- FindStat

Identifier

Mp00080: Set partitions —to permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000527: Posets ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 702 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2

{{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2

{{1,2,3,4,6,7},{5}} => [2,3,4,6,5,7,1] => [5,7,1,2,3,4,6] => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7) => 2

{{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => [6,1,2,3,4,7,5] => ([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7) => 2

{{1,2,3,4,6},{5},{7}} => [2,3,4,6,5,1,7] => [5,6,1,2,3,4,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2

{{1,2,3,4,7},{5,6}} => [2,3,4,7,6,5,1] => [6,5,7,1,2,3,4] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 3

{{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2

{{1,2,3,5,6},{4,7}} => [2,3,5,7,6,1,4] => [6,1,2,3,5,7,4] => ([(0,6),(1,4),(3,6),(4,5),(5,2),(5,3)],7) => 3

{{1,2,3,5,7},{4,6}} => [2,3,5,6,7,4,1] => [6,4,7,1,2,3,5] => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => 3

{{1,2,3,5},{4,6,7}} => [2,3,5,6,1,7,4] => [5,1,2,3,7,4,6] => ([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7) => 2

{{1,2,3,5,7},{4},{6}} => [2,3,5,4,7,6,1] => [4,6,7,1,2,3,5] => ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7) => 2

{{1,2,3,5},{4,7},{6}} => [2,3,5,7,1,6,4] => [5,1,2,3,6,7,4] => ([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7) => 2

{{1,2,3,5},{4},{6},{7}} => [2,3,5,4,1,6,7] => [4,5,1,2,3,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2

{{1,2,3,6,7},{4,5}} => [2,3,6,5,4,7,1] => [5,4,7,1,2,3,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => 3

{{1,2,3,6},{4,5},{7}} => [2,3,6,5,4,1,7] => [5,4,6,1,2,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 3

{{1,2,3,7},{4,5},{6}} => [2,3,7,5,4,6,1] => [5,4,6,7,1,2,3] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 3

{{1,2,3,6},{4,7},{5}} => [2,3,6,7,5,1,4] => [5,6,1,2,3,7,4] => ([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7) => 2

{{1,2,3,6},{4},{5},{7}} => [2,3,6,4,5,1,7] => [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 2

{{1,2,3},{4},{5,6},{7}} => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => ([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 2

{{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2

{{1,2,4,5,7},{3,6}} => [2,4,6,5,7,3,1] => [6,3,7,1,2,4,5] => ([(0,5),(1,5),(1,6),(2,3),(3,6),(6,4)],7) => 3

{{1,2,4,5},{3,6,7}} => [2,4,6,5,1,7,3] => [5,1,2,4,7,3,6] => ([(0,5),(0,6),(1,4),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 3

{{1,2,4,7},{3,5,6}} => [2,4,5,7,6,3,1] => [6,3,5,7,1,2,4] => ([(0,6),(1,3),(2,4),(2,5),(3,5),(4,6)],7) => 3

{{1,2,4},{3,5,6,7}} => [2,4,5,1,6,7,3] => [4,1,2,7,3,5,6] => ([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7) => 2

{{1,2,4,7},{3,6},{5}} => [2,4,6,7,5,3,1] => [5,6,3,7,1,2,4] => ([(0,5),(0,6),(1,4),(2,3),(3,5),(4,6)],7) => 3

{{1,2,4},{3,6,7},{5}} => [2,4,6,1,5,7,3] => [4,1,2,5,7,3,6] => ([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7) => 2

{{1,2,4},{3,6},{5,7}} => [2,4,6,1,7,3,5] => [4,1,2,6,3,7,5] => ([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7) => 2

{{1,2,4,7},{3},{5},{6}} => [2,4,3,7,5,6,1] => [3,5,6,7,1,2,4] => ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7) => 2

{{1,2,4},{3,7},{5},{6}} => [2,4,7,1,5,6,3] => [4,1,2,5,6,7,3] => ([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7) => 2

{{1,2,4},{3},{5},{6},{7}} => [2,4,3,1,5,6,7] => [3,4,1,2,5,6,7] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => 2

{{1,2,5,6,7},{3,4}} => [2,5,4,3,6,7,1] => [4,3,7,1,2,5,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(6,4)],7) => 3

{{1,2,5,6},{3,4},{7}} => [2,5,4,3,6,1,7] => [4,3,6,1,2,5,7] => ([(0,4),(0,6),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) => 3

{{1,2,5,7},{3,4},{6}} => [2,5,4,3,7,6,1] => [4,3,6,7,1,2,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(5,4)],7) => 3

{{1,2,5},{3,4},{6,7}} => [2,5,4,3,1,7,6] => [4,3,5,1,2,7,6] => ([(0,4),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7) => 3

{{1,2,5},{3,4},{6},{7}} => [2,5,4,3,1,6,7] => [4,3,5,1,2,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 3

{{1,2,6},{3,4,5},{7}} => [2,6,4,5,3,1,7] => [5,3,4,6,1,2,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3

{{1,2,7},{3,4,5,6}} => [2,7,4,5,6,3,1] => [6,3,4,5,7,1,2] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => 3

{{1,2},{3,4,5,6,7}} => [2,1,4,5,6,7,3] => [2,1,7,3,4,5,6] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) => 2

{{1,2},{3,4,5,6},{7}} => [2,1,4,5,6,3,7] => [2,1,6,3,4,5,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => 2

{{1,2},{3,4,5,7},{6}} => [2,1,4,5,7,6,3] => [2,1,6,7,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7) => 2

{{1,2},{3,4,5},{6,7}} => [2,1,4,5,3,7,6] => [2,1,5,3,4,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => 2

{{1,2},{3,4,5},{6},{7}} => [2,1,4,5,3,6,7] => [2,1,5,3,4,6,7] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => 2

{{1,2,6,7},{3,4},{5}} => [2,6,4,3,5,7,1] => [4,3,5,7,1,2,6] => ([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7) => 3

{{1,2,6},{3,4},{5,7}} => [2,6,4,3,7,1,5] => [4,3,6,1,2,7,5] => ([(0,4),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(4,5)],7) => 3

{{1,2,6},{3,4},{5},{7}} => [2,6,4,3,5,1,7] => [4,3,5,6,1,2,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 3

{{1,2},{3,4,6,7},{5}} => [2,1,4,6,5,7,3] => [2,1,5,7,3,4,6] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7) => 2

{{1,2},{3,4,6},{5,7}} => [2,1,4,6,7,3,5] => [2,1,6,3,4,7,5] => ([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7) => 2

{{1,2},{3,4,6},{5},{7}} => [2,1,4,6,5,3,7] => [2,1,5,6,3,4,7] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => 2

{{1,2,7},{3,4},{5,6}} => [2,7,4,3,6,5,1] => [4,3,6,5,7,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,6),(5,6)],7) => 3

{{1,2},{3,4},{5,6,7}} => [2,1,4,3,6,7,5] => [2,1,4,3,7,5,6] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 2

{{1,2},{3,4},{5,6},{7}} => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => ([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 2

{{1,2,7},{3,4},{5},{6}} => [2,7,4,3,5,6,1] => [4,3,5,6,7,1,2] => ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 3

{{1,2},{3,4,7},{5},{6}} => [2,1,4,7,5,6,3] => [2,1,5,6,7,3,4] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7) => 2

{{1,2},{3,4},{5,7},{6}} => [2,1,4,3,7,6,5] => [2,1,4,3,6,7,5] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 2

{{1,2},{3,4},{5},{6,7}} => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => 2

{{1,2},{3,4},{5},{6},{7}} => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => 2

{{1,2,5},{3,7},{4,6}} => [2,5,7,6,1,4,3] => [5,1,2,6,4,7,3] => ([(0,6),(1,4),(3,5),(4,2),(4,3),(4,6),(6,5)],7) => 3

{{1,2,5},{3},{4},{6},{7}} => [2,5,3,4,1,6,7] => [3,4,5,1,2,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => 2

{{1,2,6},{3,5},{4},{7}} => [2,6,5,4,3,1,7] => [4,5,3,6,1,2,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 3

{{1,2},{3,5,6,7},{4}} => [2,1,5,4,6,7,3] => [2,1,4,7,3,5,6] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7) => 2

{{1,2},{3,5,6},{4,7}} => [2,1,5,7,6,3,4] => [2,1,6,3,5,7,4] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(5,2),(5,3),(6,4)],7) => 3

{{1,2},{3,5,6},{4},{7}} => [2,1,5,4,6,3,7] => [2,1,4,6,3,5,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => 2

{{1,2},{3,5},{4,6,7}} => [2,1,5,6,3,7,4] => [2,1,5,3,7,4,6] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) => 2

{{1,2},{3,5},{4,6},{7}} => [2,1,5,6,3,4,7] => [2,1,5,3,6,4,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => 2

{{1,2},{3,5,7},{4},{6}} => [2,1,5,4,7,6,3] => [2,1,4,6,7,3,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7) => 2

{{1,2},{3,5},{4,7},{6}} => [2,1,5,7,3,6,4] => [2,1,5,3,6,7,4] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7) => 2

{{1,2},{3,5},{4},{6,7}} => [2,1,5,4,3,7,6] => [2,1,4,5,3,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => 2

{{1,2},{3,5},{4},{6},{7}} => [2,1,5,4,3,6,7] => [2,1,4,5,3,6,7] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => 2

{{1,2,6},{3,7},{4,5}} => [2,6,7,5,4,1,3] => [5,4,6,1,2,7,3] => ([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7) => 3

{{1,2,7},{3,6},{4,5}} => [2,7,6,5,4,3,1] => [5,4,6,3,7,1,2] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 4

{{1,2},{3,6},{4,5,7}} => [2,1,6,5,7,3,4] => [2,1,6,3,7,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7) => 2

{{1,2},{3},{4,5,6,7}} => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6] => ([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => 2

{{1,2},{3},{4,5,6},{7}} => [2,1,3,5,6,4,7] => [2,1,3,6,4,5,7] => ([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => 2

{{1,2},{3},{4,5,7},{6}} => [2,1,3,5,7,6,4] => [2,1,3,6,7,4,5] => ([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) => 2

{{1,2},{3},{4,5},{6,7}} => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => 2

{{1,2},{3},{4,5},{6},{7}} => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => 2

{{1,2,6,7},{3},{4},{5}} => [2,6,3,4,5,7,1] => [3,4,5,7,1,2,6] => ([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7) => 2

{{1,2,6},{3},{4},{5},{7}} => [2,6,3,4,5,1,7] => [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 2

{{1,2,7},{3,6},{4},{5}} => [2,7,6,4,5,3,1] => [4,5,6,3,7,1,2] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => 3

{{1,2},{3,6,7},{4},{5}} => [2,1,6,4,5,7,3] => [2,1,4,5,7,3,6] => ([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7) => 2

{{1,2},{3,6},{4,7},{5}} => [2,1,6,7,5,3,4] => [2,1,5,6,3,7,4] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7) => 2

{{1,2},{3,6},{4},{5,7}} => [2,1,6,4,7,3,5] => [2,1,4,6,3,7,5] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) => 2

{{1,2},{3,6},{4},{5},{7}} => [2,1,6,4,5,3,7] => [2,1,4,5,6,3,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => 2

{{1,2},{3},{4,6,7},{5}} => [2,1,3,6,5,7,4] => [2,1,3,5,7,4,6] => ([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => 2

{{1,2},{3},{4,6},{5,7}} => [2,1,3,6,7,4,5] => [2,1,3,6,4,7,5] => ([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => 2

{{1,2},{3},{4,6},{5},{7}} => [2,1,3,6,5,4,7] => [2,1,3,5,6,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => 2

{{1,2},{3,7},{4},{5,6}} => [2,1,7,4,6,5,3] => [2,1,4,6,5,7,3] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7) => 3

{{1,2},{3},{4,7},{5,6}} => [2,1,3,7,6,5,4] => [2,1,3,6,5,7,4] => ([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7) => 3

{{1,2},{3},{4},{5,6,7}} => [2,1,3,4,6,7,5] => [2,1,3,4,7,5,6] => ([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => 2

{{1,2},{3},{4},{5,6},{7}} => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => ([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => 2

{{1,2},{3,7},{4},{5},{6}} => [2,1,7,4,5,6,3] => [2,1,4,5,6,7,3] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) => 2

{{1,2},{3},{4,7},{5},{6}} => [2,1,3,7,5,6,4] => [2,1,3,5,6,7,4] => ([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => 2

{{1,2},{3},{4},{5,7},{6}} => [2,1,3,4,7,6,5] => [2,1,3,4,6,7,5] => ([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => 2

{{1,2},{3},{4},{5},{6,7}} => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => ([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => 2

{{1,2},{3},{4},{5},{6},{7}} => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 2

{{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => [2,7,1,3,4,5,6] => ([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7) => 2

{{1,3,4,5,6},{2,7}} => [3,7,4,5,6,1,2] => [6,1,3,4,5,7,2] => ([(0,6),(1,2),(1,5),(3,6),(4,3),(5,4)],7) => 3

{{1,3,4,5,7},{2,6}} => [3,6,4,5,7,2,1] => [6,2,7,1,3,4,5] => ([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7) => 3

{{1,3,4,5},{2,6,7}} => [3,6,4,5,1,7,2] => [5,1,3,4,7,2,6] => ([(0,5),(0,6),(1,2),(1,4),(2,6),(3,5),(3,6),(4,3)],7) => 3

{{1,3,4,5},{2,6},{7}} => [3,6,4,5,1,2,7] => [5,1,3,4,6,2,7] => ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => 3

{{1,3,4,5,7},{2},{6}} => [3,2,4,5,7,6,1] => [2,6,7,1,3,4,5] => ([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7) => 2

{{1,3,4,6,7},{2,5}} => [3,5,4,6,2,7,1] => [5,2,7,1,3,4,6] => ([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7) => 3

{{1,3,4,6},{2,5},{7}} => [3,5,4,6,2,1,7] => [5,2,6,1,3,4,7] => ([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 3

{{1,3,4,7},{2,5},{6}} => [3,5,4,7,2,6,1] => [5,2,6,7,1,3,4] => ([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7) => 3

{{1,3,4,6},{2,7},{5}} => [3,7,4,6,5,1,2] => [5,6,1,3,4,7,2] => ([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7) => 3

{{1,3,4,6},{2},{5,7}} => [3,2,4,6,7,1,5] => [2,6,1,3,4,7,5] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7) => 2

{{1,3,4,7},{2},{5,6}} => [3,2,4,7,6,5,1] => [2,6,5,7,1,3,4] => ([(0,6),(1,3),(1,4),(1,6),(3,5),(4,5),(6,2)],7) => 3

{{1,3,4,7},{2},{5},{6}} => [3,2,4,7,5,6,1] => [2,5,6,7,1,3,4] => ([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7) => 2

{{1,3,4},{2},{5},{6,7}} => [3,2,4,1,5,7,6] => [2,4,1,3,5,7,6] => ([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => 2

{{1,3,5,6},{2,4,7}} => [3,4,5,7,6,1,2] => [6,1,3,5,7,2,4] => ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => 3

{{1,3,5},{2,4},{6,7}} => [3,4,5,2,1,7,6] => [4,2,5,1,3,7,6] => ([(0,6),(1,5),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 3

{{1,3,5},{2,4},{6},{7}} => [3,4,5,2,1,6,7] => [4,2,5,1,3,6,7] => ([(0,5),(1,4),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 3

{{1,3,7},{2,4,5,6}} => [3,4,7,5,6,2,1] => [6,2,4,5,7,1,3] => ([(0,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => 3

{{1,3},{2,4,5,6,7}} => [3,4,1,5,6,7,2] => [3,1,7,2,4,5,6] => ([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7) => 2

{{1,3,6,7},{2,4},{5}} => [3,4,6,2,5,7,1] => [4,2,5,7,1,3,6] => ([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 3

{{1,3,6},{2,4},{5},{7}} => [3,4,6,2,5,1,7] => [4,2,5,6,1,3,7] => ([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 3

{{1,3,7},{2,4,6},{5}} => [3,4,7,6,5,2,1] => [5,6,2,4,7,1,3] => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6)],7) => 3

{{1,3},{2,4,6},{5,7}} => [3,4,1,6,7,2,5] => [3,1,6,2,4,7,5] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7) => 2

{{1,3,7},{2,4},{5,6}} => [3,4,7,2,6,5,1] => [4,2,6,5,7,1,3] => ([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 3

{{1,3,7},{2,4},{5},{6}} => [3,4,7,2,5,6,1] => [4,2,5,6,7,1,3] => ([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7) => 3

{{1,3},{2,4},{5},{6,7}} => [3,4,1,2,5,7,6] => [3,1,4,2,5,7,6] => ([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => 2

{{1,3,5,6,7},{2},{4}} => [3,2,5,4,6,7,1] => [2,4,7,1,3,5,6] => ([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7) => 2

{{1,3,5,7},{2},{4,6}} => [3,2,5,6,7,4,1] => [2,6,4,7,1,3,5] => ([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(3,5),(6,4)],7) => 3

{{1,3,5},{2},{4,6,7}} => [3,2,5,6,1,7,4] => [2,5,1,3,7,4,6] => ([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7) => 2

{{1,3,5},{2},{4,7},{6}} => [3,2,5,7,1,6,4] => [2,5,1,3,6,7,4] => ([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) => 2

{{1,3,5},{2},{4},{6,7}} => [3,2,5,4,1,7,6] => [2,4,5,1,3,7,6] => ([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7) => 2

{{1,3,5},{2},{4},{6},{7}} => [3,2,5,4,1,6,7] => [2,4,5,1,3,6,7] => ([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => 2

{{1,3,6},{2,5},{4,7}} => [3,5,6,7,2,1,4] => [5,2,6,1,3,7,4] => ([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 3

{{1,3},{2,5,6,7},{4}} => [3,5,1,4,6,7,2] => [3,1,4,7,2,5,6] => ([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) => 2

{{1,3},{2,5},{4,6,7}} => [3,5,1,6,2,7,4] => [3,1,5,2,7,4,6] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) => 2

{{1,3,7},{2,5},{4},{6}} => [3,5,7,4,2,6,1] => [4,5,2,6,7,1,3] => ([(0,5),(1,5),(1,6),(2,3),(3,6),(6,4)],7) => 3

{{1,3},{2,5},{4,7},{6}} => [3,5,1,7,2,6,4] => [3,1,5,2,6,7,4] => ([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7) => 2

{{1,3,6,7},{2},{4,5}} => [3,2,6,5,4,7,1] => [2,5,4,7,1,3,6] => ([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 3

{{1,3,6},{2,7},{4,5}} => [3,7,6,5,4,1,2] => [5,4,6,1,3,7,2] => ([(0,5),(1,5),(2,3),(2,4),(4,6),(5,6)],7) => 4

{{1,3,6},{2},{4,5},{7}} => [3,2,6,5,4,1,7] => [2,5,4,6,1,3,7] => ([(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(5,4),(6,4)],7) => 3

{{1,3,7},{2,6},{4,5}} => [3,6,7,5,4,2,1] => [5,4,6,2,7,1,3] => ([(0,4),(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 4

{{1,3},{2,7},{4,5,6}} => [3,7,1,5,6,4,2] => [3,1,6,4,5,7,2] => ([(0,5),(0,6),(1,2),(1,5),(1,6),(3,4),(5,3),(6,4)],7) => 3

{{1,3,7},{2},{4,5},{6}} => [3,2,7,5,4,6,1] => [2,5,4,6,7,1,3] => ([(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(6,2)],7) => 3

{{1,3,6,7},{2},{4},{5}} => [3,2,6,4,5,7,1] => [2,4,5,7,1,3,6] => ([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7) => 2

{{1,3,6},{2,7},{4},{5}} => [3,7,6,4,5,1,2] => [4,5,6,1,3,7,2] => ([(0,5),(1,2),(1,4),(3,6),(4,6),(5,3)],7) => 3

{{1,3,6},{2},{4,7},{5}} => [3,2,6,7,5,1,4] => [2,5,6,1,3,7,4] => ([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7) => 2

{{1,3,7},{2,6},{4},{5}} => [3,6,7,4,5,2,1] => [4,5,6,2,7,1,3] => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => 3

{{1,3},{2,6,7},{4},{5}} => [3,6,1,4,5,7,2] => [3,1,4,5,7,2,6] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7) => 2

{{1,3},{2,6},{4},{5,7}} => [3,6,1,4,7,2,5] => [3,1,4,6,2,7,5] => ([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7) => 2

{{1,3},{2,7},{4,6},{5}} => [3,7,1,6,5,4,2] => [3,1,5,6,4,7,2] => ([(0,5),(0,6),(1,2),(1,5),(1,6),(3,4),(5,3),(6,4)],7) => 3

{{1,3},{2,7},{4},{5,6}} => [3,7,1,4,6,5,2] => [3,1,4,6,5,7,2] => ([(0,6),(1,2),(1,6),(3,5),(4,5),(6,3),(6,4)],7) => 3

{{1,3},{2},{4},{5,6},{7}} => [3,2,1,4,6,5,7] => [2,3,1,4,6,5,7] => ([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 2

{{1,3,7},{2},{4},{5},{6}} => [3,2,7,4,5,6,1] => [2,4,5,6,7,1,3] => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7) => 2

{{1,3},{2,7},{4},{5},{6}} => [3,7,1,4,5,6,2] => [3,1,4,5,6,7,2] => ([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7) => 2

{{1,3},{2},{4},{5},{6},{7}} => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => 2

{{1,4,5,6,7},{2,3}} => [4,3,2,5,6,7,1] => [3,2,7,1,4,5,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 3

{{1,4,5,6},{2,3,7}} => [4,3,7,5,6,1,2] => [6,1,4,5,7,2,3] => ([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7) => 3

{{1,4,5,6},{2,3},{7}} => [4,3,2,5,6,1,7] => [3,2,6,1,4,5,7] => ([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,5),(6,3)],7) => 3

{{1,4,5,7},{2,3},{6}} => [4,3,2,5,7,6,1] => [3,2,6,7,1,4,5] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 3

{{1,4,5},{2,3},{6,7}} => [4,3,2,5,1,7,6] => [3,2,5,1,4,7,6] => ([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 3

{{1,4,5},{2,3},{6},{7}} => [4,3,2,5,1,6,7] => [3,2,5,1,4,6,7] => ([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7) => 3

{{1,4},{2,3,5},{6,7}} => [4,3,5,1,2,7,6] => [4,1,5,2,3,7,6] => ([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7) => 2

{{1,4},{2,3,5},{6},{7}} => [4,3,5,1,2,6,7] => [4,1,5,2,3,6,7] => ([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => 2

{{1,4,6,7},{2,3},{5}} => [4,3,2,6,5,7,1] => [3,2,5,7,1,4,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,4)],7) => 3

{{1,4,6},{2,3,7},{5}} => [4,3,7,6,5,1,2] => [5,6,1,4,7,2,3] => ([(0,4),(1,3),(1,5),(3,6),(4,6),(5,2)],7) => 3

{{1,4,6},{2,3},{5,7}} => [4,3,2,6,7,1,5] => [3,2,6,1,4,7,5] => ([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 3

{{1,4,6},{2,3},{5},{7}} => [4,3,2,6,5,1,7] => [3,2,5,6,1,4,7] => ([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3),(6,5)],7) => 3

{{1,4},{2,3,6,7},{5}} => [4,3,6,1,5,7,2] => [4,1,5,7,2,3,6] => ([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7) => 2

{{1,4,7},{2,3},{5,6}} => [4,3,2,7,6,5,1] => [3,2,6,5,7,1,4] => ([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => 3

{{1,4},{2,3},{5,6,7}} => [4,3,2,1,6,7,5] => [3,2,4,1,7,5,6] => ([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7) => 3

{{1,4},{2,3},{5,6},{7}} => [4,3,2,1,6,5,7] => [3,2,4,1,6,5,7] => ([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => 3

{{1,4,7},{2,3},{5},{6}} => [4,3,2,7,5,6,1] => [3,2,5,6,7,1,4] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,3)],7) => 3

{{1,4},{2,3,7},{5},{6}} => [4,3,7,1,5,6,2] => [4,1,5,6,7,2,3] => ([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7) => 2

{{1,4},{2,3},{5,7},{6}} => [4,3,2,1,7,6,5] => [3,2,4,1,6,7,5] => ([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7) => 3

{{1,4},{2,3},{5},{6,7}} => [4,3,2,1,5,7,6] => [3,2,4,1,5,7,6] => ([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7) => 3

{{1,4},{2,3},{5},{6},{7}} => [4,3,2,1,5,6,7] => [3,2,4,1,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 3

{{1,5,6,7},{2,3,4}} => [5,3,4,2,6,7,1] => [4,2,3,7,1,5,6] => ([(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) => 3

{{1,5,6},{2,3,4,7}} => [5,3,4,7,6,1,2] => [6,1,5,7,2,3,4] => ([(0,6),(1,3),(1,5),(3,6),(4,2),(5,4)],7) => 3

{{1,5},{2,3,4,7},{6}} => [5,3,4,7,1,6,2] => [5,1,6,7,2,3,4] => ([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7) => 2

{{1,5},{2,3,4},{6},{7}} => [5,3,4,2,1,6,7] => [4,2,3,5,1,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3

{{1,6,7},{2,3,4,5}} => [6,3,4,5,2,7,1] => [5,2,3,4,7,1,6] => ([(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7) => 3

{{1,6},{2,3,4,5,7}} => [6,3,4,5,7,1,2] => [6,1,7,2,3,4,5] => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7) => 2

{{1,6},{2,3,4,5},{7}} => [6,3,4,5,2,1,7] => [5,2,3,4,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3

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

{{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 2

{{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 2

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

{{1},{2,3,4,5,7},{6}} => [1,3,4,5,7,6,2] => [1,6,7,2,3,4,5] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 2

{{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 2

{{1,6,7},{2,3,4},{5}} => [6,3,4,2,5,7,1] => [4,2,3,5,7,1,6] => ([(0,6),(1,5),(2,3),(3,6),(6,4),(6,5)],7) => 3

{{1,6},{2,3,4,7},{5}} => [6,3,4,7,5,1,2] => [5,6,1,7,2,3,4] => ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7) => 2

{{1,6},{2,3,4},{5,7}} => [6,3,4,2,7,1,5] => [4,2,3,6,1,7,5] => ([(0,5),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(5,4)],7) => 3

{{1,6},{2,3,4},{5},{7}} => [6,3,4,2,5,1,7] => [4,2,3,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3

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

{{1},{2,3,4,6},{5},{7}} => [1,3,4,6,5,2,7] => [1,5,6,2,3,4,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 2

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

{{1},{2,3,4,7},{5},{6}} => [1,3,4,7,5,6,2] => [1,5,6,7,2,3,4] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => 2

{{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => ([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => 2

{{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => 2

{{1,5,6,7},{2,3},{4}} => [5,3,2,4,6,7,1] => [3,2,4,7,1,5,6] => ([(0,6),(1,5),(2,5),(5,3),(5,6),(6,4)],7) => 3

{{1,5,6},{2,3},{4},{7}} => [5,3,2,4,6,1,7] => [3,2,4,6,1,5,7] => ([(0,5),(1,5),(2,4),(3,6),(4,6),(5,3),(5,4)],7) => 3

{{1,5},{2,3,6},{4,7}} => [5,3,6,7,1,2,4] => [5,1,6,2,3,7,4] => ([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7) => 2

{{1,5,7},{2,3},{4,6}} => [5,3,2,6,7,4,1] => [3,2,6,4,7,1,5] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(5,3),(6,3),(6,4)],7) => 3

{{1,5},{2,3,7},{4,6}} => [5,3,7,6,1,4,2] => [5,1,6,4,7,2,3] => ([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(6,5)],7) => 3

{{1,5},{2,3},{4,6,7}} => [5,3,2,6,1,7,4] => [3,2,5,1,7,4,6] => ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 3

{{1,5},{2,3},{4,6},{7}} => [5,3,2,6,1,4,7] => [3,2,5,1,6,4,7] => ([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7) => 3

{{1,5,7},{2,3},{4},{6}} => [5,3,2,4,7,6,1] => [3,2,4,6,7,1,5] => ([(0,6),(1,6),(2,5),(3,4),(6,3),(6,5)],7) => 3

{{1,5},{2,3},{4,7},{6}} => [5,3,2,7,1,6,4] => [3,2,5,1,6,7,4] => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3)],7) => 3

{{1,5},{2,3},{4},{6,7}} => [5,3,2,4,1,7,6] => [3,2,4,5,1,7,6] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7) => 3

{{1,5},{2,3},{4},{6},{7}} => [5,3,2,4,1,6,7] => [3,2,4,5,1,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 3

{{1,6,7},{2,3,5},{4}} => [6,3,5,4,2,7,1] => [4,5,2,3,7,1,6] => ([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7) => 3

{{1,6},{2,3,5},{4},{7}} => [6,3,5,4,2,1,7] => [4,5,2,3,6,1,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 3

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

{{1},{2,3,5,6},{4},{7}} => [1,3,5,4,6,2,7] => [1,4,6,2,3,5,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 2

{{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => [1,5,2,3,6,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 2

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

{{1},{2,3,5},{4},{6,7}} => [1,3,5,4,2,7,6] => [1,4,5,2,3,7,6] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => 2

{{1},{2,3,5},{4},{6},{7}} => [1,3,5,4,2,6,7] => [1,4,5,2,3,6,7] => ([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => 2

{{1,6,7},{2,3},{4,5}} => [6,3,2,5,4,7,1] => [3,2,5,4,7,1,6] => ([(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 3

{{1,6},{2,3,7},{4,5}} => [6,3,7,5,4,1,2] => [5,4,6,1,7,2,3] => ([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7) => 3

{{1,6},{2,3},{4,5,7}} => [6,3,2,5,7,1,4] => [3,2,6,1,7,4,5] => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7) => 3

{{1,6},{2,3},{4,5},{7}} => [6,3,2,5,4,1,7] => [3,2,5,4,6,1,7] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 3

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

{{1},{2,3,6},{4,5},{7}} => [1,3,6,5,4,2,7] => [1,5,4,6,2,3,7] => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7) => 3

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

{{1},{2,3,7},{4,5,6}} => [1,3,7,5,6,4,2] => [1,6,4,5,7,2,3] => ([(0,3),(0,4),(0,5),(2,6),(3,6),(4,1),(5,2)],7) => 3

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

{{1},{2,3,7},{4,5},{6}} => [1,3,7,5,4,6,2] => [1,5,4,6,7,2,3] => ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7) => 3

{{1},{2,3},{4,5,7},{6}} => [1,3,2,5,7,6,4] => [1,3,2,6,7,4,5] => ([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => 2

{{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => ([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 2

{{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => 2

{{1,6,7},{2,3},{4},{5}} => [6,3,2,4,5,7,1] => [3,2,4,5,7,1,6] => ([(0,6),(1,5),(2,5),(3,4),(3,6),(5,3)],7) => 3

{{1,6},{2,3,7},{4},{5}} => [6,3,7,4,5,1,2] => [4,5,6,1,7,2,3] => ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7) => 2

{{1,6},{2,3},{4,7},{5}} => [6,3,2,7,5,1,4] => [3,2,5,6,1,7,4] => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3)],7) => 3

{{1,6},{2,3},{4},{5,7}} => [6,3,2,4,7,1,5] => [3,2,4,6,1,7,5] => ([(0,5),(1,5),(2,4),(2,6),(3,6),(5,3),(5,4)],7) => 3

{{1,6},{2,3},{4},{5},{7}} => [6,3,2,4,5,1,7] => [3,2,4,5,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 3

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

{{1},{2,3,6},{4},{5},{7}} => [1,3,6,4,5,2,7] => [1,4,5,6,2,3,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 2

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

{{1},{2,3,7},{4,6},{5}} => [1,3,7,6,5,4,2] => [1,5,6,4,7,2,3] => ([(0,3),(0,4),(0,5),(2,6),(3,6),(4,1),(5,2)],7) => 3

{{1},{2,3},{4,6,7},{5}} => [1,3,2,6,5,7,4] => [1,3,2,5,7,4,6] => ([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => 2

{{1},{2,3},{4,6},{5,7}} => [1,3,2,6,7,4,5] => [1,3,2,6,4,7,5] => ([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => 2

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

{{1},{2,3,7},{4},{5,6}} => [1,3,7,4,6,5,2] => [1,4,6,5,7,2,3] => ([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7) => 3

{{1},{2,3},{4,7},{5,6}} => [1,3,2,7,6,5,4] => [1,3,2,6,5,7,4] => ([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 3

{{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 2

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

{{1},{2,3,7},{4},{5},{6}} => [1,3,7,4,5,6,2] => [1,4,5,6,7,2,3] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => 2

{{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2

{{1,4,5,6,7},{2},{3}} => [4,2,3,5,6,7,1] => [2,3,7,1,4,5,6] => ([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7) => 2

{{1,4,5},{2,7},{3,6}} => [4,7,6,5,1,3,2] => [5,1,4,6,3,7,2] => ([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7) => 4

{{1,4,6},{2,5},{3,7}} => [4,5,7,6,2,1,3] => [5,2,6,1,4,7,3] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 3

{{1,4},{2,5},{3,7},{6}} => [4,5,7,1,2,6,3] => [4,1,5,2,6,7,3] => ([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7) => 2

{{1,4,7},{2,6},{3,5}} => [4,6,5,7,3,2,1] => [5,3,6,2,7,1,4] => ([(0,6),(1,5),(1,6),(2,4),(3,4),(3,6),(4,5)],7) => 4

{{1,4},{2,6,7},{3,5}} => [4,6,5,1,3,7,2] => [4,1,5,3,7,2,6] => ([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3

{{1,4},{2},{3,5,6,7}} => [4,2,5,1,6,7,3] => [2,4,1,7,3,5,6] => ([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7) => 2

{{1,4},{2,7},{3,5},{6}} => [4,7,5,1,3,6,2] => [4,1,5,3,6,7,2] => ([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7) => 3

{{1,4,6},{2},{3},{5,7}} => [4,2,3,6,7,1,5] => [2,3,6,1,4,7,5] => ([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7) => 2

{{1,4},{2,7},{3,6},{5}} => [4,7,6,1,5,3,2] => [4,1,5,6,3,7,2] => ([(0,6),(1,2),(1,4),(1,6),(3,5),(4,5),(6,3)],7) => 3

{{1,4},{2},{3,6,7},{5}} => [4,2,6,1,5,7,3] => [2,4,1,5,7,3,6] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7) => 2

{{1,4},{2},{3,6},{5,7}} => [4,2,6,1,7,3,5] => [2,4,1,6,3,7,5] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) => 2

{{1,4},{2},{3,7},{5},{6}} => [4,2,7,1,5,6,3] => [2,4,1,5,6,7,3] => ([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7) => 2

{{1,4},{2},{3},{5},{6},{7}} => [4,2,3,1,5,6,7] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => 2

{{1,5,6,7},{2,4},{3}} => [5,4,3,2,6,7,1] => [3,4,2,7,1,5,6] => ([(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) => 3

{{1,5},{2,4,7},{3,6}} => [5,4,6,7,1,3,2] => [5,1,6,3,7,2,4] => ([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(3,5),(6,4)],7) => 3

{{1,5},{2,4},{3},{6},{7}} => [5,4,3,2,1,6,7] => [3,4,2,5,1,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 3

{{1},{2,4,5,6},{3},{7}} => [1,4,3,5,6,2,7] => [1,3,6,2,4,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 2

{{1},{2,4,5,7},{3,6}} => [1,4,6,5,7,3,2] => [1,6,3,7,2,4,5] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7) => 3

{{1},{2,4,5},{3,6},{7}} => [1,4,6,5,2,3,7] => [1,5,2,4,6,3,7] => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => 3

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

{{1},{2,4,5},{3},{6},{7}} => [1,4,3,5,2,6,7] => [1,3,5,2,4,6,7] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2

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

{{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => [1,5,3,7,2,4,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => 3

{{1},{2,4,6},{3,5},{7}} => [1,4,5,6,3,2,7] => [1,5,3,6,2,4,7] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 3

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

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

{{1},{2,4,7},{3,5},{6}} => [1,4,5,7,3,6,2] => [1,5,3,6,7,2,4] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7) => 3

{{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => [1,4,2,5,3,6,7] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2

{{1,6,7},{2,4},{3},{5}} => [6,4,3,2,5,7,1] => [3,4,2,5,7,1,6] => ([(0,6),(1,5),(2,3),(3,6),(6,4),(6,5)],7) => 3

{{1,6},{2,4},{3,7},{5}} => [6,4,7,2,5,1,3] => [4,2,5,6,1,7,3] => ([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7) => 3

{{1,6},{2,4},{3},{5,7}} => [6,4,3,2,7,1,5] => [3,4,2,6,1,7,5] => ([(0,5),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(5,4)],7) => 3

{{1,6},{2,4},{3},{5},{7}} => [6,4,3,2,5,1,7] => [3,4,2,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 3

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

{{1},{2,4,6,7},{3},{5}} => [1,4,3,6,5,7,2] => [1,3,5,7,2,4,6] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 2

{{1},{2,4,6},{3,7},{5}} => [1,4,7,6,5,2,3] => [1,5,6,2,4,7,3] => ([(0,4),(0,5),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 3

{{1},{2,4,6},{3},{5},{7}} => [1,4,3,6,5,2,7] => [1,3,5,6,2,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 2

{{1},{2,4},{3,6},{5},{7}} => [1,4,6,2,5,3,7] => [1,4,2,5,6,3,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 2

{{1},{2,4,7},{3},{5,6}} => [1,4,3,7,6,5,2] => [1,3,6,5,7,2,4] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(4,6)],7) => 3

{{1},{2,4},{3,7},{5,6}} => [1,4,7,2,6,5,3] => [1,4,2,6,5,7,3] => ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7) => 3

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

{{1},{2,4,7},{3},{5},{6}} => [1,4,3,7,5,6,2] => [1,3,5,6,7,2,4] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 2

{{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => [1,3,4,2,5,7,6] => ([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => 2

{{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => 2

{{1,5,6},{2,7},{3,4}} => [5,7,4,3,6,1,2] => [4,3,6,1,5,7,2] => ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(4,5),(6,5)],7) => 3

{{1,5,7},{2,6},{3,4}} => [5,6,4,3,7,2,1] => [4,3,6,2,7,1,5] => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 4

{{1,5},{2,6,7},{3,4}} => [5,6,4,3,1,7,2] => [4,3,5,1,7,2,6] => ([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 3

{{1,5},{2,6},{3,4},{7}} => [5,6,4,3,1,2,7] => [4,3,5,1,6,2,7] => ([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => 3

{{1,5},{2,7},{3,4,6}} => [5,7,4,6,1,3,2] => [5,1,6,3,4,7,2] => ([(0,6),(1,2),(1,4),(1,6),(3,5),(4,3),(6,5)],7) => 3

{{1,5},{2,7},{3,4},{6}} => [5,7,4,3,1,6,2] => [4,3,5,1,6,7,2] => ([(0,5),(1,5),(2,4),(2,6),(5,6),(6,3)],7) => 3

{{1,6,7},{2,5},{3,4}} => [6,5,4,3,2,7,1] => [4,3,5,2,7,1,6] => ([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 4

{{1,6},{2,5,7},{3,4}} => [6,5,4,3,7,1,2] => [4,3,6,1,7,2,5] => ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7) => 3

{{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => [4,3,5,2,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 4

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

{{1},{2,5,6,7},{3,4}} => [1,5,4,3,6,7,2] => [1,4,3,7,2,5,6] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 3

{{1},{2,5,6},{3,4},{7}} => [1,5,4,3,6,2,7] => [1,4,3,6,2,5,7] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 3

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

{{1},{2,5},{3,4,6},{7}} => [1,5,4,6,2,3,7] => [1,5,2,6,3,4,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 2

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

{{1},{2,5,7},{3,4},{6}} => [1,5,4,3,7,6,2] => [1,4,3,6,7,2,5] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1)],7) => 3

{{1},{2,5},{3,4},{6,7}} => [1,5,4,3,2,7,6] => [1,4,3,5,2,7,6] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 3

{{1},{2,5},{3,4},{6},{7}} => [1,5,4,3,2,6,7] => [1,4,3,5,2,6,7] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 3

{{1,6,7},{2},{3,4,5}} => [6,2,4,5,3,7,1] => [2,5,3,4,7,1,6] => ([(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) => 3

{{1},{2,6},{3,4,5,7}} => [1,6,4,5,7,2,3] => [1,6,2,7,3,4,5] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => 2

{{1},{2,6},{3,4,5},{7}} => [1,6,4,5,3,2,7] => [1,5,3,4,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7) => 3

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

{{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => ([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7) => 2

{{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 2

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

{{1},{2,7},{3,4,5},{6}} => [1,7,4,5,3,6,2] => [1,5,3,4,6,7,2] => ([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7) => 3

{{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => [1,2,6,7,3,4,5] => ([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7) => 2

{{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 2

{{1,6},{2,7},{3,4},{5}} => [6,7,4,3,5,1,2] => [4,3,5,6,1,7,2] => ([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7) => 3

{{1,6},{2},{3,4},{5},{7}} => [6,2,4,3,5,1,7] => [2,4,3,5,6,1,7] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7) => 3

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

{{1},{2,6,7},{3,4},{5}} => [1,6,4,3,5,7,2] => [1,4,3,5,7,2,6] => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,5),(6,1),(6,5)],7) => 3

{{1},{2,6},{3,4},{5,7}} => [1,6,4,3,7,2,5] => [1,4,3,6,2,7,5] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 3

{{1},{2,6},{3,4},{5},{7}} => [1,6,4,3,5,2,7] => [1,4,3,5,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7) => 3

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

{{1},{2,7},{3,4,6},{5}} => [1,7,4,6,5,3,2] => [1,5,6,3,4,7,2] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(4,2),(5,1)],7) => 3

{{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => [1,2,5,6,3,4,7] => ([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => 2

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

{{1},{2,7},{3,4},{5,6}} => [1,7,4,3,6,5,2] => [1,4,3,6,5,7,2] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 3

{{1},{2},{3,4,7},{5},{6}} => [1,2,4,7,5,6,3] => [1,2,5,6,7,3,4] => ([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7) => 2

{{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2

{{1,5,6,7},{2},{3},{4}} => [5,2,3,4,6,7,1] => [2,3,4,7,1,5,6] => ([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7) => 2

{{1,5},{2},{3,7},{4,6}} => [5,2,7,6,1,4,3] => [2,5,1,6,4,7,3] => ([(0,2),(0,4),(0,6),(1,4),(1,5),(1,6),(2,5),(5,3),(6,3)],7) => 3

{{1,5},{2},{3},{4,6,7}} => [5,2,3,6,1,7,4] => [2,3,5,1,7,4,6] => ([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7) => 2

{{1,5},{2},{3},{4,7},{6}} => [5,2,3,7,1,6,4] => [2,3,5,1,6,7,4] => ([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7) => 2

{{1,5},{2},{3},{4},{6},{7}} => [5,2,3,4,1,6,7] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 2

{{1,6,7},{2,5},{3},{4}} => [6,5,3,4,2,7,1] => [3,4,5,2,7,1,6] => ([(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7) => 3

{{1,6},{2,5},{3},{4},{7}} => [6,5,3,4,2,1,7] => [3,4,5,2,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 3

{{1},{2,5,6},{3,7},{4}} => [1,5,7,4,6,2,3] => [1,4,6,2,5,7,3] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => 3

{{1},{2,5,6},{3},{4},{7}} => [1,5,3,4,6,2,7] => [1,3,4,6,2,5,7] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 2

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

{{1},{2,5},{3,6},{4,7}} => [1,5,6,7,2,3,4] => [1,5,2,6,3,7,4] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => 2

{{1},{2,5},{3,6},{4},{7}} => [1,5,6,4,2,3,7] => [1,4,5,2,6,3,7] => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 2

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

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

{{1},{2,5},{3},{4},{6},{7}} => [1,5,3,4,2,6,7] => [1,3,4,5,2,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 2

{{1,6,7},{2},{3,5},{4}} => [6,2,5,4,3,7,1] => [2,4,5,3,7,1,6] => ([(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) => 3

{{1},{2,6},{3,5},{4,7}} => [1,6,5,7,3,2,4] => [1,5,3,6,2,7,4] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => 3

{{1},{2,6},{3,5},{4},{7}} => [1,6,5,4,3,2,7] => [1,4,5,3,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7) => 3

{{1},{2},{3,5,6},{4},{7}} => [1,2,5,4,6,3,7] => [1,2,4,6,3,5,7] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2

{{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => [1,2,5,3,6,4,7] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2

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

{{1},{2,7},{3,5},{4},{6}} => [1,7,5,4,3,6,2] => [1,4,5,3,6,7,2] => ([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7) => 3

{{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 2

{{1},{2,6,7},{3},{4,5}} => [1,6,3,5,4,7,2] => [1,3,5,4,7,2,6] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,6),(4,1),(4,2)],7) => 3

{{1},{2,6},{3,7},{4,5}} => [1,6,7,5,4,2,3] => [1,5,4,6,2,7,3] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,6),(5,6)],7) => 3

{{1},{2,6},{3},{4,5},{7}} => [1,6,3,5,4,2,7] => [1,3,5,4,6,2,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 3

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

{{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => [1,5,4,6,3,7,2] => ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7) => 4

{{1},{2},{3,6,7},{4,5}} => [1,2,6,5,4,7,3] => [1,2,5,4,7,3,6] => ([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 3

{{1},{2},{3,6},{4,5},{7}} => [1,2,6,5,4,3,7] => [1,2,5,4,6,3,7] => ([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7) => 3

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

{{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => ([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) => 2

{{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => 2

{{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => [1,2,3,6,7,4,5] => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7) => 2

{{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 2

{{1,6,7},{2},{3},{4},{5}} => [6,2,3,4,5,7,1] => [2,3,4,5,7,1,6] => ([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7) => 2

{{1,6},{2,7},{3},{4},{5}} => [6,7,3,4,5,1,2] => [3,4,5,6,1,7,2] => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7) => 2

{{1,6},{2},{3},{4},{5,7}} => [6,2,3,4,7,1,5] => [2,3,4,6,1,7,5] => ([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7) => 2

{{1,6},{2},{3},{4},{5},{7}} => [6,2,3,4,5,1,7] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => 2

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

{{1},{2,6},{3},{4},{5},{7}} => [1,6,3,4,5,2,7] => [1,3,4,5,6,2,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 2

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

{{1},{2},{3,6},{4},{5},{7}} => [1,2,6,4,5,3,7] => [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 2

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

{{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => 2

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

{{1},{2},{3},{4,7},{5,6}} => [1,2,3,7,6,5,4] => [1,2,3,6,5,7,4] => ([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 3

{{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => ([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => 2

{{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => 2

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

{{1},{2,7},{3},{4},{5},{6}} => [1,7,3,4,5,6,2] => [1,3,4,5,6,7,2] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => 2

{{1},{2},{3,7},{4},{5},{6}} => [1,2,7,4,5,6,3] => [1,2,4,5,6,7,3] => ([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7) => 2

{{1},{2},{3},{4,7},{5},{6}} => [1,2,3,7,5,6,4] => [1,2,3,5,6,7,4] => ([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) => 2

{{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => [1,2,3,4,6,7,5] => ([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => 2

{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => ([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7) => 2

{{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

{{1,2},{3,4},{5,6},{7,8}} => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => ([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8) => 2

{{1},{2},{3},{4},{5},{6},{7},{8}} => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

{{1},{2,3},{4},{5},{6,7},{8}} => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8) => 2

{{1},{2,8},{3},{4},{5},{6},{7}} => [1,8,3,4,5,6,7,2] => [1,3,4,5,6,7,8,2] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => 2

{{1},{2,4,8},{3},{5},{6},{7}} => [1,4,3,8,5,6,7,2] => [1,3,5,6,7,8,2,4] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => 2

{{1},{2,4,6,7},{3},{5},{8}} => [1,4,3,6,5,7,2,8] => [1,3,5,7,2,4,6,8] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

{{1},{2,4,6,8},{3},{5},{7}} => [1,4,3,6,5,8,7,2] => [1,3,5,7,8,2,4,6] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 2

{{1},{2,3,8},{4},{5},{6},{7}} => [1,3,8,4,5,6,7,2] => [1,4,5,6,7,8,2,3] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => 2

{{1},{2,3,4,8},{5},{6},{7}} => [1,3,4,8,5,6,7,2] => [1,5,6,7,8,2,3,4] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => 2

{{1},{2,3,4,5,8},{6},{7}} => [1,3,4,5,8,6,7,2] => [1,6,7,8,2,3,4,5] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => 2

{{1},{2,3,4,5,6,8},{7}} => [1,3,4,5,6,8,7,2] => [1,7,8,2,3,4,5,6] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => 2

{{1},{2,3,4,5,6,7,8}} => [1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => 2

{{1,2},{3,4},{5,6,8},{7}} => [2,1,4,3,6,8,7,5] => [2,1,4,3,7,8,5,6] => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(6,5),(7,4),(7,5)],8) => 2

{{1,2},{3,4,6},{5},{7,8}} => [2,1,4,6,5,3,8,7] => [2,1,5,6,3,4,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(6,3),(7,2)],8) => 2

{{1,2},{3,4,5,8},{6},{7}} => [2,1,4,5,8,6,7,3] => [2,1,6,7,8,3,4,5] => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8) => 2

{{1,2,4},{3},{5,6},{7,8}} => [2,4,3,1,6,5,8,7] => [3,4,1,2,6,5,8,7] => ([(0,3),(1,2),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8) => 2

{{1,2,4},{3},{5,6,8},{7}} => [2,4,3,1,6,8,7,5] => [3,4,1,2,7,8,5,6] => ([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8) => 2

{{1,2,3,6},{4},{5},{7,8}} => [2,3,6,4,5,1,8,7] => [4,5,6,1,2,3,8,7] => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8) => 2

{{1,2,3,4,8},{5},{6},{7}} => [2,3,4,8,5,6,7,1] => [5,6,7,8,1,2,3,4] => ([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8) => 2

{{1,2,7},{3,6,8},{4},{5}} => [2,7,6,4,5,8,1,3] => [4,5,7,1,2,8,3,6] => ([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8) => 2

{{1,2},{3,7},{4,6,8},{5}} => [2,1,7,6,5,8,3,4] => [2,1,5,7,3,8,4,6] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8) => 2

{{1,7},{2,3,5,8},{4},{6}} => [7,3,5,4,8,6,1,2] => [4,6,7,1,8,2,3,5] => ([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8) => 2

{{1},{2},{3},{4},{5},{6},{7},{8},{9}} => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

{{1},{2,9},{3},{4},{5},{6},{7},{8}} => [1,9,3,4,5,6,7,8,2] => [1,3,4,5,6,7,8,9,2] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => 2

{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

{{1},{2,10},{3},{4},{5},{6},{7},{8},{9}} => [1,10,3,4,5,6,7,8,9,2] => [1,3,4,5,6,7,8,9,10,2] => ([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 2

{{1},{2,3,4,5,6,7,8,9}} => [1,3,4,5,6,7,8,9,2] => [1,9,2,3,4,5,6,7,8] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => 2

{{1},{2,3,4,5,6,7,9},{8}} => [1,3,4,5,6,7,9,8,2] => [1,8,9,2,3,4,5,6,7] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => 2

{{1},{2,3,4,5,6,7,8,9,10}} => [1,3,4,5,6,7,8,9,10,2] => [1,10,2,3,4,5,6,7,8,9] => ([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 2

{{1},{2,3,4,5,6,7,8,10},{9}} => [1,3,4,5,6,7,8,10,9,2] => [1,9,10,2,3,4,5,6,7,8] => ([(0,8),(0,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,1)],10) => 2

{{1},{2,6},{3,7},{4,5,8}} => [1,6,7,5,8,2,3,4] => [1,6,2,7,3,8,4,5] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => 2

{{1,5},{2,4,6},{3},{7,8}} => [5,4,3,6,1,2,8,7] => [3,5,1,6,2,4,8,7] => ([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8) => 2

{{1,6},{2,4,5,8},{3},{7}} => [6,4,3,5,8,1,7,2] => [3,6,1,7,8,2,4,5] => ([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8) => 2

{{1,5},{2,7},{3},{4,6,8}} => [5,7,3,6,1,8,2,4] => [3,5,1,7,2,8,4,6] => ([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8) => 2

{{1},{2},{3,5},{4,6},{7},{8}} => [1,2,5,6,3,4,7,8] => [1,2,5,3,6,4,7,8] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => 2

{{1},{2,5},{3,6},{4,7},{8}} => [1,5,6,7,2,3,4,8] => [1,5,2,6,3,7,4,8] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 2

{{1},{2,3,9},{4},{5},{6},{7},{8}} => [1,3,9,4,5,6,7,8,2] => [1,4,5,6,7,8,9,2,3] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => 2

{{1,3,5,8},{2,7},{4,6}} => [3,7,5,6,8,4,2,1] => [6,4,7,2,8,1,3,5] => ([(0,5),(1,4),(2,4),(2,7),(3,5),(3,6),(4,6),(5,7)],8) => 4

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$F_{1} = q$

$F_{2} = q + q^{2}$

$F_{3} = q + 4\ q^{2}$

$F_{4} = q + 13\ q^{2} + q^{3}$

$F_{5} = q + 41\ q^{2} + 10\ q^{3}$

$F_{6} = q + 131\ q^{2} + 70\ q^{3} + q^{4}$

Description

The width of the poset.
This is the size of the poset's longest antichain, also called Dilworth number.

Map

to permutation

Description

Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.

Map

inverse first fundamental transformation

Description

Let

$\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps

$\sigma$ to the permutation

$[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.

Map

permutation poset

Description

Sends a permutation to its permutation poset.
For a permutation

$\pi$ of length

$n$ , this poset has vertices

$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$
and the cover relation is given by

$(w, x) \leq (y, z)$ if

$w \leq y$ and

$x \leq z$ .
For example, the permutation

$[3,1,5,4,2]$ is mapped to the poset with cover relations

$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$