- FindStat

Identifier

Mp00080: Set partitions —to permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
St001050: Set partitions ⟶ ℤ

Values

{{1}} => [1] => [1] => {{1}} => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1194 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}} => 7

{{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}} => 1

{{1,2,3,4,5,7},{6}} => [2,3,4,5,7,6,1] => [1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}} => 2

{{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => [1,2,3,4,7,6,5] => {{1},{2},{3},{4},{5,7},{6}} => 2

{{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => {{1},{2},{3},{4},{5,6,7}} => 1

{{1,2,3,4,6,7},{5}} => [2,3,4,6,5,7,1] => [1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}} => 3

{{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => [1,2,3,7,4,5,6] => {{1},{2},{3},{4,7},{5},{6}} => 3

{{1,2,3,4,6},{5},{7}} => [2,3,4,6,5,1,7] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}} => 1

{{1,2,3,4,7},{5,6}} => [2,3,4,7,6,5,1] => [1,2,3,6,5,4,7] => {{1},{2},{3},{4,6},{5},{7}} => 3

{{1,2,3,4},{5,6,7}} => [2,3,4,1,6,7,5] => [1,2,3,7,5,6,4] => {{1},{2},{3},{4,7},{5},{6}} => 3

{{1,2,3,4},{5,6},{7}} => [2,3,4,1,6,5,7] => [1,2,3,6,5,7,4] => {{1},{2},{3},{4,6,7},{5}} => 1

{{1,2,3,4,7},{5},{6}} => [2,3,4,7,5,6,1] => [1,2,3,5,6,4,7] => {{1},{2},{3},{4,5,6},{7}} => 2

{{1,2,3,4},{5,7},{6}} => [2,3,4,1,7,6,5] => [1,2,3,7,6,5,4] => {{1},{2},{3},{4,7},{5,6}} => 2

{{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => [1,2,3,5,7,6,4] => {{1},{2},{3},{4,5,7},{6}} => 2

{{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => {{1},{2},{3},{4,5,6,7}} => 1

{{1,2,3,5,6,7},{4}} => [2,3,5,4,6,7,1] => [1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}} => 4

{{1,2,3,5,6},{4,7}} => [2,3,5,7,6,1,4] => [1,2,7,3,5,4,6] => {{1},{2},{3,7},{4},{5},{6}} => 4

{{1,2,3,5,6},{4},{7}} => [2,3,5,4,6,1,7] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}} => 1

{{1,2,3,5,7},{4,6}} => [2,3,5,6,7,4,1] => [1,2,6,3,4,5,7] => {{1},{2},{3,6},{4},{5},{7}} => 4

{{1,2,3,5},{4,6,7}} => [2,3,5,6,1,7,4] => [1,2,7,3,4,6,5] => {{1},{2},{3,7},{4},{5},{6}} => 4

{{1,2,3,5},{4,6},{7}} => [2,3,5,6,1,4,7] => [1,2,6,3,4,7,5] => {{1},{2},{3,6,7},{4},{5}} => 1

{{1,2,3,5,7},{4},{6}} => [2,3,5,4,7,6,1] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}} => 2

{{1,2,3,5},{4,7},{6}} => [2,3,5,7,1,6,4] => [1,2,7,3,6,4,5] => {{1},{2},{3,7},{4},{5,6}} => 2

{{1,2,3,5},{4},{6,7}} => [2,3,5,4,1,7,6] => [1,2,4,3,7,6,5] => {{1},{2},{3,4},{5,7},{6}} => 2

{{1,2,3,5},{4},{6},{7}} => [2,3,5,4,1,6,7] => [1,2,4,3,6,7,5] => {{1},{2},{3,4},{5,6,7}} => 1

{{1,2,3,6,7},{4,5}} => [2,3,6,5,4,7,1] => [1,2,5,4,3,6,7] => {{1},{2},{3,5},{4},{6},{7}} => 4

{{1,2,3,6},{4,5,7}} => [2,3,6,5,7,1,4] => [1,2,7,4,3,5,6] => {{1},{2},{3,7},{4},{5},{6}} => 4

{{1,2,3,6},{4,5},{7}} => [2,3,6,5,4,1,7] => [1,2,5,4,3,7,6] => {{1},{2},{3,5},{4},{6,7}} => 1

{{1,2,3,7},{4,5,6}} => [2,3,7,5,6,4,1] => [1,2,6,4,5,3,7] => {{1},{2},{3,6},{4},{5},{7}} => 4

{{1,2,3},{4,5,6,7}} => [2,3,1,5,6,7,4] => [1,2,7,4,5,6,3] => {{1},{2},{3,7},{4},{5},{6}} => 4

{{1,2,3},{4,5,6},{7}} => [2,3,1,5,6,4,7] => [1,2,6,4,5,7,3] => {{1},{2},{3,6,7},{4},{5}} => 1

{{1,2,3,7},{4,5},{6}} => [2,3,7,5,4,6,1] => [1,2,5,4,6,3,7] => {{1},{2},{3,5,6},{4},{7}} => 2

{{1,2,3},{4,5,7},{6}} => [2,3,1,5,7,6,4] => [1,2,7,4,6,5,3] => {{1},{2},{3,7},{4},{5,6}} => 2

{{1,2,3},{4,5},{6,7}} => [2,3,1,5,4,7,6] => [1,2,5,4,7,6,3] => {{1},{2},{3,5,7},{4},{6}} => 2

{{1,2,3},{4,5},{6},{7}} => [2,3,1,5,4,6,7] => [1,2,5,4,6,7,3] => {{1},{2},{3,5,6,7},{4}} => 1

{{1,2,3,6,7},{4},{5}} => [2,3,6,4,5,7,1] => [1,2,4,5,3,6,7] => {{1},{2},{3,4,5},{6},{7}} => 3

{{1,2,3,6},{4,7},{5}} => [2,3,6,7,5,1,4] => [1,2,7,5,3,4,6] => {{1},{2},{3,7},{4,5},{6}} => 3

{{1,2,3,6},{4},{5,7}} => [2,3,6,4,7,1,5] => [1,2,4,7,3,5,6] => {{1},{2},{3,4,7},{5},{6}} => 3

{{1,2,3,6},{4},{5},{7}} => [2,3,6,4,5,1,7] => [1,2,4,5,3,7,6] => {{1},{2},{3,4,5},{6,7}} => 1

{{1,2,3,7},{4,6},{5}} => [2,3,7,6,5,4,1] => [1,2,6,5,4,3,7] => {{1},{2},{3,6},{4,5},{7}} => 3

{{1,2,3},{4,6,7},{5}} => [2,3,1,6,5,7,4] => [1,2,7,5,4,6,3] => {{1},{2},{3,7},{4,5},{6}} => 3

{{1,2,3},{4,6},{5,7}} => [2,3,1,6,7,4,5] => [1,2,6,7,4,5,3] => {{1},{2},{3,6},{4,7},{5}} => 3

{{1,2,3},{4,6},{5},{7}} => [2,3,1,6,5,4,7] => [1,2,6,5,4,7,3] => {{1},{2},{3,6,7},{4,5}} => 1

{{1,2,3,7},{4},{5,6}} => [2,3,7,4,6,5,1] => [1,2,4,6,5,3,7] => {{1},{2},{3,4,6},{5},{7}} => 3

{{1,2,3},{4,7},{5,6}} => [2,3,1,7,6,5,4] => [1,2,7,6,5,4,3] => {{1},{2},{3,7},{4,6},{5}} => 3

{{1,2,3},{4},{5,6,7}} => [2,3,1,4,6,7,5] => [1,2,4,7,5,6,3] => {{1},{2},{3,4,7},{5},{6}} => 3

{{1,2,3},{4},{5,6},{7}} => [2,3,1,4,6,5,7] => [1,2,4,6,5,7,3] => {{1},{2},{3,4,6,7},{5}} => 1

{{1,2,3,7},{4},{5},{6}} => [2,3,7,4,5,6,1] => [1,2,4,5,6,3,7] => {{1},{2},{3,4,5,6},{7}} => 2

{{1,2,3},{4,7},{5},{6}} => [2,3,1,7,5,6,4] => [1,2,7,5,6,4,3] => {{1},{2},{3,7},{4,5,6}} => 2

{{1,2,3},{4},{5,7},{6}} => [2,3,1,4,7,6,5] => [1,2,4,7,6,5,3] => {{1},{2},{3,4,7},{5,6}} => 2

{{1,2,3},{4},{5},{6,7}} => [2,3,1,4,5,7,6] => [1,2,4,5,7,6,3] => {{1},{2},{3,4,5,7},{6}} => 2

{{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => {{1},{2},{3,4,5,6,7}} => 1

{{1,2,4,5,6,7},{3}} => [2,4,3,5,6,7,1] => [1,3,2,4,5,6,7] => {{1},{2,3},{4},{5},{6},{7}} => 5

{{1,2,4,5,6},{3,7}} => [2,4,7,5,6,1,3] => [1,7,2,4,5,3,6] => {{1},{2,7},{3},{4},{5},{6}} => 5

{{1,2,4,5,6},{3},{7}} => [2,4,3,5,6,1,7] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}} => 1

{{1,2,4,5,7},{3,6}} => [2,4,6,5,7,3,1] => [1,6,2,4,3,5,7] => {{1},{2,6},{3},{4},{5},{7}} => 5

{{1,2,4,5},{3,6,7}} => [2,4,6,5,1,7,3] => [1,7,2,4,3,6,5] => {{1},{2,7},{3},{4},{5},{6}} => 5

{{1,2,4,5},{3,6},{7}} => [2,4,6,5,1,3,7] => [1,6,2,4,3,7,5] => {{1},{2,6,7},{3},{4},{5}} => 1

{{1,2,4,5,7},{3},{6}} => [2,4,3,5,7,6,1] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}} => 2

{{1,2,4,5},{3,7},{6}} => [2,4,7,5,1,6,3] => [1,7,2,4,6,3,5] => {{1},{2,7},{3},{4},{5,6}} => 2

{{1,2,4,5},{3},{6,7}} => [2,4,3,5,1,7,6] => [1,3,2,4,7,6,5] => {{1},{2,3},{4},{5,7},{6}} => 2

{{1,2,4,5},{3},{6},{7}} => [2,4,3,5,1,6,7] => [1,3,2,4,6,7,5] => {{1},{2,3},{4},{5,6,7}} => 1

{{1,2,4,6,7},{3,5}} => [2,4,5,6,3,7,1] => [1,5,2,3,4,6,7] => {{1},{2,5},{3},{4},{6},{7}} => 5

{{1,2,4,6},{3,5,7}} => [2,4,5,6,7,1,3] => [1,7,2,3,4,5,6] => {{1},{2,7},{3},{4},{5},{6}} => 5

{{1,2,4,6},{3,5},{7}} => [2,4,5,6,3,1,7] => [1,5,2,3,4,7,6] => {{1},{2,5},{3},{4},{6,7}} => 1

{{1,2,4,7},{3,5,6}} => [2,4,5,7,6,3,1] => [1,6,2,3,5,4,7] => {{1},{2,6},{3},{4},{5},{7}} => 5

{{1,2,4},{3,5,6,7}} => [2,4,5,1,6,7,3] => [1,7,2,3,5,6,4] => {{1},{2,7},{3},{4},{5},{6}} => 5

{{1,2,4},{3,5,6},{7}} => [2,4,5,1,6,3,7] => [1,6,2,3,5,7,4] => {{1},{2,6,7},{3},{4},{5}} => 1

{{1,2,4,7},{3,5},{6}} => [2,4,5,7,3,6,1] => [1,5,2,3,6,4,7] => {{1},{2,5,6},{3},{4},{7}} => 2

{{1,2,4},{3,5,7},{6}} => [2,4,5,1,7,6,3] => [1,7,2,3,6,5,4] => {{1},{2,7},{3},{4},{5,6}} => 2

{{1,2,4},{3,5},{6,7}} => [2,4,5,1,3,7,6] => [1,5,2,3,7,6,4] => {{1},{2,5,7},{3},{4},{6}} => 2

{{1,2,4},{3,5},{6},{7}} => [2,4,5,1,3,6,7] => [1,5,2,3,6,7,4] => {{1},{2,5,6,7},{3},{4}} => 1

{{1,2,4,6,7},{3},{5}} => [2,4,3,6,5,7,1] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}} => 3

{{1,2,4,6},{3,7},{5}} => [2,4,7,6,5,1,3] => [1,7,2,5,4,3,6] => {{1},{2,7},{3},{4,5},{6}} => 3

{{1,2,4,6},{3},{5,7}} => [2,4,3,6,7,1,5] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,7},{5},{6}} => 3

{{1,2,4,6},{3},{5},{7}} => [2,4,3,6,5,1,7] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}} => 1

{{1,2,4,7},{3,6},{5}} => [2,4,6,7,5,3,1] => [1,6,2,5,3,4,7] => {{1},{2,6},{3},{4,5},{7}} => 3

{{1,2,4},{3,6,7},{5}} => [2,4,6,1,5,7,3] => [1,7,2,5,3,6,4] => {{1},{2,7},{3},{4,5},{6}} => 3

{{1,2,4},{3,6},{5,7}} => [2,4,6,1,7,3,5] => [1,6,2,7,3,5,4] => {{1},{2,6},{3},{4,7},{5}} => 3

{{1,2,4},{3,6},{5},{7}} => [2,4,6,1,5,3,7] => [1,6,2,5,3,7,4] => {{1},{2,6,7},{3},{4,5}} => 1

{{1,2,4,7},{3},{5,6}} => [2,4,3,7,6,5,1] => [1,3,2,6,5,4,7] => {{1},{2,3},{4,6},{5},{7}} => 3

{{1,2,4},{3,7},{5,6}} => [2,4,7,1,6,5,3] => [1,7,2,6,5,3,4] => {{1},{2,7},{3},{4,6},{5}} => 3

{{1,2,4},{3},{5,6,7}} => [2,4,3,1,6,7,5] => [1,3,2,7,5,6,4] => {{1},{2,3},{4,7},{5},{6}} => 3

{{1,2,4},{3},{5,6},{7}} => [2,4,3,1,6,5,7] => [1,3,2,6,5,7,4] => {{1},{2,3},{4,6,7},{5}} => 1

{{1,2,4,7},{3},{5},{6}} => [2,4,3,7,5,6,1] => [1,3,2,5,6,4,7] => {{1},{2,3},{4,5,6},{7}} => 2

{{1,2,4},{3,7},{5},{6}} => [2,4,7,1,5,6,3] => [1,7,2,5,6,3,4] => {{1},{2,7},{3},{4,5,6}} => 2

{{1,2,4},{3},{5,7},{6}} => [2,4,3,1,7,6,5] => [1,3,2,7,6,5,4] => {{1},{2,3},{4,7},{5,6}} => 2

{{1,2,4},{3},{5},{6,7}} => [2,4,3,1,5,7,6] => [1,3,2,5,7,6,4] => {{1},{2,3},{4,5,7},{6}} => 2

{{1,2,4},{3},{5},{6},{7}} => [2,4,3,1,5,6,7] => [1,3,2,5,6,7,4] => {{1},{2,3},{4,5,6,7}} => 1

{{1,2,5,6,7},{3,4}} => [2,5,4,3,6,7,1] => [1,4,3,2,5,6,7] => {{1},{2,4},{3},{5},{6},{7}} => 5

{{1,2,5,6},{3,4,7}} => [2,5,4,7,6,1,3] => [1,7,3,2,5,4,6] => {{1},{2,7},{3},{4},{5},{6}} => 5

{{1,2,5,6},{3,4},{7}} => [2,5,4,3,6,1,7] => [1,4,3,2,5,7,6] => {{1},{2,4},{3},{5},{6,7}} => 1

{{1,2,5,7},{3,4,6}} => [2,5,4,6,7,3,1] => [1,6,3,2,4,5,7] => {{1},{2,6},{3},{4},{5},{7}} => 5

{{1,2,5},{3,4,6,7}} => [2,5,4,6,1,7,3] => [1,7,3,2,4,6,5] => {{1},{2,7},{3},{4},{5},{6}} => 5

{{1,2,5},{3,4,6},{7}} => [2,5,4,6,1,3,7] => [1,6,3,2,4,7,5] => {{1},{2,6,7},{3},{4},{5}} => 1

{{1,2,5,7},{3,4},{6}} => [2,5,4,3,7,6,1] => [1,4,3,2,6,5,7] => {{1},{2,4},{3},{5,6},{7}} => 2

{{1,2,5},{3,4,7},{6}} => [2,5,4,7,1,6,3] => [1,7,3,2,6,4,5] => {{1},{2,7},{3},{4},{5,6}} => 2

{{1,2,5},{3,4},{6,7}} => [2,5,4,3,1,7,6] => [1,4,3,2,7,6,5] => {{1},{2,4},{3},{5,7},{6}} => 2

{{1,2,5},{3,4},{6},{7}} => [2,5,4,3,1,6,7] => [1,4,3,2,6,7,5] => {{1},{2,4},{3},{5,6,7}} => 1

{{1,2,6,7},{3,4,5}} => [2,6,4,5,3,7,1] => [1,5,3,4,2,6,7] => {{1},{2,5},{3},{4},{6},{7}} => 5

{{1,2,6},{3,4,5,7}} => [2,6,4,5,7,1,3] => [1,7,3,4,2,5,6] => {{1},{2,7},{3},{4},{5},{6}} => 5

{{1,2,6},{3,4,5},{7}} => [2,6,4,5,3,1,7] => [1,5,3,4,2,7,6] => {{1},{2,5},{3},{4},{6,7}} => 1

{{1,2,7},{3,4,5,6}} => [2,7,4,5,6,3,1] => [1,6,3,4,5,2,7] => {{1},{2,6},{3},{4},{5},{7}} => 5

{{1,2},{3,4,5,6,7}} => [2,1,4,5,6,7,3] => [1,7,3,4,5,6,2] => {{1},{2,7},{3},{4},{5},{6}} => 5

{{1,2},{3,4,5,6},{7}} => [2,1,4,5,6,3,7] => [1,6,3,4,5,7,2] => {{1},{2,6,7},{3},{4},{5}} => 1

{{1,2,7},{3,4,5},{6}} => [2,7,4,5,3,6,1] => [1,5,3,4,6,2,7] => {{1},{2,5,6},{3},{4},{7}} => 2

{{1,2},{3,4,5,7},{6}} => [2,1,4,5,7,6,3] => [1,7,3,4,6,5,2] => {{1},{2,7},{3},{4},{5,6}} => 2

{{1,2},{3,4,5},{6,7}} => [2,1,4,5,3,7,6] => [1,5,3,4,7,6,2] => {{1},{2,5,7},{3},{4},{6}} => 2

{{1,2},{3,4,5},{6},{7}} => [2,1,4,5,3,6,7] => [1,5,3,4,6,7,2] => {{1},{2,5,6,7},{3},{4}} => 1

{{1,2,6,7},{3,4},{5}} => [2,6,4,3,5,7,1] => [1,4,3,5,2,6,7] => {{1},{2,4,5},{3},{6},{7}} => 3

{{1,2,6},{3,4,7},{5}} => [2,6,4,7,5,1,3] => [1,7,3,5,2,4,6] => {{1},{2,7},{3},{4,5},{6}} => 3

{{1,2,6},{3,4},{5,7}} => [2,6,4,3,7,1,5] => [1,4,3,7,2,5,6] => {{1},{2,4,7},{3},{5},{6}} => 3

{{1,2,6},{3,4},{5},{7}} => [2,6,4,3,5,1,7] => [1,4,3,5,2,7,6] => {{1},{2,4,5},{3},{6,7}} => 1

{{1,2,7},{3,4,6},{5}} => [2,7,4,6,5,3,1] => [1,6,3,5,4,2,7] => {{1},{2,6},{3},{4,5},{7}} => 3

{{1,2},{3,4,6,7},{5}} => [2,1,4,6,5,7,3] => [1,7,3,5,4,6,2] => {{1},{2,7},{3},{4,5},{6}} => 3

{{1,2},{3,4,6},{5,7}} => [2,1,4,6,7,3,5] => [1,6,3,7,4,5,2] => {{1},{2,6},{3},{4,7},{5}} => 3

{{1,2},{3,4,6},{5},{7}} => [2,1,4,6,5,3,7] => [1,6,3,5,4,7,2] => {{1},{2,6,7},{3},{4,5}} => 1

{{1,2,7},{3,4},{5,6}} => [2,7,4,3,6,5,1] => [1,4,3,6,5,2,7] => {{1},{2,4,6},{3},{5},{7}} => 3

{{1,2},{3,4,7},{5,6}} => [2,1,4,7,6,5,3] => [1,7,3,6,5,4,2] => {{1},{2,7},{3},{4,6},{5}} => 3

{{1,2},{3,4},{5,6,7}} => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => {{1},{2,4,7},{3},{5},{6}} => 3

{{1,2},{3,4},{5,6},{7}} => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => {{1},{2,4,6,7},{3},{5}} => 1

{{1,2,7},{3,4},{5},{6}} => [2,7,4,3,5,6,1] => [1,4,3,5,6,2,7] => {{1},{2,4,5,6},{3},{7}} => 2

{{1,2},{3,4,7},{5},{6}} => [2,1,4,7,5,6,3] => [1,7,3,5,6,4,2] => {{1},{2,7},{3},{4,5,6}} => 2

{{1,2},{3,4},{5,7},{6}} => [2,1,4,3,7,6,5] => [1,4,3,7,6,5,2] => {{1},{2,4,7},{3},{5,6}} => 2

{{1,2},{3,4},{5},{6,7}} => [2,1,4,3,5,7,6] => [1,4,3,5,7,6,2] => {{1},{2,4,5,7},{3},{6}} => 2

{{1,2},{3,4},{5},{6},{7}} => [2,1,4,3,5,6,7] => [1,4,3,5,6,7,2] => {{1},{2,4,5,6,7},{3}} => 1

{{1,2,5,6,7},{3},{4}} => [2,5,3,4,6,7,1] => [1,3,4,2,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => 4

{{1,2,5,6},{3,7},{4}} => [2,5,7,4,6,1,3] => [1,7,4,2,5,3,6] => {{1},{2,7},{3,4},{5},{6}} => 4

{{1,2,5,6},{3},{4,7}} => [2,5,3,7,6,1,4] => [1,3,7,2,5,4,6] => {{1},{2,3,7},{4},{5},{6}} => 4

{{1,2,5,6},{3},{4},{7}} => [2,5,3,4,6,1,7] => [1,3,4,2,5,7,6] => {{1},{2,3,4},{5},{6,7}} => 1

{{1,2,5,7},{3,6},{4}} => [2,5,6,4,7,3,1] => [1,6,4,2,3,5,7] => {{1},{2,6},{3,4},{5},{7}} => 4

{{1,2,5},{3,6,7},{4}} => [2,5,6,4,1,7,3] => [1,7,4,2,3,6,5] => {{1},{2,7},{3,4},{5},{6}} => 4

{{1,2,5},{3,6},{4,7}} => [2,5,6,7,1,3,4] => [1,6,7,2,3,4,5] => {{1},{2,6},{3,7},{4},{5}} => 4

{{1,2,5},{3,6},{4},{7}} => [2,5,6,4,1,3,7] => [1,6,4,2,3,7,5] => {{1},{2,6,7},{3,4},{5}} => 1

{{1,2,5,7},{3},{4,6}} => [2,5,3,6,7,4,1] => [1,3,6,2,4,5,7] => {{1},{2,3,6},{4},{5},{7}} => 4

{{1,2,5},{3,7},{4,6}} => [2,5,7,6,1,4,3] => [1,7,6,2,4,3,5] => {{1},{2,7},{3,6},{4},{5}} => 4

{{1,2,5},{3},{4,6,7}} => [2,5,3,6,1,7,4] => [1,3,7,2,4,6,5] => {{1},{2,3,7},{4},{5},{6}} => 4

{{1,2,5},{3},{4,6},{7}} => [2,5,3,6,1,4,7] => [1,3,6,2,4,7,5] => {{1},{2,3,6,7},{4},{5}} => 1

{{1,2,5,7},{3},{4},{6}} => [2,5,3,4,7,6,1] => [1,3,4,2,6,5,7] => {{1},{2,3,4},{5,6},{7}} => 2

{{1,2,5},{3,7},{4},{6}} => [2,5,7,4,1,6,3] => [1,7,4,2,6,3,5] => {{1},{2,7},{3,4},{5,6}} => 2

{{1,2,5},{3},{4,7},{6}} => [2,5,3,7,1,6,4] => [1,3,7,2,6,4,5] => {{1},{2,3,7},{4},{5,6}} => 2

{{1,2,5},{3},{4},{6,7}} => [2,5,3,4,1,7,6] => [1,3,4,2,7,6,5] => {{1},{2,3,4},{5,7},{6}} => 2

{{1,2,5},{3},{4},{6},{7}} => [2,5,3,4,1,6,7] => [1,3,4,2,6,7,5] => {{1},{2,3,4},{5,6,7}} => 1

{{1,2,6,7},{3,5},{4}} => [2,6,5,4,3,7,1] => [1,5,4,3,2,6,7] => {{1},{2,5},{3,4},{6},{7}} => 4

{{1,2,6},{3,5,7},{4}} => [2,6,5,4,7,1,3] => [1,7,4,3,2,5,6] => {{1},{2,7},{3,4},{5},{6}} => 4

{{1,2,6},{3,5},{4,7}} => [2,6,5,7,3,1,4] => [1,5,7,3,2,4,6] => {{1},{2,5},{3,7},{4},{6}} => 4

{{1,2,6},{3,5},{4},{7}} => [2,6,5,4,3,1,7] => [1,5,4,3,2,7,6] => {{1},{2,5},{3,4},{6,7}} => 1

{{1,2,7},{3,5,6},{4}} => [2,7,5,4,6,3,1] => [1,6,4,3,5,2,7] => {{1},{2,6},{3,4},{5},{7}} => 4

{{1,2},{3,5,6,7},{4}} => [2,1,5,4,6,7,3] => [1,7,4,3,5,6,2] => {{1},{2,7},{3,4},{5},{6}} => 4

{{1,2},{3,5,6},{4,7}} => [2,1,5,7,6,3,4] => [1,6,7,3,5,4,2] => {{1},{2,6},{3,7},{4},{5}} => 4

{{1,2},{3,5,6},{4},{7}} => [2,1,5,4,6,3,7] => [1,6,4,3,5,7,2] => {{1},{2,6,7},{3,4},{5}} => 1

{{1,2,7},{3,5},{4,6}} => [2,7,5,6,3,4,1] => [1,5,6,3,4,2,7] => {{1},{2,5},{3,6},{4},{7}} => 4

{{1,2},{3,5,7},{4,6}} => [2,1,5,6,7,4,3] => [1,7,6,3,4,5,2] => {{1},{2,7},{3,6},{4},{5}} => 4

{{1,2},{3,5},{4,6,7}} => [2,1,5,6,3,7,4] => [1,5,7,3,4,6,2] => {{1},{2,5},{3,7},{4},{6}} => 4

{{1,2},{3,5},{4,6},{7}} => [2,1,5,6,3,4,7] => [1,5,6,3,4,7,2] => {{1},{2,5},{3,6,7},{4}} => 1

{{1,2,7},{3,5},{4},{6}} => [2,7,5,4,3,6,1] => [1,5,4,3,6,2,7] => {{1},{2,5,6},{3,4},{7}} => 2

{{1,2},{3,5,7},{4},{6}} => [2,1,5,4,7,6,3] => [1,7,4,3,6,5,2] => {{1},{2,7},{3,4},{5,6}} => 2

{{1,2},{3,5},{4,7},{6}} => [2,1,5,7,3,6,4] => [1,5,7,3,6,4,2] => {{1},{2,5,6},{3,7},{4}} => 2

{{1,2},{3,5},{4},{6,7}} => [2,1,5,4,3,7,6] => [1,5,4,3,7,6,2] => {{1},{2,5,7},{3,4},{6}} => 2

{{1,2},{3,5},{4},{6},{7}} => [2,1,5,4,3,6,7] => [1,5,4,3,6,7,2] => {{1},{2,5,6,7},{3,4}} => 1

{{1,2,6,7},{3},{4,5}} => [2,6,3,5,4,7,1] => [1,3,5,4,2,6,7] => {{1},{2,3,5},{4},{6},{7}} => 4

{{1,2,6},{3,7},{4,5}} => [2,6,7,5,4,1,3] => [1,7,5,4,2,3,6] => {{1},{2,7},{3,5},{4},{6}} => 4

{{1,2,6},{3},{4,5,7}} => [2,6,3,5,7,1,4] => [1,3,7,4,2,5,6] => {{1},{2,3,7},{4},{5},{6}} => 4

{{1,2,6},{3},{4,5},{7}} => [2,6,3,5,4,1,7] => [1,3,5,4,2,7,6] => {{1},{2,3,5},{4},{6,7}} => 1

{{1,2,7},{3,6},{4,5}} => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => {{1},{2,6},{3,5},{4},{7}} => 4

{{1,2},{3,6,7},{4,5}} => [2,1,6,5,4,7,3] => [1,7,5,4,3,6,2] => {{1},{2,7},{3,5},{4},{6}} => 4

{{1,2},{3,6},{4,5,7}} => [2,1,6,5,7,3,4] => [1,6,7,4,3,5,2] => {{1},{2,6},{3,7},{4},{5}} => 4

{{1,2},{3,6},{4,5},{7}} => [2,1,6,5,4,3,7] => [1,6,5,4,3,7,2] => {{1},{2,6,7},{3,5},{4}} => 1

{{1,2,7},{3},{4,5,6}} => [2,7,3,5,6,4,1] => [1,3,6,4,5,2,7] => {{1},{2,3,6},{4},{5},{7}} => 4

{{1,2},{3,7},{4,5,6}} => [2,1,7,5,6,4,3] => [1,7,6,4,5,3,2] => {{1},{2,7},{3,6},{4},{5}} => 4

{{1,2},{3},{4,5,6,7}} => [2,1,3,5,6,7,4] => [1,3,7,4,5,6,2] => {{1},{2,3,7},{4},{5},{6}} => 4

{{1,2},{3},{4,5,6},{7}} => [2,1,3,5,6,4,7] => [1,3,6,4,5,7,2] => {{1},{2,3,6,7},{4},{5}} => 1

{{1,2,7},{3},{4,5},{6}} => [2,7,3,5,4,6,1] => [1,3,5,4,6,2,7] => {{1},{2,3,5,6},{4},{7}} => 2

{{1,2},{3,7},{4,5},{6}} => [2,1,7,5,4,6,3] => [1,7,5,4,6,3,2] => {{1},{2,7},{3,5,6},{4}} => 2

{{1,2},{3},{4,5,7},{6}} => [2,1,3,5,7,6,4] => [1,3,7,4,6,5,2] => {{1},{2,3,7},{4},{5,6}} => 2

{{1,2},{3},{4,5},{6,7}} => [2,1,3,5,4,7,6] => [1,3,5,4,7,6,2] => {{1},{2,3,5,7},{4},{6}} => 2

{{1,2},{3},{4,5},{6},{7}} => [2,1,3,5,4,6,7] => [1,3,5,4,6,7,2] => {{1},{2,3,5,6,7},{4}} => 1

{{1,2,6,7},{3},{4},{5}} => [2,6,3,4,5,7,1] => [1,3,4,5,2,6,7] => {{1},{2,3,4,5},{6},{7}} => 3

{{1,2,6},{3,7},{4},{5}} => [2,6,7,4,5,1,3] => [1,7,4,5,2,3,6] => {{1},{2,7},{3,4,5},{6}} => 3

{{1,2,6},{3},{4,7},{5}} => [2,6,3,7,5,1,4] => [1,3,7,5,2,4,6] => {{1},{2,3,7},{4,5},{6}} => 3

{{1,2,6},{3},{4},{5,7}} => [2,6,3,4,7,1,5] => [1,3,4,7,2,5,6] => {{1},{2,3,4,7},{5},{6}} => 3

{{1,2,6},{3},{4},{5},{7}} => [2,6,3,4,5,1,7] => [1,3,4,5,2,7,6] => {{1},{2,3,4,5},{6,7}} => 1

{{1,2,7},{3,6},{4},{5}} => [2,7,6,4,5,3,1] => [1,6,4,5,3,2,7] => {{1},{2,6},{3,4,5},{7}} => 3

{{1,2},{3,6,7},{4},{5}} => [2,1,6,4,5,7,3] => [1,7,4,5,3,6,2] => {{1},{2,7},{3,4,5},{6}} => 3

{{1,2},{3,6},{4,7},{5}} => [2,1,6,7,5,3,4] => [1,6,7,5,3,4,2] => {{1},{2,6},{3,7},{4,5}} => 3

{{1,2},{3,6},{4},{5,7}} => [2,1,6,4,7,3,5] => [1,6,4,7,3,5,2] => {{1},{2,6},{3,4,7},{5}} => 3

{{1,2},{3,6},{4},{5},{7}} => [2,1,6,4,5,3,7] => [1,6,4,5,3,7,2] => {{1},{2,6,7},{3,4,5}} => 1

{{1,2,7},{3},{4,6},{5}} => [2,7,3,6,5,4,1] => [1,3,6,5,4,2,7] => {{1},{2,3,6},{4,5},{7}} => 3

{{1,2},{3,7},{4,6},{5}} => [2,1,7,6,5,4,3] => [1,7,6,5,4,3,2] => {{1},{2,7},{3,6},{4,5}} => 3

{{1,2},{3},{4,6,7},{5}} => [2,1,3,6,5,7,4] => [1,3,7,5,4,6,2] => {{1},{2,3,7},{4,5},{6}} => 3

{{1,2},{3},{4,6},{5,7}} => [2,1,3,6,7,4,5] => [1,3,6,7,4,5,2] => {{1},{2,3,6},{4,7},{5}} => 3

{{1,2},{3},{4,6},{5},{7}} => [2,1,3,6,5,4,7] => [1,3,6,5,4,7,2] => {{1},{2,3,6,7},{4,5}} => 1

{{1,2,7},{3},{4},{5,6}} => [2,7,3,4,6,5,1] => [1,3,4,6,5,2,7] => {{1},{2,3,4,6},{5},{7}} => 3

{{1,2},{3,7},{4},{5,6}} => [2,1,7,4,6,5,3] => [1,7,4,6,5,3,2] => {{1},{2,7},{3,4,6},{5}} => 3

{{1,2},{3},{4,7},{5,6}} => [2,1,3,7,6,5,4] => [1,3,7,6,5,4,2] => {{1},{2,3,7},{4,6},{5}} => 3

{{1,2},{3},{4},{5,6,7}} => [2,1,3,4,6,7,5] => [1,3,4,7,5,6,2] => {{1},{2,3,4,7},{5},{6}} => 3

{{1,2},{3},{4},{5,6},{7}} => [2,1,3,4,6,5,7] => [1,3,4,6,5,7,2] => {{1},{2,3,4,6,7},{5}} => 1

{{1,2,7},{3},{4},{5},{6}} => [2,7,3,4,5,6,1] => [1,3,4,5,6,2,7] => {{1},{2,3,4,5,6},{7}} => 2

{{1,2},{3,7},{4},{5},{6}} => [2,1,7,4,5,6,3] => [1,7,4,5,6,3,2] => {{1},{2,7},{3,4,5,6}} => 2

{{1,2},{3},{4,7},{5},{6}} => [2,1,3,7,5,6,4] => [1,3,7,5,6,4,2] => {{1},{2,3,7},{4,5,6}} => 2

{{1,2},{3},{4},{5,7},{6}} => [2,1,3,4,7,6,5] => [1,3,4,7,6,5,2] => {{1},{2,3,4,7},{5,6}} => 2

{{1,2},{3},{4},{5},{6,7}} => [2,1,3,4,5,7,6] => [1,3,4,5,7,6,2] => {{1},{2,3,4,5,7},{6}} => 2

{{1,2},{3},{4},{5},{6},{7}} => [2,1,3,4,5,6,7] => [1,3,4,5,6,7,2] => {{1},{2,3,4,5,6,7}} => 1

{{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => [2,1,3,4,5,6,7] => {{1,2},{3},{4},{5},{6},{7}} => 6

{{1,3,4,5,6},{2,7}} => [3,7,4,5,6,1,2] => [7,1,3,4,5,2,6] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,3,4,5,6},{2},{7}} => [3,2,4,5,6,1,7] => [2,1,3,4,5,7,6] => {{1,2},{3},{4},{5},{6,7}} => 1

{{1,3,4,5,7},{2,6}} => [3,6,4,5,7,2,1] => [6,1,3,4,2,5,7] => {{1,6},{2},{3},{4},{5},{7}} => 6

{{1,3,4,5},{2,6,7}} => [3,6,4,5,1,7,2] => [7,1,3,4,2,6,5] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,3,4,5},{2,6},{7}} => [3,6,4,5,1,2,7] => [6,1,3,4,2,7,5] => {{1,6,7},{2},{3},{4},{5}} => 1

{{1,3,4,5,7},{2},{6}} => [3,2,4,5,7,6,1] => [2,1,3,4,6,5,7] => {{1,2},{3},{4},{5,6},{7}} => 2

{{1,3,4,5},{2,7},{6}} => [3,7,4,5,1,6,2] => [7,1,3,4,6,2,5] => {{1,7},{2},{3},{4},{5,6}} => 2

{{1,3,4,5},{2},{6,7}} => [3,2,4,5,1,7,6] => [2,1,3,4,7,6,5] => {{1,2},{3},{4},{5,7},{6}} => 2

{{1,3,4,5},{2},{6},{7}} => [3,2,4,5,1,6,7] => [2,1,3,4,6,7,5] => {{1,2},{3},{4},{5,6,7}} => 1

{{1,3,4,6,7},{2,5}} => [3,5,4,6,2,7,1] => [5,1,3,2,4,6,7] => {{1,5},{2},{3},{4},{6},{7}} => 6

{{1,3,4,6},{2,5,7}} => [3,5,4,6,7,1,2] => [7,1,3,2,4,5,6] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,3,4,6},{2,5},{7}} => [3,5,4,6,2,1,7] => [5,1,3,2,4,7,6] => {{1,5},{2},{3},{4},{6,7}} => 1

{{1,3,4,7},{2,5,6}} => [3,5,4,7,6,2,1] => [6,1,3,2,5,4,7] => {{1,6},{2},{3},{4},{5},{7}} => 6

{{1,3,4},{2,5,6,7}} => [3,5,4,1,6,7,2] => [7,1,3,2,5,6,4] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,3,4},{2,5,6},{7}} => [3,5,4,1,6,2,7] => [6,1,3,2,5,7,4] => {{1,6,7},{2},{3},{4},{5}} => 1

{{1,3,4,7},{2,5},{6}} => [3,5,4,7,2,6,1] => [5,1,3,2,6,4,7] => {{1,5,6},{2},{3},{4},{7}} => 2

{{1,3,4},{2,5,7},{6}} => [3,5,4,1,7,6,2] => [7,1,3,2,6,5,4] => {{1,7},{2},{3},{4},{5,6}} => 2

{{1,3,4},{2,5},{6,7}} => [3,5,4,1,2,7,6] => [5,1,3,2,7,6,4] => {{1,5,7},{2},{3},{4},{6}} => 2

{{1,3,4},{2,5},{6},{7}} => [3,5,4,1,2,6,7] => [5,1,3,2,6,7,4] => {{1,5,6,7},{2},{3},{4}} => 1

{{1,3,4,6,7},{2},{5}} => [3,2,4,6,5,7,1] => [2,1,3,5,4,6,7] => {{1,2},{3},{4,5},{6},{7}} => 3

{{1,3,4,6},{2,7},{5}} => [3,7,4,6,5,1,2] => [7,1,3,5,4,2,6] => {{1,7},{2},{3},{4,5},{6}} => 3

{{1,3,4,6},{2},{5,7}} => [3,2,4,6,7,1,5] => [2,1,3,7,4,5,6] => {{1,2},{3},{4,7},{5},{6}} => 3

{{1,3,4,6},{2},{5},{7}} => [3,2,4,6,5,1,7] => [2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}} => 1

{{1,3,4,7},{2,6},{5}} => [3,6,4,7,5,2,1] => [6,1,3,5,2,4,7] => {{1,6},{2},{3},{4,5},{7}} => 3

{{1,3,4},{2,6,7},{5}} => [3,6,4,1,5,7,2] => [7,1,3,5,2,6,4] => {{1,7},{2},{3},{4,5},{6}} => 3

{{1,3,4},{2,6},{5,7}} => [3,6,4,1,7,2,5] => [6,1,3,7,2,5,4] => {{1,6},{2},{3},{4,7},{5}} => 3

{{1,3,4},{2,6},{5},{7}} => [3,6,4,1,5,2,7] => [6,1,3,5,2,7,4] => {{1,6,7},{2},{3},{4,5}} => 1

{{1,3,4,7},{2},{5,6}} => [3,2,4,7,6,5,1] => [2,1,3,6,5,4,7] => {{1,2},{3},{4,6},{5},{7}} => 3

{{1,3,4},{2,7},{5,6}} => [3,7,4,1,6,5,2] => [7,1,3,6,5,2,4] => {{1,7},{2},{3},{4,6},{5}} => 3

{{1,3,4},{2},{5,6,7}} => [3,2,4,1,6,7,5] => [2,1,3,7,5,6,4] => {{1,2},{3},{4,7},{5},{6}} => 3

{{1,3,4},{2},{5,6},{7}} => [3,2,4,1,6,5,7] => [2,1,3,6,5,7,4] => {{1,2},{3},{4,6,7},{5}} => 1

{{1,3,4,7},{2},{5},{6}} => [3,2,4,7,5,6,1] => [2,1,3,5,6,4,7] => {{1,2},{3},{4,5,6},{7}} => 2

{{1,3,4},{2,7},{5},{6}} => [3,7,4,1,5,6,2] => [7,1,3,5,6,2,4] => {{1,7},{2},{3},{4,5,6}} => 2

{{1,3,4},{2},{5,7},{6}} => [3,2,4,1,7,6,5] => [2,1,3,7,6,5,4] => {{1,2},{3},{4,7},{5,6}} => 2

{{1,3,4},{2},{5},{6,7}} => [3,2,4,1,5,7,6] => [2,1,3,5,7,6,4] => {{1,2},{3},{4,5,7},{6}} => 2

{{1,3,4},{2},{5},{6},{7}} => [3,2,4,1,5,6,7] => [2,1,3,5,6,7,4] => {{1,2},{3},{4,5,6,7}} => 1

{{1,3,5,6,7},{2,4}} => [3,4,5,2,6,7,1] => [4,1,2,3,5,6,7] => {{1,4},{2},{3},{5},{6},{7}} => 6

{{1,3,5,6},{2,4,7}} => [3,4,5,7,6,1,2] => [7,1,2,3,5,4,6] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,3,5,6},{2,4},{7}} => [3,4,5,2,6,1,7] => [4,1,2,3,5,7,6] => {{1,4},{2},{3},{5},{6,7}} => 1

{{1,3,5,7},{2,4,6}} => [3,4,5,6,7,2,1] => [6,1,2,3,4,5,7] => {{1,6},{2},{3},{4},{5},{7}} => 6

{{1,3,5},{2,4,6,7}} => [3,4,5,6,1,7,2] => [7,1,2,3,4,6,5] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,3,5},{2,4,6},{7}} => [3,4,5,6,1,2,7] => [6,1,2,3,4,7,5] => {{1,6,7},{2},{3},{4},{5}} => 1

{{1,3,5,7},{2,4},{6}} => [3,4,5,2,7,6,1] => [4,1,2,3,6,5,7] => {{1,4},{2},{3},{5,6},{7}} => 2

{{1,3,5},{2,4,7},{6}} => [3,4,5,7,1,6,2] => [7,1,2,3,6,4,5] => {{1,7},{2},{3},{4},{5,6}} => 2

{{1,3,5},{2,4},{6,7}} => [3,4,5,2,1,7,6] => [4,1,2,3,7,6,5] => {{1,4},{2},{3},{5,7},{6}} => 2

{{1,3,5},{2,4},{6},{7}} => [3,4,5,2,1,6,7] => [4,1,2,3,6,7,5] => {{1,4},{2},{3},{5,6,7}} => 1

{{1,3,6,7},{2,4,5}} => [3,4,6,5,2,7,1] => [5,1,2,4,3,6,7] => {{1,5},{2},{3},{4},{6},{7}} => 6

{{1,3,6},{2,4,5,7}} => [3,4,6,5,7,1,2] => [7,1,2,4,3,5,6] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,3,6},{2,4,5},{7}} => [3,4,6,5,2,1,7] => [5,1,2,4,3,7,6] => {{1,5},{2},{3},{4},{6,7}} => 1

{{1,3,7},{2,4,5,6}} => [3,4,7,5,6,2,1] => [6,1,2,4,5,3,7] => {{1,6},{2},{3},{4},{5},{7}} => 6

{{1,3},{2,4,5,6,7}} => [3,4,1,5,6,7,2] => [7,1,2,4,5,6,3] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,3},{2,4,5,6},{7}} => [3,4,1,5,6,2,7] => [6,1,2,4,5,7,3] => {{1,6,7},{2},{3},{4},{5}} => 1

{{1,3,7},{2,4,5},{6}} => [3,4,7,5,2,6,1] => [5,1,2,4,6,3,7] => {{1,5,6},{2},{3},{4},{7}} => 2

{{1,3},{2,4,5,7},{6}} => [3,4,1,5,7,6,2] => [7,1,2,4,6,5,3] => {{1,7},{2},{3},{4},{5,6}} => 2

{{1,3},{2,4,5},{6,7}} => [3,4,1,5,2,7,6] => [5,1,2,4,7,6,3] => {{1,5,7},{2},{3},{4},{6}} => 2

{{1,3},{2,4,5},{6},{7}} => [3,4,1,5,2,6,7] => [5,1,2,4,6,7,3] => {{1,5,6,7},{2},{3},{4}} => 1

{{1,3,6,7},{2,4},{5}} => [3,4,6,2,5,7,1] => [4,1,2,5,3,6,7] => {{1,4,5},{2},{3},{6},{7}} => 3

{{1,3,6},{2,4,7},{5}} => [3,4,6,7,5,1,2] => [7,1,2,5,3,4,6] => {{1,7},{2},{3},{4,5},{6}} => 3

{{1,3,6},{2,4},{5,7}} => [3,4,6,2,7,1,5] => [4,1,2,7,3,5,6] => {{1,4,7},{2},{3},{5},{6}} => 3

{{1,3,6},{2,4},{5},{7}} => [3,4,6,2,5,1,7] => [4,1,2,5,3,7,6] => {{1,4,5},{2},{3},{6,7}} => 1

{{1,3,7},{2,4,6},{5}} => [3,4,7,6,5,2,1] => [6,1,2,5,4,3,7] => {{1,6},{2},{3},{4,5},{7}} => 3

{{1,3},{2,4,6,7},{5}} => [3,4,1,6,5,7,2] => [7,1,2,5,4,6,3] => {{1,7},{2},{3},{4,5},{6}} => 3

{{1,3},{2,4,6},{5,7}} => [3,4,1,6,7,2,5] => [6,1,2,7,4,5,3] => {{1,6},{2},{3},{4,7},{5}} => 3

{{1,3},{2,4,6},{5},{7}} => [3,4,1,6,5,2,7] => [6,1,2,5,4,7,3] => {{1,6,7},{2},{3},{4,5}} => 1

{{1,3,7},{2,4},{5,6}} => [3,4,7,2,6,5,1] => [4,1,2,6,5,3,7] => {{1,4,6},{2},{3},{5},{7}} => 3

{{1,3},{2,4,7},{5,6}} => [3,4,1,7,6,5,2] => [7,1,2,6,5,4,3] => {{1,7},{2},{3},{4,6},{5}} => 3

{{1,3},{2,4},{5,6,7}} => [3,4,1,2,6,7,5] => [4,1,2,7,5,6,3] => {{1,4,7},{2},{3},{5},{6}} => 3

{{1,3},{2,4},{5,6},{7}} => [3,4,1,2,6,5,7] => [4,1,2,6,5,7,3] => {{1,4,6,7},{2},{3},{5}} => 1

{{1,3,7},{2,4},{5},{6}} => [3,4,7,2,5,6,1] => [4,1,2,5,6,3,7] => {{1,4,5,6},{2},{3},{7}} => 2

{{1,3},{2,4,7},{5},{6}} => [3,4,1,7,5,6,2] => [7,1,2,5,6,4,3] => {{1,7},{2},{3},{4,5,6}} => 2

{{1,3},{2,4},{5,7},{6}} => [3,4,1,2,7,6,5] => [4,1,2,7,6,5,3] => {{1,4,7},{2},{3},{5,6}} => 2

{{1,3},{2,4},{5},{6,7}} => [3,4,1,2,5,7,6] => [4,1,2,5,7,6,3] => {{1,4,5,7},{2},{3},{6}} => 2

{{1,3},{2,4},{5},{6},{7}} => [3,4,1,2,5,6,7] => [4,1,2,5,6,7,3] => {{1,4,5,6,7},{2},{3}} => 1

{{1,3,5,6,7},{2},{4}} => [3,2,5,4,6,7,1] => [2,1,4,3,5,6,7] => {{1,2},{3,4},{5},{6},{7}} => 4

{{1,3,5,6},{2,7},{4}} => [3,7,5,4,6,1,2] => [7,1,4,3,5,2,6] => {{1,7},{2},{3,4},{5},{6}} => 4

{{1,3,5,6},{2},{4,7}} => [3,2,5,7,6,1,4] => [2,1,7,3,5,4,6] => {{1,2},{3,7},{4},{5},{6}} => 4

{{1,3,5,6},{2},{4},{7}} => [3,2,5,4,6,1,7] => [2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}} => 1

{{1,3,5,7},{2,6},{4}} => [3,6,5,4,7,2,1] => [6,1,4,3,2,5,7] => {{1,6},{2},{3,4},{5},{7}} => 4

{{1,3,5},{2,6,7},{4}} => [3,6,5,4,1,7,2] => [7,1,4,3,2,6,5] => {{1,7},{2},{3,4},{5},{6}} => 4

{{1,3,5},{2,6},{4,7}} => [3,6,5,7,1,2,4] => [6,1,7,3,2,4,5] => {{1,6},{2},{3,7},{4},{5}} => 4

{{1,3,5},{2,6},{4},{7}} => [3,6,5,4,1,2,7] => [6,1,4,3,2,7,5] => {{1,6,7},{2},{3,4},{5}} => 1

{{1,3,5,7},{2},{4,6}} => [3,2,5,6,7,4,1] => [2,1,6,3,4,5,7] => {{1,2},{3,6},{4},{5},{7}} => 4

{{1,3,5},{2,7},{4,6}} => [3,7,5,6,1,4,2] => [7,1,6,3,4,2,5] => {{1,7},{2},{3,6},{4},{5}} => 4

{{1,3,5},{2},{4,6,7}} => [3,2,5,6,1,7,4] => [2,1,7,3,4,6,5] => {{1,2},{3,7},{4},{5},{6}} => 4

{{1,3,5},{2},{4,6},{7}} => [3,2,5,6,1,4,7] => [2,1,6,3,4,7,5] => {{1,2},{3,6,7},{4},{5}} => 1

{{1,3,5,7},{2},{4},{6}} => [3,2,5,4,7,6,1] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}} => 2

{{1,3,5},{2,7},{4},{6}} => [3,7,5,4,1,6,2] => [7,1,4,3,6,2,5] => {{1,7},{2},{3,4},{5,6}} => 2

{{1,3,5},{2},{4,7},{6}} => [3,2,5,7,1,6,4] => [2,1,7,3,6,4,5] => {{1,2},{3,7},{4},{5,6}} => 2

{{1,3,5},{2},{4},{6,7}} => [3,2,5,4,1,7,6] => [2,1,4,3,7,6,5] => {{1,2},{3,4},{5,7},{6}} => 2

{{1,3,5},{2},{4},{6},{7}} => [3,2,5,4,1,6,7] => [2,1,4,3,6,7,5] => {{1,2},{3,4},{5,6,7}} => 1

{{1,3,6,7},{2,5},{4}} => [3,5,6,4,2,7,1] => [5,1,4,2,3,6,7] => {{1,5},{2},{3,4},{6},{7}} => 4

{{1,3,6},{2,5,7},{4}} => [3,5,6,4,7,1,2] => [7,1,4,2,3,5,6] => {{1,7},{2},{3,4},{5},{6}} => 4

{{1,3,6},{2,5},{4,7}} => [3,5,6,7,2,1,4] => [5,1,7,2,3,4,6] => {{1,5},{2},{3,7},{4},{6}} => 4

{{1,3,6},{2,5},{4},{7}} => [3,5,6,4,2,1,7] => [5,1,4,2,3,7,6] => {{1,5},{2},{3,4},{6,7}} => 1

{{1,3,7},{2,5,6},{4}} => [3,5,7,4,6,2,1] => [6,1,4,2,5,3,7] => {{1,6},{2},{3,4},{5},{7}} => 4

{{1,3},{2,5,6,7},{4}} => [3,5,1,4,6,7,2] => [7,1,4,2,5,6,3] => {{1,7},{2},{3,4},{5},{6}} => 4

{{1,3},{2,5,6},{4,7}} => [3,5,1,7,6,2,4] => [6,1,7,2,5,4,3] => {{1,6},{2},{3,7},{4},{5}} => 4

{{1,3},{2,5,6},{4},{7}} => [3,5,1,4,6,2,7] => [6,1,4,2,5,7,3] => {{1,6,7},{2},{3,4},{5}} => 1

{{1,3,7},{2,5},{4,6}} => [3,5,7,6,2,4,1] => [5,1,6,2,4,3,7] => {{1,5},{2},{3,6},{4},{7}} => 4

{{1,3},{2,5,7},{4,6}} => [3,5,1,6,7,4,2] => [7,1,6,2,4,5,3] => {{1,7},{2},{3,6},{4},{5}} => 4

{{1,3},{2,5},{4,6,7}} => [3,5,1,6,2,7,4] => [5,1,7,2,4,6,3] => {{1,5},{2},{3,7},{4},{6}} => 4

{{1,3},{2,5},{4,6},{7}} => [3,5,1,6,2,4,7] => [5,1,6,2,4,7,3] => {{1,5},{2},{3,6,7},{4}} => 1

{{1,3,7},{2,5},{4},{6}} => [3,5,7,4,2,6,1] => [5,1,4,2,6,3,7] => {{1,5,6},{2},{3,4},{7}} => 2

{{1,3},{2,5,7},{4},{6}} => [3,5,1,4,7,6,2] => [7,1,4,2,6,5,3] => {{1,7},{2},{3,4},{5,6}} => 2

{{1,3},{2,5},{4,7},{6}} => [3,5,1,7,2,6,4] => [5,1,7,2,6,4,3] => {{1,5,6},{2},{3,7},{4}} => 2

{{1,3},{2,5},{4},{6,7}} => [3,5,1,4,2,7,6] => [5,1,4,2,7,6,3] => {{1,5,7},{2},{3,4},{6}} => 2

{{1,3},{2,5},{4},{6},{7}} => [3,5,1,4,2,6,7] => [5,1,4,2,6,7,3] => {{1,5,6,7},{2},{3,4}} => 1

{{1,3,6,7},{2},{4,5}} => [3,2,6,5,4,7,1] => [2,1,5,4,3,6,7] => {{1,2},{3,5},{4},{6},{7}} => 4

{{1,3,6},{2,7},{4,5}} => [3,7,6,5,4,1,2] => [7,1,5,4,3,2,6] => {{1,7},{2},{3,5},{4},{6}} => 4

{{1,3,6},{2},{4,5,7}} => [3,2,6,5,7,1,4] => [2,1,7,4,3,5,6] => {{1,2},{3,7},{4},{5},{6}} => 4

{{1,3,6},{2},{4,5},{7}} => [3,2,6,5,4,1,7] => [2,1,5,4,3,7,6] => {{1,2},{3,5},{4},{6,7}} => 1

{{1,3,7},{2,6},{4,5}} => [3,6,7,5,4,2,1] => [6,1,5,4,2,3,7] => {{1,6},{2},{3,5},{4},{7}} => 4

{{1,3},{2,6,7},{4,5}} => [3,6,1,5,4,7,2] => [7,1,5,4,2,6,3] => {{1,7},{2},{3,5},{4},{6}} => 4

{{1,3},{2,6},{4,5,7}} => [3,6,1,5,7,2,4] => [6,1,7,4,2,5,3] => {{1,6},{2},{3,7},{4},{5}} => 4

{{1,3},{2,6},{4,5},{7}} => [3,6,1,5,4,2,7] => [6,1,5,4,2,7,3] => {{1,6,7},{2},{3,5},{4}} => 1

{{1,3,7},{2},{4,5,6}} => [3,2,7,5,6,4,1] => [2,1,6,4,5,3,7] => {{1,2},{3,6},{4},{5},{7}} => 4

{{1,3},{2,7},{4,5,6}} => [3,7,1,5,6,4,2] => [7,1,6,4,5,2,3] => {{1,7},{2},{3,6},{4},{5}} => 4

{{1,3},{2},{4,5,6,7}} => [3,2,1,5,6,7,4] => [2,1,7,4,5,6,3] => {{1,2},{3,7},{4},{5},{6}} => 4

{{1,3},{2},{4,5,6},{7}} => [3,2,1,5,6,4,7] => [2,1,6,4,5,7,3] => {{1,2},{3,6,7},{4},{5}} => 1

{{1,3,7},{2},{4,5},{6}} => [3,2,7,5,4,6,1] => [2,1,5,4,6,3,7] => {{1,2},{3,5,6},{4},{7}} => 2

{{1,3},{2,7},{4,5},{6}} => [3,7,1,5,4,6,2] => [7,1,5,4,6,2,3] => {{1,7},{2},{3,5,6},{4}} => 2

{{1,3},{2},{4,5,7},{6}} => [3,2,1,5,7,6,4] => [2,1,7,4,6,5,3] => {{1,2},{3,7},{4},{5,6}} => 2

{{1,3},{2},{4,5},{6,7}} => [3,2,1,5,4,7,6] => [2,1,5,4,7,6,3] => {{1,2},{3,5,7},{4},{6}} => 2

{{1,3},{2},{4,5},{6},{7}} => [3,2,1,5,4,6,7] => [2,1,5,4,6,7,3] => {{1,2},{3,5,6,7},{4}} => 1

{{1,3,6,7},{2},{4},{5}} => [3,2,6,4,5,7,1] => [2,1,4,5,3,6,7] => {{1,2},{3,4,5},{6},{7}} => 3

{{1,3,6},{2,7},{4},{5}} => [3,7,6,4,5,1,2] => [7,1,4,5,3,2,6] => {{1,7},{2},{3,4,5},{6}} => 3

{{1,3,6},{2},{4,7},{5}} => [3,2,6,7,5,1,4] => [2,1,7,5,3,4,6] => {{1,2},{3,7},{4,5},{6}} => 3

{{1,3,6},{2},{4},{5,7}} => [3,2,6,4,7,1,5] => [2,1,4,7,3,5,6] => {{1,2},{3,4,7},{5},{6}} => 3

{{1,3,6},{2},{4},{5},{7}} => [3,2,6,4,5,1,7] => [2,1,4,5,3,7,6] => {{1,2},{3,4,5},{6,7}} => 1

{{1,3,7},{2,6},{4},{5}} => [3,6,7,4,5,2,1] => [6,1,4,5,2,3,7] => {{1,6},{2},{3,4,5},{7}} => 3

{{1,3},{2,6,7},{4},{5}} => [3,6,1,4,5,7,2] => [7,1,4,5,2,6,3] => {{1,7},{2},{3,4,5},{6}} => 3

{{1,3},{2,6},{4,7},{5}} => [3,6,1,7,5,2,4] => [6,1,7,5,2,4,3] => {{1,6},{2},{3,7},{4,5}} => 3

{{1,3},{2,6},{4},{5,7}} => [3,6,1,4,7,2,5] => [6,1,4,7,2,5,3] => {{1,6},{2},{3,4,7},{5}} => 3

{{1,3},{2,6},{4},{5},{7}} => [3,6,1,4,5,2,7] => [6,1,4,5,2,7,3] => {{1,6,7},{2},{3,4,5}} => 1

{{1,3,7},{2},{4,6},{5}} => [3,2,7,6,5,4,1] => [2,1,6,5,4,3,7] => {{1,2},{3,6},{4,5},{7}} => 3

{{1,3},{2,7},{4,6},{5}} => [3,7,1,6,5,4,2] => [7,1,6,5,4,2,3] => {{1,7},{2},{3,6},{4,5}} => 3

{{1,3},{2},{4,6,7},{5}} => [3,2,1,6,5,7,4] => [2,1,7,5,4,6,3] => {{1,2},{3,7},{4,5},{6}} => 3

{{1,3},{2},{4,6},{5,7}} => [3,2,1,6,7,4,5] => [2,1,6,7,4,5,3] => {{1,2},{3,6},{4,7},{5}} => 3

{{1,3},{2},{4,6},{5},{7}} => [3,2,1,6,5,4,7] => [2,1,6,5,4,7,3] => {{1,2},{3,6,7},{4,5}} => 1

{{1,3,7},{2},{4},{5,6}} => [3,2,7,4,6,5,1] => [2,1,4,6,5,3,7] => {{1,2},{3,4,6},{5},{7}} => 3

{{1,3},{2,7},{4},{5,6}} => [3,7,1,4,6,5,2] => [7,1,4,6,5,2,3] => {{1,7},{2},{3,4,6},{5}} => 3

{{1,3},{2},{4,7},{5,6}} => [3,2,1,7,6,5,4] => [2,1,7,6,5,4,3] => {{1,2},{3,7},{4,6},{5}} => 3

{{1,3},{2},{4},{5,6,7}} => [3,2,1,4,6,7,5] => [2,1,4,7,5,6,3] => {{1,2},{3,4,7},{5},{6}} => 3

{{1,3},{2},{4},{5,6},{7}} => [3,2,1,4,6,5,7] => [2,1,4,6,5,7,3] => {{1,2},{3,4,6,7},{5}} => 1

{{1,3,7},{2},{4},{5},{6}} => [3,2,7,4,5,6,1] => [2,1,4,5,6,3,7] => {{1,2},{3,4,5,6},{7}} => 2

{{1,3},{2,7},{4},{5},{6}} => [3,7,1,4,5,6,2] => [7,1,4,5,6,2,3] => {{1,7},{2},{3,4,5,6}} => 2

{{1,3},{2},{4,7},{5},{6}} => [3,2,1,7,5,6,4] => [2,1,7,5,6,4,3] => {{1,2},{3,7},{4,5,6}} => 2

{{1,3},{2},{4},{5,7},{6}} => [3,2,1,4,7,6,5] => [2,1,4,7,6,5,3] => {{1,2},{3,4,7},{5,6}} => 2

{{1,3},{2},{4},{5},{6,7}} => [3,2,1,4,5,7,6] => [2,1,4,5,7,6,3] => {{1,2},{3,4,5,7},{6}} => 2

{{1,3},{2},{4},{5},{6},{7}} => [3,2,1,4,5,6,7] => [2,1,4,5,6,7,3] => {{1,2},{3,4,5,6,7}} => 1

{{1,4,5,6,7},{2,3}} => [4,3,2,5,6,7,1] => [3,2,1,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}} => 6

{{1,4,5,6},{2,3,7}} => [4,3,7,5,6,1,2] => [7,2,1,4,5,3,6] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,4,5,6},{2,3},{7}} => [4,3,2,5,6,1,7] => [3,2,1,4,5,7,6] => {{1,3},{2},{4},{5},{6,7}} => 1

{{1,4,5,7},{2,3,6}} => [4,3,6,5,7,2,1] => [6,2,1,4,3,5,7] => {{1,6},{2},{3},{4},{5},{7}} => 6

{{1,4,5},{2,3,6,7}} => [4,3,6,5,1,7,2] => [7,2,1,4,3,6,5] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,4,5},{2,3,6},{7}} => [4,3,6,5,1,2,7] => [6,2,1,4,3,7,5] => {{1,6,7},{2},{3},{4},{5}} => 1

{{1,4,5,7},{2,3},{6}} => [4,3,2,5,7,6,1] => [3,2,1,4,6,5,7] => {{1,3},{2},{4},{5,6},{7}} => 2

{{1,4,5},{2,3,7},{6}} => [4,3,7,5,1,6,2] => [7,2,1,4,6,3,5] => {{1,7},{2},{3},{4},{5,6}} => 2

{{1,4,5},{2,3},{6,7}} => [4,3,2,5,1,7,6] => [3,2,1,4,7,6,5] => {{1,3},{2},{4},{5,7},{6}} => 2

{{1,4,5},{2,3},{6},{7}} => [4,3,2,5,1,6,7] => [3,2,1,4,6,7,5] => {{1,3},{2},{4},{5,6,7}} => 1

{{1,4,6,7},{2,3,5}} => [4,3,5,6,2,7,1] => [5,2,1,3,4,6,7] => {{1,5},{2},{3},{4},{6},{7}} => 6

{{1,4,6},{2,3,5,7}} => [4,3,5,6,7,1,2] => [7,2,1,3,4,5,6] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,4,6},{2,3,5},{7}} => [4,3,5,6,2,1,7] => [5,2,1,3,4,7,6] => {{1,5},{2},{3},{4},{6,7}} => 1

{{1,4,7},{2,3,5,6}} => [4,3,5,7,6,2,1] => [6,2,1,3,5,4,7] => {{1,6},{2},{3},{4},{5},{7}} => 6

{{1,4},{2,3,5,6,7}} => [4,3,5,1,6,7,2] => [7,2,1,3,5,6,4] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,4},{2,3,5,6},{7}} => [4,3,5,1,6,2,7] => [6,2,1,3,5,7,4] => {{1,6,7},{2},{3},{4},{5}} => 1

{{1,4,7},{2,3,5},{6}} => [4,3,5,7,2,6,1] => [5,2,1,3,6,4,7] => {{1,5,6},{2},{3},{4},{7}} => 2

{{1,4},{2,3,5,7},{6}} => [4,3,5,1,7,6,2] => [7,2,1,3,6,5,4] => {{1,7},{2},{3},{4},{5,6}} => 2

{{1,4},{2,3,5},{6,7}} => [4,3,5,1,2,7,6] => [5,2,1,3,7,6,4] => {{1,5,7},{2},{3},{4},{6}} => 2

{{1,4},{2,3,5},{6},{7}} => [4,3,5,1,2,6,7] => [5,2,1,3,6,7,4] => {{1,5,6,7},{2},{3},{4}} => 1

{{1,4,6,7},{2,3},{5}} => [4,3,2,6,5,7,1] => [3,2,1,5,4,6,7] => {{1,3},{2},{4,5},{6},{7}} => 3

{{1,4,6},{2,3,7},{5}} => [4,3,7,6,5,1,2] => [7,2,1,5,4,3,6] => {{1,7},{2},{3},{4,5},{6}} => 3

{{1,4,6},{2,3},{5,7}} => [4,3,2,6,7,1,5] => [3,2,1,7,4,5,6] => {{1,3},{2},{4,7},{5},{6}} => 3

{{1,4,6},{2,3},{5},{7}} => [4,3,2,6,5,1,7] => [3,2,1,5,4,7,6] => {{1,3},{2},{4,5},{6,7}} => 1

{{1,4,7},{2,3,6},{5}} => [4,3,6,7,5,2,1] => [6,2,1,5,3,4,7] => {{1,6},{2},{3},{4,5},{7}} => 3

{{1,4},{2,3,6,7},{5}} => [4,3,6,1,5,7,2] => [7,2,1,5,3,6,4] => {{1,7},{2},{3},{4,5},{6}} => 3

{{1,4},{2,3,6},{5,7}} => [4,3,6,1,7,2,5] => [6,2,1,7,3,5,4] => {{1,6},{2},{3},{4,7},{5}} => 3

{{1,4},{2,3,6},{5},{7}} => [4,3,6,1,5,2,7] => [6,2,1,5,3,7,4] => {{1,6,7},{2},{3},{4,5}} => 1

{{1,4,7},{2,3},{5,6}} => [4,3,2,7,6,5,1] => [3,2,1,6,5,4,7] => {{1,3},{2},{4,6},{5},{7}} => 3

{{1,4},{2,3,7},{5,6}} => [4,3,7,1,6,5,2] => [7,2,1,6,5,3,4] => {{1,7},{2},{3},{4,6},{5}} => 3

{{1,4},{2,3},{5,6,7}} => [4,3,2,1,6,7,5] => [3,2,1,7,5,6,4] => {{1,3},{2},{4,7},{5},{6}} => 3

{{1,4},{2,3},{5,6},{7}} => [4,3,2,1,6,5,7] => [3,2,1,6,5,7,4] => {{1,3},{2},{4,6,7},{5}} => 1

{{1,4,7},{2,3},{5},{6}} => [4,3,2,7,5,6,1] => [3,2,1,5,6,4,7] => {{1,3},{2},{4,5,6},{7}} => 2

{{1,4},{2,3,7},{5},{6}} => [4,3,7,1,5,6,2] => [7,2,1,5,6,3,4] => {{1,7},{2},{3},{4,5,6}} => 2

{{1,4},{2,3},{5,7},{6}} => [4,3,2,1,7,6,5] => [3,2,1,7,6,5,4] => {{1,3},{2},{4,7},{5,6}} => 2

{{1,4},{2,3},{5},{6,7}} => [4,3,2,1,5,7,6] => [3,2,1,5,7,6,4] => {{1,3},{2},{4,5,7},{6}} => 2

{{1,4},{2,3},{5},{6},{7}} => [4,3,2,1,5,6,7] => [3,2,1,5,6,7,4] => {{1,3},{2},{4,5,6,7}} => 1

{{1,5,6,7},{2,3,4}} => [5,3,4,2,6,7,1] => [4,2,3,1,5,6,7] => {{1,4},{2},{3},{5},{6},{7}} => 6

{{1,5,6},{2,3,4,7}} => [5,3,4,7,6,1,2] => [7,2,3,1,5,4,6] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,5,6},{2,3,4},{7}} => [5,3,4,2,6,1,7] => [4,2,3,1,5,7,6] => {{1,4},{2},{3},{5},{6,7}} => 1

{{1,5,7},{2,3,4,6}} => [5,3,4,6,7,2,1] => [6,2,3,1,4,5,7] => {{1,6},{2},{3},{4},{5},{7}} => 6

{{1,5},{2,3,4,6,7}} => [5,3,4,6,1,7,2] => [7,2,3,1,4,6,5] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,5},{2,3,4,6},{7}} => [5,3,4,6,1,2,7] => [6,2,3,1,4,7,5] => {{1,6,7},{2},{3},{4},{5}} => 1

{{1,5,7},{2,3,4},{6}} => [5,3,4,2,7,6,1] => [4,2,3,1,6,5,7] => {{1,4},{2},{3},{5,6},{7}} => 2

{{1,5},{2,3,4,7},{6}} => [5,3,4,7,1,6,2] => [7,2,3,1,6,4,5] => {{1,7},{2},{3},{4},{5,6}} => 2

{{1,5},{2,3,4},{6,7}} => [5,3,4,2,1,7,6] => [4,2,3,1,7,6,5] => {{1,4},{2},{3},{5,7},{6}} => 2

{{1,5},{2,3,4},{6},{7}} => [5,3,4,2,1,6,7] => [4,2,3,1,6,7,5] => {{1,4},{2},{3},{5,6,7}} => 1

{{1,6,7},{2,3,4,5}} => [6,3,4,5,2,7,1] => [5,2,3,4,1,6,7] => {{1,5},{2},{3},{4},{6},{7}} => 6

{{1,6},{2,3,4,5,7}} => [6,3,4,5,7,1,2] => [7,2,3,4,1,5,6] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1,6},{2,3,4,5},{7}} => [6,3,4,5,2,1,7] => [5,2,3,4,1,7,6] => {{1,5},{2},{3},{4},{6,7}} => 1

{{1,7},{2,3,4,5,6}} => [7,3,4,5,6,2,1] => [6,2,3,4,5,1,7] => {{1,6},{2},{3},{4},{5},{7}} => 6

{{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => [7,2,3,4,5,6,1] => {{1,7},{2},{3},{4},{5},{6}} => 6

{{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => [6,2,3,4,5,7,1] => {{1,6,7},{2},{3},{4},{5}} => 1

{{1,7},{2,3,4,5},{6}} => [7,3,4,5,2,6,1] => [5,2,3,4,6,1,7] => {{1,5,6},{2},{3},{4},{7}} => 2

{{1},{2,3,4,5,7},{6}} => [1,3,4,5,7,6,2] => [7,2,3,4,6,5,1] => {{1,7},{2},{3},{4},{5,6}} => 2

{{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => [5,2,3,4,7,6,1] => {{1,5,7},{2},{3},{4},{6}} => 2

{{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => [5,2,3,4,6,7,1] => {{1,5,6,7},{2},{3},{4}} => 1

{{1,6,7},{2,3,4},{5}} => [6,3,4,2,5,7,1] => [4,2,3,5,1,6,7] => {{1,4,5},{2},{3},{6},{7}} => 3

{{1,6},{2,3,4,7},{5}} => [6,3,4,7,5,1,2] => [7,2,3,5,1,4,6] => {{1,7},{2},{3},{4,5},{6}} => 3

{{1,6},{2,3,4},{5,7}} => [6,3,4,2,7,1,5] => [4,2,3,7,1,5,6] => {{1,4,7},{2},{3},{5},{6}} => 3

{{1,6},{2,3,4},{5},{7}} => [6,3,4,2,5,1,7] => [4,2,3,5,1,7,6] => {{1,4,5},{2},{3},{6,7}} => 1

{{1,7},{2,3,4,6},{5}} => [7,3,4,6,5,2,1] => [6,2,3,5,4,1,7] => {{1,6},{2},{3},{4,5},{7}} => 3

{{1},{2,3,4,6,7},{5}} => [1,3,4,6,5,7,2] => [7,2,3,5,4,6,1] => {{1,7},{2},{3},{4,5},{6}} => 3

{{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => [6,2,3,7,4,5,1] => {{1,6},{2},{3},{4,7},{5}} => 3

{{1},{2,3,4,6},{5},{7}} => [1,3,4,6,5,2,7] => [6,2,3,5,4,7,1] => {{1,6,7},{2},{3},{4,5}} => 1

{{1,7},{2,3,4},{5,6}} => [7,3,4,2,6,5,1] => [4,2,3,6,5,1,7] => {{1,4,6},{2},{3},{5},{7}} => 3

{{1},{2,3,4,7},{5,6}} => [1,3,4,7,6,5,2] => [7,2,3,6,5,4,1] => {{1,7},{2},{3},{4,6},{5}} => 3

{{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => [4,2,3,7,5,6,1] => {{1,4,7},{2},{3},{5},{6}} => 3

{{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => [4,2,3,6,5,7,1] => {{1,4,6,7},{2},{3},{5}} => 1

{{1,7},{2,3,4},{5},{6}} => [7,3,4,2,5,6,1] => [4,2,3,5,6,1,7] => {{1,4,5,6},{2},{3},{7}} => 2

{{1},{2,3,4,7},{5},{6}} => [1,3,4,7,5,6,2] => [7,2,3,5,6,4,1] => {{1,7},{2},{3},{4,5,6}} => 2

{{1},{2,3,4},{5,7},{6}} => [1,3,4,2,7,6,5] => [4,2,3,7,6,5,1] => {{1,4,7},{2},{3},{5,6}} => 2

{{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => [4,2,3,5,7,6,1] => {{1,4,5,7},{2},{3},{6}} => 2

{{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => [4,2,3,5,6,7,1] => {{1,4,5,6,7},{2},{3}} => 1

{{1,5,6,7},{2,3},{4}} => [5,3,2,4,6,7,1] => [3,2,4,1,5,6,7] => {{1,3,4},{2},{5},{6},{7}} => 4

{{1,5,6},{2,3,7},{4}} => [5,3,7,4,6,1,2] => [7,2,4,1,5,3,6] => {{1,7},{2},{3,4},{5},{6}} => 4

{{1,5,6},{2,3},{4,7}} => [5,3,2,7,6,1,4] => [3,2,7,1,5,4,6] => {{1,3,7},{2},{4},{5},{6}} => 4

{{1,5,6},{2,3},{4},{7}} => [5,3,2,4,6,1,7] => [3,2,4,1,5,7,6] => {{1,3,4},{2},{5},{6,7}} => 1

{{1,5,7},{2,3,6},{4}} => [5,3,6,4,7,2,1] => [6,2,4,1,3,5,7] => {{1,6},{2},{3,4},{5},{7}} => 4

{{1,5},{2,3,6,7},{4}} => [5,3,6,4,1,7,2] => [7,2,4,1,3,6,5] => {{1,7},{2},{3,4},{5},{6}} => 4

{{1,5},{2,3,6},{4,7}} => [5,3,6,7,1,2,4] => [6,2,7,1,3,4,5] => {{1,6},{2},{3,7},{4},{5}} => 4

{{1,5},{2,3,6},{4},{7}} => [5,3,6,4,1,2,7] => [6,2,4,1,3,7,5] => {{1,6,7},{2},{3,4},{5}} => 1

{{1,5,7},{2,3},{4,6}} => [5,3,2,6,7,4,1] => [3,2,6,1,4,5,7] => {{1,3,6},{2},{4},{5},{7}} => 4

{{1,5},{2,3,7},{4,6}} => [5,3,7,6,1,4,2] => [7,2,6,1,4,3,5] => {{1,7},{2},{3,6},{4},{5}} => 4

{{1,5},{2,3},{4,6,7}} => [5,3,2,6,1,7,4] => [3,2,7,1,4,6,5] => {{1,3,7},{2},{4},{5},{6}} => 4

{{1,5},{2,3},{4,6},{7}} => [5,3,2,6,1,4,7] => [3,2,6,1,4,7,5] => {{1,3,6,7},{2},{4},{5}} => 1

{{1,5,7},{2,3},{4},{6}} => [5,3,2,4,7,6,1] => [3,2,4,1,6,5,7] => {{1,3,4},{2},{5,6},{7}} => 2

{{1,5},{2,3,7},{4},{6}} => [5,3,7,4,1,6,2] => [7,2,4,1,6,3,5] => {{1,7},{2},{3,4},{5,6}} => 2

{{1,5},{2,3},{4,7},{6}} => [5,3,2,7,1,6,4] => [3,2,7,1,6,4,5] => {{1,3,7},{2},{4},{5,6}} => 2

{{1,5},{2,3},{4},{6,7}} => [5,3,2,4,1,7,6] => [3,2,4,1,7,6,5] => {{1,3,4},{2},{5,7},{6}} => 2

{{1,5},{2,3},{4},{6},{7}} => [5,3,2,4,1,6,7] => [3,2,4,1,6,7,5] => {{1,3,4},{2},{5,6,7}} => 1

{{1,6,7},{2,3,5},{4}} => [6,3,5,4,2,7,1] => [5,2,4,3,1,6,7] => {{1,5},{2},{3,4},{6},{7}} => 4

{{1,6},{2,3,5,7},{4}} => [6,3,5,4,7,1,2] => [7,2,4,3,1,5,6] => {{1,7},{2},{3,4},{5},{6}} => 4

{{1,6},{2,3,5},{4,7}} => [6,3,5,7,2,1,4] => [5,2,7,3,1,4,6] => {{1,5},{2},{3,7},{4},{6}} => 4

{{1,6},{2,3,5},{4},{7}} => [6,3,5,4,2,1,7] => [5,2,4,3,1,7,6] => {{1,5},{2},{3,4},{6,7}} => 1

{{1,7},{2,3,5,6},{4}} => [7,3,5,4,6,2,1] => [6,2,4,3,5,1,7] => {{1,6},{2},{3,4},{5},{7}} => 4

{{1},{2,3,5,6,7},{4}} => [1,3,5,4,6,7,2] => [7,2,4,3,5,6,1] => {{1,7},{2},{3,4},{5},{6}} => 4

{{1},{2,3,5,6},{4,7}} => [1,3,5,7,6,2,4] => [6,2,7,3,5,4,1] => {{1,6},{2},{3,7},{4},{5}} => 4

{{1},{2,3,5,6},{4},{7}} => [1,3,5,4,6,2,7] => [6,2,4,3,5,7,1] => {{1,6,7},{2},{3,4},{5}} => 1

{{1,7},{2,3,5},{4,6}} => [7,3,5,6,2,4,1] => [5,2,6,3,4,1,7] => {{1,5},{2},{3,6},{4},{7}} => 4

{{1},{2,3,5,7},{4,6}} => [1,3,5,6,7,4,2] => [7,2,6,3,4,5,1] => {{1,7},{2},{3,6},{4},{5}} => 4

{{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => [5,2,7,3,4,6,1] => {{1,5},{2},{3,7},{4},{6}} => 4

{{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => [5,2,6,3,4,7,1] => {{1,5},{2},{3,6,7},{4}} => 1

{{1,7},{2,3,5},{4},{6}} => [7,3,5,4,2,6,1] => [5,2,4,3,6,1,7] => {{1,5,6},{2},{3,4},{7}} => 2

{{1},{2,3,5,7},{4},{6}} => [1,3,5,4,7,6,2] => [7,2,4,3,6,5,1] => {{1,7},{2},{3,4},{5,6}} => 2

{{1},{2,3,5},{4,7},{6}} => [1,3,5,7,2,6,4] => [5,2,7,3,6,4,1] => {{1,5,6},{2},{3,7},{4}} => 2

{{1},{2,3,5},{4},{6,7}} => [1,3,5,4,2,7,6] => [5,2,4,3,7,6,1] => {{1,5,7},{2},{3,4},{6}} => 2

{{1},{2,3,5},{4},{6},{7}} => [1,3,5,4,2,6,7] => [5,2,4,3,6,7,1] => {{1,5,6,7},{2},{3,4}} => 1

{{1,6,7},{2,3},{4,5}} => [6,3,2,5,4,7,1] => [3,2,5,4,1,6,7] => {{1,3,5},{2},{4},{6},{7}} => 4

{{1,6},{2,3,7},{4,5}} => [6,3,7,5,4,1,2] => [7,2,5,4,1,3,6] => {{1,7},{2},{3,5},{4},{6}} => 4

{{1,6},{2,3},{4,5,7}} => [6,3,2,5,7,1,4] => [3,2,7,4,1,5,6] => {{1,3,7},{2},{4},{5},{6}} => 4

{{1,6},{2,3},{4,5},{7}} => [6,3,2,5,4,1,7] => [3,2,5,4,1,7,6] => {{1,3,5},{2},{4},{6,7}} => 1

{{1,7},{2,3,6},{4,5}} => [7,3,6,5,4,2,1] => [6,2,5,4,3,1,7] => {{1,6},{2},{3,5},{4},{7}} => 4

{{1},{2,3,6,7},{4,5}} => [1,3,6,5,4,7,2] => [7,2,5,4,3,6,1] => {{1,7},{2},{3,5},{4},{6}} => 4

{{1},{2,3,6},{4,5,7}} => [1,3,6,5,7,2,4] => [6,2,7,4,3,5,1] => {{1,6},{2},{3,7},{4},{5}} => 4

{{1},{2,3,6},{4,5},{7}} => [1,3,6,5,4,2,7] => [6,2,5,4,3,7,1] => {{1,6,7},{2},{3,5},{4}} => 1

{{1,7},{2,3},{4,5,6}} => [7,3,2,5,6,4,1] => [3,2,6,4,5,1,7] => {{1,3,6},{2},{4},{5},{7}} => 4

{{1},{2,3,7},{4,5,6}} => [1,3,7,5,6,4,2] => [7,2,6,4,5,3,1] => {{1,7},{2},{3,6},{4},{5}} => 4

{{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => [3,2,7,4,5,6,1] => {{1,3,7},{2},{4},{5},{6}} => 4

{{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => [3,2,6,4,5,7,1] => {{1,3,6,7},{2},{4},{5}} => 1

{{1,7},{2,3},{4,5},{6}} => [7,3,2,5,4,6,1] => [3,2,5,4,6,1,7] => {{1,3,5,6},{2},{4},{7}} => 2

{{1},{2,3,7},{4,5},{6}} => [1,3,7,5,4,6,2] => [7,2,5,4,6,3,1] => {{1,7},{2},{3,5,6},{4}} => 2

{{1},{2,3},{4,5,7},{6}} => [1,3,2,5,7,6,4] => [3,2,7,4,6,5,1] => {{1,3,7},{2},{4},{5,6}} => 2

{{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => [3,2,5,4,7,6,1] => {{1,3,5,7},{2},{4},{6}} => 2

{{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => [3,2,5,4,6,7,1] => {{1,3,5,6,7},{2},{4}} => 1

{{1,6,7},{2,3},{4},{5}} => [6,3,2,4,5,7,1] => [3,2,4,5,1,6,7] => {{1,3,4,5},{2},{6},{7}} => 3

{{1,6},{2,3,7},{4},{5}} => [6,3,7,4,5,1,2] => [7,2,4,5,1,3,6] => {{1,7},{2},{3,4,5},{6}} => 3

{{1,6},{2,3},{4,7},{5}} => [6,3,2,7,5,1,4] => [3,2,7,5,1,4,6] => {{1,3,7},{2},{4,5},{6}} => 3

{{1,6},{2,3},{4},{5,7}} => [6,3,2,4,7,1,5] => [3,2,4,7,1,5,6] => {{1,3,4,7},{2},{5},{6}} => 3

{{1,6},{2,3},{4},{5},{7}} => [6,3,2,4,5,1,7] => [3,2,4,5,1,7,6] => {{1,3,4,5},{2},{6,7}} => 1

{{1,7},{2,3,6},{4},{5}} => [7,3,6,4,5,2,1] => [6,2,4,5,3,1,7] => {{1,6},{2},{3,4,5},{7}} => 3

{{1},{2,3,6,7},{4},{5}} => [1,3,6,4,5,7,2] => [7,2,4,5,3,6,1] => {{1,7},{2},{3,4,5},{6}} => 3

{{1},{2,3,6},{4,7},{5}} => [1,3,6,7,5,2,4] => [6,2,7,5,3,4,1] => {{1,6},{2},{3,7},{4,5}} => 3

{{1},{2,3,6},{4},{5,7}} => [1,3,6,4,7,2,5] => [6,2,4,7,3,5,1] => {{1,6},{2},{3,4,7},{5}} => 3

{{1},{2,3,6},{4},{5},{7}} => [1,3,6,4,5,2,7] => [6,2,4,5,3,7,1] => {{1,6,7},{2},{3,4,5}} => 1

{{1,7},{2,3},{4,6},{5}} => [7,3,2,6,5,4,1] => [3,2,6,5,4,1,7] => {{1,3,6},{2},{4,5},{7}} => 3

{{1},{2,3,7},{4,6},{5}} => [1,3,7,6,5,4,2] => [7,2,6,5,4,3,1] => {{1,7},{2},{3,6},{4,5}} => 3

{{1},{2,3},{4,6,7},{5}} => [1,3,2,6,5,7,4] => [3,2,7,5,4,6,1] => {{1,3,7},{2},{4,5},{6}} => 3

{{1},{2,3},{4,6},{5,7}} => [1,3,2,6,7,4,5] => [3,2,6,7,4,5,1] => {{1,3,6},{2},{4,7},{5}} => 3

{{1},{2,3},{4,6},{5},{7}} => [1,3,2,6,5,4,7] => [3,2,6,5,4,7,1] => {{1,3,6,7},{2},{4,5}} => 1

{{1,7},{2,3},{4},{5,6}} => [7,3,2,4,6,5,1] => [3,2,4,6,5,1,7] => {{1,3,4,6},{2},{5},{7}} => 3

{{1},{2,3,7},{4},{5,6}} => [1,3,7,4,6,5,2] => [7,2,4,6,5,3,1] => {{1,7},{2},{3,4,6},{5}} => 3

{{1},{2,3},{4,7},{5,6}} => [1,3,2,7,6,5,4] => [3,2,7,6,5,4,1] => {{1,3,7},{2},{4,6},{5}} => 3

{{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => [3,2,4,7,5,6,1] => {{1,3,4,7},{2},{5},{6}} => 3

{{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => [3,2,4,6,5,7,1] => {{1,3,4,6,7},{2},{5}} => 1

{{1,7},{2,3},{4},{5},{6}} => [7,3,2,4,5,6,1] => [3,2,4,5,6,1,7] => {{1,3,4,5,6},{2},{7}} => 2

{{1},{2,3,7},{4},{5},{6}} => [1,3,7,4,5,6,2] => [7,2,4,5,6,3,1] => {{1,7},{2},{3,4,5,6}} => 2

{{1},{2,3},{4,7},{5},{6}} => [1,3,2,7,5,6,4] => [3,2,7,5,6,4,1] => {{1,3,7},{2},{4,5,6}} => 2

{{1},{2,3},{4},{5,7},{6}} => [1,3,2,4,7,6,5] => [3,2,4,7,6,5,1] => {{1,3,4,7},{2},{5,6}} => 2

{{1},{2,3},{4},{5},{6,7}} => [1,3,2,4,5,7,6] => [3,2,4,5,7,6,1] => {{1,3,4,5,7},{2},{6}} => 2

{{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => [3,2,4,5,6,7,1] => {{1,3,4,5,6,7},{2}} => 1

{{1,4,5,6,7},{2},{3}} => [4,2,3,5,6,7,1] => [2,3,1,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => 5

{{1,4,5,6},{2,7},{3}} => [4,7,3,5,6,1,2] => [7,3,1,4,5,2,6] => {{1,7},{2,3},{4},{5},{6}} => 5

{{1,4,5,6},{2},{3,7}} => [4,2,7,5,6,1,3] => [2,7,1,4,5,3,6] => {{1,2,7},{3},{4},{5},{6}} => 5

{{1,4,5,6},{2},{3},{7}} => [4,2,3,5,6,1,7] => [2,3,1,4,5,7,6] => {{1,2,3},{4},{5},{6,7}} => 1

{{1,4,5,7},{2,6},{3}} => [4,6,3,5,7,2,1] => [6,3,1,4,2,5,7] => {{1,6},{2,3},{4},{5},{7}} => 5

{{1,4,5},{2,6,7},{3}} => [4,6,3,5,1,7,2] => [7,3,1,4,2,6,5] => {{1,7},{2,3},{4},{5},{6}} => 5

{{1,4,5},{2,6},{3,7}} => [4,6,7,5,1,2,3] => [6,7,1,4,2,3,5] => {{1,6},{2,7},{3},{4},{5}} => 5

{{1,4,5},{2,6},{3},{7}} => [4,6,3,5,1,2,7] => [6,3,1,4,2,7,5] => {{1,6,7},{2,3},{4},{5}} => 1

{{1,4,5,7},{2},{3,6}} => [4,2,6,5,7,3,1] => [2,6,1,4,3,5,7] => {{1,2,6},{3},{4},{5},{7}} => 5

{{1,4,5},{2,7},{3,6}} => [4,7,6,5,1,3,2] => [7,6,1,4,3,2,5] => {{1,7},{2,6},{3},{4},{5}} => 5

{{1,4,5},{2},{3,6,7}} => [4,2,6,5,1,7,3] => [2,7,1,4,3,6,5] => {{1,2,7},{3},{4},{5},{6}} => 5

{{1,4,5},{2},{3,6},{7}} => [4,2,6,5,1,3,7] => [2,6,1,4,3,7,5] => {{1,2,6,7},{3},{4},{5}} => 1

{{1,4,5,7},{2},{3},{6}} => [4,2,3,5,7,6,1] => [2,3,1,4,6,5,7] => {{1,2,3},{4},{5,6},{7}} => 2

{{1,4,5},{2,7},{3},{6}} => [4,7,3,5,1,6,2] => [7,3,1,4,6,2,5] => {{1,7},{2,3},{4},{5,6}} => 2

{{1,4,5},{2},{3,7},{6}} => [4,2,7,5,1,6,3] => [2,7,1,4,6,3,5] => {{1,2,7},{3},{4},{5,6}} => 2

{{1,4,5},{2},{3},{6,7}} => [4,2,3,5,1,7,6] => [2,3,1,4,7,6,5] => {{1,2,3},{4},{5,7},{6}} => 2

{{1,4,5},{2},{3},{6},{7}} => [4,2,3,5,1,6,7] => [2,3,1,4,6,7,5] => {{1,2,3},{4},{5,6,7}} => 1

{{1,4,6,7},{2,5},{3}} => [4,5,3,6,2,7,1] => [5,3,1,2,4,6,7] => {{1,5},{2,3},{4},{6},{7}} => 5

{{1,4,6},{2,5,7},{3}} => [4,5,3,6,7,1,2] => [7,3,1,2,4,5,6] => {{1,7},{2,3},{4},{5},{6}} => 5

{{1,4,6},{2,5},{3,7}} => [4,5,7,6,2,1,3] => [5,7,1,2,4,3,6] => {{1,5},{2,7},{3},{4},{6}} => 5

{{1,4,6},{2,5},{3},{7}} => [4,5,3,6,2,1,7] => [5,3,1,2,4,7,6] => {{1,5},{2,3},{4},{6,7}} => 1

{{1,4,7},{2,5,6},{3}} => [4,5,3,7,6,2,1] => [6,3,1,2,5,4,7] => {{1,6},{2,3},{4},{5},{7}} => 5

{{1,4},{2,5,6,7},{3}} => [4,5,3,1,6,7,2] => [7,3,1,2,5,6,4] => {{1,7},{2,3},{4},{5},{6}} => 5

{{1,4},{2,5,6},{3,7}} => [4,5,7,1,6,2,3] => [6,7,1,2,5,3,4] => {{1,6},{2,7},{3},{4},{5}} => 5

{{1,4},{2,5,6},{3},{7}} => [4,5,3,1,6,2,7] => [6,3,1,2,5,7,4] => {{1,6,7},{2,3},{4},{5}} => 1

{{1,4,7},{2,5},{3,6}} => [4,5,6,7,2,3,1] => [5,6,1,2,3,4,7] => {{1,5},{2,6},{3},{4},{7}} => 5

{{1,4},{2,5,7},{3,6}} => [4,5,6,1,7,3,2] => [7,6,1,2,3,5,4] => {{1,7},{2,6},{3},{4},{5}} => 5

{{1,4},{2,5},{3,6,7}} => [4,5,6,1,2,7,3] => [5,7,1,2,3,6,4] => {{1,5},{2,7},{3},{4},{6}} => 5

{{1,4},{2,5},{3,6},{7}} => [4,5,6,1,2,3,7] => [5,6,1,2,3,7,4] => {{1,5},{2,6,7},{3},{4}} => 1

{{1,4,7},{2,5},{3},{6}} => [4,5,3,7,2,6,1] => [5,3,1,2,6,4,7] => {{1,5,6},{2,3},{4},{7}} => 2

{{1,4},{2,5,7},{3},{6}} => [4,5,3,1,7,6,2] => [7,3,1,2,6,5,4] => {{1,7},{2,3},{4},{5,6}} => 2

{{1,4},{2,5},{3,7},{6}} => [4,5,7,1,2,6,3] => [5,7,1,2,6,3,4] => {{1,5,6},{2,7},{3},{4}} => 2

{{1,4},{2,5},{3},{6,7}} => [4,5,3,1,2,7,6] => [5,3,1,2,7,6,4] => {{1,5,7},{2,3},{4},{6}} => 2

{{1,4},{2,5},{3},{6},{7}} => [4,5,3,1,2,6,7] => [5,3,1,2,6,7,4] => {{1,5,6,7},{2,3},{4}} => 1

{{1,4,6,7},{2},{3,5}} => [4,2,5,6,3,7,1] => [2,5,1,3,4,6,7] => {{1,2,5},{3},{4},{6},{7}} => 5

{{1,4,6},{2,7},{3,5}} => [4,7,5,6,3,1,2] => [7,5,1,3,4,2,6] => {{1,7},{2,5},{3},{4},{6}} => 5

{{1,4,6},{2},{3,5,7}} => [4,2,5,6,7,1,3] => [2,7,1,3,4,5,6] => {{1,2,7},{3},{4},{5},{6}} => 5

{{1,4,6},{2},{3,5},{7}} => [4,2,5,6,3,1,7] => [2,5,1,3,4,7,6] => {{1,2,5},{3},{4},{6,7}} => 1

{{1,4,7},{2,6},{3,5}} => [4,6,5,7,3,2,1] => [6,5,1,3,2,4,7] => {{1,6},{2,5},{3},{4},{7}} => 5

{{1,4},{2,6,7},{3,5}} => [4,6,5,1,3,7,2] => [7,5,1,3,2,6,4] => {{1,7},{2,5},{3},{4},{6}} => 5

{{1,4},{2,6},{3,5,7}} => [4,6,5,1,7,2,3] => [6,7,1,3,2,5,4] => {{1,6},{2,7},{3},{4},{5}} => 5

{{1,4},{2,6},{3,5},{7}} => [4,6,5,1,3,2,7] => [6,5,1,3,2,7,4] => {{1,6,7},{2,5},{3},{4}} => 1

{{1,4,7},{2},{3,5,6}} => [4,2,5,7,6,3,1] => [2,6,1,3,5,4,7] => {{1,2,6},{3},{4},{5},{7}} => 5

{{1,4},{2,7},{3,5,6}} => [4,7,5,1,6,3,2] => [7,6,1,3,5,2,4] => {{1,7},{2,6},{3},{4},{5}} => 5

{{1,4},{2},{3,5,6,7}} => [4,2,5,1,6,7,3] => [2,7,1,3,5,6,4] => {{1,2,7},{3},{4},{5},{6}} => 5

{{1,4},{2},{3,5,6},{7}} => [4,2,5,1,6,3,7] => [2,6,1,3,5,7,4] => {{1,2,6,7},{3},{4},{5}} => 1

{{1,4,7},{2},{3,5},{6}} => [4,2,5,7,3,6,1] => [2,5,1,3,6,4,7] => {{1,2,5,6},{3},{4},{7}} => 2

{{1,4},{2,7},{3,5},{6}} => [4,7,5,1,3,6,2] => [7,5,1,3,6,2,4] => {{1,7},{2,5,6},{3},{4}} => 2

{{1,4},{2},{3,5,7},{6}} => [4,2,5,1,7,6,3] => [2,7,1,3,6,5,4] => {{1,2,7},{3},{4},{5,6}} => 2

{{1,4},{2},{3,5},{6,7}} => [4,2,5,1,3,7,6] => [2,5,1,3,7,6,4] => {{1,2,5,7},{3},{4},{6}} => 2

{{1,4},{2},{3,5},{6},{7}} => [4,2,5,1,3,6,7] => [2,5,1,3,6,7,4] => {{1,2,5,6,7},{3},{4}} => 1

{{1,4,6,7},{2},{3},{5}} => [4,2,3,6,5,7,1] => [2,3,1,5,4,6,7] => {{1,2,3},{4,5},{6},{7}} => 3

{{1,4,6},{2,7},{3},{5}} => [4,7,3,6,5,1,2] => [7,3,1,5,4,2,6] => {{1,7},{2,3},{4,5},{6}} => 3

{{1,4,6},{2},{3,7},{5}} => [4,2,7,6,5,1,3] => [2,7,1,5,4,3,6] => {{1,2,7},{3},{4,5},{6}} => 3

{{1,4,6},{2},{3},{5,7}} => [4,2,3,6,7,1,5] => [2,3,1,7,4,5,6] => {{1,2,3},{4,7},{5},{6}} => 3

{{1,4,6},{2},{3},{5},{7}} => [4,2,3,6,5,1,7] => [2,3,1,5,4,7,6] => {{1,2,3},{4,5},{6,7}} => 1

{{1,4,7},{2,6},{3},{5}} => [4,6,3,7,5,2,1] => [6,3,1,5,2,4,7] => {{1,6},{2,3},{4,5},{7}} => 3

{{1,4},{2,6,7},{3},{5}} => [4,6,3,1,5,7,2] => [7,3,1,5,2,6,4] => {{1,7},{2,3},{4,5},{6}} => 3

{{1,4},{2,6},{3,7},{5}} => [4,6,7,1,5,2,3] => [6,7,1,5,2,3,4] => {{1,6},{2,7},{3},{4,5}} => 3

{{1,4},{2,6},{3},{5,7}} => [4,6,3,1,7,2,5] => [6,3,1,7,2,5,4] => {{1,6},{2,3},{4,7},{5}} => 3

{{1,4},{2,6},{3},{5},{7}} => [4,6,3,1,5,2,7] => [6,3,1,5,2,7,4] => {{1,6,7},{2,3},{4,5}} => 1

{{1,4,7},{2},{3,6},{5}} => [4,2,6,7,5,3,1] => [2,6,1,5,3,4,7] => {{1,2,6},{3},{4,5},{7}} => 3

{{1,4},{2,7},{3,6},{5}} => [4,7,6,1,5,3,2] => [7,6,1,5,3,2,4] => {{1,7},{2,6},{3},{4,5}} => 3

{{1,4},{2},{3,6,7},{5}} => [4,2,6,1,5,7,3] => [2,7,1,5,3,6,4] => {{1,2,7},{3},{4,5},{6}} => 3

{{1,4},{2},{3,6},{5,7}} => [4,2,6,1,7,3,5] => [2,6,1,7,3,5,4] => {{1,2,6},{3},{4,7},{5}} => 3

{{1,4},{2},{3,6},{5},{7}} => [4,2,6,1,5,3,7] => [2,6,1,5,3,7,4] => {{1,2,6,7},{3},{4,5}} => 1

{{1,4,7},{2},{3},{5,6}} => [4,2,3,7,6,5,1] => [2,3,1,6,5,4,7] => {{1,2,3},{4,6},{5},{7}} => 3

{{1,4},{2,7},{3},{5,6}} => [4,7,3,1,6,5,2] => [7,3,1,6,5,2,4] => {{1,7},{2,3},{4,6},{5}} => 3

{{1,4},{2},{3,7},{5,6}} => [4,2,7,1,6,5,3] => [2,7,1,6,5,3,4] => {{1,2,7},{3},{4,6},{5}} => 3

{{1,4},{2},{3},{5,6,7}} => [4,2,3,1,6,7,5] => [2,3,1,7,5,6,4] => {{1,2,3},{4,7},{5},{6}} => 3

{{1,4},{2},{3},{5,6},{7}} => [4,2,3,1,6,5,7] => [2,3,1,6,5,7,4] => {{1,2,3},{4,6,7},{5}} => 1

{{1,4,7},{2},{3},{5},{6}} => [4,2,3,7,5,6,1] => [2,3,1,5,6,4,7] => {{1,2,3},{4,5,6},{7}} => 2

{{1,4},{2,7},{3},{5},{6}} => [4,7,3,1,5,6,2] => [7,3,1,5,6,2,4] => {{1,7},{2,3},{4,5,6}} => 2

{{1,4},{2},{3,7},{5},{6}} => [4,2,7,1,5,6,3] => [2,7,1,5,6,3,4] => {{1,2,7},{3},{4,5,6}} => 2

{{1,4},{2},{3},{5,7},{6}} => [4,2,3,1,7,6,5] => [2,3,1,7,6,5,4] => {{1,2,3},{4,7},{5,6}} => 2

{{1,4},{2},{3},{5},{6,7}} => [4,2,3,1,5,7,6] => [2,3,1,5,7,6,4] => {{1,2,3},{4,5,7},{6}} => 2

{{1,4},{2},{3},{5},{6},{7}} => [4,2,3,1,5,6,7] => [2,3,1,5,6,7,4] => {{1,2,3},{4,5,6,7}} => 1

{{1,5,6,7},{2,4},{3}} => [5,4,3,2,6,7,1] => [4,3,2,1,5,6,7] => {{1,4},{2,3},{5},{6},{7}} => 5

{{1,5,6},{2,4,7},{3}} => [5,4,3,7,6,1,2] => [7,3,2,1,5,4,6] => {{1,7},{2,3},{4},{5},{6}} => 5

{{1,5,6},{2,4},{3,7}} => [5,4,7,2,6,1,3] => [4,7,2,1,5,3,6] => {{1,4},{2,7},{3},{5},{6}} => 5

{{1,5,6},{2,4},{3},{7}} => [5,4,3,2,6,1,7] => [4,3,2,1,5,7,6] => {{1,4},{2,3},{5},{6,7}} => 1

{{1,5,7},{2,4,6},{3}} => [5,4,3,6,7,2,1] => [6,3,2,1,4,5,7] => {{1,6},{2,3},{4},{5},{7}} => 5

{{1,5},{2,4,6,7},{3}} => [5,4,3,6,1,7,2] => [7,3,2,1,4,6,5] => {{1,7},{2,3},{4},{5},{6}} => 5

{{1,5},{2,4,6},{3,7}} => [5,4,7,6,1,2,3] => [6,7,2,1,4,3,5] => {{1,6},{2,7},{3},{4},{5}} => 5

{{1,5},{2,4,6},{3},{7}} => [5,4,3,6,1,2,7] => [6,3,2,1,4,7,5] => {{1,6,7},{2,3},{4},{5}} => 1

{{1,5,7},{2,4},{3,6}} => [5,4,6,2,7,3,1] => [4,6,2,1,3,5,7] => {{1,4},{2,6},{3},{5},{7}} => 5

{{1,5},{2,4,7},{3,6}} => [5,4,6,7,1,3,2] => [7,6,2,1,3,4,5] => {{1,7},{2,6},{3},{4},{5}} => 5

{{1,5},{2,4},{3,6,7}} => [5,4,6,2,1,7,3] => [4,7,2,1,3,6,5] => {{1,4},{2,7},{3},{5},{6}} => 5

{{1,5},{2,4},{3,6},{7}} => [5,4,6,2,1,3,7] => [4,6,2,1,3,7,5] => {{1,4},{2,6,7},{3},{5}} => 1

{{1,5,7},{2,4},{3},{6}} => [5,4,3,2,7,6,1] => [4,3,2,1,6,5,7] => {{1,4},{2,3},{5,6},{7}} => 2

{{1,5},{2,4,7},{3},{6}} => [5,4,3,7,1,6,2] => [7,3,2,1,6,4,5] => {{1,7},{2,3},{4},{5,6}} => 2

{{1,5},{2,4},{3,7},{6}} => [5,4,7,2,1,6,3] => [4,7,2,1,6,3,5] => {{1,4},{2,7},{3},{5,6}} => 2

{{1,5},{2,4},{3},{6,7}} => [5,4,3,2,1,7,6] => [4,3,2,1,7,6,5] => {{1,4},{2,3},{5,7},{6}} => 2

{{1,5},{2,4},{3},{6},{7}} => [5,4,3,2,1,6,7] => [4,3,2,1,6,7,5] => {{1,4},{2,3},{5,6,7}} => 1

{{1,6,7},{2,4,5},{3}} => [6,4,3,5,2,7,1] => [5,3,2,4,1,6,7] => {{1,5},{2,3},{4},{6},{7}} => 5

{{1,6},{2,4,5,7},{3}} => [6,4,3,5,7,1,2] => [7,3,2,4,1,5,6] => {{1,7},{2,3},{4},{5},{6}} => 5

{{1,6},{2,4,5},{3,7}} => [6,4,7,5,2,1,3] => [5,7,2,4,1,3,6] => {{1,5},{2,7},{3},{4},{6}} => 5

{{1,6},{2,4,5},{3},{7}} => [6,4,3,5,2,1,7] => [5,3,2,4,1,7,6] => {{1,5},{2,3},{4},{6,7}} => 1

{{1,7},{2,4,5,6},{3}} => [7,4,3,5,6,2,1] => [6,3,2,4,5,1,7] => {{1,6},{2,3},{4},{5},{7}} => 5

{{1},{2,4,5,6,7},{3}} => [1,4,3,5,6,7,2] => [7,3,2,4,5,6,1] => {{1,7},{2,3},{4},{5},{6}} => 5

{{1},{2,4,5,6},{3,7}} => [1,4,7,5,6,2,3] => [6,7,2,4,5,3,1] => {{1,6},{2,7},{3},{4},{5}} => 5

{{1},{2,4,5,6},{3},{7}} => [1,4,3,5,6,2,7] => [6,3,2,4,5,7,1] => {{1,6,7},{2,3},{4},{5}} => 1

{{1,7},{2,4,5},{3,6}} => [7,4,6,5,2,3,1] => [5,6,2,4,3,1,7] => {{1,5},{2,6},{3},{4},{7}} => 5

{{1},{2,4,5,7},{3,6}} => [1,4,6,5,7,3,2] => [7,6,2,4,3,5,1] => {{1,7},{2,6},{3},{4},{5}} => 5

{{1},{2,4,5},{3,6,7}} => [1,4,6,5,2,7,3] => [5,7,2,4,3,6,1] => {{1,5},{2,7},{3},{4},{6}} => 5

{{1},{2,4,5},{3,6},{7}} => [1,4,6,5,2,3,7] => [5,6,2,4,3,7,1] => {{1,5},{2,6,7},{3},{4}} => 1

{{1,7},{2,4,5},{3},{6}} => [7,4,3,5,2,6,1] => [5,3,2,4,6,1,7] => {{1,5,6},{2,3},{4},{7}} => 2

{{1},{2,4,5,7},{3},{6}} => [1,4,3,5,7,6,2] => [7,3,2,4,6,5,1] => {{1,7},{2,3},{4},{5,6}} => 2

{{1},{2,4,5},{3,7},{6}} => [1,4,7,5,2,6,3] => [5,7,2,4,6,3,1] => {{1,5,6},{2,7},{3},{4}} => 2

{{1},{2,4,5},{3},{6,7}} => [1,4,3,5,2,7,6] => [5,3,2,4,7,6,1] => {{1,5,7},{2,3},{4},{6}} => 2

{{1},{2,4,5},{3},{6},{7}} => [1,4,3,5,2,6,7] => [5,3,2,4,6,7,1] => {{1,5,6,7},{2,3},{4}} => 1

{{1,6,7},{2,4},{3,5}} => [6,4,5,2,3,7,1] => [4,5,2,3,1,6,7] => {{1,4},{2,5},{3},{6},{7}} => 5

{{1,6},{2,4,7},{3,5}} => [6,4,5,7,3,1,2] => [7,5,2,3,1,4,6] => {{1,7},{2,5},{3},{4},{6}} => 5

{{1,6},{2,4},{3,5,7}} => [6,4,5,2,7,1,3] => [4,7,2,3,1,5,6] => {{1,4},{2,7},{3},{5},{6}} => 5

{{1,6},{2,4},{3,5},{7}} => [6,4,5,2,3,1,7] => [4,5,2,3,1,7,6] => {{1,4},{2,5},{3},{6,7}} => 1

{{1,7},{2,4,6},{3,5}} => [7,4,5,6,3,2,1] => [6,5,2,3,4,1,7] => {{1,6},{2,5},{3},{4},{7}} => 5

{{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => [7,5,2,3,4,6,1] => {{1,7},{2,5},{3},{4},{6}} => 5

{{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => [6,7,2,3,4,5,1] => {{1,6},{2,7},{3},{4},{5}} => 5

{{1},{2,4,6},{3,5},{7}} => [1,4,5,6,3,2,7] => [6,5,2,3,4,7,1] => {{1,6,7},{2,5},{3},{4}} => 1

{{1,7},{2,4},{3,5,6}} => [7,4,5,2,6,3,1] => [4,6,2,3,5,1,7] => {{1,4},{2,6},{3},{5},{7}} => 5

{{1},{2,4,7},{3,5,6}} => [1,4,5,7,6,3,2] => [7,6,2,3,5,4,1] => {{1,7},{2,6},{3},{4},{5}} => 5

{{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => [4,7,2,3,5,6,1] => {{1,4},{2,7},{3},{5},{6}} => 5

{{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => [4,6,2,3,5,7,1] => {{1,4},{2,6,7},{3},{5}} => 1

{{1,7},{2,4},{3,5},{6}} => [7,4,5,2,3,6,1] => [4,5,2,3,6,1,7] => {{1,4},{2,5,6},{3},{7}} => 2

{{1},{2,4,7},{3,5},{6}} => [1,4,5,7,3,6,2] => [7,5,2,3,6,4,1] => {{1,7},{2,5,6},{3},{4}} => 2

{{1},{2,4},{3,5,7},{6}} => [1,4,5,2,7,6,3] => [4,7,2,3,6,5,1] => {{1,4},{2,7},{3},{5,6}} => 2

{{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => [4,5,2,3,7,6,1] => {{1,4},{2,5,7},{3},{6}} => 2

{{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => [4,5,2,3,6,7,1] => {{1,4},{2,5,6,7},{3}} => 1

{{1,6,7},{2,4},{3},{5}} => [6,4,3,2,5,7,1] => [4,3,2,5,1,6,7] => {{1,4,5},{2,3},{6},{7}} => 3

{{1,6},{2,4,7},{3},{5}} => [6,4,3,7,5,1,2] => [7,3,2,5,1,4,6] => {{1,7},{2,3},{4,5},{6}} => 3

{{1,6},{2,4},{3,7},{5}} => [6,4,7,2,5,1,3] => [4,7,2,5,1,3,6] => {{1,4,5},{2,7},{3},{6}} => 3

{{1,6},{2,4},{3},{5,7}} => [6,4,3,2,7,1,5] => [4,3,2,7,1,5,6] => {{1,4,7},{2,3},{5},{6}} => 3

{{1,6},{2,4},{3},{5},{7}} => [6,4,3,2,5,1,7] => [4,3,2,5,1,7,6] => {{1,4,5},{2,3},{6,7}} => 1

{{1,7},{2,4,6},{3},{5}} => [7,4,3,6,5,2,1] => [6,3,2,5,4,1,7] => {{1,6},{2,3},{4,5},{7}} => 3

{{1},{2,4,6,7},{3},{5}} => [1,4,3,6,5,7,2] => [7,3,2,5,4,6,1] => {{1,7},{2,3},{4,5},{6}} => 3

{{1},{2,4,6},{3,7},{5}} => [1,4,7,6,5,2,3] => [6,7,2,5,4,3,1] => {{1,6},{2,7},{3},{4,5}} => 3

{{1},{2,4,6},{3},{5,7}} => [1,4,3,6,7,2,5] => [6,3,2,7,4,5,1] => {{1,6},{2,3},{4,7},{5}} => 3

{{1},{2,4,6},{3},{5},{7}} => [1,4,3,6,5,2,7] => [6,3,2,5,4,7,1] => {{1,6,7},{2,3},{4,5}} => 1

{{1,7},{2,4},{3,6},{5}} => [7,4,6,2,5,3,1] => [4,6,2,5,3,1,7] => {{1,4,5},{2,6},{3},{7}} => 3

{{1},{2,4,7},{3,6},{5}} => [1,4,6,7,5,3,2] => [7,6,2,5,3,4,1] => {{1,7},{2,6},{3},{4,5}} => 3

{{1},{2,4},{3,6,7},{5}} => [1,4,6,2,5,7,3] => [4,7,2,5,3,6,1] => {{1,4,5},{2,7},{3},{6}} => 3

{{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => [4,6,2,7,3,5,1] => {{1,4,7},{2,6},{3},{5}} => 3

{{1},{2,4},{3,6},{5},{7}} => [1,4,6,2,5,3,7] => [4,6,2,5,3,7,1] => {{1,4,5},{2,6,7},{3}} => 1

{{1,7},{2,4},{3},{5,6}} => [7,4,3,2,6,5,1] => [4,3,2,6,5,1,7] => {{1,4,6},{2,3},{5},{7}} => 3

{{1},{2,4,7},{3},{5,6}} => [1,4,3,7,6,5,2] => [7,3,2,6,5,4,1] => {{1,7},{2,3},{4,6},{5}} => 3

{{1},{2,4},{3,7},{5,6}} => [1,4,7,2,6,5,3] => [4,7,2,6,5,3,1] => {{1,4,6},{2,7},{3},{5}} => 3

{{1},{2,4},{3},{5,6,7}} => [1,4,3,2,6,7,5] => [4,3,2,7,5,6,1] => {{1,4,7},{2,3},{5},{6}} => 3

{{1},{2,4},{3},{5,6},{7}} => [1,4,3,2,6,5,7] => [4,3,2,6,5,7,1] => {{1,4,6,7},{2,3},{5}} => 1

{{1,7},{2,4},{3},{5},{6}} => [7,4,3,2,5,6,1] => [4,3,2,5,6,1,7] => {{1,4,5,6},{2,3},{7}} => 2

{{1},{2,4,7},{3},{5},{6}} => [1,4,3,7,5,6,2] => [7,3,2,5,6,4,1] => {{1,7},{2,3},{4,5,6}} => 2

{{1},{2,4},{3,7},{5},{6}} => [1,4,7,2,5,6,3] => [4,7,2,5,6,3,1] => {{1,4,5,6},{2,7},{3}} => 2

{{1},{2,4},{3},{5,7},{6}} => [1,4,3,2,7,6,5] => [4,3,2,7,6,5,1] => {{1,4,7},{2,3},{5,6}} => 2

{{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => [4,3,2,5,7,6,1] => {{1,4,5,7},{2,3},{6}} => 2

{{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => [4,3,2,5,6,7,1] => {{1,4,5,6,7},{2,3}} => 1

{{1,5,6,7},{2},{3,4}} => [5,2,4,3,6,7,1] => [2,4,3,1,5,6,7] => {{1,2,4},{3},{5},{6},{7}} => 5

{{1,5,6},{2,7},{3,4}} => [5,7,4,3,6,1,2] => [7,4,3,1,5,2,6] => {{1,7},{2,4},{3},{5},{6}} => 5

{{1,5,6},{2},{3,4,7}} => [5,2,4,7,6,1,3] => [2,7,3,1,5,4,6] => {{1,2,7},{3},{4},{5},{6}} => 5

{{1,5,6},{2},{3,4},{7}} => [5,2,4,3,6,1,7] => [2,4,3,1,5,7,6] => {{1,2,4},{3},{5},{6,7}} => 1

{{1,5,7},{2,6},{3,4}} => [5,6,4,3,7,2,1] => [6,4,3,1,2,5,7] => {{1,6},{2,4},{3},{5},{7}} => 5

{{1,5},{2,6,7},{3,4}} => [5,6,4,3,1,7,2] => [7,4,3,1,2,6,5] => {{1,7},{2,4},{3},{5},{6}} => 5

{{1,5},{2,6},{3,4,7}} => [5,6,4,7,1,2,3] => [6,7,3,1,2,4,5] => {{1,6},{2,7},{3},{4},{5}} => 5

{{1,5},{2,6},{3,4},{7}} => [5,6,4,3,1,2,7] => [6,4,3,1,2,7,5] => {{1,6,7},{2,4},{3},{5}} => 1

{{1,5,7},{2},{3,4,6}} => [5,2,4,6,7,3,1] => [2,6,3,1,4,5,7] => {{1,2,6},{3},{4},{5},{7}} => 5

{{1,5},{2,7},{3,4,6}} => [5,7,4,6,1,3,2] => [7,6,3,1,4,2,5] => {{1,7},{2,6},{3},{4},{5}} => 5

{{1,5},{2},{3,4,6,7}} => [5,2,4,6,1,7,3] => [2,7,3,1,4,6,5] => {{1,2,7},{3},{4},{5},{6}} => 5

{{1,5},{2},{3,4,6},{7}} => [5,2,4,6,1,3,7] => [2,6,3,1,4,7,5] => {{1,2,6,7},{3},{4},{5}} => 1

{{1,5,7},{2},{3,4},{6}} => [5,2,4,3,7,6,1] => [2,4,3,1,6,5,7] => {{1,2,4},{3},{5,6},{7}} => 2

{{1,5},{2,7},{3,4},{6}} => [5,7,4,3,1,6,2] => [7,4,3,1,6,2,5] => {{1,7},{2,4},{3},{5,6}} => 2

{{1,5},{2},{3,4,7},{6}} => [5,2,4,7,1,6,3] => [2,7,3,1,6,4,5] => {{1,2,7},{3},{4},{5,6}} => 2

{{1,5},{2},{3,4},{6,7}} => [5,2,4,3,1,7,6] => [2,4,3,1,7,6,5] => {{1,2,4},{3},{5,7},{6}} => 2

{{1,5},{2},{3,4},{6},{7}} => [5,2,4,3,1,6,7] => [2,4,3,1,6,7,5] => {{1,2,4},{3},{5,6,7}} => 1

{{1,6,7},{2,5},{3,4}} => [6,5,4,3,2,7,1] => [5,4,3,2,1,6,7] => {{1,5},{2,4},{3},{6},{7}} => 5

{{1,6},{2,5,7},{3,4}} => [6,5,4,3,7,1,2] => [7,4,3,2,1,5,6] => {{1,7},{2,4},{3},{5},{6}} => 5

{{1,6},{2,5},{3,4,7}} => [6,5,4,7,2,1,3] => [5,7,3,2,1,4,6] => {{1,5},{2,7},{3},{4},{6}} => 5

{{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => [5,4,3,2,1,7,6] => {{1,5},{2,4},{3},{6,7}} => 1

{{1,7},{2,5,6},{3,4}} => [7,5,4,3,6,2,1] => [6,4,3,2,5,1,7] => {{1,6},{2,4},{3},{5},{7}} => 5

{{1},{2,5,6,7},{3,4}} => [1,5,4,3,6,7,2] => [7,4,3,2,5,6,1] => {{1,7},{2,4},{3},{5},{6}} => 5

{{1},{2,5,6},{3,4,7}} => [1,5,4,7,6,2,3] => [6,7,3,2,5,4,1] => {{1,6},{2,7},{3},{4},{5}} => 5

{{1},{2,5,6},{3,4},{7}} => [1,5,4,3,6,2,7] => [6,4,3,2,5,7,1] => {{1,6,7},{2,4},{3},{5}} => 1

{{1,7},{2,5},{3,4,6}} => [7,5,4,6,2,3,1] => [5,6,3,2,4,1,7] => {{1,5},{2,6},{3},{4},{7}} => 5

{{1},{2,5,7},{3,4,6}} => [1,5,4,6,7,3,2] => [7,6,3,2,4,5,1] => {{1,7},{2,6},{3},{4},{5}} => 5

{{1},{2,5},{3,4,6,7}} => [1,5,4,6,2,7,3] => [5,7,3,2,4,6,1] => {{1,5},{2,7},{3},{4},{6}} => 5

{{1},{2,5},{3,4,6},{7}} => [1,5,4,6,2,3,7] => [5,6,3,2,4,7,1] => {{1,5},{2,6,7},{3},{4}} => 1

{{1,7},{2,5},{3,4},{6}} => [7,5,4,3,2,6,1] => [5,4,3,2,6,1,7] => {{1,5,6},{2,4},{3},{7}} => 2

{{1},{2,5,7},{3,4},{6}} => [1,5,4,3,7,6,2] => [7,4,3,2,6,5,1] => {{1,7},{2,4},{3},{5,6}} => 2

{{1},{2,5},{3,4,7},{6}} => [1,5,4,7,2,6,3] => [5,7,3,2,6,4,1] => {{1,5,6},{2,7},{3},{4}} => 2

{{1},{2,5},{3,4},{6,7}} => [1,5,4,3,2,7,6] => [5,4,3,2,7,6,1] => {{1,5,7},{2,4},{3},{6}} => 2

{{1},{2,5},{3,4},{6},{7}} => [1,5,4,3,2,6,7] => [5,4,3,2,6,7,1] => {{1,5,6,7},{2,4},{3}} => 1

{{1,6,7},{2},{3,4,5}} => [6,2,4,5,3,7,1] => [2,5,3,4,1,6,7] => {{1,2,5},{3},{4},{6},{7}} => 5

{{1,6},{2,7},{3,4,5}} => [6,7,4,5,3,1,2] => [7,5,3,4,1,2,6] => {{1,7},{2,5},{3},{4},{6}} => 5

{{1,6},{2},{3,4,5,7}} => [6,2,4,5,7,1,3] => [2,7,3,4,1,5,6] => {{1,2,7},{3},{4},{5},{6}} => 5

{{1,6},{2},{3,4,5},{7}} => [6,2,4,5,3,1,7] => [2,5,3,4,1,7,6] => {{1,2,5},{3},{4},{6,7}} => 1

{{1,7},{2,6},{3,4,5}} => [7,6,4,5,3,2,1] => [6,5,3,4,2,1,7] => {{1,6},{2,5},{3},{4},{7}} => 5

{{1},{2,6,7},{3,4,5}} => [1,6,4,5,3,7,2] => [7,5,3,4,2,6,1] => {{1,7},{2,5},{3},{4},{6}} => 5

{{1},{2,6},{3,4,5,7}} => [1,6,4,5,7,2,3] => [6,7,3,4,2,5,1] => {{1,6},{2,7},{3},{4},{5}} => 5

{{1},{2,6},{3,4,5},{7}} => [1,6,4,5,3,2,7] => [6,5,3,4,2,7,1] => {{1,6,7},{2,5},{3},{4}} => 1

{{1,7},{2},{3,4,5,6}} => [7,2,4,5,6,3,1] => [2,6,3,4,5,1,7] => {{1,2,6},{3},{4},{5},{7}} => 5

{{1},{2,7},{3,4,5,6}} => [1,7,4,5,6,3,2] => [7,6,3,4,5,2,1] => {{1,7},{2,6},{3},{4},{5}} => 5

{{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => [2,7,3,4,5,6,1] => {{1,2,7},{3},{4},{5},{6}} => 5

{{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => [2,6,3,4,5,7,1] => {{1,2,6,7},{3},{4},{5}} => 1

{{1,7},{2},{3,4,5},{6}} => [7,2,4,5,3,6,1] => [2,5,3,4,6,1,7] => {{1,2,5,6},{3},{4},{7}} => 2

{{1},{2,7},{3,4,5},{6}} => [1,7,4,5,3,6,2] => [7,5,3,4,6,2,1] => {{1,7},{2,5,6},{3},{4}} => 2

{{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => [2,7,3,4,6,5,1] => {{1,2,7},{3},{4},{5,6}} => 2

{{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => [2,5,3,4,7,6,1] => {{1,2,5,7},{3},{4},{6}} => 2

{{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => [2,5,3,4,6,7,1] => {{1,2,5,6,7},{3},{4}} => 1

{{1,6,7},{2},{3,4},{5}} => [6,2,4,3,5,7,1] => [2,4,3,5,1,6,7] => {{1,2,4,5},{3},{6},{7}} => 3

{{1,6},{2,7},{3,4},{5}} => [6,7,4,3,5,1,2] => [7,4,3,5,1,2,6] => {{1,7},{2,4,5},{3},{6}} => 3

{{1,6},{2},{3,4,7},{5}} => [6,2,4,7,5,1,3] => [2,7,3,5,1,4,6] => {{1,2,7},{3},{4,5},{6}} => 3

{{1,6},{2},{3,4},{5,7}} => [6,2,4,3,7,1,5] => [2,4,3,7,1,5,6] => {{1,2,4,7},{3},{5},{6}} => 3

{{1,6},{2},{3,4},{5},{7}} => [6,2,4,3,5,1,7] => [2,4,3,5,1,7,6] => {{1,2,4,5},{3},{6,7}} => 1

{{1,7},{2,6},{3,4},{5}} => [7,6,4,3,5,2,1] => [6,4,3,5,2,1,7] => {{1,6},{2,4,5},{3},{7}} => 3

{{1},{2,6,7},{3,4},{5}} => [1,6,4,3,5,7,2] => [7,4,3,5,2,6,1] => {{1,7},{2,4,5},{3},{6}} => 3

{{1},{2,6},{3,4,7},{5}} => [1,6,4,7,5,2,3] => [6,7,3,5,2,4,1] => {{1,6},{2,7},{3},{4,5}} => 3

{{1},{2,6},{3,4},{5,7}} => [1,6,4,3,7,2,5] => [6,4,3,7,2,5,1] => {{1,6},{2,4,7},{3},{5}} => 3

{{1},{2,6},{3,4},{5},{7}} => [1,6,4,3,5,2,7] => [6,4,3,5,2,7,1] => {{1,6,7},{2,4,5},{3}} => 1

{{1,7},{2},{3,4,6},{5}} => [7,2,4,6,5,3,1] => [2,6,3,5,4,1,7] => {{1,2,6},{3},{4,5},{7}} => 3

{{1},{2,7},{3,4,6},{5}} => [1,7,4,6,5,3,2] => [7,6,3,5,4,2,1] => {{1,7},{2,6},{3},{4,5}} => 3

{{1},{2},{3,4,6,7},{5}} => [1,2,4,6,5,7,3] => [2,7,3,5,4,6,1] => {{1,2,7},{3},{4,5},{6}} => 3

{{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => [2,6,3,7,4,5,1] => {{1,2,6},{3},{4,7},{5}} => 3

{{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => [2,6,3,5,4,7,1] => {{1,2,6,7},{3},{4,5}} => 1

{{1,7},{2},{3,4},{5,6}} => [7,2,4,3,6,5,1] => [2,4,3,6,5,1,7] => {{1,2,4,6},{3},{5},{7}} => 3

{{1},{2,7},{3,4},{5,6}} => [1,7,4,3,6,5,2] => [7,4,3,6,5,2,1] => {{1,7},{2,4,6},{3},{5}} => 3

{{1},{2},{3,4,7},{5,6}} => [1,2,4,7,6,5,3] => [2,7,3,6,5,4,1] => {{1,2,7},{3},{4,6},{5}} => 3

{{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => [2,4,3,7,5,6,1] => {{1,2,4,7},{3},{5},{6}} => 3

{{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => [2,4,3,6,5,7,1] => {{1,2,4,6,7},{3},{5}} => 1

{{1,7},{2},{3,4},{5},{6}} => [7,2,4,3,5,6,1] => [2,4,3,5,6,1,7] => {{1,2,4,5,6},{3},{7}} => 2

{{1},{2,7},{3,4},{5},{6}} => [1,7,4,3,5,6,2] => [7,4,3,5,6,2,1] => {{1,7},{2,4,5,6},{3}} => 2

{{1},{2},{3,4,7},{5},{6}} => [1,2,4,7,5,6,3] => [2,7,3,5,6,4,1] => {{1,2,7},{3},{4,5,6}} => 2

{{1},{2},{3,4},{5,7},{6}} => [1,2,4,3,7,6,5] => [2,4,3,7,6,5,1] => {{1,2,4,7},{3},{5,6}} => 2

{{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => [2,4,3,5,7,6,1] => {{1,2,4,5,7},{3},{6}} => 2

{{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => [2,4,3,5,6,7,1] => {{1,2,4,5,6,7},{3}} => 1

{{1,5,6,7},{2},{3},{4}} => [5,2,3,4,6,7,1] => [2,3,4,1,5,6,7] => {{1,2,3,4},{5},{6},{7}} => 4

{{1,5,6},{2,7},{3},{4}} => [5,7,3,4,6,1,2] => [7,3,4,1,5,2,6] => {{1,7},{2,3,4},{5},{6}} => 4

{{1,5,6},{2},{3,7},{4}} => [5,2,7,4,6,1,3] => [2,7,4,1,5,3,6] => {{1,2,7},{3,4},{5},{6}} => 4

{{1,5,6},{2},{3},{4,7}} => [5,2,3,7,6,1,4] => [2,3,7,1,5,4,6] => {{1,2,3,7},{4},{5},{6}} => 4

{{1,5,6},{2},{3},{4},{7}} => [5,2,3,4,6,1,7] => [2,3,4,1,5,7,6] => {{1,2,3,4},{5},{6,7}} => 1

{{1,5,7},{2,6},{3},{4}} => [5,6,3,4,7,2,1] => [6,3,4,1,2,5,7] => {{1,6},{2,3,4},{5},{7}} => 4

{{1,5},{2,6,7},{3},{4}} => [5,6,3,4,1,7,2] => [7,3,4,1,2,6,5] => {{1,7},{2,3,4},{5},{6}} => 4

{{1,5},{2,6},{3,7},{4}} => [5,6,7,4,1,2,3] => [6,7,4,1,2,3,5] => {{1,6},{2,7},{3,4},{5}} => 4

{{1,5},{2,6},{3},{4,7}} => [5,6,3,7,1,2,4] => [6,3,7,1,2,4,5] => {{1,6},{2,3,7},{4},{5}} => 4

{{1,5},{2,6},{3},{4},{7}} => [5,6,3,4,1,2,7] => [6,3,4,1,2,7,5] => {{1,6,7},{2,3,4},{5}} => 1

{{1,5,7},{2},{3,6},{4}} => [5,2,6,4,7,3,1] => [2,6,4,1,3,5,7] => {{1,2,6},{3,4},{5},{7}} => 4

{{1,5},{2,7},{3,6},{4}} => [5,7,6,4,1,3,2] => [7,6,4,1,3,2,5] => {{1,7},{2,6},{3,4},{5}} => 4

{{1,5},{2},{3,6,7},{4}} => [5,2,6,4,1,7,3] => [2,7,4,1,3,6,5] => {{1,2,7},{3,4},{5},{6}} => 4

{{1,5},{2},{3,6},{4,7}} => [5,2,6,7,1,3,4] => [2,6,7,1,3,4,5] => {{1,2,6},{3,7},{4},{5}} => 4

{{1,5},{2},{3,6},{4},{7}} => [5,2,6,4,1,3,7] => [2,6,4,1,3,7,5] => {{1,2,6,7},{3,4},{5}} => 1

{{1,5,7},{2},{3},{4,6}} => [5,2,3,6,7,4,1] => [2,3,6,1,4,5,7] => {{1,2,3,6},{4},{5},{7}} => 4

{{1,5},{2,7},{3},{4,6}} => [5,7,3,6,1,4,2] => [7,3,6,1,4,2,5] => {{1,7},{2,3,6},{4},{5}} => 4

{{1,5},{2},{3,7},{4,6}} => [5,2,7,6,1,4,3] => [2,7,6,1,4,3,5] => {{1,2,7},{3,6},{4},{5}} => 4

{{1,5},{2},{3},{4,6,7}} => [5,2,3,6,1,7,4] => [2,3,7,1,4,6,5] => {{1,2,3,7},{4},{5},{6}} => 4

{{1,5},{2},{3},{4,6},{7}} => [5,2,3,6,1,4,7] => [2,3,6,1,4,7,5] => {{1,2,3,6,7},{4},{5}} => 1

{{1,5,7},{2},{3},{4},{6}} => [5,2,3,4,7,6,1] => [2,3,4,1,6,5,7] => {{1,2,3,4},{5,6},{7}} => 2

{{1,5},{2,7},{3},{4},{6}} => [5,7,3,4,1,6,2] => [7,3,4,1,6,2,5] => {{1,7},{2,3,4},{5,6}} => 2

{{1,5},{2},{3,7},{4},{6}} => [5,2,7,4,1,6,3] => [2,7,4,1,6,3,5] => {{1,2,7},{3,4},{5,6}} => 2

{{1,5},{2},{3},{4,7},{6}} => [5,2,3,7,1,6,4] => [2,3,7,1,6,4,5] => {{1,2,3,7},{4},{5,6}} => 2

{{1,5},{2},{3},{4},{6,7}} => [5,2,3,4,1,7,6] => [2,3,4,1,7,6,5] => {{1,2,3,4},{5,7},{6}} => 2

{{1,5},{2},{3},{4},{6},{7}} => [5,2,3,4,1,6,7] => [2,3,4,1,6,7,5] => {{1,2,3,4},{5,6,7}} => 1

{{1,6,7},{2,5},{3},{4}} => [6,5,3,4,2,7,1] => [5,3,4,2,1,6,7] => {{1,5},{2,3,4},{6},{7}} => 4

{{1,6},{2,5,7},{3},{4}} => [6,5,3,4,7,1,2] => [7,3,4,2,1,5,6] => {{1,7},{2,3,4},{5},{6}} => 4

{{1,6},{2,5},{3,7},{4}} => [6,5,7,4,2,1,3] => [5,7,4,2,1,3,6] => {{1,5},{2,7},{3,4},{6}} => 4

{{1,6},{2,5},{3},{4,7}} => [6,5,3,7,2,1,4] => [5,3,7,2,1,4,6] => {{1,5},{2,3,7},{4},{6}} => 4

{{1,6},{2,5},{3},{4},{7}} => [6,5,3,4,2,1,7] => [5,3,4,2,1,7,6] => {{1,5},{2,3,4},{6,7}} => 1

{{1,7},{2,5,6},{3},{4}} => [7,5,3,4,6,2,1] => [6,3,4,2,5,1,7] => {{1,6},{2,3,4},{5},{7}} => 4

{{1},{2,5,6,7},{3},{4}} => [1,5,3,4,6,7,2] => [7,3,4,2,5,6,1] => {{1,7},{2,3,4},{5},{6}} => 4

{{1},{2,5,6},{3,7},{4}} => [1,5,7,4,6,2,3] => [6,7,4,2,5,3,1] => {{1,6},{2,7},{3,4},{5}} => 4

{{1},{2,5,6},{3},{4,7}} => [1,5,3,7,6,2,4] => [6,3,7,2,5,4,1] => {{1,6},{2,3,7},{4},{5}} => 4

{{1},{2,5,6},{3},{4},{7}} => [1,5,3,4,6,2,7] => [6,3,4,2,5,7,1] => {{1,6,7},{2,3,4},{5}} => 1

{{1,7},{2,5},{3,6},{4}} => [7,5,6,4,2,3,1] => [5,6,4,2,3,1,7] => {{1,5},{2,6},{3,4},{7}} => 4

{{1},{2,5,7},{3,6},{4}} => [1,5,6,4,7,3,2] => [7,6,4,2,3,5,1] => {{1,7},{2,6},{3,4},{5}} => 4

{{1},{2,5},{3,6,7},{4}} => [1,5,6,4,2,7,3] => [5,7,4,2,3,6,1] => {{1,5},{2,7},{3,4},{6}} => 4

{{1},{2,5},{3,6},{4,7}} => [1,5,6,7,2,3,4] => [5,6,7,2,3,4,1] => {{1,5},{2,6},{3,7},{4}} => 4

{{1},{2,5},{3,6},{4},{7}} => [1,5,6,4,2,3,7] => [5,6,4,2,3,7,1] => {{1,5},{2,6,7},{3,4}} => 1

{{1,7},{2,5},{3},{4,6}} => [7,5,3,6,2,4,1] => [5,3,6,2,4,1,7] => {{1,5},{2,3,6},{4},{7}} => 4

{{1},{2,5,7},{3},{4,6}} => [1,5,3,6,7,4,2] => [7,3,6,2,4,5,1] => {{1,7},{2,3,6},{4},{5}} => 4

{{1},{2,5},{3,7},{4,6}} => [1,5,7,6,2,4,3] => [5,7,6,2,4,3,1] => {{1,5},{2,7},{3,6},{4}} => 4

{{1},{2,5},{3},{4,6,7}} => [1,5,3,6,2,7,4] => [5,3,7,2,4,6,1] => {{1,5},{2,3,7},{4},{6}} => 4

{{1},{2,5},{3},{4,6},{7}} => [1,5,3,6,2,4,7] => [5,3,6,2,4,7,1] => {{1,5},{2,3,6,7},{4}} => 1

{{1,7},{2,5},{3},{4},{6}} => [7,5,3,4,2,6,1] => [5,3,4,2,6,1,7] => {{1,5,6},{2,3,4},{7}} => 2

{{1},{2,5,7},{3},{4},{6}} => [1,5,3,4,7,6,2] => [7,3,4,2,6,5,1] => {{1,7},{2,3,4},{5,6}} => 2

{{1},{2,5},{3,7},{4},{6}} => [1,5,7,4,2,6,3] => [5,7,4,2,6,3,1] => {{1,5,6},{2,7},{3,4}} => 2

{{1},{2,5},{3},{4,7},{6}} => [1,5,3,7,2,6,4] => [5,3,7,2,6,4,1] => {{1,5,6},{2,3,7},{4}} => 2

{{1},{2,5},{3},{4},{6,7}} => [1,5,3,4,2,7,6] => [5,3,4,2,7,6,1] => {{1,5,7},{2,3,4},{6}} => 2

{{1},{2,5},{3},{4},{6},{7}} => [1,5,3,4,2,6,7] => [5,3,4,2,6,7,1] => {{1,5,6,7},{2,3,4}} => 1

{{1,6,7},{2},{3,5},{4}} => [6,2,5,4,3,7,1] => [2,5,4,3,1,6,7] => {{1,2,5},{3,4},{6},{7}} => 4

{{1,6},{2,7},{3,5},{4}} => [6,7,5,4,3,1,2] => [7,5,4,3,1,2,6] => {{1,7},{2,5},{3,4},{6}} => 4

{{1,6},{2},{3,5,7},{4}} => [6,2,5,4,7,1,3] => [2,7,4,3,1,5,6] => {{1,2,7},{3,4},{5},{6}} => 4

{{1,6},{2},{3,5},{4,7}} => [6,2,5,7,3,1,4] => [2,5,7,3,1,4,6] => {{1,2,5},{3,7},{4},{6}} => 4

{{1,6},{2},{3,5},{4},{7}} => [6,2,5,4,3,1,7] => [2,5,4,3,1,7,6] => {{1,2,5},{3,4},{6,7}} => 1

{{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => [6,5,4,3,2,1,7] => {{1,6},{2,5},{3,4},{7}} => 4

{{1},{2,6,7},{3,5},{4}} => [1,6,5,4,3,7,2] => [7,5,4,3,2,6,1] => {{1,7},{2,5},{3,4},{6}} => 4

{{1},{2,6},{3,5,7},{4}} => [1,6,5,4,7,2,3] => [6,7,4,3,2,5,1] => {{1,6},{2,7},{3,4},{5}} => 4

{{1},{2,6},{3,5},{4,7}} => [1,6,5,7,3,2,4] => [6,5,7,3,2,4,1] => {{1,6},{2,5},{3,7},{4}} => 4

{{1},{2,6},{3,5},{4},{7}} => [1,6,5,4,3,2,7] => [6,5,4,3,2,7,1] => {{1,6,7},{2,5},{3,4}} => 1

{{1,7},{2},{3,5,6},{4}} => [7,2,5,4,6,3,1] => [2,6,4,3,5,1,7] => {{1,2,6},{3,4},{5},{7}} => 4

{{1},{2,7},{3,5,6},{4}} => [1,7,5,4,6,3,2] => [7,6,4,3,5,2,1] => {{1,7},{2,6},{3,4},{5}} => 4

{{1},{2},{3,5,6,7},{4}} => [1,2,5,4,6,7,3] => [2,7,4,3,5,6,1] => {{1,2,7},{3,4},{5},{6}} => 4

{{1},{2},{3,5,6},{4,7}} => [1,2,5,7,6,3,4] => [2,6,7,3,5,4,1] => {{1,2,6},{3,7},{4},{5}} => 4

{{1},{2},{3,5,6},{4},{7}} => [1,2,5,4,6,3,7] => [2,6,4,3,5,7,1] => {{1,2,6,7},{3,4},{5}} => 1

{{1,7},{2},{3,5},{4,6}} => [7,2,5,6,3,4,1] => [2,5,6,3,4,1,7] => {{1,2,5},{3,6},{4},{7}} => 4

{{1},{2,7},{3,5},{4,6}} => [1,7,5,6,3,4,2] => [7,5,6,3,4,2,1] => {{1,7},{2,5},{3,6},{4}} => 4

{{1},{2},{3,5,7},{4,6}} => [1,2,5,6,7,4,3] => [2,7,6,3,4,5,1] => {{1,2,7},{3,6},{4},{5}} => 4

{{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => [2,5,7,3,4,6,1] => {{1,2,5},{3,7},{4},{6}} => 4

{{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => [2,5,6,3,4,7,1] => {{1,2,5},{3,6,7},{4}} => 1

{{1,7},{2},{3,5},{4},{6}} => [7,2,5,4,3,6,1] => [2,5,4,3,6,1,7] => {{1,2,5,6},{3,4},{7}} => 2

{{1},{2,7},{3,5},{4},{6}} => [1,7,5,4,3,6,2] => [7,5,4,3,6,2,1] => {{1,7},{2,5,6},{3,4}} => 2

{{1},{2},{3,5,7},{4},{6}} => [1,2,5,4,7,6,3] => [2,7,4,3,6,5,1] => {{1,2,7},{3,4},{5,6}} => 2

{{1},{2},{3,5},{4,7},{6}} => [1,2,5,7,3,6,4] => [2,5,7,3,6,4,1] => {{1,2,5,6},{3,7},{4}} => 2

{{1},{2},{3,5},{4},{6,7}} => [1,2,5,4,3,7,6] => [2,5,4,3,7,6,1] => {{1,2,5,7},{3,4},{6}} => 2

{{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => [2,5,4,3,6,7,1] => {{1,2,5,6,7},{3,4}} => 1

{{1,6,7},{2},{3},{4,5}} => [6,2,3,5,4,7,1] => [2,3,5,4,1,6,7] => {{1,2,3,5},{4},{6},{7}} => 4

{{1,6},{2,7},{3},{4,5}} => [6,7,3,5,4,1,2] => [7,3,5,4,1,2,6] => {{1,7},{2,3,5},{4},{6}} => 4

{{1,6},{2},{3,7},{4,5}} => [6,2,7,5,4,1,3] => [2,7,5,4,1,3,6] => {{1,2,7},{3,5},{4},{6}} => 4

{{1,6},{2},{3},{4,5,7}} => [6,2,3,5,7,1,4] => [2,3,7,4,1,5,6] => {{1,2,3,7},{4},{5},{6}} => 4

{{1,6},{2},{3},{4,5},{7}} => [6,2,3,5,4,1,7] => [2,3,5,4,1,7,6] => {{1,2,3,5},{4},{6,7}} => 1

{{1,7},{2,6},{3},{4,5}} => [7,6,3,5,4,2,1] => [6,3,5,4,2,1,7] => {{1,6},{2,3,5},{4},{7}} => 4

{{1},{2,6,7},{3},{4,5}} => [1,6,3,5,4,7,2] => [7,3,5,4,2,6,1] => {{1,7},{2,3,5},{4},{6}} => 4

{{1},{2,6},{3,7},{4,5}} => [1,6,7,5,4,2,3] => [6,7,5,4,2,3,1] => {{1,6},{2,7},{3,5},{4}} => 4

{{1},{2,6},{3},{4,5,7}} => [1,6,3,5,7,2,4] => [6,3,7,4,2,5,1] => {{1,6},{2,3,7},{4},{5}} => 4

{{1},{2,6},{3},{4,5},{7}} => [1,6,3,5,4,2,7] => [6,3,5,4,2,7,1] => {{1,6,7},{2,3,5},{4}} => 1

{{1,7},{2},{3,6},{4,5}} => [7,2,6,5,4,3,1] => [2,6,5,4,3,1,7] => {{1,2,6},{3,5},{4},{7}} => 4

{{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => [7,6,5,4,3,2,1] => {{1,7},{2,6},{3,5},{4}} => 4

{{1},{2},{3,6,7},{4,5}} => [1,2,6,5,4,7,3] => [2,7,5,4,3,6,1] => {{1,2,7},{3,5},{4},{6}} => 4

{{1},{2},{3,6},{4,5,7}} => [1,2,6,5,7,3,4] => [2,6,7,4,3,5,1] => {{1,2,6},{3,7},{4},{5}} => 4

{{1},{2},{3,6},{4,5},{7}} => [1,2,6,5,4,3,7] => [2,6,5,4,3,7,1] => {{1,2,6,7},{3,5},{4}} => 1

{{1,7},{2},{3},{4,5,6}} => [7,2,3,5,6,4,1] => [2,3,6,4,5,1,7] => {{1,2,3,6},{4},{5},{7}} => 4

{{1},{2,7},{3},{4,5,6}} => [1,7,3,5,6,4,2] => [7,3,6,4,5,2,1] => {{1,7},{2,3,6},{4},{5}} => 4

{{1},{2},{3,7},{4,5,6}} => [1,2,7,5,6,4,3] => [2,7,6,4,5,3,1] => {{1,2,7},{3,6},{4},{5}} => 4

{{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => [2,3,7,4,5,6,1] => {{1,2,3,7},{4},{5},{6}} => 4

{{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => [2,3,6,4,5,7,1] => {{1,2,3,6,7},{4},{5}} => 1

{{1,7},{2},{3},{4,5},{6}} => [7,2,3,5,4,6,1] => [2,3,5,4,6,1,7] => {{1,2,3,5,6},{4},{7}} => 2

{{1},{2,7},{3},{4,5},{6}} => [1,7,3,5,4,6,2] => [7,3,5,4,6,2,1] => {{1,7},{2,3,5,6},{4}} => 2

{{1},{2},{3,7},{4,5},{6}} => [1,2,7,5,4,6,3] => [2,7,5,4,6,3,1] => {{1,2,7},{3,5,6},{4}} => 2

{{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => [2,3,7,4,6,5,1] => {{1,2,3,7},{4},{5,6}} => 2

{{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => [2,3,5,4,7,6,1] => {{1,2,3,5,7},{4},{6}} => 2

{{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => [2,3,5,4,6,7,1] => {{1,2,3,5,6,7},{4}} => 1

{{1,6,7},{2},{3},{4},{5}} => [6,2,3,4,5,7,1] => [2,3,4,5,1,6,7] => {{1,2,3,4,5},{6},{7}} => 3

{{1,6},{2,7},{3},{4},{5}} => [6,7,3,4,5,1,2] => [7,3,4,5,1,2,6] => {{1,7},{2,3,4,5},{6}} => 3

{{1,6},{2},{3,7},{4},{5}} => [6,2,7,4,5,1,3] => [2,7,4,5,1,3,6] => {{1,2,7},{3,4,5},{6}} => 3

{{1,6},{2},{3},{4,7},{5}} => [6,2,3,7,5,1,4] => [2,3,7,5,1,4,6] => {{1,2,3,7},{4,5},{6}} => 3

{{1,6},{2},{3},{4},{5,7}} => [6,2,3,4,7,1,5] => [2,3,4,7,1,5,6] => {{1,2,3,4,7},{5},{6}} => 3

{{1,6},{2},{3},{4},{5},{7}} => [6,2,3,4,5,1,7] => [2,3,4,5,1,7,6] => {{1,2,3,4,5},{6,7}} => 1

{{1,7},{2,6},{3},{4},{5}} => [7,6,3,4,5,2,1] => [6,3,4,5,2,1,7] => {{1,6},{2,3,4,5},{7}} => 3

{{1},{2,6,7},{3},{4},{5}} => [1,6,3,4,5,7,2] => [7,3,4,5,2,6,1] => {{1,7},{2,3,4,5},{6}} => 3

{{1},{2,6},{3,7},{4},{5}} => [1,6,7,4,5,2,3] => [6,7,4,5,2,3,1] => {{1,6},{2,7},{3,4,5}} => 3

{{1},{2,6},{3},{4,7},{5}} => [1,6,3,7,5,2,4] => [6,3,7,5,2,4,1] => {{1,6},{2,3,7},{4,5}} => 3

{{1},{2,6},{3},{4},{5,7}} => [1,6,3,4,7,2,5] => [6,3,4,7,2,5,1] => {{1,6},{2,3,4,7},{5}} => 3

{{1},{2,6},{3},{4},{5},{7}} => [1,6,3,4,5,2,7] => [6,3,4,5,2,7,1] => {{1,6,7},{2,3,4,5}} => 1

{{1,7},{2},{3,6},{4},{5}} => [7,2,6,4,5,3,1] => [2,6,4,5,3,1,7] => {{1,2,6},{3,4,5},{7}} => 3

{{1},{2,7},{3,6},{4},{5}} => [1,7,6,4,5,3,2] => [7,6,4,5,3,2,1] => {{1,7},{2,6},{3,4,5}} => 3

{{1},{2},{3,6,7},{4},{5}} => [1,2,6,4,5,7,3] => [2,7,4,5,3,6,1] => {{1,2,7},{3,4,5},{6}} => 3

{{1},{2},{3,6},{4,7},{5}} => [1,2,6,7,5,3,4] => [2,6,7,5,3,4,1] => {{1,2,6},{3,7},{4,5}} => 3

{{1},{2},{3,6},{4},{5,7}} => [1,2,6,4,7,3,5] => [2,6,4,7,3,5,1] => {{1,2,6},{3,4,7},{5}} => 3

{{1},{2},{3,6},{4},{5},{7}} => [1,2,6,4,5,3,7] => [2,6,4,5,3,7,1] => {{1,2,6,7},{3,4,5}} => 1

{{1,7},{2},{3},{4,6},{5}} => [7,2,3,6,5,4,1] => [2,3,6,5,4,1,7] => {{1,2,3,6},{4,5},{7}} => 3

{{1},{2,7},{3},{4,6},{5}} => [1,7,3,6,5,4,2] => [7,3,6,5,4,2,1] => {{1,7},{2,3,6},{4,5}} => 3

{{1},{2},{3,7},{4,6},{5}} => [1,2,7,6,5,4,3] => [2,7,6,5,4,3,1] => {{1,2,7},{3,6},{4,5}} => 3

{{1},{2},{3},{4,6,7},{5}} => [1,2,3,6,5,7,4] => [2,3,7,5,4,6,1] => {{1,2,3,7},{4,5},{6}} => 3

{{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => [2,3,6,7,4,5,1] => {{1,2,3,6},{4,7},{5}} => 3

{{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => [2,3,6,5,4,7,1] => {{1,2,3,6,7},{4,5}} => 1

{{1,7},{2},{3},{4},{5,6}} => [7,2,3,4,6,5,1] => [2,3,4,6,5,1,7] => {{1,2,3,4,6},{5},{7}} => 3

{{1},{2,7},{3},{4},{5,6}} => [1,7,3,4,6,5,2] => [7,3,4,6,5,2,1] => {{1,7},{2,3,4,6},{5}} => 3

{{1},{2},{3,7},{4},{5,6}} => [1,2,7,4,6,5,3] => [2,7,4,6,5,3,1] => {{1,2,7},{3,4,6},{5}} => 3

{{1},{2},{3},{4,7},{5,6}} => [1,2,3,7,6,5,4] => [2,3,7,6,5,4,1] => {{1,2,3,7},{4,6},{5}} => 3

{{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => [2,3,4,7,5,6,1] => {{1,2,3,4,7},{5},{6}} => 3

{{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => [2,3,4,6,5,7,1] => {{1,2,3,4,6,7},{5}} => 1

{{1,7},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,1] => [2,3,4,5,6,1,7] => {{1,2,3,4,5,6},{7}} => 2

{{1},{2,7},{3},{4},{5},{6}} => [1,7,3,4,5,6,2] => [7,3,4,5,6,2,1] => {{1,7},{2,3,4,5,6}} => 2

{{1},{2},{3,7},{4},{5},{6}} => [1,2,7,4,5,6,3] => [2,7,4,5,6,3,1] => {{1,2,7},{3,4,5,6}} => 2

{{1},{2},{3},{4,7},{5},{6}} => [1,2,3,7,5,6,4] => [2,3,7,5,6,4,1] => {{1,2,3,7},{4,5,6}} => 2

{{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => [2,3,4,7,6,5,1] => {{1,2,3,4,7},{5,6}} => 2

{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [2,3,4,5,7,6,1] => {{1,2,3,4,5,7},{6}} => 2

{{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => [2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}} => 1

{{1},{2},{3},{4},{5},{6},{7},{8}} => [1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => 1

{{1},{2},{3},{4},{5},{6},{7,8}} => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,8,7,1] => {{1,2,3,4,5,6,8},{7}} => 2

{{1},{2,4,6,8},{3},{5},{7}} => [1,4,3,6,5,8,7,2] => [8,3,2,5,4,7,6,1] => {{1,8},{2,3},{4,5},{6,7}} => 2

{{1},{2,4,8},{3},{5,7},{6}} => [1,4,3,8,7,6,5,2] => [8,3,2,7,6,5,4,1] => {{1,8},{2,3},{4,7},{5,6}} => 3

{{1},{2,6,8},{3,5},{4},{7}} => [1,6,5,4,3,8,7,2] => [8,5,4,3,2,7,6,1] => {{1,8},{2,5},{3,4},{6,7}} => 2

{{1},{2,8},{3,5,7},{4},{6}} => [1,8,5,4,7,6,3,2] => [8,7,4,3,6,5,2,1] => {{1,8},{2,7},{3,4},{5,6}} => 3

{{1},{2,8},{3,7},{4,6},{5}} => [1,8,7,6,5,4,3,2] => [8,7,6,5,4,3,2,1] => {{1,8},{2,7},{3,6},{4,5}} => 4

{{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,3,4,5,6,7,8] => [1,3,4,5,6,7,8,2] => {{1},{2,3,4,5,6,7,8}} => 1

{{1,2},{3},{4},{5},{6},{7,8}} => [2,1,3,4,5,6,8,7] => [1,3,4,5,6,8,7,2] => {{1},{2,3,4,5,6,8},{7}} => 2

{{1,2},{3,4},{5},{6},{7},{8}} => [2,1,4,3,5,6,7,8] => [1,4,3,5,6,7,8,2] => {{1},{2,4,5,6,7,8},{3}} => 1

{{1,3},{2},{4},{5},{6},{7},{8}} => [3,2,1,4,5,6,7,8] => [2,1,4,5,6,7,8,3] => {{1,2},{3,4,5,6,7,8}} => 1

{{1,3},{2},{4,6,8},{5},{7}} => [3,2,1,6,5,8,7,4] => [2,1,8,5,4,7,6,3] => {{1,2},{3,8},{4,5},{6,7}} => 2

{{1,3},{2},{4,8},{5,7},{6}} => [3,2,1,8,7,6,5,4] => [2,1,8,7,6,5,4,3] => {{1,2},{3,8},{4,7},{5,6}} => 3

{{1,7},{2},{3},{4},{5},{6},{8}} => [7,2,3,4,5,6,1,8] => [2,3,4,5,6,1,8,7] => {{1,2,3,4,5,6},{7,8}} => 1

{{1,8},{2},{3},{4},{5},{6},{7}} => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => 2

{{1,8},{2},{3},{4},{5},{6,7}} => [8,2,3,4,5,7,6,1] => [2,3,4,5,7,6,1,8] => {{1,2,3,4,5,7},{6},{8}} => 3

{{1,3,5},{2},{4},{6,8},{7}} => [3,2,5,4,1,8,7,6] => [2,1,4,3,8,7,6,5] => {{1,2},{3,4},{5,8},{6,7}} => 2

{{1,3,5,7},{2},{4},{6},{8}} => [3,2,5,4,7,6,1,8] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}} => 1

{{1,3,7},{2},{4,6},{5},{8}} => [3,2,7,6,5,4,1,8] => [2,1,6,5,4,3,8,7] => {{1,2},{3,6},{4,5},{7,8}} => 1

{{1,2,3},{4},{5},{6},{7},{8}} => [2,3,1,4,5,6,7,8] => [1,2,4,5,6,7,8,3] => {{1},{2},{3,4,5,6,7,8}} => 1

{{1,5},{2,4},{3},{6,8},{7}} => [5,4,3,2,1,8,7,6] => [4,3,2,1,8,7,6,5] => {{1,4},{2,3},{5,8},{6,7}} => 2

{{1,5,7},{2,4},{3},{6},{8}} => [5,4,3,2,7,6,1,8] => [4,3,2,1,6,5,8,7] => {{1,4},{2,3},{5,6},{7,8}} => 1

{{1,7},{2,4,6},{3},{5},{8}} => [7,4,3,6,5,2,1,8] => [6,3,2,5,4,1,8,7] => {{1,6},{2,3},{4,5},{7,8}} => 1

{{1,7},{2,6},{3,5},{4},{8}} => [7,6,5,4,3,2,1,8] => [6,5,4,3,2,1,8,7] => {{1,6},{2,5},{3,4},{7,8}} => 1

{{1,4,7},{2,6},{3},{5},{8}} => [4,6,3,7,5,2,1,8] => [6,3,1,5,2,4,8,7] => {{1,6},{2,3},{4,5},{7,8}} => 1

{{1,3},{2,4},{5},{6},{7},{8}} => [3,4,1,2,5,6,7,8] => [4,1,2,5,6,7,8,3] => {{1,4,5,6,7,8},{2},{3}} => 1

{{1,9},{2},{3},{4},{5},{6},{7},{8}} => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1,9] => {{1,2,3,4,5,6,7,8},{9}} => 2

{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1,10] => {{1,2,3,4,5,6,7,8,9},{10}} => 2

{{1},{2,4,7},{3},{5,8},{6}} => [1,4,3,7,8,6,2,5] => [7,3,2,8,6,4,5,1] => {{1,7},{2,3},{4,8},{5,6}} => 3

{{1},{2,5,8},{3,7},{4},{6}} => [1,5,7,4,8,6,3,2] => [8,7,4,2,6,3,5,1] => {{1,8},{2,7},{3,4},{5,6}} => 3

{{1},{2,6},{3,7},{4,8},{5}} => [1,6,7,8,5,2,3,4] => [6,7,8,5,2,3,4,1] => {{1,6},{2,7},{3,8},{4,5}} => 4

{{1},{2,5,7},{3,8},{4},{6}} => [1,5,8,4,7,6,2,3] => [7,8,4,2,6,5,3,1] => {{1,7},{2,8},{3,4},{5,6}} => 3

{{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,2] => {{1},{2,3,4,5,6,7,8,9}} => 1

{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,3,4,5,6,7,8,9,10] => [1,3,4,5,6,7,8,9,10,2] => {{1},{2,3,4,5,6,7,8,9,10}} => 1

{{1,6},{2,4,8},{3},{5},{7}} => [6,4,3,8,5,1,7,2] => [8,3,2,5,1,7,4,6] => {{1,8},{2,3},{4,5},{6,7}} => 2

{{1},{2,10},{3,9},{4,8},{5,7},{6}} => [1,10,9,8,7,6,5,4,3,2] => [10,9,8,7,6,5,4,3,2,1] => {{1,10},{2,9},{3,8},{4,7},{5,6}} => 5

{{1,7},{2,5},{3,6},{4},{8}} => [7,5,6,4,2,3,1,8] => [5,6,4,2,3,1,8,7] => {{1,5},{2,6},{3,4},{7,8}} => 1

{{1,3,5,7,9},{2},{4},{6},{8},{10}} => [3,2,5,4,7,6,9,8,1,10] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => 1

{{1,3,5,7,9,11},{2},{4},{6},{8},{10},{12}} => [3,2,5,4,7,6,9,8,11,10,1,12] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => 1

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Description

The number of terminal closers of a set partition.
A closer of a set partition is a number that is maximal in its block. In particular, a singleton is a closer. This statistic counts the number of terminal closers. In other words, this is the number of closers such that all larger elements are also closers.

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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 $i\leq\pi(i)$.

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to permutation

Description

Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.

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Inverse Kreweras complement

Description

Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.