{1,4,7},{2},{3,6,8},{5}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,6,1,3,7,2,8] => {{1,5},{2,4},{3,6,7},{8}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,7,5,2,3,8,6] => {{1,4,5},{2},{3,7,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,4,5,8,3,7,6] => {{1},{2},{3,4,5,8},{6},{7}} => [1,1,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,2,3,4,1,6,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,1,4,6,3,2,5] => {{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,6,4,7,8,2,5] => {{1,3,6,8},{2},{4},{5,7}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,5,7,4,3,2,6] => {{1},{2,8},{3,5},{4,7},{6}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,4,7,5,1,3,8,6] => {{1,2,4,5},{3,7,8},{6}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,8,4,6,1,3,2,5] => {{1,7},{2,8},{3,4,6},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,6,4,1,8,2,7] => {{1,3,6,8},{2,5},{4},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,4,5,1,3,8,7] => {{1,2,6},{3,4,5},{7,8}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,6,5,8,4,3,2,7] => {{1},{2,6},{3,5},{4,8},{7}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,6,5,1,4,3,2,8] => {{1,7},{2,6},{3,5},{4},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,4,6,2,7,1,5,8] => {{1,3,6},{2,4},{5,7},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,7,5,4,1,6,8] => {{1,3,7},{2},{4,5},{6},{8}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,6,2,8,1,5,7] => {{1,4},{2,3,6},{5,8},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,2,5,4,7,8,3] => {{1,6,7,8},{2},{3},{4,5}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,4,5,1,3,7,8] => {{1,6},{2},{3,4,5},{7},{8}} => [2,1,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,6,8,1,7,2,5] => {{1,4,8},{2,3,6,7},{5}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,6,4,1,7,2,8] => {{1,5},{2,3,6,7},{4},{8}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,6,3,7,5,8,2] => {{1},{2,4},{3,6},{5,7,8}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,7,2,5,8,1,3] => {{1,4},{2,6,8},{3,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,1,7,5,3,8] => {{1,2,4},{3,6},{5,7},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,4,6,2,8,1,3] => {{1,7},{2,5},{3,4,6,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,7,5,4,3,8,6,2] => {{1},{2,7},{3,5},{4},{6,8}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,8,4,3,6,7,2] => {{1},{2,5},{3,8},{4},{6},{7}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,6,3,2,7,1,8,4] => {{1,5,7,8},{2,6},{3},{4}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,6,3,2,7,1,4] => {{1,8},{2,5},{3,6,7},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,6,2,8,1,7,3] => {{1,5,8},{2,4},{3,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,1,7,8,5,3,6] => {{1,2,4,7},{3},{5,8},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,8,2,1,6,4,7] => {{1,5},{2,3,8},{4},{6},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,7,5,8,2,1,4,6] => {{1,3,5},{2,7},{4,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,2,8,5,1,6,4] => {{1,7},{2,3},{4,8},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,6,4,3,2,1,7,5] => {{1,8},{2,6},{3,4},{5},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,6,4,3,2,1,8,5] => {{1,7,8},{2,6},{3,4},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,4,3,2,1,6,5] => {{1,7},{2,8},{3,4},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,4,7,2,1,8,6,3] => {{1,5},{2,4},{3,7},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,2,5,1,8,4] => {{1,6},{2,3,7,8},{4},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,5,7,8,4,1,3] => {{1,6},{2},{3,5,8},{4,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,7,8,6,3,4] => {{1,2},{3,5,8},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,2,8,1,4,5] => {{1,3,7},{2,6},{4},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,2,8,1,4,5] => {{1,6},{2,3,7},{4},{5,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,2,1,8,4,6] => {{1,7},{2,3,5},{4},{6,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,4,1,3,7,8,6] => {{1,2,5},{3,4},{6,7,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,4,1,7,8,3,6,5] => {{1,2,4,7},{3},{5,8},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,2,8,6,1,4,5] => {{1,3},{2,7},{4,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,8,2,1,7,4,5] => {{1,3,8},{2,6,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,8,2,1,4,7,6] => {{1,5},{2,3,8},{4},{6},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,3,5,2,1,4,7,6] => {{1,8},{2,3,5},{4},{6},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,3,2,8,6,1,4,5] => {{1,7},{2,3},{4,8},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,1,6,3,2,8,7] => {{1,5},{2,4,6},{3},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,1,6,2,3,8,7] => {{1,5},{2,4,6},{3},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,1,6,2,8,3,4] => {{1,5},{2,7},{3},{4,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,1,6,2,8,4,3] => {{1,5},{2,7},{3},{4,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,5,1,8,3,4] => {{1,2,7},{3,6,8},{4,5}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,7,6,5,1,8,4,3] => {{1,2,7},{3,6,8},{4,5}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,6,5,1,4,8,7] => {{1,2,3,6},{4,5},{7,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,6,4,1,5,8,7] => {{1,2,3,6},{4},{5},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,6,1,5,4,8,7] => {{1,2,3,6},{4},{5},{7,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,1,4,8,5,3] => {{1,2,7},{3,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,1,4,8,3,5] => {{1,2,7},{3,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,1,8,4,2,6] => {{1,7},{2,3,5,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,1,8,6,4,2] => {{1,7},{2,3,5,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,1,5,8,4,3] => {{1,2,7},{3,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,4,1,8,5,3] => {{1,2,7},{3,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,6,3,8,5,4] => {{1,2},{3,7},{4,6,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,6,3,8,4,5] => {{1,2},{3,7},{4,6,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,3,6,2,8,4,1] => {{1,5},{2,7},{3},{4,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,4,1,8,3,5] => {{1,2,7},{3,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,1,8,6,2,4] => {{1,7},{2,3,5,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,1,8,2,4,7] => {{1,6},{2,3,5,8},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,8,7,6,1,5] => {{1,2,3,4,8},{5,7},{6}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,8,5,7,1,6] => {{1,2,3,4,8},{5},{6,7}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,3,5,4,8,1,2,6] => {{1,7},{2,3,5,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,3,5,8,7,2,1] => {{1,6,7},{2,4,5,8},{3}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,1,4,5,8,7,3,6] => {{1,2},{3,4,5,8},{6,7}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,4,3,5,8,7,1,2] => {{1,6,7},{2,4,5,8},{3}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,3,5,4,8,1,6,2] => {{1,7},{2,3,5,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,8,7,5,6,1] => {{1,2,3,4,8},{5,7},{6}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,8,7,5,1,6] => {{1,2,3,4,8},{5,7},{6}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,7,6,5,4,8,1,3] => {{1,2,7},{3,6,8},{4,5}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,3,5,6,8,4,1,2] => {{1,7},{2,3,5,8},{4,6}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,3,5,6,8,1,4,2] => {{1,7},{2,3,5,8},{4,6}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,3,5,6,8,1,2,4] => {{1,7},{2,3,5,8},{4,6}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,4,1,5,8,7,2,3] => {{1,6,7},{2,4,5,8},{3}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,4,1,5,8,7,3,2] => {{1,6,7},{2,4,5,8},{3}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,4,1,5,8,3,7,2] => {{1,6},{2,4,5,8},{3},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,1,6,3,8,2,4] => {{1,5},{2,7},{3},{4,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,1,5,8,3,2,7] => {{1,6},{2,4,5,8},{3},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,1,5,8,2,3,6] => {{1,7},{2,4,5,8},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,1,5,8,2,6,3] => {{1,7},{2,4,5,8},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,7,8,2,1,4] => {{1,6},{2,3,5,8},{4,7}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,3,5,7,8,2,4,1] => {{1,6},{2,3,5,8},{4,7}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,7,6,4,5,8,3,1] => {{1,2,7},{3,6,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,3,6,1,8,4,2] => {{1,5},{2,7},{3},{4,6,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,5,8,6,3,7] => {{1,2},{3,4,5,8},{6},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,4,8,6,2,1] => {{1,7},{2,3,5,8},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,8,5,6,1,7] => {{1,2,3,4,8},{5},{6},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,8,7,1,6,5] => {{1,2,3,4,8},{5,7},{6}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,8,1,7,6,5] => {{1,2,3,4,8},{5},{6,7}} => [5,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,3,4,8,1,6,7,5] => {{1,2,3,4,8},{5},{6},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,8,5,1,7,6] => {{1,2,3,4,8},{5},{6},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,4,8,2,7,1] => {{1,6},{2,3,5,8},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,3,5,8,2,1,6] => {{1,7},{2,4,5,8},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,4,5,8,3,7,6] => {{1,2},{3,4,5,8},{6},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,3,5,8,2,6,1] => {{1,7},{2,4,5,8},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,4,8,2,1,7] => {{1,6},{2,3,5,8},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,8,5,1,6,7] => {{1,2,3,4,8},{5},{6},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,8,1,6,5,7] => {{1,2,3,4,8},{5},{6},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,3,4,8,1,5,7,6] => {{1,2,3,4,8},{5},{6},{7}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,5,7,2,6,3,4] => {{1},{2,8},{3,5},{4,7},{6}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,8,6,7,1,5,3,4] => {{1,2,8},{3,6},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,5,7,1,6,3,4] => {{1,2,8},{3,5},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,4,7,1,6,3,5] => {{1,2,8},{3,4,7},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,4,7,2,6,3,5] => {{1},{2,8},{3,4,7},{5},{6}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,4,7,5,6,2,3] => {{1},{2,8},{3,4,7},{5},{6}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,8,4,7,5,6,1,2] => {{1,3,4,7},{2,8},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,4,7,5,6,1,3] => {{1,2,8},{3,4,7},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,2,8,6,4,1,3] => {{1,7},{2,5,6},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,1,8,6,2,3,4] => {{1,7},{2,5,6},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,8,6,1,5,2,3] => {{1,7},{2,4,6},{3,8},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,8,6,2,5,1,4] => {{1,7},{2,3,8},{4,6},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,2,8,6,1,3,5] => {{1,7},{2,4,8},{3},{5,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,1,8,4,2,5,6] => {{1,7},{2,3},{4,8},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,6,3,7,8,5,4,1] => {{1,2,6},{3},{4,7},{5,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,3,7,8,4,5,1] => {{1,2,6},{3},{4,7},{5,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,7,3,5,6,8,1] => {{1,2,4},{3,7,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,3,7,8,1,6,4] => {{1,2,5,8},{3},{4,7},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,5,4,7,8,2,6] => {{1,3,5,7},{2},{4},{6,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,4,8,6,1,3,7] => {{1,5,6},{2},{3,4,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,3,8,4,6,7,1] => {{1,5},{2},{3},{4,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,8,1,3,6,7,2,5] => {{1,4},{2,8},{3},{5,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,8,2,4,7,1,6] => {{1,5},{2,3,8},{4},{6,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,2,8,1,3,7,5] => {{1,6},{2,4,8},{3},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,8,2,5,1,7,4] => {{1,6},{2,3,8},{4},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,8,1,4,7,2,5] => {{1,6,7},{2,3,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,1,2,7,6,3] => {{1,5},{2,8},{3,4},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,1,2,8,7,3,4] => {{1,6,7},{2,5,8},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,1,4,2,8,7] => {{1,6},{2,5},{3},{4},{7,8}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,1,6,4,2,7,8] => {{1,5},{2,3},{4,6},{7},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,6,1,7,5,2,8,3] => {{1,4,7,8},{2,6},{3},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,1,7,2,6,3,8] => {{1,4,7},{2,5},{3},{6},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,5,6,1,2,8,7,4] => {{1,3,6,8},{2,5},{4},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,7,1,8,6,2,4] => {{1,3,7},{2,5,8},{4},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,7,5,1,8,4] => {{1,3},{2,6},{4,7,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,7,1,8,6,3] => {{1,4,7},{2},{3,5},{6,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,7,2,8,6,1,5] => {{1,3,7},{2,4},{5,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,5,8,2,7,1,6] => {{1,3,5},{2,4,8},{6,7}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,6,2,8,1,5,7] => {{1,3,6},{2,4},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,2,6,8,1,7,4] => {{1,3},{2,5,8},{4,6},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,6,1,3,8,7] => {{1,4,6},{2},{3,5},{7,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,1,2,5,6,8,7] => {{1,4},{2,3},{5},{6},{7,8}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,6,8,4,7,2,1] => {{1,5},{2,3,6,7},{4,8}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,7,2,5,4,8,6,1] => {{1,3},{2,7},{4,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,2,5,7,3,6,1] => {{1,8},{2,4,5,7},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,2,5,8,3,6,1] => {{1,4,5,8},{2,7},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,6,5,4,8,2,7] => {{1,3,6,8},{2},{4,5},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,6,5,8,3,2,7] => {{1,4,5,8},{2},{3,6},{7}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,7,6,3,2,1] => {{1,8},{2,5,6},{3,4,7}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,7,1,5,4,3,8,6] => {{1,2,7,8},{3},{4,5},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,2,1,5,4,3,7,6] => {{1,8},{2},{3},{4,5},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,4,1,5,7,3,2,6] => {{1,8},{2,4,5,7},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,6,7,1,3,2,4] => {{1,8},{2,5},{3,6},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,6,1,7,3,2,5] => {{1,8},{2,4},{3,6},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,6,1,4,7,2,5] => {{1,8},{2,3,6,7},{4},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,1,4,3,8,5] => {{1,2,7,8},{3,6},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,8,5,1,3,2,4] => {{1,6},{2,7},{3,8},{4,5}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,6,8,2,3,4,1] => {{1,5},{2,7},{3,6},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,2,8,3,5,1] => {{1,4},{2,7},{3,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,6,2,4,7,5,1] => {{1,8},{2,3,6,7},{4},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,6,2,4,8,5,1] => {{1,3,6,8},{2,7},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,3,5,8,6,2,1] => {{1,4,5,8},{2,7},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,2,1,4,3,6,5] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,7,3,1,4,6,2,5] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,7,6,8,4,1,2,3] => {{1,5},{2,7},{3,6},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,5,8,1,2,3] => {{1,4,5,8},{2,7},{3,6}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,7,6,5,1,8,2,4] => {{1,3,6,8},{2,7},{4,5}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,1,2,3,4,5,6,7,9] => {{1,8},{2},{3},{4},{5},{6},{7},{9}} => [2,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 8

[9,1,2,3,4,5,6,7,8,10] => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => [2,1,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 9

[3,6,4,8,7,5,1,2] => {{1,3,4,8},{2,6},{5,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,4,7,2,8,1,6,5] => {{1,3,7},{2,4},{5,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,7,2,5,8,6,3] => {{1},{2,4},{3,7},{5},{6,8}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,8,5,3,4,7,1,2] => {{1,6,7},{2,8},{3,5},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,5,4,2,8,7,3] => {{1},{2,6,8},{3,5},{4},{7}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,5,2,7,3,6,4] => {{1},{2,8},{3,5,7},{4},{6}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,7,5,1,8,6,3] => {{1,4,5},{2},{3,7},{6,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,1,4,2,6,5,3] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,3,6,4,8,2,5,7] => {{1},{2,3,6},{4},{5,8},{7}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,5,1,3,4,2,8,7] => {{1,6},{2,5},{3},{4},{7,8}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,8,5,3,1,7,2,6] => {{1,4},{2,8},{3,5},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,5,3,2,8,1,6] => {{1,7},{2,4},{3,5},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,6,4,1,3,7] => {{1,2,5},{3,8},{4,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,5,8,1,7,4] => {{1,3},{2,6},{4,5,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,2,1,4,5,6,8,3] => {{1,7,8},{2},{3},{4},{5},{6}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,6,5,8,1,4,2,3] => {{1,7},{2,6},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,6,7,3,2,1,4] => {{1,5},{2,8},{3,6},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,4,3,7,2,8,5] => {{1},{2,6},{3,4},{5,7,8}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,3,4,8,7,1,5] => {{1,2,6,7},{3},{4},{5,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,3,4,5,2,8,6] => {{1,7,8},{2},{3},{4},{5},{6}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,2,4,6,3,1,5] => {{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,2,6,4,7,8,1,5] => {{1,3,6,8},{2},{4},{5,7}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,5,7,4,3,1,6] => {{1,2,8},{3,5},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,8,7,1,2,6,4] => {{1,5},{2,3,8},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,7,8,4,1,2,6] => {{1,3,7},{2,5},{4,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,7,5,3,8,2,6] => {{1},{2,4,5},{3,7},{6,8}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,7,3,1,8,5] => {{1,2,4,7,8},{3,6},{5}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,8,4,6,3,1,2,5] => {{1,7},{2,8},{3,4,6},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,5,8,4,2,1,7] => {{1,3,5},{2,6},{4,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,6,5,3,2,7,1] => {{1,4,5},{2,8},{3,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,5,8,2,1,4,3] => {{1,6},{2,7},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,8,5,7,6,2,4] => {{1},{2,3,8},{4,5,7},{6}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,2,5,6,1,7,4] => {{1,3},{2,8},{4,5,6},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,1,5,6,3,7,4] => {{1,2,8},{3},{4,5,6},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,8,6,2,7,3,4] => {{1,5},{2},{3,8},{4,6,7}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,1,5,7,2,3,4] => {{1,8},{2,6},{3},{4,5,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,5,8,1,2,4,3] => {{1,7},{2,6},{3,5},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,7,6,8,4,2,3] => {{1,5,8},{2},{3,7},{4,6}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,8,5,7,6,1,4] => {{1,3,8},{2},{4,5,7},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,8,6,1,7,3,4] => {{1,5},{2},{3,8},{4,6,7}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,8,6,5,7,3,4] => {{1},{2},{3,8},{4,6,7},{5}} => [1,1,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,1,3,6,7,8,5] => {{1,4},{2},{3},{5,6,7,8}} => [2,1,1,4] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,2,5,6,3,7,1,4] => {{1,8},{2},{3,5},{4,6,7}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,2,6,5,4,1,8,3] => {{1,7,8},{2},{3,6},{4,5}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,3,5,4,7,8,2] => {{1,6,7,8},{2},{3},{4,5}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,5,3,4,7,8,2] => {{1,6,7,8},{2},{3,5},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,6,2,4,1,8,3] => {{1,7,8},{2,5},{3,6},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,2,6,3,7,1,4] => {{1,8},{2,5},{3},{4,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,1,2,6,7,8,5] => {{1,4},{2,3},{5,6,7,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,1,6,5,7,3,2,4] => {{1,8},{2},{3,6},{4,5,7}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,1,6,3,7,2,4] => {{1,5},{2,8},{3},{4,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,5,6,3,7,2,4] => {{1},{2,8},{3,5},{4,6,7}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,6,5,4,2,8,3] => {{1},{2,7,8},{3,6},{4,5}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,6,1,4,2,8,3] => {{1,5},{2,7,8},{3,6},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,4,2,6,5,8,3] => {{1,7,8},{2},{3,4},{5,6}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,4,1,5,6,8,3] => {{1,2,7,8},{3,4},{5},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,6,4,1,2,8,3] => {{1,5},{2,7,8},{3,6},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,1,5,2,8,3] => {{1,4},{2,7,8},{3,6},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,3,6,5,7,2,4] => {{1},{2,8},{3},{4,6,7},{5}} => [1,2,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,8,1,6,5,7,2,4] => {{1,3},{2,8},{4,6,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,5,4,3,7,8,2] => {{1,6,7,8},{2},{3,5},{4}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,6,4,2,1,8,3] => {{1,7,8},{2,5},{3,6},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,2,6,5,7,1,4] => {{1,8},{2,3},{4,6,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,6,2,5,1,8,3] => {{1,7,8},{2,4},{3,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,4,3,5,7,8,2] => {{1,6,7,8},{2},{3,4},{5}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,3,4,5,7,8,2] => {{1,6,7,8},{2},{3},{4},{5}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,4,7,8,5,6,1,2] => {{1,3,7},{2,4,8},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,7,2,5,1,6,8] => {{1,3,7},{2,4},{5},{6},{8}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,7,2,5,8,3,6] => {{1},{2,4},{3,7},{5},{6,8}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,8,3,4,5,7,1,2] => {{1,6,7},{2,8},{3},{4},{5}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,7,5,8,4,1,2] => {{1,6},{2,3,7},{4,5,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,3,8,6,4,5,1,2] => {{1,7},{2,3,8},{4,6},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,7,6,5,1,4,8] => {{1,3,7},{2},{4,6},{5},{8}} => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,3,8,6,4,1,5,7] => {{1,2,3,8},{4,6},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,6,2,5,1,8,7] => {{1,4},{2,3,6},{5},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,8,3,2,5,1,4,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,1,2,5,6,3,4] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,1,8,6,4,7,3,5] => {{1,2},{3,8},{4,6,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,5,7,4,2,8,3] => {{1,6},{2},{3,5},{4,7,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,7,5,1,8,3,6] => {{1,2,4,5},{3,7},{6,8}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,8,3,4,5,1,7,6] => {{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,3,7,4,8,2,5,6] => {{1},{2,3,7},{4},{5,8},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,7,4,1,6,2,8] => {{1,5},{2,3,7},{4},{6},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,8,7,6,3,1,2,4] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,6,8,1,4,3,2] => {{1,7},{2,5},{3,6},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,7,1,6,5,3,8] => {{1,2,4},{3,7},{5,6},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,7,8,5,4,3,6] => {{1},{2},{3,7},{4,8},{5},{6}} => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,2,1,3,6,5,8,7] => {{1,4},{2},{3},{5,6},{7,8}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,8,1,4,5,6,3,7] => {{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,2,1,4,5,3,6] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,4,1,5,3,6,2] => {{1,7},{2,8},{3,4},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,4,6,1,5,8,7,2] => {{1,3,6,8},{2,4},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,1,6,4,3,8,2] => {{1,7,8},{2,5},{3},{4,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,1,8,2,7,4,3] => {{1,6,7},{2,5},{3},{4,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,1,7,4,8,2,3] => {{1,5},{2,6,8},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,1,5,7,4,2,8] => {{1,3},{2,6},{4,5,7},{8}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,6,1,7,4,8,3] => {{1,2,5,7,8},{3,6},{4}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,1,7,6,4,8,3,2] => {{1,5},{2},{3,7},{4,6,8}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,5,7,3,4,8,1] => {{1,2,6},{3,5},{4,7,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,6,4,7,5,8,2,3] => {{1},{2,6,8},{3,4,7},{5}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,3,6,2,7,4,1] => {{1,8},{2,5},{3},{4,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,7,4,6,8,2,5] => {{1},{2,3,7},{4},{5,6,8}} => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,6,5,4,8,2,3] => {{1},{2,7},{3,6,8},{4,5}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,1,6,5,7,2,4,3] => {{1,8},{2},{3,6},{4,5,7}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,7,5,3,8,2,4] => {{1,6,8},{2},{3,7},{4,5}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,7,5,6,8,3,4] => {{1,2},{3,7},{4,5,6,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,1,7,6,8,2,3] => {{1,5,6,8},{2,4,7},{3}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,8,6,4,2,7,5,1] => {{1,3,6,7},{2,8},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,6,3,7,4,5,1] => {{1,2,8},{3,6},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,4,1,7,2,6,5] => {{1,3,4},{2,8},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,7,1,8,3,2,6] => {{1,5,8},{2,4},{3,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,4,1,8,5,2,6] => {{1,3,4},{2,7},{5,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,1,3,7,2,6,4] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,4,2,1,7,3,6,5] => {{1,8},{2,4},{3},{5,7},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,7,6,8,4,5,2,1] => {{1,3,6},{2,7},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,8,5,3,4,1] => {{1,2,7},{3,6},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,8,6,7,5,2,3] => {{1},{2,4,6},{3,8},{5,7}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,6,7,3,5,1] => {{1,2,4,6},{3,8},{5,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,3,8,5,4,6,2,1] => {{1,7},{2,3,8},{4,5},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,8,5,6,7,2,1] => {{1,3,8},{2,4,5,6,7}} => [3,5] => ([(4,7),(5,7),(6,7)],8) => 2

[5,4,3,8,6,7,2,1] => {{1,5,6,7},{2,4,8},{3}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,2,8,7,3,6,1] => {{1,5,7},{2,4,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,5,8,7,3,4,1] => {{1,6},{2},{3,5,7},{4,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,8,5,7,4,6,1] => {{1,3,8},{2},{4,5,7},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,8,5,7,6,2,4] => {{1,3,8},{2},{4,5,7},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,1,5,8,7,4,2,3] => {{1,6},{2},{3,5,7},{4,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,1,8,7,6,2,3] => {{1,5,7},{2,4,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,6,7,4,3,2,1] => {{1,5},{2,8},{3,6},{4,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,1,4,3,5,8,7] => {{1,6},{2},{3},{4},{5},{7,8}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,1,4,3,8,5,7] => {{1,6,8},{2},{3},{4},{5},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,2,1,4,3,6,5,7] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

[8,2,4,1,3,6,5,7] => {{1,8},{2},{3,4},{5},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,6,1,4,3,5,8,7] => {{1,2,6},{3},{4},{5},{7,8}} => [3,1,1,1,2] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,6,4,1,3,5,8,7] => {{1,2,6},{3,4},{5},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,2,1,3,6,5,7] => {{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,6,2,1,8,3,5,7] => {{1,4},{2,6},{3},{5,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,8,4,3,6,5,7] => {{1,2},{3,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,8,1,4,3,6,5,7] => {{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,8,4,1,3,6,5,7] => {{1,2,8},{3,4},{5},{6},{7}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,8,2,1,3,6,5,7] => {{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,8,2,1,4,3,5,7] => {{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,6,4,1,8,3,5,7] => {{1,2,6},{3,4},{5,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,4,8,1,3,5,7] => {{1,2,6},{3,4,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,2,1,4,6,3,5,7] => {{1,8},{2},{3},{4},{5,6},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,1,4,8,3,5,7] => {{1,6},{2},{3},{4},{5,8},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,2,1,6,3,8,5,7] => {{1,4,6,8},{2},{3},{5},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,2,1,3,8,6,5,7] => {{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[4,2,1,8,6,3,5,7] => {{1,4,8},{2},{3},{5,6},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,2,8,1,4,3,5,7] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,4,1,8,3,6,5,7] => {{1,2,4,8},{3},{5},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,4,8,3,6,5,7] => {{1,2},{3,4,8},{5},{6},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,4,8,6,3,5,7] => {{1,2},{3,4,8},{5,6},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,1,6,3,5,7] => {{1,2,4},{3,8},{5,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,6,1,3,5,7] => {{1,2,4,6},{3,8},{5},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,8,4,1,3,5,7] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,4,8,2,1,3,5,7] => {{1,6},{2,4},{3,8},{5},{7}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,6,1,5,2,8,7] => {{1,4},{2,3,6},{5},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,5,2,8,1,7,6] => {{1,4},{2,3,5,8},{6},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,8,2,6,1,7,5] => {{1,4},{2,3,8},{5,6},{7}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,8,1,7,2,6,5] => {{1,4},{2,3,8},{5,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,7,6,8,3,4,2] => {{1,5,8},{2},{3,7},{4,6}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,7,1,8,5,6,2] => {{1,4},{2,3,7},{5,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,6,5,8,1,7,2] => {{1,4,5,8},{2,3,6},{7}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,3,5,4,7,2,8,1] => {{1,6},{2,3,5,7,8},{4}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,3,5,4,8,1,7,2] => {{1,6},{2,3,5,8},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,6,5,8,1,3,2] => {{1,7},{2,4,5,8},{3,6}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,5,1,7,2,6,4] => {{1,8},{2,3,5,7},{4},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,5,2,6,1,7,4] => {{1,8},{2,3,5,6},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,2,4,1,5,3,7,6] => {{1,8},{2},{3,4},{5},{6},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,2,8,1,5,4,7,6] => {{1,3,8},{2},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,2,7,6,8,1,5,4] => {{1,3,7},{2},{4,6},{5,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,6,5,8,1,7,4] => {{1,3,6},{2},{4,5,8},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,2,4,3,8,1] => {{1,6},{2,5},{3,7,8},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,8,5,6,2,4,3] => {{1,7},{2},{3,8},{4,5,6}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,7,2,6,3,8,1] => {{1,5,6},{2,4},{3,7,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,8,2,6,1,7,3] => {{1,5,6},{2,4},{3,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,8,1,7,2,4,3] => {{1,6},{2,5,7},{3,8},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,5,8,3,7,4] => {{1,2},{3,6},{4,5,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,4,8,1,3,2] => {{1,6},{2,5,8},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,7,1,8,3,4,2] => {{1,6},{2,5,8},{3,7},{4}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,7,1,8,3,6,2] => {{1,5,8},{2,4},{3,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,6,3,8,1,7,2] => {{1,5,8},{2,4},{3,6},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,3,1,5,4,6,7] => {{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[2,5,3,4,7,1,8,6] => {{1,2,5,7,8},{3},{4},{6}} => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,3,5,7,6,1] => {{1,2,4},{3,8},{5},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,3,1,8,6,7] => {{1,4},{2},{3,5},{6,8},{7}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,8,4,3,2,6,7] => {{1},{2,5},{3,8},{4},{6},{7}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,8,5,4,3,2,6,7] => {{1},{2,8},{3,5},{4},{6},{7}} => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,5,7,3,8,4,2,6] => {{1},{2,5,8},{3,7},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,1,4,7,8,3,2,6] => {{1,5,8},{2},{3,4,7},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,1,5,7,3,6,2] => {{1,4,5,7},{2,8},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,8,5,3,7,4,2] => {{1},{2,6,7},{3,8},{4,5}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,1,7,3,5,2] => {{1,6},{2,4},{3,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,7,1,5,2,3] => {{1,6},{2,4,7},{3,8},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,6,4,1,3,8,2,5] => {{1,7},{2,6,8},{3,4},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,5,6,3,2,8,4] => {{1},{2,7,8},{3,5},{4,6}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,4,6,3,1,8,5] => {{1,2,7,8},{3,4,6},{5}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,6,8,4,3,7,5,1] => {{1,2,6,7},{3,8},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,4,8,3,7,5,1] => {{1,6,7},{2},{3,4,8},{5}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,7,3,1,4,8,5] => {{1,2,6},{3,7,8},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,8,7,4,5,6,3] => {{1},{2},{3,8},{4,7},{5},{6}} => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,3,7,1,5,6,2,4] => {{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,5,2,6,7,4,3] => {{1},{2,8},{3,5,6,7},{4}} => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,2,1,8,6,7,4,3] => {{1,5,6,7},{2},{3},{4,8}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,8,6,1,5,2,4] => {{1,7},{2,3,8},{4,6},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,2,1,4,8,7] => {{1,6},{2,3,5},{4},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,3,6,1,2,8,7] => {{1,4,6},{2,5},{3},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,4,6,2,8,7] => {{1,3},{2,5,6},{4},{7,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,4,5,7,2,1,6] => {{1,8},{2,3,4,5,7},{6}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,7,4,6,3,8,2,1] => {{1,5},{2,7},{3,4,6,8}} => [2,2,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,8,4,6,3,7,1,5] => {{1,2,8},{3,4,6,7},{5}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,3,4,7,5,1,2,6] => {{1,8},{2,3,4,7},{5},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,1,4,7,3,2,6] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,8,5,7,4,3,6] => {{1,2},{3,8},{4,5,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,7,1,8,4,2] => {{1,6,8},{2,5},{3},{4,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,1,4,7,8,3,2] => {{1,6,8},{2,5,7},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,4,6,8,3,7,2] => {{1,5,8},{2},{3,4,6},{7}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,6,4,1,7,2,5] => {{1,3,6,7},{2,8},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,7,5,4,1,3,6] => {{1,2,8},{3,7},{4,5},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,6,7,4,2,1,5] => {{1,3,6},{2,8},{4,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,6,8,4,2,3,1] => {{1,5},{2,7},{3,6},{4,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,7,8,2,4,6,1] => {{1,5},{2,3,7},{4,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,6,2,1,4,7,5] => {{1,8},{2,3,6},{4},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,7,8,6,4,2,1,3] => {{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,7,3,5,1,8,2,4] => {{1,6,8},{2,7},{3},{4,5}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,6,7,5,8,3,4] => {{1,2},{3,6,8},{4,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,5,7,3,6,8,4] => {{1,2},{3,5},{4,7,8},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,3,6,1,2,8,4] => {{1,5},{2,7,8},{3},{4,6}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,2,1,8,7,5,3] => {{1,4},{2,6,7},{3},{5,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,6,2,7,8,5,1] => {{1,3,6,8},{2,4},{5,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,6,3,1,8,7,2,4] => {{1,5,8},{2,6,7},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,6,1,5,7,8,2] => {{1,3,6,7,8},{2,4},{5}} => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,8,2,7,6,1,5,4] => {{1,3},{2,8},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,2,7,6,5,1,4] => {{1,3},{2,8},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,2,7,6,5,4,1] => {{1,3},{2,8},{4,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,2,6,5,3,1] => {{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,2,6,5,1,3] => {{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,2,6,1,5,3] => {{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,3,6,2,5,1] => {{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,3,6,2,1,5] => {{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,3,6,1,5,2] => {{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,3,6,5,1,2] => {{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,3,6,5,2,1] => {{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,3,4,2,1] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,3,1,4,2] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,3,2,4,1] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,2,4,3,1] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,2,1,4,3] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,4,2,3,1] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,4,2,1,3] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,4,1,3,2] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,6,4,3,1,2] => {{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,4,2,1,6,5,8] => {{1,7},{2,3,4},{5},{6},{8}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,3,5,2,6,1,4,8] => {{1,7},{2,3,5,6},{4},{8}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,5,2,6,4,1,8] => {{1,7},{2,3,5,6},{4},{8}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,2,7,4,8,1] => {{1,6},{2,3,5,7,8},{4}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,2,1,5,6,4,3,8] => {{1,7},{2},{3},{4,5,6},{8}} => [2,1,1,3,1] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,3,5,1,6,4,2,8] => {{1,7},{2,3,5,6},{4},{8}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,4,5,6,1,3,2,8] => {{1,7},{2,4,6},{3,5},{8}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,5,7,3,2,8,6] => {{1},{2,4,7,8},{3,5},{6}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,6,7,3,8,2,5] => {{1},{2,4,7},{3,6,8},{5}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,5,7,3,1,8,2] => {{1,6},{2,4,7,8},{3,5}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,4,5,7,1,3,8,2] => {{1,6},{2,4,7,8},{3,5}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,3,5,1,7,4,8,2] => {{1,6},{2,3,5,7,8},{4}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,2,1,5,7,4,8,3] => {{1,6},{2},{3},{4,5,7,8}} => [2,1,1,4] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,5,7,4,8,6] => {{1,3},{2},{4,5,7,8},{6}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,7,3,8,1,5] => {{1,2,4,7},{3,6,8},{5}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,4,6,7,3,8,5,2] => {{1},{2,4,7},{3,6,8},{5}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,6,7,8,3,4,2] => {{1},{2,5,8},{3,6},{4,7}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,6,7,8,3,1,4] => {{1,2,5,8},{3,6},{4,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,2,1,6,7,8,4,5] => {{1,3},{2},{4,6,8},{5,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,6,1,7,8,4,2] => {{1,5,7},{2,3,6,8},{4}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,6,7,1,8,3,2] => {{1,5},{2,4,7},{3,6,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,5,6,7,8,3,2,4] => {{1},{2,5,8},{3,6},{4,7}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,5,7,2,1,8,3] => {{1,6},{2,4,7,8},{3,5}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,4,6,7,2,8,3,1] => {{1,5},{2,4,7},{3,6,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,6,2,7,8,4,1] => {{1,5,7},{2,3,6,8},{4}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,6,2,7,8,1,4] => {{1,5,7},{2,3,6,8},{4}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,3,5,2,7,1,8,4] => {{1,6},{2,3,5,7,8},{4}} => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,3,4,1,2,7,8,6] => {{1,5},{2,3,4},{6,7,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,6,2,7,8,1,5] => {{1,4},{2,3,6,8},{5,7}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,3,6,2,7,8,5,1] => {{1,4},{2,3,6,8},{5,7}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,3,6,2,7,8,5,4] => {{1},{2,3,6,8},{4},{5,7}} => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,6,7,2,8,5,3] => {{1},{2,4,7},{3,6,8},{5}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,1,6,7,8,3,5] => {{1,4,6,8},{2},{3},{5,7}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,6,1,7,8,2,5] => {{1,4},{2,3,6,8},{5,7}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,5,6,7,8,2,4,3] => {{1},{2,5,8},{3,6},{4,7}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,6,7,8,4,2,3] => {{1},{2,5,8},{3,6},{4,7}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,6,1,7,8,5,2] => {{1,4},{2,3,6,8},{5,7}} => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,2,1,6,7,8,5,3] => {{1,4,6,8},{2},{3},{5,7}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,6,7,1,8,5,3] => {{1,2,4,7},{3,6,8},{5}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[2,5,6,7,8,1,4,3] => {{1,2,5,8},{3,6},{4,7}} => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,1,2,3,4,5,6,8,9] => {{1,7},{2},{3},{4},{5},{6},{8},{9}} => [2,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 8

[1,4,3,7,6,8,2,5] => {{1},{2,4,7},{3},{5,6,8}} => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,3,7,4,8,2,6] => {{1},{2,5},{3},{4,7},{6,8}} => [1,2,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,2,6,5,8,4,7] => {{1},{2,3},{4,6,8},{5},{7}} => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,4,8,3,7,2,6] => {{1},{2,5},{3,4,8},{6,7}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,1,8,6,2,4,3] => {{1,7},{2,5,6},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,3,8,5,2,4,7] => {{1},{2,6},{3},{4,8},{5},{7}} => [1,2,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,3,1,8,4,2,6,5] => {{1,7},{2,3},{4,8},{5},{6}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,2,3,8,4,7,6] => {{1},{2,5,8},{3},{4},{6},{7}} => [1,3,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,2,3,8,4,7,6] => {{1,5,8},{2},{3},{4},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,2,3,8,1,4,7,6] => {{1,5},{2},{3},{4,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,8,1,3,5,4,7] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,2,4,1,8,7,3,5] => {{1,6,7},{2},{3,4},{5,8}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,1,4,2,8,5,7] => {{1,6,8},{2,3},{4},{5},{7}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,6,3,8,7,1,5,4] => {{1,2,6},{3},{4,8},{5,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,1,3,7,6,5] => {{1,2,4},{3,8},{5},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,3,7,1,6,5] => {{1,2,4},{3,8},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,3,7,6,1,5] => {{1,2,4},{3,8},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,3,8,1,7,4,6] => {{1,2,5},{3},{4,8},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,4,1,3,8,7,6] => {{1,2,5},{3,4},{6,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,5,4,8,2,7,6] => {{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,2,3,8,4,7,1,6] => {{1,5},{2},{3},{4,8},{6,7}} => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,8,3,7,2,6,5] => {{1},{2,4},{3,8},{5,7},{6}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,8,1,5,2,4,7] => {{1,6},{2,3,8},{4},{5},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,8,1,2,4,7,6] => {{1,5},{2,3,8},{4},{6},{7}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,1,3,8,2,4,7,6] => {{1,5},{2},{3},{4,8},{6},{7}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,5,4,8,2,7,6,3] => {{1},{2,5},{3,4,8},{6,7}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,4,8,2,7,6,3] => {{1,5},{2},{3,4,8},{6,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,8,1,2,7,6,3] => {{1,5},{2,4},{3,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,1,2,8,7,4,3] => {{1,6,7},{2,5,8},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,1,6,4,2,8,7] => {{1,5},{2,3},{4,6},{7,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,6,2,8,7,4,3] => {{1,5,8},{2},{3,6,7},{4}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,8,2,7,6,3] => {{1,4,8},{2},{3,5},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,2,5,8,7,6,3] => {{1,4,5,8},{2},{3},{6,7}} => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,4,2,5,8,7,6,3] => {{1},{2,4,5,8},{3},{6,7}} => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,5,2,8,7,4,6] => {{1},{2,3,5,8},{4},{6,7}} => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,2,8,7,4,6] => {{1,3},{2,5,8},{4},{6,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,2,8,7,5,1,4] => {{1,3},{2,6},{4,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,6,1,8,7,3,5] => {{1,4},{2},{3,6,7},{5,8}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,1,5,8,2,7,6] => {{1,4,5,8},{2,3},{6},{7}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,2,8,7,1,4,6] => {{1,3},{2,5,7},{4,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,8,7,2,6,1,5] => {{1,3,8},{2,4,7},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,8,7,1,2,6,5] => {{1,3,8},{2,4,7},{5},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,8,1,7,2,6,5] => {{1,3,8},{2,4},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,4,8,7,2,6,5] => {{1},{2,3,4,8},{5,7},{6}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,8,1,2,7,6,5] => {{1,3,8},{2,4},{5},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,8,2,7,1,6,5] => {{1,3,8},{2,4},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,4,8,2,7,6,1,5] => {{1,3,8},{2,4},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,5,8,1,7,6,3] => {{1,4,8},{2},{3,5},{6,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,1,2,5,8,7,6] => {{1,4},{2,3},{5},{6,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,1,4,2,5,8,7,6] => {{1,3,4},{2},{5},{6,8},{7}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,2,1,5,3,6,4] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,4,1,2,7,3,5,8] => {{1,6},{2,4},{3},{5,7},{8}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,2,1,5,4,7,3,8] => {{1,6,7},{2},{3},{4,5},{8}} => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,3,6,2,4,7,1,8] => {{1,5},{2,3,6,7},{4},{8}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,2,1,7,3,8,5] => {{1,6},{2,4},{3},{5,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,7,5,8,6,1,2] => {{1,4,5,8},{2,3,7},{6}} => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,2,6,7,4,8,1,5] => {{1,3,6,8},{2},{4,7},{5}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,6,7,4,8,5,2] => {{1,3,6,8},{2},{4,7},{5}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,6,5,3,8,4,2] => {{1},{2,7},{3,6,8},{4,5}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,5,3,8,1,4] => {{1,2,7},{3,6,8},{4,5}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,7,6,5,2,4,8,3] => {{1},{2,7,8},{3,6},{4,5}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,5,3,1,4,8] => {{1,2,7},{3,6},{4,5},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,6,4,8,5,1,2] => {{1,3,6},{2,7},{4},{5,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,7,6,3,8,4,1,2] => {{1,5,8},{2,7},{3,6},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,5,2,1,3,8] => {{1,4,5},{2,7},{3,6},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,5,2,8,1,3] => {{1,4,5},{2,7},{3,6,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,7,6,5,1,8,3,2] => {{1,4,5},{2,7},{3,6,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[1,7,6,5,2,8,3,4] => {{1},{2,7},{3,6,8},{4,5}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,6,5,3,2,8,4] => {{1},{2,7,8},{3,6},{4,5}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,5,1,2,8,3] => {{1,4,5},{2,7,8},{3,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[4,7,6,5,3,1,8,2] => {{1,4,5},{2,7,8},{3,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[5,1,6,2,4,7,8,3] => {{1,5},{2},{3,6,7,8},{4}} => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,1,6,2,3,8,5] => {{1,4,6},{2,7,8},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,6,7,4,2,8,5] => {{1,3,6},{2},{4,7,8},{5}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,3,5,8,1,2] => {{1,4},{2,7},{3,6,8},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,6,5,2,4,1,8] => {{1,3,6},{2,7},{4,5},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,7,6,5,8,2,4,3] => {{1},{2,7},{3,6},{4,5,8}} => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,6,5,8,1,4,2] => {{1,3,6},{2,7},{4,5,8}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,7,6,5,1,2,4,8] => {{1,3,6},{2,7},{4,5},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,6,8,3,5,1,2] => {{1,4,8},{2,7},{3,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,6,5,1,4,3,8] => {{1,2,7},{3,6},{4,5},{8}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,2,1,7,4,8,5] => {{1,6},{2,3},{4},{5,7,8}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,3,1,5,4,2,8,6] => {{1,7,8},{2,3},{4,5},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,5,2,7,6,3] => {{1,8},{2,4,5},{3},{6,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,7,2,1,5,8,6] => {{1,4},{2,3,7,8},{5},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,4,2,1,8,5] => {{1,6},{2,3,7,8},{4},{5}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,2,5,3,1,8,6] => {{1,4,5},{2,7,8},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,5,4,1,3,8,6] => {{1,2,7,8},{3,5},{4},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,4,3,2,1,8,6] => {{1,7,8},{2,5},{3,4},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,6,3,2,8,1,5,7] => {{1,4},{2,6},{3},{5,8},{7}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,7,4,3,2,8,1,6] => {{1,5},{2,7},{3,4},{6,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,7,3,6,4,8,1,5] => {{1,2,7},{3},{4,6,8},{5}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,7,5,3,8,1,4] => {{1,6,8},{2},{3,7},{4,5}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,1,6,2,7,4,3] => {{1,5},{2,8},{3},{4,6,7}} => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,5,7,4,3,6,2] => {{1},{2,8},{3,5},{4,7},{6}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,8,5,7,2,4,6,3] => {{1},{2,8},{3,5},{4,7},{6}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,8,6,1,7,2,5,4] => {{1,3,6},{2,8},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,4,6,7,1,3,2] => {{1,5,7},{2,8},{3,4,6}} => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[7,2,8,5,6,1,4,3] => {{1,7},{2},{3,8},{4,5,6}} => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,5,8,2,1,4] => {{1,6},{2,3,7},{4,5,8}} => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,7,2,6,8,4,1,5] => {{1,3},{2,7},{4,6},{5,8}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,5,8,1,4,2,7] => {{1,3,5},{2,6},{4,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,5,8,4,1,3,7] => {{1,2,6},{3,5},{4,8},{7}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,4,8,3,2,1,7] => {{1,6},{2,5},{3,4,8},{7}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,3,7,2,1,6,5] => {{1,8},{2,4,7},{3},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,3,6,8,2,1,5,7] => {{1,4,8},{2,3,6},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,5,1,8,4,2,7] => {{1,6},{2,3,5,8},{4},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,1,5,7,3,6,2] => {{1,8},{2,4,5,7},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,2,5,8,3,1,7] => {{1,6},{2,4,5,8},{3},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,1,6,8,2,3,7] => {{1,5,8},{2,4,6},{3},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,2,1,7,8,3,4] => {{1,6,8},{2,5,7},{3},{4}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,4,8,5,2,1] => {{1,6},{2,3,7},{4},{5,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,2,5,8,6,3,1] => {{1,4,5,8},{2,7},{3},{6}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,1,8,4,7,5,2] => {{1,6,7},{2,3},{4,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,2,8,7,3,5,1] => {{1,6},{2,4,8},{3},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,5,3,8,7,4,1,2] => {{1,6},{2,5,7},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,3,7,6,4,2,1] => {{1,8},{2,5,6},{3},{4,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,4,8,1,7,6,2,3] => {{1,5,7},{2,4},{3,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,8,2,1,7,5,3] => {{1,6,7},{2,4},{3,8},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,8,1,4,7,5,2] => {{1,3,8},{2,6,7},{4},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,4,7,8,1,5,3,2] => {{1,6},{2,4,8},{3,7},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,3,7,8,5,2,4,1] => {{1,6},{2,3,7},{4,8},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,7,1,3,6,4] => {{1,2,5},{3,8},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,8,7,2,1,6,4] => {{1,5},{2,3,8},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,7,6,1,5,4,2] => {{1,8},{2,3,7},{4,6},{5}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,8,7,6,2,1,5] => {{1,4,7},{2,3,8},{5,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[3,5,8,7,2,6,1,4] => {{1,3,8},{2,5},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,3,8,6,5,1,2] => {{1,4,8},{2,7},{3},{5,6}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,8,6,4,3,2,1] => {{1,7},{2,5},{3,8},{4,6}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,3,6,4,2,1] => {{1,5,6},{2,8},{3,7},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,8,7,6,2,5,3,1] => {{1,4,6},{2,8},{3,7},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,7,6,5,1,4,2] => {{1,3,7},{2,8},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,7,6,5,4,1,3] => {{1,2,8},{3,7},{4,6},{5}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,1,4,5,6,7,8,9] => {{1,3},{2},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 8

[3,2,1,4,5,6,7,8,9,10] => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => [2,1,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 9

[3,6,5,1,2,4,8,7] => {{1,3,5},{2,6},{4},{7,8}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,7,5,8,2,4,1,6] => {{1,3,5},{2,7},{4,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,8,5,7,2,4,1,6] => {{1,3,5},{2,8},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,1,7,8,4,3,2,6] => {{1,5},{2},{3,7},{4,8},{6}} => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[4,1,5,7,8,3,2,6] => {{1,4,7},{2},{3,5,8},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,5,8,7,3,2,6] => {{1,4,8},{2},{3,5,7},{6}} => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,5,3,8,1,4,2,6] => {{1,7},{2,5},{3},{4,8},{6}} => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,1,5,8,7,3,4,6] => {{1,2},{3,5,7},{4,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,7,1,6,3,2,8,5] => {{1,4,6},{2,7,8},{3},{5}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[7,1,2,3,5,8,6,4] => {{1,7},{2},{3},{4},{5},{6,8}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,8,1,4,3,7,2,5] => {{1,6,7},{2,8},{3},{4},{5}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,7,3,2,4,1,6,5] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,8,3,2,4,1,6,5] => {{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,2,3,5,7,6,4] => {{1,8},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,2,3,6,7,5,4] => {{1,8},{2},{3},{4},{5,6,7}} => [2,1,1,1,3] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,1,2,3,7,5,6,4] => {{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,1,2,3,6,5,7,4] => {{1,8},{2},{3},{4},{5,6},{7}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[3,5,7,8,2,4,1,6] => {{1,3,7},{2,5},{4,8},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,6,7,1,4,2,8,5] => {{1,3,7,8},{2,6},{4},{5}} => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,2,4,3,6,1,5] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,1,2,3,5,6,8,4] => {{1,7,8},{2},{3},{4},{5},{6}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[5,1,2,3,7,8,6,4] => {{1,5,7},{2},{3},{4},{6,8}} => [3,1,1,1,2] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,1,2,3,8,6,7,4] => {{1,5,8},{2},{3},{4},{6},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[6,1,2,3,5,8,7,4] => {{1,6,8},{2},{3},{4},{5},{7}} => [3,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,6,2,4,3,1,8,5] => {{1,7,8},{2,6},{3},{4},{5}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,1,2,3,5,7,8,4] => {{1,6,7,8},{2},{3},{4},{5}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,1,2,3,6,8,7,4] => {{1,5,6,8},{2},{3},{4},{7}} => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,8,1,2,6,3,5,4] => {{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,8,2,7,3,5,6] => {{1},{2,4},{3,8},{5,7},{6}} => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,8,5,4,2,7,6] => {{1},{2,3,8},{4,5},{6},{7}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,3,6,8,4,7,5,2] => {{1},{2,3,6,7},{4,8},{5}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,4,8,1,7,3,6,5] => {{1,2,4},{3,8},{5,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,6,8,4,5,7,3] => {{1},{2},{3,6},{4,8},{5},{7}} => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,5,1,2,4,3,6,8] => {{1,7},{2,5},{3},{4},{6},{8}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,4,6,1,5,2,3,8] => {{1,7},{2,4},{3,6},{5},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,6,3,8,5,4,2,7] => {{1},{2,6},{3},{4,8},{5},{7}} => [1,2,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,1,3,6,5,4,2,8] => {{1,7},{2},{3},{4,6},{5},{8}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,3,1,6,5,4,2,8] => {{1,7},{2,3},{4,6},{5},{8}} => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[7,2,1,4,6,3,5,8] => {{1,7},{2},{3},{4},{5,6},{8}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,2,3,6,5,1,4,8] => {{1,7},{2},{3},{4,6},{5},{8}} => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[7,1,2,3,6,5,4,8] => {{1,7},{2},{3},{4},{5,6},{8}} => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,5,8,2,7,6,3,4] => {{1},{2,5,7},{3,8},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,8,2,7,6,3,4,1] => {{1,5,6},{2,8},{3},{4,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,2,8,1,7,3,5,4] => {{1,6},{2},{3,8},{4},{5,7}} => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[3,6,4,1,2,8,5,7] => {{1,3,4},{2,6,8},{5},{7}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,1,8,7,6,3,4] => {{1,2,5,7},{3},{4,8},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,3,8,7,4,6,1] => {{1,2,5,7},{3},{4,8},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,2,5,3,8,7,4,6] => {{1},{2},{3,5,8},{4},{6,7}} => [1,1,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,5,3,8,7,1,6,4] => {{1,2,5,7},{3},{4,8},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,5,8,4,1,7,6,3] => {{1,2,5},{3,8},{4},{6,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,8,7,1,4,2,6] => {{1,3,8},{2,5},{4,7},{6}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,3,8,4,1,7,6,2] => {{1,5},{2,3,8},{4},{6,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,8,7,6,3,5,1] => {{1,4,7},{2},{3,8},{5,6}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,2,8,7,6,5,3,1] => {{1,4,7},{2},{3,8},{5,6}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,1,8,7,6,5,3,2] => {{1,4,7},{2},{3,8},{5,6}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,8,7,6,5,1,2] => {{1,4,7},{2,3,8},{5,6}} => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[6,3,1,8,7,2,5,4] => {{1,6},{2,3},{4,8},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,3,7,6,1,4,2] => {{1,5,6},{2,8},{3},{4,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,5,3,8,7,6,2,4] => {{1},{2,5,7},{3},{4,8},{6}} => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,5,8,4,7,2,6,3] => {{1},{2,5,7},{3,8},{4},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[5,8,7,4,6,1,2,3] => {{1,5,6},{2,8},{3,7},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,8,1,7,2,3,6] => {{1,4},{2,5,7},{3,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,8,1,7,2,6,3] => {{1,4},{2,5,7},{3,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,2,5,8,7,4,6] => {{1},{2,3},{4,5,8},{6,7}} => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,8,7,4,6,2] => {{1,3},{2,5,7},{4,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,5,1,8,7,2,6,4] => {{1,3},{2,5,7},{4,8},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,3,6,1,2,8,5,7] => {{1,4},{2,3,6,8},{5},{7}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,8,3,1,7,2,6] => {{1,4},{2,5},{3,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,2,8,7,1,3,6] => {{1,4,8},{2,5,7},{3},{6}} => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,8,7,1,6,4] => {{1,3,5,7},{2},{4,8},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,1,4,8,7,6,2,5] => {{1,3,4,8},{2},{5,7},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,4,8,7,6,2,5] => {{1},{2,3,4,8},{5,7},{6}} => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[3,2,5,8,7,4,6,1] => {{1,3,5,7},{2},{4,8},{6}} => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[4,5,8,3,1,7,6,2] => {{1,4},{2,5},{3,8},{6,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,1,3,5,8,7,4,6] => {{1,2},{3},{4,5,8},{6,7}} => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,3,7,8,2,6,5,4] => {{1},{2,3,7},{4,8},{5},{6}} => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,8,1,6,7,3,5,4] => {{1,2,8},{3},{4,6},{5,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,6,8,3,7,1,5,4] => {{1,2,6},{3,8},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,6,4,7,1,5,3] => {{1,2,8},{3,6},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,3,4,1,7,5,2] => {{1,6,7},{2,8},{3},{4},{5}} => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,6,8,3,7,5,1,4] => {{1,2,6},{3,8},{4},{5,7}} => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[2,8,1,6,7,5,3,4] => {{1,2,8},{3},{4,6},{5,7}} => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,5,7,4,1,6,2] => {{1,8},{2,3,5},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,2,4,7,1,6,3] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,7,1,2,4,6,3,5] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[1,6,8,3,7,2,5,4] => {{1},{2,6},{3,8},{4},{5,7}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[8,3,5,7,1,2,6,4] => {{1,8},{2,3,5},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,7,1,6,2,3] => {{1,8},{2,5},{3,4,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,4,7,1,2,6,3] => {{1,8},{2,5},{3,4,7},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,1,4,7,2,6,3] => {{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[1,4,6,8,2,7,5,3] => {{1},{2,4,8},{3,6,7},{5}} => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,5,8,2,7,4,3] => {{1},{2,6,7},{3,5},{4,8}} => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,5,6,3,1,7,4,2] => {{1,8},{2,5},{3,6,7},{4}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,6,2,8,1,7,4,3] => {{1,5},{2,6,7},{3},{4,8}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,8,4,5,7,2,6,3] => {{1},{2,8},{3,4,5,7},{6}} => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[5,8,7,3,6,1,2,4] => {{1,5,6},{2,8},{3,7},{4}} => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,5,7,1,6,2,4] => {{1,8},{2,3,5},{4,7},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[1,6,8,3,7,5,2,4] => {{1},{2,6},{3,8},{4},{5,7}} => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[6,3,8,2,7,5,1,4] => {{1,6},{2,3,8},{4},{5,7}} => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[6,8,4,2,7,1,5,3] => {{1,6},{2,8},{3,4},{5,7}} => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,6,4,7,3,1,5,2] => {{1,8},{2,6},{3,4,7},{5}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,5,7,3,1,6,2] => {{1,8},{2,4,7},{3,5},{6}} => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,4,2,5,7,1,6,3] => {{1,8},{2,4,5,7},{3},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,3,4,7,2,6,1,5] => {{1,8},{2,3,4,7},{5},{6}} => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,1,3,4,6,2,5] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,3,7,2,4,6,1,5] => {{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 5

[2,8,4,5,7,1,6,3] => {{1,2,8},{3,4,5,7},{6}} => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 3

[8,7,3,4,5,1,6,2] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

[8,7,4,5,2,6,1,3] => {{1,8},{2,7},{3,4,5},{6}} => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 4

[8,7,2,3,4,6,1,5] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

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Description

The order of the largest clique of the graph.
A clique in a graph $G$ is a subset $U \subseteq V(G)$ such that any pair of vertices in $U$ are adjacent. I.e. the subgraph induced by $U$ is a complete graph.

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to composition

Description

The integer composition of block sizes of a set partition.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.

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to threshold graph

Description

The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.

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weak exceedance partition

Description

The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.