- FindStat

Identifier

Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000439: Dyck paths ⟶ ℤ (values match St000025The number of initial rises of a Dyck path.)

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 821 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9

[[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,9,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2

[[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,9,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2

[[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => [1,2,9,8,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2

[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => [1,9,8,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2

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

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

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

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

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

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

[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11

[[1,3,4,5,6,7,8,9],[2]] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3

[[1,4,5,6,7,8,9],[2],[3]] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4

[[1,7],[2,9],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,9,1,7] => [6,8,5,4,3,2,1,9,7] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 7

[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 9

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

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

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

[[1,8],[2,9],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,9,1,8] => [7,6,5,4,3,2,1,9,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 8

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

[[1,3],[2,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,2,4,1,3] => [2,1,9,8,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3

[[1,2,4],[3,5],[6],[7],[8],[9]] => [9,8,7,6,3,5,1,2,4] => [1,3,2,9,8,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

[[1,2,3,4,5,6,8],[7,9]] => [7,9,1,2,3,4,5,6,8] => [1,2,3,4,5,7,6,9,8] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2

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

[[1,2,9],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2,9] => [1,8,7,6,5,4,3,2,9] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2

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

[[1,3,5,6,7,8,9],[2],[4]] => [4,2,1,3,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3

[[1,8],[2],[3],[4],[5],[6],[7],[9]] => [9,7,6,5,4,3,2,1,8] => [7,9,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 8

[[1,3,4,5,6,7,8],[2,9]] => [2,9,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,9,8] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3

[[1,3,4,5,6,7],[2,8,9]] => [2,8,9,1,3,4,5,6,7] => [2,1,3,4,5,6,8,9,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3

[[1,3,4],[2],[5],[6],[7],[8],[9]] => [9,8,7,6,5,2,1,3,4] => [2,1,9,8,7,6,5,3,4] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3

[[1,3],[2],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,2,1,3] => [2,9,8,7,6,5,4,1,3] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3

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

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

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

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

[[1,2,5,6,7,8,9],[3],[4]] => [4,3,1,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2

[[1,2,4,5,6,7,8],[3,9]] => [3,9,1,2,4,5,6,7,8] => [1,3,2,4,5,6,7,9,8] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2

[[1,2,3,4,5,6],[7,9],[8]] => [8,7,9,1,2,3,4,5,6] => [1,2,3,4,5,8,7,9,6] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2

[[1,3,4,5,6,7,9],[2,8]] => [2,8,1,3,4,5,6,7,9] => [2,1,3,4,5,6,8,7,9] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3

[[1,2,4,5,6,7],[3,8,9]] => [3,8,9,1,2,4,5,6,7] => [1,3,2,4,5,6,8,9,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2

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$F_{1} = q^{2}$

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

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

$F_{4} = 5\ q^{2} + 3\ q^{3} + q^{4} + q^{5}$

$F_{5} = 13\ q^{2} + 8\ q^{3} + 3\ q^{4} + q^{5} + q^{6}$

$F_{6} = 38\ q^{2} + 24\ q^{3} + 9\ q^{4} + 3\ q^{5} + q^{6} + q^{7}$

$F_{7} = 116\ q^{2} + 74\ q^{3} + 28\ q^{4} + 9\ q^{5} + 3\ q^{6} + q^{7} + q^{8}$

Description

The position of the first down step of a Dyck path.

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

left-to-right-maxima to Dyck path

Description

The left-to-right maxima of a permutation as a Dyck path.
Let

$(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are

$c_1, c_1+c_2, \dots, c_1+\dots+c_k$ .
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.

Map

Foata bijection

Description

Sends a permutation to its image under the Foata bijection.
The Foata bijection

$\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word

$w_1 w_2 ... w_n$ , compute the image inductively by starting with

$\phi(w_1) = w_1$ .
At the

$i$ -th step, if

$\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$ , define

$\phi(w_1 w_2 ... w_i w_{i+1})$ by placing

$w_{i+1}$ on the end of the word

$v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.

If $w_{i+1} \geq v_i$ , place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$ .
If $w_{i+1} < v_i$ , place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$ .

In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute

$\phi([1,4,2,5,3])$ , the sequence of words is

$1$
$|1|4 \to 14$
$|14|2 \to 412$
$|4|1|2|5 \to 4125$
$|4|125|3 \to 45123.$

In total, this gives

$\phi([1,4,2,5,3]) = [4,5,1,2,3]$ .
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).