- FindStat

Identifier

Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000536: Graphs ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 613 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{2} = 2$

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

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

$F_{5} = 2 + 11\ q + 11\ q^{2} + 2\ q^{3}$

$F_{6} = 2 + 18\ q + 36\ q^{2} + 18\ q^{3} + 2\ q^{4}$

$F_{7} = 2 + 24\ q + 88\ q^{2} + 90\ q^{3} + 26\ q^{4} + 2\ q^{5}$

Description

The pathwidth of a graph.

Map

reading word permutation

Description

Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.

Map

graph of inversions

Description

The graph of inversions of a permutation.
For a permutation of

$\{1,\dots,n\}$ , this is the graph with vertices

$\{1,\dots,n\}$ , where

$(i,j)$ is an edge if and only if it is an inversion of the permutation.

Map

restriction

Description

The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.