Identifier
-
Mp00080:
Set partitions
—to permutation⟶
Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001161: Dyck paths ⟶ ℤ
Values
{{1}} => [1] => [1] => [1,0] => 0
{{1,2}} => [2,1] => [2,1] => [1,1,0,0] => 0
{{1},{2}} => [1,2] => [1,2] => [1,0,1,0] => 1
{{1,2,3}} => [2,3,1] => [3,1,2] => [1,1,1,0,0,0] => 0
{{1,2},{3}} => [2,1,3] => [2,1,3] => [1,1,0,0,1,0] => 2
{{1,3},{2}} => [3,2,1] => [2,3,1] => [1,1,0,1,0,0] => 2
{{1},{2,3}} => [1,3,2] => [1,3,2] => [1,0,1,1,0,0] => 1
{{1},{2},{3}} => [1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 3
{{1,2,3,4}} => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => 0
{{1,2,3},{4}} => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 3
{{1,2,4},{3}} => [2,4,3,1] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 3
{{1,2},{3,4}} => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 2
{{1,2},{3},{4}} => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 5
{{1,3,4},{2}} => [3,2,4,1] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => 2
{{1,3},{2,4}} => [3,4,1,2] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 3
{{1,3},{2},{4}} => [3,2,1,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => 5
{{1,4},{2,3}} => [4,3,2,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 3
{{1},{2,3,4}} => [1,3,4,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => 1
{{1},{2,3},{4}} => [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => 4
{{1,4},{2},{3}} => [4,2,3,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 5
{{1},{2,4},{3}} => [1,4,3,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 4
{{1},{2},{3,4}} => [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 3
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 6
{{1,2,3,4,5}} => [2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => 0
{{1,2,3,4},{5}} => [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 4
{{1,2,3,5},{4}} => [2,3,5,4,1] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,3},{4,5}} => [2,3,1,5,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 3
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 7
{{1,2,4,5},{3}} => [2,4,3,5,1] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => 3
{{1,2,4},{3,5}} => [2,4,5,1,3] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => 4
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => 7
{{1,2,5},{3,4}} => [2,5,4,3,1] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 4
{{1,2},{3,4,5}} => [2,1,4,5,3] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 2
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 6
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => 7
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 6
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 5
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 9
{{1,3,4,5},{2}} => [3,2,4,5,1] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => 2
{{1,3,4},{2,5}} => [3,5,4,1,2] => [4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0] => 4
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => 6
{{1,3,5},{2,4}} => [3,4,5,2,1] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => 4
{{1,3},{2,4,5}} => [3,4,1,5,2] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 3
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 7
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => 6
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => 7
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 5
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 9
{{1,4,5},{2,3}} => [4,3,2,5,1] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => 3
{{1,4},{2,3,5}} => [4,3,5,1,2] => [4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => 4
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => 7
{{1,5},{2,3,4}} => [5,3,4,2,1] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 4
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => 1
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => 5
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 7
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => 5
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => 8
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => 5
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => 7
{{1,4},{2},{3,5}} => [4,2,5,1,3] => [2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => 6
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 9
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 7
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => 4
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 5
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 8
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 6
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => 5
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 3
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 7
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 9
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 8
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 7
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 6
{{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] => 10
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 9
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => [4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 4
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => [5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => [4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 9
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => [5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 5
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => [3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 8
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 9
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => [3,1,2,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => 8
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => [3,1,2,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 7
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 12
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => [3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
{{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => [5,1,2,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => [3,5,1,2,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 8
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => [5,3,6,1,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 5
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => [4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => [4,1,2,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 9
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => [3,5,6,1,2,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => 8
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => [4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => 9
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => [3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => 7
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 12
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => [4,3,6,1,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 4
>>> Load all 1594 entries. <<<{{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => [5,1,2,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 5
{{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => [4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 9
{{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => [5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 5
{{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => [2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
{{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => [2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 7
{{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => [4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 9
{{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => [2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => 7
{{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
{{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => 11
{{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => [3,4,6,1,2,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => 7
{{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => [4,5,1,2,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => 9
{{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => [3,5,1,2,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => 8
{{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => [3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 12
{{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => [4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 9
{{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => [2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0] => 6
{{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => [2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0] => 7
{{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => 11
{{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => [3,5,4,6,1,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => 8
{{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => [2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0] => 7
{{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => [2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => 5
{{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => 10
{{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => 12
{{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => [2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => 11
{{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => 10
{{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => 9
{{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 14
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
{{1,3,4,5},{2,6}} => [3,6,4,5,1,2] => [5,1,3,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
{{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => [2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
{{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => [5,2,6,1,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 5
{{1,3,4},{2,5,6}} => [3,5,4,1,6,2] => [4,1,3,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
{{1,3,4},{2,5},{6}} => [3,5,4,1,2,6] => [4,1,3,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 9
{{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => [2,5,6,1,3,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => 7
{{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => [4,1,3,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => 9
{{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => [2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => 6
{{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => [2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 11
{{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => [4,2,6,1,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 4
{{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => [5,1,3,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 5
{{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => [4,2,5,1,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 9
{{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => [5,2,4,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 5
{{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => [3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
{{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => [3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 8
{{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => [4,2,5,6,1,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => 9
{{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => [3,1,5,6,2,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => 8
{{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => [3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => 7
{{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 12
{{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => [2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 6
{{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => [4,5,1,3,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => 9
{{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => [2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => 7
{{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => [2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => 11
{{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => [4,5,2,6,1,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => 9
{{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => [3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => 7
{{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => [3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => 8
{{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => [3,1,4,5,2,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 12
{{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => [2,5,4,6,1,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => 7
{{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => [3,1,5,4,6,2] => [1,1,1,0,0,1,1,0,0,1,0,0] => 8
{{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => [2,3,1,6,4,5] => [1,1,0,1,0,0,1,1,1,0,0,0] => 5
{{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => 10
{{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => [2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => 11
{{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => [3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0] => 12
{{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => 10
{{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => 9
{{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => 14
{{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => [3,2,6,1,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
{{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => [5,1,4,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 5
{{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => [3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 8
{{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 5
{{1,4},{2,3,5,6}} => [4,3,5,1,6,2] => [4,1,6,2,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 4
{{1,4},{2,3,5},{6}} => [4,3,5,1,2,6] => [4,1,5,2,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 9
{{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => [3,2,5,6,1,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => 8
{{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => [4,1,5,6,2,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => 9
{{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => [3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => 7
{{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => [3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 12
{{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => [4,2,3,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
{{1,5},{2,3,4,6}} => [5,3,4,6,1,2] => [5,1,6,2,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 5
{{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => [4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 9
{{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 5
{{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
{{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
{{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 9
{{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => 6
{{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => [1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
{{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 10
{{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => [3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => 7
{{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => [4,5,1,6,2,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => 9
{{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => [3,2,5,1,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => 8
{{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => [3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 12
{{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 9
{{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => 5
{{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => [1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
{{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => [1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => 10
{{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => [3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => 8
{{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => [1,5,4,6,2,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => 6
{{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
{{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => 9
{{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 12
{{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => [1,4,5,6,2,3] => [1,0,1,1,1,0,1,0,1,0,0,0] => 10
{{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => 9
{{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
{{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => 13
{{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => [2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => 5
{{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => [3,5,1,4,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => 8
{{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => [2,5,1,4,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => 7
{{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => [2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => 10
{{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => [3,5,2,6,1,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => 8
{{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => [3,4,1,6,2,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => 7
{{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
{{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => [3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 12
{{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => [2,5,3,6,1,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => 7
{{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => [4,1,5,3,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
{{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => [2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => 6
{{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => [2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => 11
{{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => [2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => 10
{{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => [3,4,1,5,6,2] => [1,1,1,0,1,0,0,1,0,1,0,0] => 12
{{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => [2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0] => 11
{{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => [2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => 9
{{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => 14
{{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => [3,4,2,6,1,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => 7
{{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => [3,5,1,6,2,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => 8
{{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => [4,2,5,1,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
{{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => [3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 12
{{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => [3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 8
{{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => [1,3,6,2,4,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => 4
{{1},{2,4,5},{3,6}} => [1,4,6,5,2,3] => [1,5,2,4,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
{{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => 9
{{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => [4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
{{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => [1,5,3,6,2,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => 6
{{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => [1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => 5
{{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => [1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => 10
{{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 12
{{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => [1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0] => 9
{{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => [1,4,2,5,6,3] => [1,0,1,1,1,0,0,1,0,1,0,0] => 10
{{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => 8
{{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => 13
{{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => [2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => 6
{{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => [4,3,5,1,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
{{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => [2,5,1,6,3,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => 7
{{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => [2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => 11
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
{{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => [1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => 5
{{1},{2,5},{3,4,6}} => [1,5,4,6,2,3] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => 6
{{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => [1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => 10
{{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 7
{{1},{2,6},{3,4,5}} => [1,6,4,5,3,2] => [1,5,3,4,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
{{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => [1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
{{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 8
{{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 11
{{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => [1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => 10
{{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => [1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => 8
{{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
{{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => 12
{{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => [2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => 9
{{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => [3,4,5,1,6,2] => [1,1,1,0,1,0,1,0,0,1,0,0] => 12
{{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => [2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0] => 11
{{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => [2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0] => 10
{{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => 14
{{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 12
{{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => [1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0] => 8
{{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => [1,4,5,2,6,3] => [1,0,1,1,1,0,1,0,0,1,0,0] => 10
{{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => [1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0] => 9
{{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => [1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => 13
{{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 11
{{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => [1,4,5,3,6,2] => [1,0,1,1,1,0,1,0,0,1,0,0] => 10
{{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => [1,2,4,6,3,5] => [1,0,1,0,1,1,0,1,1,0,0,0] => 7
{{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => [1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0] => 8
{{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => 12
{{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 10
{{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => [1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => 9
{{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => [1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => 8
{{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => [1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
{{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => 11
{{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 14
{{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => 13
{{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => [1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => 12
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => 11
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => 10
{{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] => 15
{{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
{{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
{{1,2,3,4,5,7},{6}} => [2,3,4,5,7,6,1] => [6,7,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
{{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => [5,1,2,3,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
{{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 11
{{1,2,3,4,6,7},{5}} => [2,3,4,6,5,7,1] => [5,7,1,2,3,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 5
{{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => [6,1,2,3,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6
{{1,2,3,4,6},{5},{7}} => [2,3,4,6,5,1,7] => [5,6,1,2,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11
{{1,2,3,4,7},{5,6}} => [2,3,4,7,6,5,1] => [6,5,7,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 6
{{1,2,3,4},{5,6,7}} => [2,3,4,1,6,7,5] => [4,1,2,3,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
{{1,2,3,4},{5,6},{7}} => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 10
{{1,2,3,4,7},{5},{6}} => [2,3,4,7,5,6,1] => [5,6,7,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 11
{{1,2,3,4},{5,7},{6}} => [2,3,4,1,7,6,5] => [4,1,2,3,6,7,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 10
{{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 9
{{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 15
{{1,2,3,5,6,7},{4}} => [2,3,5,4,6,7,1] => [4,7,1,2,3,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 4
{{1,2,3,5,6},{4,7}} => [2,3,5,7,6,1,4] => [6,1,2,3,5,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6
{{1,2,3,5,6},{4},{7}} => [2,3,5,4,6,1,7] => [4,6,1,2,3,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 10
{{1,2,3,5,7},{4,6}} => [2,3,5,6,7,4,1] => [6,4,7,1,2,3,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 6
{{1,2,3,5},{4,6,7}} => [2,3,5,6,1,7,4] => [5,1,2,3,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 5
{{1,2,3,5},{4,6},{7}} => [2,3,5,6,1,4,7] => [5,1,2,3,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
{{1,2,3,5,7},{4},{6}} => [2,3,5,4,7,6,1] => [4,6,7,1,2,3,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 10
{{1,2,3,5},{4,7},{6}} => [2,3,5,7,1,6,4] => [5,1,2,3,6,7,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 11
{{1,2,3,5},{4},{6,7}} => [2,3,5,4,1,7,6] => [4,5,1,2,3,7,6] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 9
{{1,2,3,5},{4},{6},{7}} => [2,3,5,4,1,6,7] => [4,5,1,2,3,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 15
{{1,2,3,6,7},{4,5}} => [2,3,6,5,4,7,1] => [5,4,7,1,2,3,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 5
{{1,2,3,6},{4,5,7}} => [2,3,6,5,7,1,4] => [6,1,2,3,7,4,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
{{1,2,3,6},{4,5},{7}} => [2,3,6,5,4,1,7] => [5,4,6,1,2,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11
{{1,2,3,7},{4,5,6}} => [2,3,7,5,6,4,1] => [6,4,5,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
{{1,2,3},{4,5,6,7}} => [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
{{1,2,3},{4,5,6},{7}} => [2,3,1,5,6,4,7] => [3,1,2,6,4,5,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 9
{{1,2,3,7},{4,5},{6}} => [2,3,7,5,4,6,1] => [5,4,6,7,1,2,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 11
{{1,2,3},{4,5,7},{6}} => [2,3,1,5,7,6,4] => [3,1,2,6,7,4,5] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 9
{{1,2,3},{4,5},{6,7}} => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
{{1,2,3},{4,5},{6},{7}} => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 14
{{1,2,3,6,7},{4},{5}} => [2,3,6,4,5,7,1] => [4,5,7,1,2,3,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 9
{{1,2,3,6},{4,7},{5}} => [2,3,6,7,5,1,4] => [5,6,1,2,3,7,4] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 11
{{1,2,3,6},{4},{5,7}} => [2,3,6,4,7,1,5] => [4,6,1,2,3,7,5] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 10
{{1,2,3,6},{4},{5},{7}} => [2,3,6,4,5,1,7] => [4,5,6,1,2,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 15
{{1,2,3,7},{4,6},{5}} => [2,3,7,6,5,4,1] => [5,6,4,7,1,2,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 11
{{1,2,3},{4,6,7},{5}} => [2,3,1,6,5,7,4] => [3,1,2,5,7,4,6] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 8
{{1,2,3},{4,6},{5,7}} => [2,3,1,6,7,4,5] => [3,1,2,6,4,7,5] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 9
{{1,2,3},{4,6},{5},{7}} => [2,3,1,6,5,4,7] => [3,1,2,5,6,4,7] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 14
{{1,2,3,7},{4},{5,6}} => [2,3,7,4,6,5,1] => [4,6,5,7,1,2,3] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 10
{{1,2,3},{4,7},{5,6}} => [2,3,1,7,6,5,4] => [3,1,2,6,5,7,4] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 9
{{1,2,3},{4},{5,6,7}} => [2,3,1,4,6,7,5] => [3,1,2,4,7,5,6] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
{{1,2,3},{4},{5,6},{7}} => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 13
{{1,2,3,7},{4},{5},{6}} => [2,3,7,4,5,6,1] => [4,5,6,7,1,2,3] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 15
{{1,2,3},{4,7},{5},{6}} => [2,3,1,7,5,6,4] => [3,1,2,5,6,7,4] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 14
{{1,2,3},{4},{5,7},{6}} => [2,3,1,4,7,6,5] => [3,1,2,4,6,7,5] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 13
{{1,2,3},{4},{5},{6,7}} => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 12
{{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 18
{{1,2,4,5,6,7},{3}} => [2,4,3,5,6,7,1] => [3,7,1,2,4,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
{{1,2,4,5,6},{3,7}} => [2,4,7,5,6,1,3] => [6,1,2,4,5,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6
{{1,2,4,5,6},{3},{7}} => [2,4,3,5,6,1,7] => [3,6,1,2,4,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 9
{{1,2,4,5,7},{3,6}} => [2,4,6,5,7,3,1] => [6,3,7,1,2,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 6
{{1,2,4,5},{3,6,7}} => [2,4,6,5,1,7,3] => [5,1,2,4,7,3,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 5
{{1,2,4,5},{3,6},{7}} => [2,4,6,5,1,3,7] => [5,1,2,4,6,3,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
{{1,2,4,5,7},{3},{6}} => [2,4,3,5,7,6,1] => [3,6,7,1,2,4,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 9
{{1,2,4,5},{3,7},{6}} => [2,4,7,5,1,6,3] => [5,1,2,4,6,7,3] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 11
{{1,2,4,5},{3},{6,7}} => [2,4,3,5,1,7,6] => [3,5,1,2,4,7,6] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
{{1,2,4,5},{3},{6},{7}} => [2,4,3,5,1,6,7] => [3,5,1,2,4,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 14
{{1,2,4,6,7},{3,5}} => [2,4,5,6,3,7,1] => [5,3,7,1,2,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 5
{{1,2,4,6},{3,5,7}} => [2,4,5,6,7,1,3] => [6,1,2,4,7,3,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
{{1,2,4,6},{3,5},{7}} => [2,4,5,6,3,1,7] => [5,3,6,1,2,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11
{{1,2,4,7},{3,5,6}} => [2,4,5,7,6,3,1] => [6,3,5,7,1,2,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
{{1,2,4},{3,5,6,7}} => [2,4,5,1,6,7,3] => [4,1,2,7,3,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 4
{{1,2,4},{3,5,6},{7}} => [2,4,5,1,6,3,7] => [4,1,2,6,3,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 10
{{1,2,4,7},{3,5},{6}} => [2,4,5,7,3,6,1] => [5,3,6,7,1,2,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 11
{{1,2,4},{3,5,7},{6}} => [2,4,5,1,7,6,3] => [4,1,2,6,7,3,5] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 10
{{1,2,4},{3,5},{6,7}} => [2,4,5,1,3,7,6] => [4,1,2,5,3,7,6] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 9
{{1,2,4},{3,5},{6},{7}} => [2,4,5,1,3,6,7] => [4,1,2,5,3,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 15
{{1,2,4,6,7},{3},{5}} => [2,4,3,6,5,7,1] => [3,5,7,1,2,4,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
{{1,2,4,6},{3,7},{5}} => [2,4,7,6,5,1,3] => [5,6,1,2,4,7,3] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 11
{{1,2,4,6},{3},{5,7}} => [2,4,3,6,7,1,5] => [3,6,1,2,4,7,5] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 9
{{1,2,4,6},{3},{5},{7}} => [2,4,3,6,5,1,7] => [3,5,6,1,2,4,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 14
{{1,2,4,7},{3,6},{5}} => [2,4,6,7,5,3,1] => [5,6,3,7,1,2,4] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 11
{{1,2,4},{3,6,7},{5}} => [2,4,6,1,5,7,3] => [4,1,2,5,7,3,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 9
{{1,2,4},{3,6},{5,7}} => [2,4,6,1,7,3,5] => [4,1,2,6,3,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10
{{1,2,4},{3,6},{5},{7}} => [2,4,6,1,5,3,7] => [4,1,2,5,6,3,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 15
{{1,2,4,7},{3},{5,6}} => [2,4,3,7,6,5,1] => [3,6,5,7,1,2,4] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 9
{{1,2,4},{3,7},{5,6}} => [2,4,7,1,6,5,3] => [4,1,2,6,5,7,3] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10
{{1,2,4},{3},{5,6,7}} => [2,4,3,1,6,7,5] => [3,4,1,2,7,5,6] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 7
{{1,2,4},{3},{5,6},{7}} => [2,4,3,1,6,5,7] => [3,4,1,2,6,5,7] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 13
{{1,2,4,7},{3},{5},{6}} => [2,4,3,7,5,6,1] => [3,5,6,7,1,2,4] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 14
{{1,2,4},{3,7},{5},{6}} => [2,4,7,1,5,6,3] => [4,1,2,5,6,7,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 15
{{1,2,4},{3},{5,7},{6}} => [2,4,3,1,7,6,5] => [3,4,1,2,6,7,5] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 13
{{1,2,4},{3},{5},{6,7}} => [2,4,3,1,5,7,6] => [3,4,1,2,5,7,6] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 12
{{1,2,4},{3},{5},{6},{7}} => [2,4,3,1,5,6,7] => [3,4,1,2,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 18
{{1,2,5,6,7},{3,4}} => [2,5,4,3,6,7,1] => [4,3,7,1,2,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 4
{{1,2,5,6},{3,4,7}} => [2,5,4,7,6,1,3] => [6,1,2,5,7,3,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
{{1,2,5,6},{3,4},{7}} => [2,5,4,3,6,1,7] => [4,3,6,1,2,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 10
{{1,2,5,7},{3,4,6}} => [2,5,4,6,7,3,1] => [6,3,4,7,1,2,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
{{1,2,5},{3,4,6,7}} => [2,5,4,6,1,7,3] => [5,1,2,7,3,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 5
{{1,2,5},{3,4,6},{7}} => [2,5,4,6,1,3,7] => [5,1,2,6,3,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11
{{1,2,5,7},{3,4},{6}} => [2,5,4,3,7,6,1] => [4,3,6,7,1,2,5] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 10
{{1,2,5},{3,4,7},{6}} => [2,5,4,7,1,6,3] => [5,1,2,6,7,3,4] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 11
{{1,2,5},{3,4},{6,7}} => [2,5,4,3,1,7,6] => [4,3,5,1,2,7,6] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 9
{{1,2,5},{3,4},{6},{7}} => [2,5,4,3,1,6,7] => [4,3,5,1,2,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 15
{{1,2,6,7},{3,4,5}} => [2,6,4,5,3,7,1] => [5,3,4,7,1,2,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 5
{{1,2,6},{3,4,5,7}} => [2,6,4,5,7,1,3] => [6,1,2,7,3,4,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
{{1,2,6},{3,4,5},{7}} => [2,6,4,5,3,1,7] => [5,3,4,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11
{{1,2,7},{3,4,5,6}} => [2,7,4,5,6,3,1] => [6,3,4,5,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
{{1,2},{3,4,5,6,7}} => [2,1,4,5,6,7,3] => [2,1,7,3,4,5,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
{{1,2},{3,4,5,6},{7}} => [2,1,4,5,6,3,7] => [2,1,6,3,4,5,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 8
{{1,2,7},{3,4,5},{6}} => [2,7,4,5,3,6,1] => [5,3,4,6,7,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 11
{{1,2},{3,4,5,7},{6}} => [2,1,4,5,7,6,3] => [2,1,6,7,3,4,5] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 8
{{1,2},{3,4,5},{6,7}} => [2,1,4,5,3,7,6] => [2,1,5,3,4,7,6] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
{{1,2},{3,4,5},{6},{7}} => [2,1,4,5,3,6,7] => [2,1,5,3,4,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 13
{{1,2,6,7},{3,4},{5}} => [2,6,4,3,5,7,1] => [4,3,5,7,1,2,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 9
{{1,2,6},{3,4,7},{5}} => [2,6,4,7,5,1,3] => [5,6,1,2,7,3,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 11
{{1,2,6},{3,4},{5,7}} => [2,6,4,3,7,1,5] => [4,3,6,1,2,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 10
{{1,2,6},{3,4},{5},{7}} => [2,6,4,3,5,1,7] => [4,3,5,6,1,2,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 15
{{1,2,7},{3,4,6},{5}} => [2,7,4,6,5,3,1] => [5,6,3,4,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 11
{{1,2},{3,4,6,7},{5}} => [2,1,4,6,5,7,3] => [2,1,5,7,3,4,6] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 7
{{1,2},{3,4,6},{5,7}} => [2,1,4,6,7,3,5] => [2,1,6,3,4,7,5] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 8
{{1,2},{3,4,6},{5},{7}} => [2,1,4,6,5,3,7] => [2,1,5,6,3,4,7] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 13
{{1,2,7},{3,4},{5,6}} => [2,7,4,3,6,5,1] => [4,3,6,5,7,1,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 10
{{1,2},{3,4,7},{5,6}} => [2,1,4,7,6,5,3] => [2,1,6,5,7,3,4] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 8
{{1,2},{3,4},{5,6,7}} => [2,1,4,3,6,7,5] => [2,1,4,3,7,5,6] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
{{1,2},{3,4},{5,6},{7}} => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
{{1,2,7},{3,4},{5},{6}} => [2,7,4,3,5,6,1] => [4,3,5,6,7,1,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 15
{{1,2},{3,4,7},{5},{6}} => [2,1,4,7,5,6,3] => [2,1,5,6,7,3,4] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 13
{{1,2},{3,4},{5,7},{6}} => [2,1,4,3,7,6,5] => [2,1,4,3,6,7,5] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 12
{{1,2},{3,4},{5},{6,7}} => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
{{1,2},{3,4},{5},{6},{7}} => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 17
{{1,2,5,6,7},{3},{4}} => [2,5,3,4,6,7,1] => [3,4,7,1,2,5,6] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
{{1,2,5,6},{3,7},{4}} => [2,5,7,4,6,1,3] => [4,6,1,2,5,7,3] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 10
{{1,2,5,6},{3},{4,7}} => [2,5,3,7,6,1,4] => [3,6,1,2,5,7,4] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 9
{{1,2,5,6},{3},{4},{7}} => [2,5,3,4,6,1,7] => [3,4,6,1,2,5,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 13
{{1,2,5,7},{3,6},{4}} => [2,5,6,4,7,3,1] => [4,6,3,7,1,2,5] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 10
{{1,2,5},{3,6,7},{4}} => [2,5,6,4,1,7,3] => [4,5,1,2,7,3,6] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 9
{{1,2,5},{3,6},{4,7}} => [2,5,6,7,1,3,4] => [5,1,2,6,3,7,4] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
{{1,2,5},{3,6},{4},{7}} => [2,5,6,4,1,3,7] => [4,5,1,2,6,3,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 15
{{1,2,5,7},{3},{4,6}} => [2,5,3,6,7,4,1] => [3,6,4,7,1,2,5] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 9
{{1,2,5},{3,7},{4,6}} => [2,5,7,6,1,4,3] => [5,1,2,6,4,7,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
{{1,2,5},{3},{4,6,7}} => [2,5,3,6,1,7,4] => [3,5,1,2,7,4,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
{{1,2,5},{3},{4,6},{7}} => [2,5,3,6,1,4,7] => [3,5,1,2,6,4,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 14
{{1,2,5,7},{3},{4},{6}} => [2,5,3,4,7,6,1] => [3,4,6,7,1,2,5] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 13
{{1,2,5},{3,7},{4},{6}} => [2,5,7,4,1,6,3] => [4,5,1,2,6,7,3] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 15
{{1,2,5},{3},{4,7},{6}} => [2,5,3,7,1,6,4] => [3,5,1,2,6,7,4] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 14
{{1,2,5},{3},{4},{6,7}} => [2,5,3,4,1,7,6] => [3,4,5,1,2,7,6] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 12
{{1,2,5},{3},{4},{6},{7}} => [2,5,3,4,1,6,7] => [3,4,5,1,2,6,7] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 18
{{1,2,6,7},{3,5},{4}} => [2,6,5,4,3,7,1] => [4,5,3,7,1,2,6] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 9
{{1,2,6},{3,5,7},{4}} => [2,6,5,4,7,1,3] => [4,6,1,2,7,3,5] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 10
{{1,2,6},{3,5},{4,7}} => [2,6,5,7,3,1,4] => [5,3,6,1,2,7,4] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
{{1,2,6},{3,5},{4},{7}} => [2,6,5,4,3,1,7] => [4,5,3,6,1,2,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 15
{{1,2,7},{3,5,6},{4}} => [2,7,5,4,6,3,1] => [4,6,3,5,7,1,2] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 10
{{1,2},{3,5,6,7},{4}} => [2,1,5,4,6,7,3] => [2,1,4,7,3,5,6] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 6
{{1,2},{3,5,6},{4,7}} => [2,1,5,7,6,3,4] => [2,1,6,3,5,7,4] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 8
{{1,2},{3,5,6},{4},{7}} => [2,1,5,4,6,3,7] => [2,1,4,6,3,5,7] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 12
{{1,2,7},{3,5},{4,6}} => [2,7,5,6,3,4,1] => [5,3,6,4,7,1,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11
{{1,2},{3,5,7},{4,6}} => [2,1,5,6,7,4,3] => [2,1,6,4,7,3,5] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 8
{{1,2},{3,5},{4,6,7}} => [2,1,5,6,3,7,4] => [2,1,5,3,7,4,6] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
{{1,2},{3,5},{4,6},{7}} => [2,1,5,6,3,4,7] => [2,1,5,3,6,4,7] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 13
{{1,2,7},{3,5},{4},{6}} => [2,7,5,4,3,6,1] => [4,5,3,6,7,1,2] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 15
{{1,2},{3,5,7},{4},{6}} => [2,1,5,4,7,6,3] => [2,1,4,6,7,3,5] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 12
{{1,2},{3,5},{4,7},{6}} => [2,1,5,7,3,6,4] => [2,1,5,3,6,7,4] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 13
{{1,2},{3,5},{4},{6,7}} => [2,1,5,4,3,7,6] => [2,1,4,5,3,7,6] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 11
{{1,2},{3,5},{4},{6},{7}} => [2,1,5,4,3,6,7] => [2,1,4,5,3,6,7] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 17
{{1,2,6,7},{3},{4,5}} => [2,6,3,5,4,7,1] => [3,5,4,7,1,2,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
{{1,2,6},{3,7},{4,5}} => [2,6,7,5,4,1,3] => [5,4,6,1,2,7,3] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
{{1,2,6},{3},{4,5,7}} => [2,6,3,5,7,1,4] => [3,6,1,2,7,4,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 9
{{1,2,6},{3},{4,5},{7}} => [2,6,3,5,4,1,7] => [3,5,4,6,1,2,7] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 14
{{1,2,7},{3,6},{4,5}} => [2,7,6,5,4,3,1] => [5,4,6,3,7,1,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11
{{1,2},{3,6,7},{4,5}} => [2,1,6,5,4,7,3] => [2,1,5,4,7,3,6] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
{{1,2},{3,6},{4,5,7}} => [2,1,6,5,7,3,4] => [2,1,6,3,7,4,5] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 8
{{1,2},{3,6},{4,5},{7}} => [2,1,6,5,4,3,7] => [2,1,5,4,6,3,7] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 13
{{1,2,7},{3},{4,5,6}} => [2,7,3,5,6,4,1] => [3,6,4,5,7,1,2] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 9
{{1,2},{3,7},{4,5,6}} => [2,1,7,5,6,4,3] => [2,1,6,4,5,7,3] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 8
{{1,2},{3},{4,5,6,7}} => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
{{1,2},{3},{4,5,6},{7}} => [2,1,3,5,6,4,7] => [2,1,3,6,4,5,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
{{1,2,7},{3},{4,5},{6}} => [2,7,3,5,4,6,1] => [3,5,4,6,7,1,2] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 14
{{1,2},{3,7},{4,5},{6}} => [2,1,7,5,4,6,3] => [2,1,5,4,6,7,3] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 13
{{1,2},{3},{4,5,7},{6}} => [2,1,3,5,7,6,4] => [2,1,3,6,7,4,5] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 11
{{1,2},{3},{4,5},{6,7}} => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
{{1,2},{3},{4,5},{6},{7}} => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 16
{{1,2,6,7},{3},{4},{5}} => [2,6,3,4,5,7,1] => [3,4,5,7,1,2,6] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 12
{{1,2,6},{3,7},{4},{5}} => [2,6,7,4,5,1,3] => [4,5,6,1,2,7,3] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 15
{{1,2,6},{3},{4,7},{5}} => [2,6,3,7,5,1,4] => [3,5,6,1,2,7,4] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 14
{{1,2,6},{3},{4},{5,7}} => [2,6,3,4,7,1,5] => [3,4,6,1,2,7,5] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 13
{{1,2,6},{3},{4},{5},{7}} => [2,6,3,4,5,1,7] => [3,4,5,6,1,2,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 18
{{1,2,7},{3,6},{4},{5}} => [2,7,6,4,5,3,1] => [4,5,6,3,7,1,2] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 15
{{1,2},{3,6,7},{4},{5}} => [2,1,6,4,5,7,3] => [2,1,4,5,7,3,6] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 11
{{1,2},{3,6},{4,7},{5}} => [2,1,6,7,5,3,4] => [2,1,5,6,3,7,4] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 13
{{1,2},{3,6},{4},{5,7}} => [2,1,6,4,7,3,5] => [2,1,4,6,3,7,5] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 12
{{1,2},{3,6},{4},{5},{7}} => [2,1,6,4,5,3,7] => [2,1,4,5,6,3,7] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 17
{{1,2,7},{3},{4,6},{5}} => [2,7,3,6,5,4,1] => [3,5,6,4,7,1,2] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 14
{{1,2},{3,7},{4,6},{5}} => [2,1,7,6,5,4,3] => [2,1,5,6,4,7,3] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 13
{{1,2},{3},{4,6,7},{5}} => [2,1,3,6,5,7,4] => [2,1,3,5,7,4,6] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 10
{{1,2},{3},{4,6},{5,7}} => [2,1,3,6,7,4,5] => [2,1,3,6,4,7,5] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 11
{{1,2},{3},{4,6},{5},{7}} => [2,1,3,6,5,4,7] => [2,1,3,5,6,4,7] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 16
{{1,2,7},{3},{4},{5,6}} => [2,7,3,4,6,5,1] => [3,4,6,5,7,1,2] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 13
{{1,2},{3,7},{4},{5,6}} => [2,1,7,4,6,5,3] => [2,1,4,6,5,7,3] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 12
{{1,2},{3},{4,7},{5,6}} => [2,1,3,7,6,5,4] => [2,1,3,6,5,7,4] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 11
{{1,2},{3},{4},{5,6,7}} => [2,1,3,4,6,7,5] => [2,1,3,4,7,5,6] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
{{1,2},{3},{4},{5,6},{7}} => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 15
{{1,2,7},{3},{4},{5},{6}} => [2,7,3,4,5,6,1] => [3,4,5,6,7,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 18
{{1,2},{3,7},{4},{5},{6}} => [2,1,7,4,5,6,3] => [2,1,4,5,6,7,3] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 17
{{1,2},{3},{4,7},{5},{6}} => [2,1,3,7,5,6,4] => [2,1,3,5,6,7,4] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 16
{{1,2},{3},{4},{5,7},{6}} => [2,1,3,4,7,6,5] => [2,1,3,4,6,7,5] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 15
{{1,2},{3},{4},{5},{6,7}} => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 14
{{1,2},{3},{4},{5},{6},{7}} => [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] => 20
{{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => [2,7,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
{{1,3,4,5,6},{2,7}} => [3,7,4,5,6,1,2] => [6,1,3,4,5,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6
{{1,3,4,5,6},{2},{7}} => [3,2,4,5,6,1,7] => [2,6,1,3,4,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 8
{{1,3,4,5,7},{2,6}} => [3,6,4,5,7,2,1] => [6,2,7,1,3,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 6
{{1,3,4,5},{2,6,7}} => [3,6,4,5,1,7,2] => [5,1,3,4,7,2,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 5
{{1,3,4,5},{2,6},{7}} => [3,6,4,5,1,2,7] => [5,1,3,4,6,2,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
{{1,3,4,5,7},{2},{6}} => [3,2,4,5,7,6,1] => [2,6,7,1,3,4,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 8
{{1,3,4,5},{2,7},{6}} => [3,7,4,5,1,6,2] => [5,1,3,4,6,7,2] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 11
{{1,3,4,5},{2},{6,7}} => [3,2,4,5,1,7,6] => [2,5,1,3,4,7,6] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 7
{{1,3,4,5},{2},{6},{7}} => [3,2,4,5,1,6,7] => [2,5,1,3,4,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 13
{{1,3,4,6,7},{2,5}} => [3,5,4,6,2,7,1] => [5,2,7,1,3,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 5
{{1,3,4,6},{2,5,7}} => [3,5,4,6,7,1,2] => [6,1,3,4,7,2,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
{{1,3,4,6},{2,5},{7}} => [3,5,4,6,2,1,7] => [5,2,6,1,3,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11
{{1,3,4,7},{2,5,6}} => [3,5,4,7,6,2,1] => [6,2,5,7,1,3,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
{{1,3,4},{2,5,6,7}} => [3,5,4,1,6,7,2] => [4,1,3,7,2,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 4
{{1,3,4},{2,5,6},{7}} => [3,5,4,1,6,2,7] => [4,1,3,6,2,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 10
{{1,3,4,7},{2,5},{6}} => [3,5,4,7,2,6,1] => [5,2,6,7,1,3,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 11
{{1,3,4},{2,5,7},{6}} => [3,5,4,1,7,6,2] => [4,1,3,6,7,2,5] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 10
{{1,3,4},{2,5},{6,7}} => [3,5,4,1,2,7,6] => [4,1,3,5,2,7,6] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 9
{{1,3,4},{2,5},{6},{7}} => [3,5,4,1,2,6,7] => [4,1,3,5,2,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 15
{{1,3,4,6,7},{2},{5}} => [3,2,4,6,5,7,1] => [2,5,7,1,3,4,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 7
{{1,3,4,6},{2,7},{5}} => [3,7,4,6,5,1,2] => [5,6,1,3,4,7,2] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 11
{{1,3,4,6},{2},{5,7}} => [3,2,4,6,7,1,5] => [2,6,1,3,4,7,5] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 8
{{1,3,4,6},{2},{5},{7}} => [3,2,4,6,5,1,7] => [2,5,6,1,3,4,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 13
{{1,3,4,7},{2,6},{5}} => [3,6,4,7,5,2,1] => [5,6,2,7,1,3,4] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 11
{{1,3,4},{2,6,7},{5}} => [3,6,4,1,5,7,2] => [4,1,3,5,7,2,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 9
{{1,3,4},{2,6},{5,7}} => [3,6,4,1,7,2,5] => [4,1,3,6,2,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10
{{1,3,4},{2,6},{5},{7}} => [3,6,4,1,5,2,7] => [4,1,3,5,6,2,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 15
{{1,3,4,7},{2},{5,6}} => [3,2,4,7,6,5,1] => [2,6,5,7,1,3,4] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 8
{{1,3,4},{2,7},{5,6}} => [3,7,4,1,6,5,2] => [4,1,3,6,5,7,2] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10
{{1,3,4},{2},{5,6,7}} => [3,2,4,1,6,7,5] => [2,4,1,3,7,5,6] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 6
{{1,3,4},{2},{5,6},{7}} => [3,2,4,1,6,5,7] => [2,4,1,3,6,5,7] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 12
{{1,3,4,7},{2},{5},{6}} => [3,2,4,7,5,6,1] => [2,5,6,7,1,3,4] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 13
{{1,3,4},{2,7},{5},{6}} => [3,7,4,1,5,6,2] => [4,1,3,5,6,7,2] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 15
{{1,3,4},{2},{5,7},{6}} => [3,2,4,1,7,6,5] => [2,4,1,3,6,7,5] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 12
{{1,3,4},{2},{5},{6,7}} => [3,2,4,1,5,7,6] => [2,4,1,3,5,7,6] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 11
{{1,3,4},{2},{5},{6},{7}} => [3,2,4,1,5,6,7] => [2,4,1,3,5,6,7] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 17
{{1,3,5,6,7},{2,4}} => [3,4,5,2,6,7,1] => [4,2,7,1,3,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 4
{{1,3,5,6},{2,4,7}} => [3,4,5,7,6,1,2] => [6,1,3,5,7,2,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
{{1,3,5,6},{2,4},{7}} => [3,4,5,2,6,1,7] => [4,2,6,1,3,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 10
{{1,3,5,7},{2,4,6}} => [3,4,5,6,7,2,1] => [6,2,4,7,1,3,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
{{1,3,5},{2,4,6,7}} => [3,4,5,6,1,7,2] => [5,1,3,7,2,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 5
{{1,3,5},{2,4,6},{7}} => [3,4,5,6,1,2,7] => [5,1,3,6,2,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11
{{1,3,5,7},{2,4},{6}} => [3,4,5,2,7,6,1] => [4,2,6,7,1,3,5] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 10
{{1,3,5},{2,4,7},{6}} => [3,4,5,7,1,6,2] => [5,1,3,6,7,2,4] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 11
{{1,3,5},{2,4},{6,7}} => [3,4,5,2,1,7,6] => [4,2,5,1,3,7,6] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 9
{{1,3,5},{2,4},{6},{7}} => [3,4,5,2,1,6,7] => [4,2,5,1,3,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 15
{{1,3,6,7},{2,4,5}} => [3,4,6,5,2,7,1] => [5,2,4,7,1,3,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 5
{{1,3,6},{2,4,5,7}} => [3,4,6,5,7,1,2] => [6,1,3,7,2,4,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
{{1,3,6},{2,4,5},{7}} => [3,4,6,5,2,1,7] => [5,2,4,6,1,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11
{{1,3,7},{2,4,5,6}} => [3,4,7,5,6,2,1] => [6,2,4,5,7,1,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
{{1,3},{2,4,5,6,7}} => [3,4,1,5,6,7,2] => [3,1,7,2,4,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 3
{{1,3},{2,4,5,6},{7}} => [3,4,1,5,6,2,7] => [3,1,6,2,4,5,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 9
{{1,3,7},{2,4,5},{6}} => [3,4,7,5,2,6,1] => [5,2,4,6,7,1,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 11
{{1,3},{2,4,5,7},{6}} => [3,4,1,5,7,6,2] => [3,1,6,7,2,4,5] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 9
{{1,3},{2,4,5},{6,7}} => [3,4,1,5,2,7,6] => [3,1,5,2,4,7,6] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 8
{{1,3},{2,4,5},{6},{7}} => [3,4,1,5,2,6,7] => [3,1,5,2,4,6,7] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 14
{{1,3,6,7},{2,4},{5}} => [3,4,6,2,5,7,1] => [4,2,5,7,1,3,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 9
{{1,3,6},{2,4,7},{5}} => [3,4,6,7,5,1,2] => [5,6,1,3,7,2,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 11
{{1,3,6},{2,4},{5,7}} => [3,4,6,2,7,1,5] => [4,2,6,1,3,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 10
{{1,3,6},{2,4},{5},{7}} => [3,4,6,2,5,1,7] => [4,2,5,6,1,3,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 15
{{1,3,7},{2,4,6},{5}} => [3,4,7,6,5,2,1] => [5,6,2,4,7,1,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 11
{{1,3},{2,4,6,7},{5}} => [3,4,1,6,5,7,2] => [3,1,5,7,2,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
{{1,3},{2,4,6},{5,7}} => [3,4,1,6,7,2,5] => [3,1,6,2,4,7,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 9
{{1,3},{2,4,6},{5},{7}} => [3,4,1,6,5,2,7] => [3,1,5,6,2,4,7] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 14
{{1,3,7},{2,4},{5,6}} => [3,4,7,2,6,5,1] => [4,2,6,5,7,1,3] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 10
{{1,3},{2,4,7},{5,6}} => [3,4,1,7,6,5,2] => [3,1,6,5,7,2,4] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 9
{{1,3},{2,4},{5,6,7}} => [3,4,1,2,6,7,5] => [3,1,4,2,7,5,6] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7
{{1,3},{2,4},{5,6},{7}} => [3,4,1,2,6,5,7] => [3,1,4,2,6,5,7] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 13
{{1,3,7},{2,4},{5},{6}} => [3,4,7,2,5,6,1] => [4,2,5,6,7,1,3] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 15
{{1,3},{2,4,7},{5},{6}} => [3,4,1,7,5,6,2] => [3,1,5,6,7,2,4] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 14
{{1,3},{2,4},{5,7},{6}} => [3,4,1,2,7,6,5] => [3,1,4,2,6,7,5] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 13
{{1,3},{2,4},{5},{6,7}} => [3,4,1,2,5,7,6] => [3,1,4,2,5,7,6] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 12
{{1,3},{2,4},{5},{6},{7}} => [3,4,1,2,5,6,7] => [3,1,4,2,5,6,7] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 18
{{1,3,5,6,7},{2},{4}} => [3,2,5,4,6,7,1] => [2,4,7,1,3,5,6] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 6
{{1,3,5,6},{2,7},{4}} => [3,7,5,4,6,1,2] => [4,6,1,3,5,7,2] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 10
{{1,3,5,6},{2},{4,7}} => [3,2,5,7,6,1,4] => [2,6,1,3,5,7,4] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 8
{{1,3,5,6},{2},{4},{7}} => [3,2,5,4,6,1,7] => [2,4,6,1,3,5,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 12
{{1,3,5,7},{2,6},{4}} => [3,6,5,4,7,2,1] => [4,6,2,7,1,3,5] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 10
{{1,3,5},{2,6,7},{4}} => [3,6,5,4,1,7,2] => [4,5,1,3,7,2,6] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 9
{{1,3,5},{2,6},{4,7}} => [3,6,5,7,1,2,4] => [5,1,3,6,2,7,4] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
{{1,3,5},{2,6},{4},{7}} => [3,6,5,4,1,2,7] => [4,5,1,3,6,2,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 15
{{1,3,5,7},{2},{4,6}} => [3,2,5,6,7,4,1] => [2,6,4,7,1,3,5] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 8
{{1,3,5},{2,7},{4,6}} => [3,7,5,6,1,4,2] => [5,1,3,6,4,7,2] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
{{1,3,5},{2},{4,6,7}} => [3,2,5,6,1,7,4] => [2,5,1,3,7,4,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 7
{{1,3,5},{2},{4,6},{7}} => [3,2,5,6,1,4,7] => [2,5,1,3,6,4,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 13
{{1,3,5,7},{2},{4},{6}} => [3,2,5,4,7,6,1] => [2,4,6,7,1,3,5] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12
{{1,3,5},{2,7},{4},{6}} => [3,7,5,4,1,6,2] => [4,5,1,3,6,7,2] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 15
{{1,3,5},{2},{4,7},{6}} => [3,2,5,7,1,6,4] => [2,5,1,3,6,7,4] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 13
{{1,3,5},{2},{4},{6,7}} => [3,2,5,4,1,7,6] => [2,4,5,1,3,7,6] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 11
{{1,3,5},{2},{4},{6},{7}} => [3,2,5,4,1,6,7] => [2,4,5,1,3,6,7] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 17
{{1,3,6,7},{2,5},{4}} => [3,5,6,4,2,7,1] => [4,5,2,7,1,3,6] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 9
{{1,3,6},{2,5,7},{4}} => [3,5,6,4,7,1,2] => [4,6,1,3,7,2,5] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 10
{{1,3,6},{2,5},{4,7}} => [3,5,6,7,2,1,4] => [5,2,6,1,3,7,4] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
{{1,3,6},{2,5},{4},{7}} => [3,5,6,4,2,1,7] => [4,5,2,6,1,3,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 15
{{1,3,7},{2,5,6},{4}} => [3,5,7,4,6,2,1] => [4,6,2,5,7,1,3] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 10
{{1,3},{2,5,6,7},{4}} => [3,5,1,4,6,7,2] => [3,1,4,7,2,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
{{1,3},{2,5,6},{4,7}} => [3,5,1,7,6,2,4] => [3,1,6,2,5,7,4] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 9
{{1,3},{2,5,6},{4},{7}} => [3,5,1,4,6,2,7] => [3,1,4,6,2,5,7] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 13
{{1,3,7},{2,5},{4,6}} => [3,5,7,6,2,4,1] => [5,2,6,4,7,1,3] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11
{{1,3},{2,5,7},{4,6}} => [3,5,1,6,7,4,2] => [3,1,6,4,7,2,5] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 9
{{1,3},{2,5},{4,6,7}} => [3,5,1,6,2,7,4] => [3,1,5,2,7,4,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 8
{{1,3},{2,5},{4,6},{7}} => [3,5,1,6,2,4,7] => [3,1,5,2,6,4,7] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 14
{{1,3,7},{2,5},{4},{6}} => [3,5,7,4,2,6,1] => [4,5,2,6,7,1,3] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 15
{{1,3},{2,5,7},{4},{6}} => [3,5,1,4,7,6,2] => [3,1,4,6,7,2,5] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 13
{{1,3},{2,5},{4,7},{6}} => [3,5,1,7,2,6,4] => [3,1,5,2,6,7,4] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 14
{{1,3},{2,5},{4},{6,7}} => [3,5,1,4,2,7,6] => [3,1,4,5,2,7,6] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 12
{{1,3},{2,5},{4},{6},{7}} => [3,5,1,4,2,6,7] => [3,1,4,5,2,6,7] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 18
{{1,3,6,7},{2},{4,5}} => [3,2,6,5,4,7,1] => [2,5,4,7,1,3,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 7
{{1,3,6},{2,7},{4,5}} => [3,7,6,5,4,1,2] => [5,4,6,1,3,7,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
{{1,3,6},{2},{4,5,7}} => [3,2,6,5,7,1,4] => [2,6,1,3,7,4,5] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 8
{{1,3,6},{2},{4,5},{7}} => [3,2,6,5,4,1,7] => [2,5,4,6,1,3,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 13
{{1,3,7},{2,6},{4,5}} => [3,6,7,5,4,2,1] => [5,4,6,2,7,1,3] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11
{{1,3},{2,6,7},{4,5}} => [3,6,1,5,4,7,2] => [3,1,5,4,7,2,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 8
{{1,3},{2,6},{4,5,7}} => [3,6,1,5,7,2,4] => [3,1,6,2,7,4,5] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 9
{{1,3},{2,6},{4,5},{7}} => [3,6,1,5,4,2,7] => [3,1,5,4,6,2,7] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 14
{{1,3,7},{2},{4,5,6}} => [3,2,7,5,6,4,1] => [2,6,4,5,7,1,3] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 8
{{1,3},{2,7},{4,5,6}} => [3,7,1,5,6,4,2] => [3,1,6,4,5,7,2] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 9
{{1,3},{2},{4,5,6,7}} => [3,2,1,5,6,7,4] => [2,3,1,7,4,5,6] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 5
{{1,3},{2},{4,5,6},{7}} => [3,2,1,5,6,4,7] => [2,3,1,6,4,5,7] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 11
{{1,3,7},{2},{4,5},{6}} => [3,2,7,5,4,6,1] => [2,5,4,6,7,1,3] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 13
{{1,3},{2,7},{4,5},{6}} => [3,7,1,5,4,6,2] => [3,1,5,4,6,7,2] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 14
{{1,3},{2},{4,5,7},{6}} => [3,2,1,5,7,6,4] => [2,3,1,6,7,4,5] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 11
{{1,3},{2},{4,5},{6,7}} => [3,2,1,5,4,7,6] => [2,3,1,5,4,7,6] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 10
{{1,3},{2},{4,5},{6},{7}} => [3,2,1,5,4,6,7] => [2,3,1,5,4,6,7] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 16
{{1,3,6,7},{2},{4},{5}} => [3,2,6,4,5,7,1] => [2,4,5,7,1,3,6] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 11
{{1,3,6},{2,7},{4},{5}} => [3,7,6,4,5,1,2] => [4,5,6,1,3,7,2] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 15
{{1,3,6},{2},{4,7},{5}} => [3,2,6,7,5,1,4] => [2,5,6,1,3,7,4] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 13
{{1,3,6},{2},{4},{5,7}} => [3,2,6,4,7,1,5] => [2,4,6,1,3,7,5] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 12
{{1,3,6},{2},{4},{5},{7}} => [3,2,6,4,5,1,7] => [2,4,5,6,1,3,7] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 17
{{1,3,7},{2,6},{4},{5}} => [3,6,7,4,5,2,1] => [4,5,6,2,7,1,3] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 15
{{1,3},{2,6,7},{4},{5}} => [3,6,1,4,5,7,2] => [3,1,4,5,7,2,6] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 12
{{1,3},{2,6},{4,7},{5}} => [3,6,1,7,5,2,4] => [3,1,5,6,2,7,4] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 14
{{1,3},{2,6},{4},{5,7}} => [3,6,1,4,7,2,5] => [3,1,4,6,2,7,5] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 13
{{1,3},{2,6},{4},{5},{7}} => [3,6,1,4,5,2,7] => [3,1,4,5,6,2,7] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 18
{{1,3,7},{2},{4,6},{5}} => [3,2,7,6,5,4,1] => [2,5,6,4,7,1,3] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 13
{{1,3},{2,7},{4,6},{5}} => [3,7,1,6,5,4,2] => [3,1,5,6,4,7,2] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 14
{{1,3},{2},{4,6,7},{5}} => [3,2,1,6,5,7,4] => [2,3,1,5,7,4,6] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 10
{{1,3},{2},{4,6},{5,7}} => [3,2,1,6,7,4,5] => [2,3,1,6,4,7,5] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 11
{{1,3},{2},{4,6},{5},{7}} => [3,2,1,6,5,4,7] => [2,3,1,5,6,4,7] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 16
{{1,3,7},{2},{4},{5,6}} => [3,2,7,4,6,5,1] => [2,4,6,5,7,1,3] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 12
{{1,3},{2,7},{4},{5,6}} => [3,7,1,4,6,5,2] => [3,1,4,6,5,7,2] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 13
{{1,3},{2},{4,7},{5,6}} => [3,2,1,7,6,5,4] => [2,3,1,6,5,7,4] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 11
{{1,3},{2},{4},{5,6,7}} => [3,2,1,4,6,7,5] => [2,3,1,4,7,5,6] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 9
{{1,3},{2},{4},{5,6},{7}} => [3,2,1,4,6,5,7] => [2,3,1,4,6,5,7] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 15
{{1,3,7},{2},{4},{5},{6}} => [3,2,7,4,5,6,1] => [2,4,5,6,7,1,3] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 17
{{1,3},{2,7},{4},{5},{6}} => [3,7,1,4,5,6,2] => [3,1,4,5,6,7,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 18
{{1,3},{2},{4,7},{5},{6}} => [3,2,1,7,5,6,4] => [2,3,1,5,6,7,4] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 16
{{1,3},{2},{4},{5,7},{6}} => [3,2,1,4,7,6,5] => [2,3,1,4,6,7,5] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 15
{{1,3},{2},{4},{5},{6,7}} => [3,2,1,4,5,7,6] => [2,3,1,4,5,7,6] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 14
{{1,3},{2},{4},{5},{6},{7}} => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 20
{{1,4,5,6,7},{2,3}} => [4,3,2,5,6,7,1] => [3,2,7,1,4,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 3
{{1,4,5,6},{2,3,7}} => [4,3,7,5,6,1,2] => [6,1,4,5,7,2,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
{{1,4,5,6},{2,3},{7}} => [4,3,2,5,6,1,7] => [3,2,6,1,4,5,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 9
{{1,4,5,7},{2,3,6}} => [4,3,6,5,7,2,1] => [6,2,3,7,1,4,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
{{1,4,5},{2,3,6,7}} => [4,3,6,5,1,7,2] => [5,1,4,7,2,3,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 5
{{1,4,5},{2,3,6},{7}} => [4,3,6,5,1,2,7] => [5,1,4,6,2,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11
{{1,4,5,7},{2,3},{6}} => [4,3,2,5,7,6,1] => [3,2,6,7,1,4,5] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 9
{{1,4,5},{2,3,7},{6}} => [4,3,7,5,1,6,2] => [5,1,4,6,7,2,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 11
{{1,4,5},{2,3},{6,7}} => [4,3,2,5,1,7,6] => [3,2,5,1,4,7,6] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 8
{{1,4,5},{2,3},{6},{7}} => [4,3,2,5,1,6,7] => [3,2,5,1,4,6,7] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 14
{{1,4,6,7},{2,3,5}} => [4,3,5,6,2,7,1] => [5,2,3,7,1,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 5
{{1,4,6},{2,3,5,7}} => [4,3,5,6,7,1,2] => [6,1,4,7,2,3,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
{{1,4,6},{2,3,5},{7}} => [4,3,5,6,2,1,7] => [5,2,3,6,1,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11
{{1,4,7},{2,3,5,6}} => [4,3,5,7,6,2,1] => [6,2,3,5,7,1,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
{{1,4},{2,3,5,6,7}} => [4,3,5,1,6,7,2] => [4,1,7,2,3,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 4
{{1,4},{2,3,5,6},{7}} => [4,3,5,1,6,2,7] => [4,1,6,2,3,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 10
{{1,4,7},{2,3,5},{6}} => [4,3,5,7,2,6,1] => [5,2,3,6,7,1,4] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 11
{{1,4},{2,3,5,7},{6}} => [4,3,5,1,7,6,2] => [4,1,6,7,2,3,5] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 10
{{1,4},{2,3,5},{6,7}} => [4,3,5,1,2,7,6] => [4,1,5,2,3,7,6] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 9
{{1,4},{2,3,5},{6},{7}} => [4,3,5,1,2,6,7] => [4,1,5,2,3,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 15
{{1,4,6,7},{2,3},{5}} => [4,3,2,6,5,7,1] => [3,2,5,7,1,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
{{1,4,6},{2,3,7},{5}} => [4,3,7,6,5,1,2] => [5,6,1,4,7,2,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 11
{{1,4,6},{2,3},{5,7}} => [4,3,2,6,7,1,5] => [3,2,6,1,4,7,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 9
{{1,4,6},{2,3},{5},{7}} => [4,3,2,6,5,1,7] => [3,2,5,6,1,4,7] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 14
{{1,4,7},{2,3,6},{5}} => [4,3,6,7,5,2,1] => [5,6,2,3,7,1,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 11
{{1,4},{2,3,6,7},{5}} => [4,3,6,1,5,7,2] => [4,1,5,7,2,3,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 9
{{1,4},{2,3,6},{5,7}} => [4,3,6,1,7,2,5] => [4,1,6,2,3,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 10
{{1,4},{2,3,6},{5},{7}} => [4,3,6,1,5,2,7] => [4,1,5,6,2,3,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 15
{{1,4,7},{2,3},{5,6}} => [4,3,2,7,6,5,1] => [3,2,6,5,7,1,4] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 9
{{1,4},{2,3,7},{5,6}} => [4,3,7,1,6,5,2] => [4,1,6,5,7,2,3] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 10
{{1,4},{2,3},{5,6,7}} => [4,3,2,1,6,7,5] => [3,2,4,1,7,5,6] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7
{{1,4},{2,3},{5,6},{7}} => [4,3,2,1,6,5,7] => [3,2,4,1,6,5,7] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 13
{{1,4,7},{2,3},{5},{6}} => [4,3,2,7,5,6,1] => [3,2,5,6,7,1,4] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 14
{{1,4},{2,3,7},{5},{6}} => [4,3,7,1,5,6,2] => [4,1,5,6,7,2,3] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 15
{{1,4},{2,3},{5,7},{6}} => [4,3,2,1,7,6,5] => [3,2,4,1,6,7,5] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 13
{{1,4},{2,3},{5},{6,7}} => [4,3,2,1,5,7,6] => [3,2,4,1,5,7,6] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 12
{{1,4},{2,3},{5},{6},{7}} => [4,3,2,1,5,6,7] => [3,2,4,1,5,6,7] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 18
{{1,5,6,7},{2,3,4}} => [5,3,4,2,6,7,1] => [4,2,3,7,1,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 4
{{1,5,6},{2,3,4,7}} => [5,3,4,7,6,1,2] => [6,1,5,7,2,3,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 6
{{1,5,6},{2,3,4},{7}} => [5,3,4,2,6,1,7] => [4,2,3,6,1,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 10
{{1,5,7},{2,3,4,6}} => [5,3,4,6,7,2,1] => [6,2,3,4,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 6
{{1,5},{2,3,4,6,7}} => [5,3,4,6,1,7,2] => [5,1,7,2,3,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 5
{{1,5},{2,3,4,6},{7}} => [5,3,4,6,1,2,7] => [5,1,6,2,3,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11
{{1,5,7},{2,3,4},{6}} => [5,3,4,2,7,6,1] => [4,2,3,6,7,1,5] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 10
{{1,5},{2,3,4,7},{6}} => [5,3,4,7,1,6,2] => [5,1,6,7,2,3,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 11
{{1,5},{2,3,4},{6,7}} => [5,3,4,2,1,7,6] => [4,2,3,5,1,7,6] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 9
{{1,5},{2,3,4},{6},{7}} => [5,3,4,2,1,6,7] => [4,2,3,5,1,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 15
{{1,6,7},{2,3,4,5}} => [6,3,4,5,2,7,1] => [5,2,3,4,7,1,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 5
{{1,6},{2,3,4,5,7}} => [6,3,4,5,7,1,2] => [6,1,7,2,3,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 6
{{1,6},{2,3,4,5},{7}} => [6,3,4,5,2,1,7] => [5,2,3,4,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
{{1,7},{2,3,4,5,6}} => [7,3,4,5,6,2,1] => [6,2,3,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6
{{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
{{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
{{1,7},{2,3,4,5},{6}} => [7,3,4,5,2,6,1] => [5,2,3,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 11
{{1},{2,3,4,5,7},{6}} => [1,3,4,5,7,6,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
{{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
{{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 12
{{1,6,7},{2,3,4},{5}} => [6,3,4,2,5,7,1] => [4,2,3,5,7,1,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 9
{{1,6},{2,3,4,7},{5}} => [6,3,4,7,5,1,2] => [5,6,1,7,2,3,4] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 11
{{1,6},{2,3,4},{5,7}} => [6,3,4,2,7,1,5] => [4,2,3,6,1,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10
{{1,6},{2,3,4},{5},{7}} => [6,3,4,2,5,1,7] => [4,2,3,5,6,1,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 15
{{1,7},{2,3,4,6},{5}} => [7,3,4,6,5,2,1] => [5,6,2,3,4,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 11
{{1},{2,3,4,6,7},{5}} => [1,3,4,6,5,7,2] => [1,5,7,2,3,4,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 6
{{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => [1,6,2,3,4,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
{{1},{2,3,4,6},{5},{7}} => [1,3,4,6,5,2,7] => [1,5,6,2,3,4,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 12
{{1,7},{2,3,4},{5,6}} => [7,3,4,2,6,5,1] => [4,2,3,6,5,7,1] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 10
{{1},{2,3,4,7},{5,6}} => [1,3,4,7,6,5,2] => [1,6,5,7,2,3,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
{{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => [1,4,2,3,7,5,6] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
{{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
{{1,7},{2,3,4},{5},{6}} => [7,3,4,2,5,6,1] => [4,2,3,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 15
{{1},{2,3,4,7},{5},{6}} => [1,3,4,7,5,6,2] => [1,5,6,7,2,3,4] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12
{{1},{2,3,4},{5,7},{6}} => [1,3,4,2,7,6,5] => [1,4,2,3,6,7,5] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 11
{{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
{{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 16
{{1,5,6,7},{2,3},{4}} => [5,3,2,4,6,7,1] => [3,2,4,7,1,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
{{1,5,6},{2,3,7},{4}} => [5,3,7,4,6,1,2] => [4,6,1,5,7,2,3] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 10
{{1,5,6},{2,3},{4,7}} => [5,3,2,7,6,1,4] => [3,2,6,1,5,7,4] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 9
{{1,5,6},{2,3},{4},{7}} => [5,3,2,4,6,1,7] => [3,2,4,6,1,5,7] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 13
{{1,5,7},{2,3,6},{4}} => [5,3,6,4,7,2,1] => [4,6,2,3,7,1,5] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 10
{{1,5},{2,3,6,7},{4}} => [5,3,6,4,1,7,2] => [4,5,1,7,2,3,6] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 9
{{1,5},{2,3,6},{4,7}} => [5,3,6,7,1,2,4] => [5,1,6,2,3,7,4] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
{{1,5},{2,3,6},{4},{7}} => [5,3,6,4,1,2,7] => [4,5,1,6,2,3,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 15
{{1,5,7},{2,3},{4,6}} => [5,3,2,6,7,4,1] => [3,2,6,4,7,1,5] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 9
{{1,5},{2,3,7},{4,6}} => [5,3,7,6,1,4,2] => [5,1,6,4,7,2,3] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11
{{1,5},{2,3},{4,6,7}} => [5,3,2,6,1,7,4] => [3,2,5,1,7,4,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 8
{{1,5},{2,3},{4,6},{7}} => [5,3,2,6,1,4,7] => [3,2,5,1,6,4,7] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 14
{{1,5,7},{2,3},{4},{6}} => [5,3,2,4,7,6,1] => [3,2,4,6,7,1,5] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 13
{{1,5},{2,3,7},{4},{6}} => [5,3,7,4,1,6,2] => [4,5,1,6,7,2,3] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 15
{{1,5},{2,3},{4,7},{6}} => [5,3,2,7,1,6,4] => [3,2,5,1,6,7,4] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 14
{{1,5},{2,3},{4},{6,7}} => [5,3,2,4,1,7,6] => [3,2,4,5,1,7,6] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 12
{{1,5},{2,3},{4},{6},{7}} => [5,3,2,4,1,6,7] => [3,2,4,5,1,6,7] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 18
{{1,6,7},{2,3,5},{4}} => [6,3,5,4,2,7,1] => [4,5,2,3,7,1,6] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 9
{{1,6},{2,3,5,7},{4}} => [6,3,5,4,7,1,2] => [4,6,1,7,2,3,5] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 10
{{1,6},{2,3,5},{4,7}} => [6,3,5,7,2,1,4] => [5,2,3,6,1,7,4] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
{{1,6},{2,3,5},{4},{7}} => [6,3,5,4,2,1,7] => [4,5,2,3,6,1,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 15
{{1,7},{2,3,5,6},{4}} => [7,3,5,4,6,2,1] => [4,6,2,3,5,7,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 10
{{1},{2,3,5,6,7},{4}} => [1,3,5,4,6,7,2] => [1,4,7,2,3,5,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
{{1},{2,3,5,6},{4,7}} => [1,3,5,7,6,2,4] => [1,6,2,3,5,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
{{1},{2,3,5,6},{4},{7}} => [1,3,5,4,6,2,7] => [1,4,6,2,3,5,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 11
{{1,7},{2,3,5},{4,6}} => [7,3,5,6,2,4,1] => [5,2,3,6,4,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
{{1},{2,3,5,7},{4,6}} => [1,3,5,6,7,4,2] => [1,6,4,7,2,3,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
{{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => [1,5,2,3,7,4,6] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 6
{{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => [1,5,2,3,6,4,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 12
{{1,7},{2,3,5},{4},{6}} => [7,3,5,4,2,6,1] => [4,5,2,3,6,7,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 15
{{1},{2,3,5,7},{4},{6}} => [1,3,5,4,7,6,2] => [1,4,6,7,2,3,5] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11
{{1},{2,3,5},{4,7},{6}} => [1,3,5,7,2,6,4] => [1,5,2,3,6,7,4] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 12
{{1},{2,3,5},{4},{6,7}} => [1,3,5,4,2,7,6] => [1,4,5,2,3,7,6] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 10
{{1},{2,3,5},{4},{6},{7}} => [1,3,5,4,2,6,7] => [1,4,5,2,3,6,7] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 16
{{1,6,7},{2,3},{4,5}} => [6,3,2,5,4,7,1] => [3,2,5,4,7,1,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 8
{{1,6},{2,3,7},{4,5}} => [6,3,7,5,4,1,2] => [5,4,6,1,7,2,3] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11
{{1,6},{2,3},{4,5,7}} => [6,3,2,5,7,1,4] => [3,2,6,1,7,4,5] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 9
{{1,6},{2,3},{4,5},{7}} => [6,3,2,5,4,1,7] => [3,2,5,4,6,1,7] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 14
{{1,7},{2,3,6},{4,5}} => [7,3,6,5,4,2,1] => [5,4,6,2,3,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
{{1},{2,3,6,7},{4,5}} => [1,3,6,5,4,7,2] => [1,5,4,7,2,3,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 6
{{1},{2,3,6},{4,5,7}} => [1,3,6,5,7,2,4] => [1,6,2,3,7,4,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
{{1},{2,3,6},{4,5},{7}} => [1,3,6,5,4,2,7] => [1,5,4,6,2,3,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 12
{{1,7},{2,3},{4,5,6}} => [7,3,2,5,6,4,1] => [3,2,6,4,5,7,1] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 9
{{1},{2,3,7},{4,5,6}} => [1,3,7,5,6,4,2] => [1,6,4,5,7,2,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
{{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
{{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => [1,3,2,6,4,5,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
{{1,7},{2,3},{4,5},{6}} => [7,3,2,5,4,6,1] => [3,2,5,4,6,7,1] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 14
{{1},{2,3,7},{4,5},{6}} => [1,3,7,5,4,6,2] => [1,5,4,6,7,2,3] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 12
{{1},{2,3},{4,5,7},{6}} => [1,3,2,5,7,6,4] => [1,3,2,6,7,4,5] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 10
{{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
{{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
{{1,6,7},{2,3},{4},{5}} => [6,3,2,4,5,7,1] => [3,2,4,5,7,1,6] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 12
{{1,6},{2,3,7},{4},{5}} => [6,3,7,4,5,1,2] => [4,5,6,1,7,2,3] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 15
{{1,6},{2,3},{4,7},{5}} => [6,3,2,7,5,1,4] => [3,2,5,6,1,7,4] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 14
{{1,6},{2,3},{4},{5,7}} => [6,3,2,4,7,1,5] => [3,2,4,6,1,7,5] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 13
{{1,6},{2,3},{4},{5},{7}} => [6,3,2,4,5,1,7] => [3,2,4,5,6,1,7] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 18
{{1,7},{2,3,6},{4},{5}} => [7,3,6,4,5,2,1] => [4,5,6,2,3,7,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 15
{{1},{2,3,6,7},{4},{5}} => [1,3,6,4,5,7,2] => [1,4,5,7,2,3,6] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 10
{{1},{2,3,6},{4,7},{5}} => [1,3,6,7,5,2,4] => [1,5,6,2,3,7,4] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 12
{{1},{2,3,6},{4},{5,7}} => [1,3,6,4,7,2,5] => [1,4,6,2,3,7,5] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 11
{{1},{2,3,6},{4},{5},{7}} => [1,3,6,4,5,2,7] => [1,4,5,6,2,3,7] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 16
{{1,7},{2,3},{4,6},{5}} => [7,3,2,6,5,4,1] => [3,2,5,6,4,7,1] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 14
{{1},{2,3,7},{4,6},{5}} => [1,3,7,6,5,4,2] => [1,5,6,4,7,2,3] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
{{1},{2,3},{4,6,7},{5}} => [1,3,2,6,5,7,4] => [1,3,2,5,7,4,6] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 9
{{1},{2,3},{4,6},{5,7}} => [1,3,2,6,7,4,5] => [1,3,2,6,4,7,5] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 10
{{1},{2,3},{4,6},{5},{7}} => [1,3,2,6,5,4,7] => [1,3,2,5,6,4,7] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 15
{{1,7},{2,3},{4},{5,6}} => [7,3,2,4,6,5,1] => [3,2,4,6,5,7,1] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 13
{{1},{2,3,7},{4},{5,6}} => [1,3,7,4,6,5,2] => [1,4,6,5,7,2,3] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 11
{{1},{2,3},{4,7},{5,6}} => [1,3,2,7,6,5,4] => [1,3,2,6,5,7,4] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 10
{{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
{{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
{{1,7},{2,3},{4},{5},{6}} => [7,3,2,4,5,6,1] => [3,2,4,5,6,7,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 18
{{1},{2,3,7},{4},{5},{6}} => [1,3,7,4,5,6,2] => [1,4,5,6,7,2,3] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 16
{{1},{2,3},{4,7},{5},{6}} => [1,3,2,7,5,6,4] => [1,3,2,5,6,7,4] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 15
{{1},{2,3},{4},{5,7},{6}} => [1,3,2,4,7,6,5] => [1,3,2,4,6,7,5] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 14
{{1},{2,3},{4},{5},{6,7}} => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
{{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 19
{{1,4,5,6,7},{2},{3}} => [4,2,3,5,6,7,1] => [2,3,7,1,4,5,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 5
{{1,4,5,6},{2,7},{3}} => [4,7,3,5,6,1,2] => [3,6,1,4,5,7,2] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 9
{{1,4,5,6},{2},{3,7}} => [4,2,7,5,6,1,3] => [2,6,1,4,5,7,3] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 8
{{1,4,5,6},{2},{3},{7}} => [4,2,3,5,6,1,7] => [2,3,6,1,4,5,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 11
{{1,4,5,7},{2,6},{3}} => [4,6,3,5,7,2,1] => [3,6,2,7,1,4,5] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 9
{{1,4,5},{2,6,7},{3}} => [4,6,3,5,1,7,2] => [3,5,1,4,7,2,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
{{1,4,5},{2,6},{3,7}} => [4,6,7,5,1,2,3] => [5,1,4,6,2,7,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
{{1,4,5},{2,6},{3},{7}} => [4,6,3,5,1,2,7] => [3,5,1,4,6,2,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 14
{{1,4,5,7},{2},{3,6}} => [4,2,6,5,7,3,1] => [2,6,3,7,1,4,5] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 8
{{1,4,5},{2,7},{3,6}} => [4,7,6,5,1,3,2] => [5,1,4,6,3,7,2] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
{{1,4,5},{2},{3,6,7}} => [4,2,6,5,1,7,3] => [2,5,1,4,7,3,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 7
{{1,4,5},{2},{3,6},{7}} => [4,2,6,5,1,3,7] => [2,5,1,4,6,3,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 13
{{1,4,5,7},{2},{3},{6}} => [4,2,3,5,7,6,1] => [2,3,6,7,1,4,5] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11
{{1,4,5},{2,7},{3},{6}} => [4,7,3,5,1,6,2] => [3,5,1,4,6,7,2] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 14
{{1,4,5},{2},{3,7},{6}} => [4,2,7,5,1,6,3] => [2,5,1,4,6,7,3] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 13
{{1,4,5},{2},{3},{6,7}} => [4,2,3,5,1,7,6] => [2,3,5,1,4,7,6] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 10
{{1,4,5},{2},{3},{6},{7}} => [4,2,3,5,1,6,7] => [2,3,5,1,4,6,7] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 16
{{1,4,6,7},{2,5},{3}} => [4,5,3,6,2,7,1] => [3,5,2,7,1,4,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
{{1,4,6},{2,5,7},{3}} => [4,5,3,6,7,1,2] => [3,6,1,4,7,2,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 9
{{1,4,6},{2,5},{3,7}} => [4,5,7,6,2,1,3] => [5,2,6,1,4,7,3] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
{{1,4,6},{2,5},{3},{7}} => [4,5,3,6,2,1,7] => [3,5,2,6,1,4,7] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 14
{{1,4,7},{2,5,6},{3}} => [4,5,3,7,6,2,1] => [3,6,2,5,7,1,4] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 9
{{1,4},{2,5,6,7},{3}} => [4,5,3,1,6,7,2] => [3,4,1,7,2,5,6] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
{{1,4},{2,5,6},{3,7}} => [4,5,7,1,6,2,3] => [4,1,6,2,5,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 10
{{1,4},{2,5,6},{3},{7}} => [4,5,3,1,6,2,7] => [3,4,1,6,2,5,7] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 13
{{1,4,7},{2,5},{3,6}} => [4,5,6,7,2,3,1] => [5,2,6,3,7,1,4] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11
{{1,4},{2,5,7},{3,6}} => [4,5,6,1,7,3,2] => [4,1,6,3,7,2,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 10
{{1,4},{2,5},{3,6,7}} => [4,5,6,1,2,7,3] => [4,1,5,2,7,3,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 9
{{1,4},{2,5},{3,6},{7}} => [4,5,6,1,2,3,7] => [4,1,5,2,6,3,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 15
{{1,4,7},{2,5},{3},{6}} => [4,5,3,7,2,6,1] => [3,5,2,6,7,1,4] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 14
{{1,4},{2,5,7},{3},{6}} => [4,5,3,1,7,6,2] => [3,4,1,6,7,2,5] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 13
{{1,4},{2,5},{3,7},{6}} => [4,5,7,1,2,6,3] => [4,1,5,2,6,7,3] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 15
{{1,4},{2,5},{3},{6,7}} => [4,5,3,1,2,7,6] => [3,4,1,5,2,7,6] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 12
{{1,4},{2,5},{3},{6},{7}} => [4,5,3,1,2,6,7] => [3,4,1,5,2,6,7] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 18
{{1,4,6,7},{2},{3,5}} => [4,2,5,6,3,7,1] => [2,5,3,7,1,4,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 7
{{1,4,6},{2,7},{3,5}} => [4,7,5,6,3,1,2] => [5,3,6,1,4,7,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
{{1,4,6},{2},{3,5,7}} => [4,2,5,6,7,1,3] => [2,6,1,4,7,3,5] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 8
{{1,4,6},{2},{3,5},{7}} => [4,2,5,6,3,1,7] => [2,5,3,6,1,4,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 13
{{1,4,7},{2,6},{3,5}} => [4,6,5,7,3,2,1] => [5,3,6,2,7,1,4] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11
{{1,4},{2,6,7},{3,5}} => [4,6,5,1,3,7,2] => [4,1,5,3,7,2,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 9
{{1,4},{2,6},{3,5,7}} => [4,6,5,1,7,2,3] => [4,1,6,2,7,3,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 10
{{1,4},{2,6},{3,5},{7}} => [4,6,5,1,3,2,7] => [4,1,5,3,6,2,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 15
{{1,4,7},{2},{3,5,6}} => [4,2,5,7,6,3,1] => [2,6,3,5,7,1,4] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 8
{{1,4},{2,7},{3,5,6}} => [4,7,5,1,6,3,2] => [4,1,6,3,5,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 10
{{1,4},{2},{3,5,6,7}} => [4,2,5,1,6,7,3] => [2,4,1,7,3,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 6
{{1,4},{2},{3,5,6},{7}} => [4,2,5,1,6,3,7] => [2,4,1,6,3,5,7] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 12
{{1,4,7},{2},{3,5},{6}} => [4,2,5,7,3,6,1] => [2,5,3,6,7,1,4] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 13
{{1,4},{2,7},{3,5},{6}} => [4,7,5,1,3,6,2] => [4,1,5,3,6,7,2] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 15
{{1,4},{2},{3,5,7},{6}} => [4,2,5,1,7,6,3] => [2,4,1,6,7,3,5] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 12
{{1,4},{2},{3,5},{6,7}} => [4,2,5,1,3,7,6] => [2,4,1,5,3,7,6] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 11
{{1,4},{2},{3,5},{6},{7}} => [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] => 17
{{1,4,6,7},{2},{3},{5}} => [4,2,3,6,5,7,1] => [2,3,5,7,1,4,6] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 10
{{1,4,6},{2,7},{3},{5}} => [4,7,3,6,5,1,2] => [3,5,6,1,4,7,2] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 14
{{1,4,6},{2},{3,7},{5}} => [4,2,7,6,5,1,3] => [2,5,6,1,4,7,3] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 13
{{1,4,6},{2},{3},{5,7}} => [4,2,3,6,7,1,5] => [2,3,6,1,4,7,5] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 11
{{1,4,6},{2},{3},{5},{7}} => [4,2,3,6,5,1,7] => [2,3,5,6,1,4,7] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 16
{{1,4,7},{2,6},{3},{5}} => [4,6,3,7,5,2,1] => [3,5,6,2,7,1,4] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 14
{{1,4},{2,6,7},{3},{5}} => [4,6,3,1,5,7,2] => [3,4,1,5,7,2,6] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 12
{{1,4},{2,6},{3,7},{5}} => [4,6,7,1,5,2,3] => [4,1,5,6,2,7,3] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 15
{{1,4},{2,6},{3},{5,7}} => [4,6,3,1,7,2,5] => [3,4,1,6,2,7,5] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 13
{{1,4},{2,6},{3},{5},{7}} => [4,6,3,1,5,2,7] => [3,4,1,5,6,2,7] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 18
{{1,4,7},{2},{3,6},{5}} => [4,2,6,7,5,3,1] => [2,5,6,3,7,1,4] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 13
{{1,4},{2,7},{3,6},{5}} => [4,7,6,1,5,3,2] => [4,1,5,6,3,7,2] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 15
{{1,4},{2},{3,6,7},{5}} => [4,2,6,1,5,7,3] => [2,4,1,5,7,3,6] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 11
{{1,4},{2},{3,6},{5,7}} => [4,2,6,1,7,3,5] => [2,4,1,6,3,7,5] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 12
{{1,4},{2},{3,6},{5},{7}} => [4,2,6,1,5,3,7] => [2,4,1,5,6,3,7] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 17
{{1,4,7},{2},{3},{5,6}} => [4,2,3,7,6,5,1] => [2,3,6,5,7,1,4] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 11
{{1,4},{2,7},{3},{5,6}} => [4,7,3,1,6,5,2] => [3,4,1,6,5,7,2] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 13
{{1,4},{2},{3,7},{5,6}} => [4,2,7,1,6,5,3] => [2,4,1,6,5,7,3] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 12
{{1,4},{2},{3},{5,6,7}} => [4,2,3,1,6,7,5] => [2,3,4,1,7,5,6] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 9
{{1,4},{2},{3},{5,6},{7}} => [4,2,3,1,6,5,7] => [2,3,4,1,6,5,7] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 15
{{1,4,7},{2},{3},{5},{6}} => [4,2,3,7,5,6,1] => [2,3,5,6,7,1,4] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 16
{{1,4},{2,7},{3},{5},{6}} => [4,7,3,1,5,6,2] => [3,4,1,5,6,7,2] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 18
{{1,4},{2},{3,7},{5},{6}} => [4,2,7,1,5,6,3] => [2,4,1,5,6,7,3] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 17
{{1,4},{2},{3},{5,7},{6}} => [4,2,3,1,7,6,5] => [2,3,4,1,6,7,5] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 15
{{1,4},{2},{3},{5},{6,7}} => [4,2,3,1,5,7,6] => [2,3,4,1,5,7,6] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 14
{{1,4},{2},{3},{5},{6},{7}} => [4,2,3,1,5,6,7] => [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 20
{{1,5,6,7},{2,4},{3}} => [5,4,3,2,6,7,1] => [3,4,2,7,1,5,6] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
{{1,5,6},{2,4,7},{3}} => [5,4,3,7,6,1,2] => [3,6,1,5,7,2,4] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 9
{{1,5,6},{2,4},{3,7}} => [5,4,7,2,6,1,3] => [4,2,6,1,5,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 10
{{1,5,6},{2,4},{3},{7}} => [5,4,3,2,6,1,7] => [3,4,2,6,1,5,7] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 13
{{1,5,7},{2,4,6},{3}} => [5,4,3,6,7,2,1] => [3,6,2,4,7,1,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 9
{{1,5},{2,4,6,7},{3}} => [5,4,3,6,1,7,2] => [3,5,1,7,2,4,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
{{1,5},{2,4,6},{3,7}} => [5,4,7,6,1,2,3] => [5,1,6,2,4,7,3] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
{{1,5},{2,4,6},{3},{7}} => [5,4,3,6,1,2,7] => [3,5,1,6,2,4,7] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 14
{{1,5,7},{2,4},{3,6}} => [5,4,6,2,7,3,1] => [4,2,6,3,7,1,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 10
{{1,5},{2,4,7},{3,6}} => [5,4,6,7,1,3,2] => [5,1,6,3,7,2,4] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11
{{1,5},{2,4},{3,6,7}} => [5,4,6,2,1,7,3] => [4,2,5,1,7,3,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 9
{{1,5},{2,4},{3,6},{7}} => [5,4,6,2,1,3,7] => [4,2,5,1,6,3,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 15
{{1,5,7},{2,4},{3},{6}} => [5,4,3,2,7,6,1] => [3,4,2,6,7,1,5] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 13
{{1,5},{2,4,7},{3},{6}} => [5,4,3,7,1,6,2] => [3,5,1,6,7,2,4] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 14
{{1,5},{2,4},{3,7},{6}} => [5,4,7,2,1,6,3] => [4,2,5,1,6,7,3] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 15
{{1,5},{2,4},{3},{6,7}} => [5,4,3,2,1,7,6] => [3,4,2,5,1,7,6] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 12
{{1,5},{2,4},{3},{6},{7}} => [5,4,3,2,1,6,7] => [3,4,2,5,1,6,7] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 18
{{1,6,7},{2,4,5},{3}} => [6,4,3,5,2,7,1] => [3,5,2,4,7,1,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
{{1,6},{2,4,5,7},{3}} => [6,4,3,5,7,1,2] => [3,6,1,7,2,4,5] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 9
{{1,6},{2,4,5},{3,7}} => [6,4,7,5,2,1,3] => [5,2,4,6,1,7,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
{{1,6},{2,4,5},{3},{7}} => [6,4,3,5,2,1,7] => [3,5,2,4,6,1,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 14
{{1,7},{2,4,5,6},{3}} => [7,4,3,5,6,2,1] => [3,6,2,4,5,7,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 9
{{1},{2,4,5,6,7},{3}} => [1,4,3,5,6,7,2] => [1,3,7,2,4,5,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 4
{{1},{2,4,5,6},{3,7}} => [1,4,7,5,6,2,3] => [1,6,2,4,5,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
{{1},{2,4,5,6},{3},{7}} => [1,4,3,5,6,2,7] => [1,3,6,2,4,5,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 10
{{1,7},{2,4,5},{3,6}} => [7,4,6,5,2,3,1] => [5,2,4,6,3,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
{{1},{2,4,5,7},{3,6}} => [1,4,6,5,7,3,2] => [1,6,3,7,2,4,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
{{1},{2,4,5},{3,6,7}} => [1,4,6,5,2,7,3] => [1,5,2,4,7,3,6] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 6
{{1},{2,4,5},{3,6},{7}} => [1,4,6,5,2,3,7] => [1,5,2,4,6,3,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 12
{{1,7},{2,4,5},{3},{6}} => [7,4,3,5,2,6,1] => [3,5,2,4,6,7,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 14
{{1},{2,4,5,7},{3},{6}} => [1,4,3,5,7,6,2] => [1,3,6,7,2,4,5] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 10
{{1},{2,4,5},{3,7},{6}} => [1,4,7,5,2,6,3] => [1,5,2,4,6,7,3] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 12
{{1},{2,4,5},{3},{6,7}} => [1,4,3,5,2,7,6] => [1,3,5,2,4,7,6] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 9
{{1},{2,4,5},{3},{6},{7}} => [1,4,3,5,2,6,7] => [1,3,5,2,4,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 15
{{1,6,7},{2,4},{3,5}} => [6,4,5,2,3,7,1] => [4,2,5,3,7,1,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 9
{{1,6},{2,4,7},{3,5}} => [6,4,5,7,3,1,2] => [5,3,6,1,7,2,4] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11
{{1,6},{2,4},{3,5,7}} => [6,4,5,2,7,1,3] => [4,2,6,1,7,3,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 10
{{1,6},{2,4},{3,5},{7}} => [6,4,5,2,3,1,7] => [4,2,5,3,6,1,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 15
{{1,7},{2,4,6},{3,5}} => [7,4,5,6,3,2,1] => [5,3,6,2,4,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
{{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => [1,5,3,7,2,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 6
{{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => [1,6,2,4,7,3,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
{{1},{2,4,6},{3,5},{7}} => [1,4,5,6,3,2,7] => [1,5,3,6,2,4,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 12
{{1,7},{2,4},{3,5,6}} => [7,4,5,2,6,3,1] => [4,2,6,3,5,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 10
{{1},{2,4,7},{3,5,6}} => [1,4,5,7,6,3,2] => [1,6,3,5,7,2,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
{{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => [1,4,2,7,3,5,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 5
{{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => [1,4,2,6,3,5,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 11
{{1,7},{2,4},{3,5},{6}} => [7,4,5,2,3,6,1] => [4,2,5,3,6,7,1] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 15
{{1},{2,4,7},{3,5},{6}} => [1,4,5,7,3,6,2] => [1,5,3,6,7,2,4] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 12
{{1},{2,4},{3,5,7},{6}} => [1,4,5,2,7,6,3] => [1,4,2,6,7,3,5] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 11
{{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => [1,4,2,5,3,7,6] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 10
{{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => [1,4,2,5,3,6,7] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 16
{{1,6,7},{2,4},{3},{5}} => [6,4,3,2,5,7,1] => [3,4,2,5,7,1,6] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 12
{{1,6},{2,4,7},{3},{5}} => [6,4,3,7,5,1,2] => [3,5,6,1,7,2,4] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 14
{{1,6},{2,4},{3,7},{5}} => [6,4,7,2,5,1,3] => [4,2,5,6,1,7,3] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 15
{{1,6},{2,4},{3},{5,7}} => [6,4,3,2,7,1,5] => [3,4,2,6,1,7,5] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 13
{{1,6},{2,4},{3},{5},{7}} => [6,4,3,2,5,1,7] => [3,4,2,5,6,1,7] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 18
{{1,7},{2,4,6},{3},{5}} => [7,4,3,6,5,2,1] => [3,5,6,2,4,7,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 14
{{1},{2,4,6,7},{3},{5}} => [1,4,3,6,5,7,2] => [1,3,5,7,2,4,6] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 9
{{1},{2,4,6},{3,7},{5}} => [1,4,7,6,5,2,3] => [1,5,6,2,4,7,3] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 12
{{1},{2,4,6},{3},{5,7}} => [1,4,3,6,7,2,5] => [1,3,6,2,4,7,5] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 10
{{1},{2,4,6},{3},{5},{7}} => [1,4,3,6,5,2,7] => [1,3,5,6,2,4,7] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 15
{{1,7},{2,4},{3,6},{5}} => [7,4,6,2,5,3,1] => [4,2,5,6,3,7,1] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 15
{{1},{2,4,7},{3,6},{5}} => [1,4,6,7,5,3,2] => [1,5,6,3,7,2,4] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
{{1},{2,4},{3,6,7},{5}} => [1,4,6,2,5,7,3] => [1,4,2,5,7,3,6] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 10
{{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => [1,4,2,6,3,7,5] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 11
{{1},{2,4},{3,6},{5},{7}} => [1,4,6,2,5,3,7] => [1,4,2,5,6,3,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 16
{{1,7},{2,4},{3},{5,6}} => [7,4,3,2,6,5,1] => [3,4,2,6,5,7,1] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 13
{{1},{2,4,7},{3},{5,6}} => [1,4,3,7,6,5,2] => [1,3,6,5,7,2,4] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 10
{{1},{2,4},{3,7},{5,6}} => [1,4,7,2,6,5,3] => [1,4,2,6,5,7,3] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 11
{{1},{2,4},{3},{5,6,7}} => [1,4,3,2,6,7,5] => [1,3,4,2,7,5,6] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 8
{{1},{2,4},{3},{5,6},{7}} => [1,4,3,2,6,5,7] => [1,3,4,2,6,5,7] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 14
{{1,7},{2,4},{3},{5},{6}} => [7,4,3,2,5,6,1] => [3,4,2,5,6,7,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 18
{{1},{2,4,7},{3},{5},{6}} => [1,4,3,7,5,6,2] => [1,3,5,6,7,2,4] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 15
{{1},{2,4},{3,7},{5},{6}} => [1,4,7,2,5,6,3] => [1,4,2,5,6,7,3] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 16
{{1},{2,4},{3},{5,7},{6}} => [1,4,3,2,7,6,5] => [1,3,4,2,6,7,5] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 14
{{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => [1,3,4,2,5,7,6] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 13
{{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 19
{{1,5,6,7},{2},{3,4}} => [5,2,4,3,6,7,1] => [2,4,3,7,1,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 6
{{1,5,6},{2,7},{3,4}} => [5,7,4,3,6,1,2] => [4,3,6,1,5,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 10
{{1,5,6},{2},{3,4,7}} => [5,2,4,7,6,1,3] => [2,6,1,5,7,3,4] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 8
{{1,5,6},{2},{3,4},{7}} => [5,2,4,3,6,1,7] => [2,4,3,6,1,5,7] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 12
{{1,5,7},{2,6},{3,4}} => [5,6,4,3,7,2,1] => [4,3,6,2,7,1,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 10
{{1,5},{2,6,7},{3,4}} => [5,6,4,3,1,7,2] => [4,3,5,1,7,2,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 9
{{1,5},{2,6},{3,4,7}} => [5,6,4,7,1,2,3] => [5,1,6,2,7,3,4] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11
{{1,5},{2,6},{3,4},{7}} => [5,6,4,3,1,2,7] => [4,3,5,1,6,2,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 15
{{1,5,7},{2},{3,4,6}} => [5,2,4,6,7,3,1] => [2,6,3,4,7,1,5] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 8
{{1,5},{2,7},{3,4,6}} => [5,7,4,6,1,3,2] => [5,1,6,3,4,7,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
{{1,5},{2},{3,4,6,7}} => [5,2,4,6,1,7,3] => [2,5,1,7,3,4,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 7
{{1,5},{2},{3,4,6},{7}} => [5,2,4,6,1,3,7] => [2,5,1,6,3,4,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 13
{{1,5,7},{2},{3,4},{6}} => [5,2,4,3,7,6,1] => [2,4,3,6,7,1,5] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 12
{{1,5},{2,7},{3,4},{6}} => [5,7,4,3,1,6,2] => [4,3,5,1,6,7,2] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 15
{{1,5},{2},{3,4,7},{6}} => [5,2,4,7,1,6,3] => [2,5,1,6,7,3,4] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 13
{{1,5},{2},{3,4},{6,7}} => [5,2,4,3,1,7,6] => [2,4,3,5,1,7,6] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 11
{{1,5},{2},{3,4},{6},{7}} => [5,2,4,3,1,6,7] => [2,4,3,5,1,6,7] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 17
{{1,6,7},{2,5},{3,4}} => [6,5,4,3,2,7,1] => [4,3,5,2,7,1,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 9
{{1,6},{2,5,7},{3,4}} => [6,5,4,3,7,1,2] => [4,3,6,1,7,2,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 10
{{1,6},{2,5},{3,4,7}} => [6,5,4,7,2,1,3] => [5,2,6,1,7,3,4] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11
{{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => [4,3,5,2,6,1,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 15
{{1,7},{2,5,6},{3,4}} => [7,5,4,3,6,2,1] => [4,3,6,2,5,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 10
{{1},{2,5,6,7},{3,4}} => [1,5,4,3,6,7,2] => [1,4,3,7,2,5,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 5
{{1},{2,5,6},{3,4,7}} => [1,5,4,7,6,2,3] => [1,6,2,5,7,3,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
{{1},{2,5,6},{3,4},{7}} => [1,5,4,3,6,2,7] => [1,4,3,6,2,5,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 11
{{1,7},{2,5},{3,4,6}} => [7,5,4,6,2,3,1] => [5,2,6,3,4,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
{{1},{2,5,7},{3,4,6}} => [1,5,4,6,7,3,2] => [1,6,3,4,7,2,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
{{1},{2,5},{3,4,6,7}} => [1,5,4,6,2,7,3] => [1,5,2,7,3,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 6
{{1},{2,5},{3,4,6},{7}} => [1,5,4,6,2,3,7] => [1,5,2,6,3,4,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 12
{{1,7},{2,5},{3,4},{6}} => [7,5,4,3,2,6,1] => [4,3,5,2,6,7,1] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 15
{{1},{2,5,7},{3,4},{6}} => [1,5,4,3,7,6,2] => [1,4,3,6,7,2,5] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 11
{{1},{2,5},{3,4,7},{6}} => [1,5,4,7,2,6,3] => [1,5,2,6,7,3,4] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 12
{{1},{2,5},{3,4},{6,7}} => [1,5,4,3,2,7,6] => [1,4,3,5,2,7,6] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 10
{{1},{2,5},{3,4},{6},{7}} => [1,5,4,3,2,6,7] => [1,4,3,5,2,6,7] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 16
{{1,6,7},{2},{3,4,5}} => [6,2,4,5,3,7,1] => [2,5,3,4,7,1,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 7
{{1,6},{2,7},{3,4,5}} => [6,7,4,5,3,1,2] => [5,3,4,6,1,7,2] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
{{1,6},{2},{3,4,5,7}} => [6,2,4,5,7,1,3] => [2,6,1,7,3,4,5] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 8
{{1,6},{2},{3,4,5},{7}} => [6,2,4,5,3,1,7] => [2,5,3,4,6,1,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 13
{{1,7},{2,6},{3,4,5}} => [7,6,4,5,3,2,1] => [5,3,4,6,2,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11
{{1},{2,6,7},{3,4,5}} => [1,6,4,5,3,7,2] => [1,5,3,4,7,2,6] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 6
{{1},{2,6},{3,4,5,7}} => [1,6,4,5,7,2,3] => [1,6,2,7,3,4,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
{{1},{2,6},{3,4,5},{7}} => [1,6,4,5,3,2,7] => [1,5,3,4,6,2,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 12
{{1,7},{2},{3,4,5,6}} => [7,2,4,5,6,3,1] => [2,6,3,4,5,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 8
{{1},{2,7},{3,4,5,6}} => [1,7,4,5,6,3,2] => [1,6,3,4,5,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
{{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
{{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
{{1,7},{2},{3,4,5},{6}} => [7,2,4,5,3,6,1] => [2,5,3,4,6,7,1] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 13
{{1},{2,7},{3,4,5},{6}} => [1,7,4,5,3,6,2] => [1,5,3,4,6,7,2] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 12
{{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => [1,2,6,7,3,4,5] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 9
{{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
{{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 14
{{1,6,7},{2},{3,4},{5}} => [6,2,4,3,5,7,1] => [2,4,3,5,7,1,6] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 11
{{1,6},{2,7},{3,4},{5}} => [6,7,4,3,5,1,2] => [4,3,5,6,1,7,2] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 15
{{1,6},{2},{3,4,7},{5}} => [6,2,4,7,5,1,3] => [2,5,6,1,7,3,4] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 13
{{1,6},{2},{3,4},{5,7}} => [6,2,4,3,7,1,5] => [2,4,3,6,1,7,5] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 12
{{1,6},{2},{3,4},{5},{7}} => [6,2,4,3,5,1,7] => [2,4,3,5,6,1,7] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 17
{{1,7},{2,6},{3,4},{5}} => [7,6,4,3,5,2,1] => [4,3,5,6,2,7,1] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 15
{{1},{2,6,7},{3,4},{5}} => [1,6,4,3,5,7,2] => [1,4,3,5,7,2,6] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 10
{{1},{2,6},{3,4,7},{5}} => [1,6,4,7,5,2,3] => [1,5,6,2,7,3,4] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
{{1},{2,6},{3,4},{5,7}} => [1,6,4,3,7,2,5] => [1,4,3,6,2,7,5] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 11
{{1},{2,6},{3,4},{5},{7}} => [1,6,4,3,5,2,7] => [1,4,3,5,6,2,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 16
{{1,7},{2},{3,4,6},{5}} => [7,2,4,6,5,3,1] => [2,5,6,3,4,7,1] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 13
{{1},{2,7},{3,4,6},{5}} => [1,7,4,6,5,3,2] => [1,5,6,3,4,7,2] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 12
{{1},{2},{3,4,6,7},{5}} => [1,2,4,6,5,7,3] => [1,2,5,7,3,4,6] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 8
{{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => [1,2,6,3,4,7,5] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 9
{{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => [1,2,5,6,3,4,7] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 14
{{1,7},{2},{3,4},{5,6}} => [7,2,4,3,6,5,1] => [2,4,3,6,5,7,1] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 12
{{1},{2,7},{3,4},{5,6}} => [1,7,4,3,6,5,2] => [1,4,3,6,5,7,2] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 11
{{1},{2},{3,4,7},{5,6}} => [1,2,4,7,6,5,3] => [1,2,6,5,7,3,4] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 9
{{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
{{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
{{1,7},{2},{3,4},{5},{6}} => [7,2,4,3,5,6,1] => [2,4,3,5,6,7,1] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 17
{{1},{2,7},{3,4},{5},{6}} => [1,7,4,3,5,6,2] => [1,4,3,5,6,7,2] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 16
{{1},{2},{3,4,7},{5},{6}} => [1,2,4,7,5,6,3] => [1,2,5,6,7,3,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 14
{{1},{2},{3,4},{5,7},{6}} => [1,2,4,3,7,6,5] => [1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 13
{{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
{{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 18
{{1,5,6,7},{2},{3},{4}} => [5,2,3,4,6,7,1] => [2,3,4,7,1,5,6] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 9
{{1,5,6},{2,7},{3},{4}} => [5,7,3,4,6,1,2] => [3,4,6,1,5,7,2] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 13
{{1,5,6},{2},{3,7},{4}} => [5,2,7,4,6,1,3] => [2,4,6,1,5,7,3] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 12
{{1,5,6},{2},{3},{4,7}} => [5,2,3,7,6,1,4] => [2,3,6,1,5,7,4] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 11
{{1,5,6},{2},{3},{4},{7}} => [5,2,3,4,6,1,7] => [2,3,4,6,1,5,7] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 15
{{1,5,7},{2,6},{3},{4}} => [5,6,3,4,7,2,1] => [3,4,6,2,7,1,5] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 13
{{1,5},{2,6,7},{3},{4}} => [5,6,3,4,1,7,2] => [3,4,5,1,7,2,6] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 12
{{1,5},{2,6},{3,7},{4}} => [5,6,7,4,1,2,3] => [4,5,1,6,2,7,3] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 15
{{1,5},{2,6},{3},{4,7}} => [5,6,3,7,1,2,4] => [3,5,1,6,2,7,4] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 14
{{1,5},{2,6},{3},{4},{7}} => [5,6,3,4,1,2,7] => [3,4,5,1,6,2,7] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 18
{{1,5,7},{2},{3,6},{4}} => [5,2,6,4,7,3,1] => [2,4,6,3,7,1,5] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 12
{{1,5},{2,7},{3,6},{4}} => [5,7,6,4,1,3,2] => [4,5,1,6,3,7,2] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 15
{{1,5},{2},{3,6,7},{4}} => [5,2,6,4,1,7,3] => [2,4,5,1,7,3,6] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 11
{{1,5},{2},{3,6},{4,7}} => [5,2,6,7,1,3,4] => [2,5,1,6,3,7,4] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 13
{{1,5},{2},{3,6},{4},{7}} => [5,2,6,4,1,3,7] => [2,4,5,1,6,3,7] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 17
{{1,5,7},{2},{3},{4,6}} => [5,2,3,6,7,4,1] => [2,3,6,4,7,1,5] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 11
{{1,5},{2,7},{3},{4,6}} => [5,7,3,6,1,4,2] => [3,5,1,6,4,7,2] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 14
{{1,5},{2},{3,7},{4,6}} => [5,2,7,6,1,4,3] => [2,5,1,6,4,7,3] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 13
{{1,5},{2},{3},{4,6,7}} => [5,2,3,6,1,7,4] => [2,3,5,1,7,4,6] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 10
{{1,5},{2},{3},{4,6},{7}} => [5,2,3,6,1,4,7] => [2,3,5,1,6,4,7] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 16
{{1,5,7},{2},{3},{4},{6}} => [5,2,3,4,7,6,1] => [2,3,4,6,7,1,5] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 15
{{1,5},{2,7},{3},{4},{6}} => [5,7,3,4,1,6,2] => [3,4,5,1,6,7,2] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 18
{{1,5},{2},{3,7},{4},{6}} => [5,2,7,4,1,6,3] => [2,4,5,1,6,7,3] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 17
{{1,5},{2},{3},{4,7},{6}} => [5,2,3,7,1,6,4] => [2,3,5,1,6,7,4] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 16
{{1,5},{2},{3},{4},{6,7}} => [5,2,3,4,1,7,6] => [2,3,4,5,1,7,6] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 14
{{1,5},{2},{3},{4},{6},{7}} => [5,2,3,4,1,6,7] => [2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 20
{{1,6,7},{2,5},{3},{4}} => [6,5,3,4,2,7,1] => [3,4,5,2,7,1,6] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 12
{{1,6},{2,5,7},{3},{4}} => [6,5,3,4,7,1,2] => [3,4,6,1,7,2,5] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 13
{{1,6},{2,5},{3,7},{4}} => [6,5,7,4,2,1,3] => [4,5,2,6,1,7,3] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 15
{{1,6},{2,5},{3},{4,7}} => [6,5,3,7,2,1,4] => [3,5,2,6,1,7,4] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 14
{{1,6},{2,5},{3},{4},{7}} => [6,5,3,4,2,1,7] => [3,4,5,2,6,1,7] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 18
{{1,7},{2,5,6},{3},{4}} => [7,5,3,4,6,2,1] => [3,4,6,2,5,7,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 13
{{1},{2,5,6,7},{3},{4}} => [1,5,3,4,6,7,2] => [1,3,4,7,2,5,6] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 8
{{1},{2,5,6},{3,7},{4}} => [1,5,7,4,6,2,3] => [1,4,6,2,5,7,3] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 11
{{1},{2,5,6},{3},{4,7}} => [1,5,3,7,6,2,4] => [1,3,6,2,5,7,4] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 10
{{1},{2,5,6},{3},{4},{7}} => [1,5,3,4,6,2,7] => [1,3,4,6,2,5,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 14
{{1,7},{2,5},{3,6},{4}} => [7,5,6,4,2,3,1] => [4,5,2,6,3,7,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 15
{{1},{2,5,7},{3,6},{4}} => [1,5,6,4,7,3,2] => [1,4,6,3,7,2,5] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 11
{{1},{2,5},{3,6,7},{4}} => [1,5,6,4,2,7,3] => [1,4,5,2,7,3,6] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 10
{{1},{2,5},{3,6},{4,7}} => [1,5,6,7,2,3,4] => [1,5,2,6,3,7,4] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 12
{{1},{2,5},{3,6},{4},{7}} => [1,5,6,4,2,3,7] => [1,4,5,2,6,3,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 16
{{1,7},{2,5},{3},{4,6}} => [7,5,3,6,2,4,1] => [3,5,2,6,4,7,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 14
{{1},{2,5,7},{3},{4,6}} => [1,5,3,6,7,4,2] => [1,3,6,4,7,2,5] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 10
{{1},{2,5},{3,7},{4,6}} => [1,5,7,6,2,4,3] => [1,5,2,6,4,7,3] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 12
{{1},{2,5},{3},{4,6,7}} => [1,5,3,6,2,7,4] => [1,3,5,2,7,4,6] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 9
{{1},{2,5},{3},{4,6},{7}} => [1,5,3,6,2,4,7] => [1,3,5,2,6,4,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 15
{{1,7},{2,5},{3},{4},{6}} => [7,5,3,4,2,6,1] => [3,4,5,2,6,7,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 18
{{1},{2,5,7},{3},{4},{6}} => [1,5,3,4,7,6,2] => [1,3,4,6,7,2,5] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 14
{{1},{2,5},{3,7},{4},{6}} => [1,5,7,4,2,6,3] => [1,4,5,2,6,7,3] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 16
{{1},{2,5},{3},{4,7},{6}} => [1,5,3,7,2,6,4] => [1,3,5,2,6,7,4] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 15
{{1},{2,5},{3},{4},{6,7}} => [1,5,3,4,2,7,6] => [1,3,4,5,2,7,6] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 13
{{1},{2,5},{3},{4},{6},{7}} => [1,5,3,4,2,6,7] => [1,3,4,5,2,6,7] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 19
{{1,6,7},{2},{3,5},{4}} => [6,2,5,4,3,7,1] => [2,4,5,3,7,1,6] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 11
{{1,6},{2,7},{3,5},{4}} => [6,7,5,4,3,1,2] => [4,5,3,6,1,7,2] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 15
{{1,6},{2},{3,5,7},{4}} => [6,2,5,4,7,1,3] => [2,4,6,1,7,3,5] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 12
{{1,6},{2},{3,5},{4,7}} => [6,2,5,7,3,1,4] => [2,5,3,6,1,7,4] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 13
{{1,6},{2},{3,5},{4},{7}} => [6,2,5,4,3,1,7] => [2,4,5,3,6,1,7] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 17
{{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => [4,5,3,6,2,7,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 15
{{1},{2,6,7},{3,5},{4}} => [1,6,5,4,3,7,2] => [1,4,5,3,7,2,6] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 10
{{1},{2,6},{3,5,7},{4}} => [1,6,5,4,7,2,3] => [1,4,6,2,7,3,5] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 11
{{1},{2,6},{3,5},{4,7}} => [1,6,5,7,3,2,4] => [1,5,3,6,2,7,4] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 12
{{1},{2,6},{3,5},{4},{7}} => [1,6,5,4,3,2,7] => [1,4,5,3,6,2,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 16
{{1,7},{2},{3,5,6},{4}} => [7,2,5,4,6,3,1] => [2,4,6,3,5,7,1] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 12
{{1},{2,7},{3,5,6},{4}} => [1,7,5,4,6,3,2] => [1,4,6,3,5,7,2] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 11
{{1},{2},{3,5,6,7},{4}} => [1,2,5,4,6,7,3] => [1,2,4,7,3,5,6] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7
{{1},{2},{3,5,6},{4,7}} => [1,2,5,7,6,3,4] => [1,2,6,3,5,7,4] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 9
{{1},{2},{3,5,6},{4},{7}} => [1,2,5,4,6,3,7] => [1,2,4,6,3,5,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 13
{{1,7},{2},{3,5},{4,6}} => [7,2,5,6,3,4,1] => [2,5,3,6,4,7,1] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 13
{{1},{2,7},{3,5},{4,6}} => [1,7,5,6,3,4,2] => [1,5,3,6,4,7,2] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 12
{{1},{2},{3,5,7},{4,6}} => [1,2,5,6,7,4,3] => [1,2,6,4,7,3,5] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 9
{{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => [1,2,5,3,7,4,6] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 8
{{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => [1,2,5,3,6,4,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 14
{{1,7},{2},{3,5},{4},{6}} => [7,2,5,4,3,6,1] => [2,4,5,3,6,7,1] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 17
{{1},{2,7},{3,5},{4},{6}} => [1,7,5,4,3,6,2] => [1,4,5,3,6,7,2] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 16
{{1},{2},{3,5,7},{4},{6}} => [1,2,5,4,7,6,3] => [1,2,4,6,7,3,5] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 13
{{1},{2},{3,5},{4,7},{6}} => [1,2,5,7,3,6,4] => [1,2,5,3,6,7,4] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 14
{{1},{2},{3,5},{4},{6,7}} => [1,2,5,4,3,7,6] => [1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 12
{{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 18
{{1,6,7},{2},{3},{4,5}} => [6,2,3,5,4,7,1] => [2,3,5,4,7,1,6] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 10
{{1,6},{2,7},{3},{4,5}} => [6,7,3,5,4,1,2] => [3,5,4,6,1,7,2] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 14
{{1,6},{2},{3,7},{4,5}} => [6,2,7,5,4,1,3] => [2,5,4,6,1,7,3] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 13
{{1,6},{2},{3},{4,5,7}} => [6,2,3,5,7,1,4] => [2,3,6,1,7,4,5] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 11
{{1,6},{2},{3},{4,5},{7}} => [6,2,3,5,4,1,7] => [2,3,5,4,6,1,7] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 16
{{1,7},{2,6},{3},{4,5}} => [7,6,3,5,4,2,1] => [3,5,4,6,2,7,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 14
{{1},{2,6,7},{3},{4,5}} => [1,6,3,5,4,7,2] => [1,3,5,4,7,2,6] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 9
{{1},{2,6},{3,7},{4,5}} => [1,6,7,5,4,2,3] => [1,5,4,6,2,7,3] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 12
{{1},{2,6},{3},{4,5,7}} => [1,6,3,5,7,2,4] => [1,3,6,2,7,4,5] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 10
{{1},{2,6},{3},{4,5},{7}} => [1,6,3,5,4,2,7] => [1,3,5,4,6,2,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 15
{{1,7},{2},{3,6},{4,5}} => [7,2,6,5,4,3,1] => [2,5,4,6,3,7,1] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 13
{{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => [1,5,4,6,3,7,2] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 12
{{1},{2},{3,6,7},{4,5}} => [1,2,6,5,4,7,3] => [1,2,5,4,7,3,6] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 8
{{1},{2},{3,6},{4,5,7}} => [1,2,6,5,7,3,4] => [1,2,6,3,7,4,5] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 9
{{1},{2},{3,6},{4,5},{7}} => [1,2,6,5,4,3,7] => [1,2,5,4,6,3,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 14
{{1,7},{2},{3},{4,5,6}} => [7,2,3,5,6,4,1] => [2,3,6,4,5,7,1] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 11
{{1},{2,7},{3},{4,5,6}} => [1,7,3,5,6,4,2] => [1,3,6,4,5,7,2] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 10
{{1},{2},{3,7},{4,5,6}} => [1,2,7,5,6,4,3] => [1,2,6,4,5,7,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 9
{{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
{{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
{{1,7},{2},{3},{4,5},{6}} => [7,2,3,5,4,6,1] => [2,3,5,4,6,7,1] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 16
{{1},{2,7},{3},{4,5},{6}} => [1,7,3,5,4,6,2] => [1,3,5,4,6,7,2] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 15
{{1},{2},{3,7},{4,5},{6}} => [1,2,7,5,4,6,3] => [1,2,5,4,6,7,3] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 14
{{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => [1,2,3,6,7,4,5] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 12
{{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
{{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 17
{{1,6,7},{2},{3},{4},{5}} => [6,2,3,4,5,7,1] => [2,3,4,5,7,1,6] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 14
{{1,6},{2,7},{3},{4},{5}} => [6,7,3,4,5,1,2] => [3,4,5,6,1,7,2] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 18
{{1,6},{2},{3,7},{4},{5}} => [6,2,7,4,5,1,3] => [2,4,5,6,1,7,3] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 17
{{1,6},{2},{3},{4,7},{5}} => [6,2,3,7,5,1,4] => [2,3,5,6,1,7,4] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 16
{{1,6},{2},{3},{4},{5,7}} => [6,2,3,4,7,1,5] => [2,3,4,6,1,7,5] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 15
{{1,6},{2},{3},{4},{5},{7}} => [6,2,3,4,5,1,7] => [2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 20
{{1,7},{2,6},{3},{4},{5}} => [7,6,3,4,5,2,1] => [3,4,5,6,2,7,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 18
{{1},{2,6,7},{3},{4},{5}} => [1,6,3,4,5,7,2] => [1,3,4,5,7,2,6] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 13
{{1},{2,6},{3,7},{4},{5}} => [1,6,7,4,5,2,3] => [1,4,5,6,2,7,3] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 16
{{1},{2,6},{3},{4,7},{5}} => [1,6,3,7,5,2,4] => [1,3,5,6,2,7,4] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 15
{{1},{2,6},{3},{4},{5,7}} => [1,6,3,4,7,2,5] => [1,3,4,6,2,7,5] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 14
{{1},{2,6},{3},{4},{5},{7}} => [1,6,3,4,5,2,7] => [1,3,4,5,6,2,7] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 19
{{1,7},{2},{3,6},{4},{5}} => [7,2,6,4,5,3,1] => [2,4,5,6,3,7,1] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 17
{{1},{2,7},{3,6},{4},{5}} => [1,7,6,4,5,3,2] => [1,4,5,6,3,7,2] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 16
{{1},{2},{3,6,7},{4},{5}} => [1,2,6,4,5,7,3] => [1,2,4,5,7,3,6] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 12
{{1},{2},{3,6},{4,7},{5}} => [1,2,6,7,5,3,4] => [1,2,5,6,3,7,4] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 14
{{1},{2},{3,6},{4},{5,7}} => [1,2,6,4,7,3,5] => [1,2,4,6,3,7,5] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 13
{{1},{2},{3,6},{4},{5},{7}} => [1,2,6,4,5,3,7] => [1,2,4,5,6,3,7] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 18
{{1,7},{2},{3},{4,6},{5}} => [7,2,3,6,5,4,1] => [2,3,5,6,4,7,1] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 16
{{1},{2,7},{3},{4,6},{5}} => [1,7,3,6,5,4,2] => [1,3,5,6,4,7,2] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 15
{{1},{2},{3,7},{4,6},{5}} => [1,2,7,6,5,4,3] => [1,2,5,6,4,7,3] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 14
{{1},{2},{3},{4,6,7},{5}} => [1,2,3,6,5,7,4] => [1,2,3,5,7,4,6] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 11
{{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => [1,2,3,6,4,7,5] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 12
{{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 17
{{1,7},{2},{3},{4},{5,6}} => [7,2,3,4,6,5,1] => [2,3,4,6,5,7,1] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 15
{{1},{2,7},{3},{4},{5,6}} => [1,7,3,4,6,5,2] => [1,3,4,6,5,7,2] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 14
{{1},{2},{3,7},{4},{5,6}} => [1,2,7,4,6,5,3] => [1,2,4,6,5,7,3] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 13
{{1},{2},{3},{4,7},{5,6}} => [1,2,3,7,6,5,4] => [1,2,3,6,5,7,4] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 12
{{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
{{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 16
{{1,7},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,1] => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 20
{{1},{2,7},{3},{4},{5},{6}} => [1,7,3,4,5,6,2] => [1,3,4,5,6,7,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 19
{{1},{2},{3,7},{4},{5},{6}} => [1,2,7,4,5,6,3] => [1,2,4,5,6,7,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 18
{{1},{2},{3},{4,7},{5},{6}} => [1,2,3,7,5,6,4] => [1,2,3,5,6,7,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 17
{{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => [1,2,3,4,6,7,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 16
{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 15
{{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] => 21
{{1,2},{3,4},{5,6},{7,8}} => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
{{1,2},{3,5},{4,6},{7,8}} => [2,1,5,6,3,4,8,7] => [2,1,5,3,6,4,8,7] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 13
{{1,2},{3,6},{4,5},{7,8}} => [2,1,6,5,4,3,8,7] => [2,1,5,4,6,3,8,7] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 13
{{1,2},{3,7},{4,5},{6,8}} => [2,1,7,5,4,8,3,6] => [2,1,5,4,7,3,8,6] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 14
{{1,2},{3,8},{4,5},{6,7}} => [2,1,8,5,4,7,6,3] => [2,1,5,4,7,6,8,3] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 14
{{1,2},{3,8},{4,6},{5,7}} => [2,1,8,6,7,4,5,3] => [2,1,6,4,7,5,8,3] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 15
{{1,2},{3,7},{4,6},{5,8}} => [2,1,7,6,8,4,3,5] => [2,1,6,4,7,3,8,5] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 15
{{1,2},{3,6},{4,7},{5,8}} => [2,1,6,7,8,3,4,5] => [2,1,6,3,7,4,8,5] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 15
{{1,2},{3,5},{4,7},{6,8}} => [2,1,5,7,3,8,4,6] => [2,1,5,3,7,4,8,6] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 14
{{1,2},{3,4},{5,7},{6,8}} => [2,1,4,3,7,8,5,6] => [2,1,4,3,7,5,8,6] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 13
{{1,2},{3,4},{5,8},{6,7}} => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,6,8,5] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 13
{{1,2},{3,5},{4,8},{6,7}} => [2,1,5,8,3,7,6,4] => [2,1,5,3,7,6,8,4] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 14
{{1,2},{3,6},{4,8},{5,7}} => [2,1,6,8,7,3,5,4] => [2,1,6,3,7,5,8,4] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 15
{{1,2},{3,7},{4,8},{5,6}} => [2,1,7,8,6,5,3,4] => [2,1,6,5,7,3,8,4] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 15
{{1,2},{3,8},{4,7},{5,6}} => [2,1,8,7,6,5,4,3] => [2,1,6,5,7,4,8,3] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 15
{{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] => 28
{{1},{2},{3},{4},{5},{6},{7,8}} => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 21
{{1},{2},{3},{4},{5},{6,8},{7}} => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,8,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 22
{{1},{2},{3},{4},{5},{6,7,8}} => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
{{1},{2},{3},{4},{5,8},{6},{7}} => [1,2,3,4,8,6,7,5] => [1,2,3,4,6,7,8,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 23
{{1},{2},{3},{4},{5,7,8},{6}} => [1,2,3,4,7,6,8,5] => [1,2,3,4,6,8,5,7] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 16
{{1},{2},{3},{4},{5,8},{6,7}} => [1,2,3,4,8,7,6,5] => [1,2,3,4,7,6,8,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 17
{{1},{2},{3},{4},{5,6,8},{7}} => [1,2,3,4,6,8,7,5] => [1,2,3,4,7,8,5,6] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 17
{{1},{2},{3},{4},{5,6,7,8}} => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,5,6,7] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
{{1},{2},{3},{4,8},{5},{6},{7}} => [1,2,3,8,5,6,7,4] => [1,2,3,5,6,7,8,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 24
{{1},{2},{3},{4,6,8},{5},{7}} => [1,2,3,6,5,8,7,4] => [1,2,3,5,7,8,4,6] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 18
{{1},{2},{3},{4,6,7,8},{5}} => [1,2,3,6,5,7,8,4] => [1,2,3,5,8,4,6,7] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 11
{{1},{2},{3},{4,7,8},{5,6}} => [1,2,3,7,6,5,8,4] => [1,2,3,6,5,8,4,7] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 12
{{1},{2},{3},{4,5,8},{6},{7}} => [1,2,3,5,8,6,7,4] => [1,2,3,6,7,8,4,5] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 19
{{1},{2},{3},{4,8},{5,6,7}} => [1,2,3,8,6,7,5,4] => [1,2,3,7,5,6,8,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 13
{{1},{2},{3},{4,5,6,8},{7}} => [1,2,3,5,6,8,7,4] => [1,2,3,7,8,4,5,6] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 13
{{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
{{1},{2},{3,4},{5,6},{7},{8}} => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
{{1},{2},{3,4},{5,8},{6,7}} => [1,2,4,3,8,7,6,5] => [1,2,4,3,7,6,8,5] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 14
{{1},{2},{3,4},{5,6,7,8}} => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,5,6,7] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
{{1},{2},{3,5},{4},{6,7,8}} => [1,2,5,4,3,7,8,6] => [1,2,4,5,3,8,6,7] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 12
{{1},{2},{3,8},{4},{5},{6},{7}} => [1,2,8,4,5,6,7,3] => [1,2,4,5,6,7,8,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 25
{{1},{2},{3,7,8},{4},{5,6}} => [1,2,7,4,6,5,8,3] => [1,2,4,6,5,8,3,7] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 13
{{1},{2},{3,5,8},{4},{6},{7}} => [1,2,5,4,8,6,7,3] => [1,2,4,6,7,8,3,5] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 20
{{1},{2},{3,5,7,8},{4},{6}} => [1,2,5,4,7,6,8,3] => [1,2,4,6,8,3,5,7] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 13
{{1},{2},{3,8},{4},{5,6,7}} => [1,2,8,4,6,7,5,3] => [1,2,4,7,5,6,8,3] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 14
{{1},{2},{3,5,8},{4},{6,7}} => [1,2,5,4,8,7,6,3] => [1,2,4,7,6,8,3,5] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 14
{{1},{2},{3,5,6,7,8},{4}} => [1,2,5,4,6,7,8,3] => [1,2,4,8,3,5,6,7] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 7
{{1},{2},{3,4,5},{6,7,8}} => [1,2,4,5,3,7,8,6] => [1,2,5,3,4,8,6,7] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
{{1},{2},{3,6,7,8},{4,5}} => [1,2,6,5,4,7,8,3] => [1,2,5,4,8,3,6,7] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
{{1},{2},{3,4,8},{5},{6},{7}} => [1,2,4,8,5,6,7,3] => [1,2,5,6,7,8,3,4] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 21
{{1},{2},{3,8},{4,6,7},{5}} => [1,2,8,6,5,7,4,3] => [1,2,5,7,4,6,8,3] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 15
{{1},{2},{3,4,5,6},{7,8}} => [1,2,4,5,6,3,8,7] => [1,2,6,3,4,5,8,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
{{1},{2},{3,7,8},{4,5,6}} => [1,2,7,5,6,4,8,3] => [1,2,6,4,5,8,3,7] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 9
{{1},{2},{3,4,7,8},{5,6}} => [1,2,4,7,6,5,8,3] => [1,2,6,5,8,3,4,7] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 9
{{1},{2},{3,4,5,8},{6},{7}} => [1,2,4,5,8,6,7,3] => [1,2,6,7,8,3,4,5] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 16
{{1},{2},{3,4,5,6,7},{8}} => [1,2,4,5,6,7,3,8] => [1,2,7,3,4,5,6,8] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
{{1},{2},{3,8},{4,5,6,7}} => [1,2,8,5,6,7,4,3] => [1,2,7,4,5,6,8,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10
{{1},{2},{3,4,8},{5,6,7}} => [1,2,4,8,6,7,5,3] => [1,2,7,5,6,8,3,4] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10
{{1},{2},{3,4,5,8},{6,7}} => [1,2,4,5,8,7,6,3] => [1,2,7,6,8,3,4,5] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10
{{1},{2},{3,4,5,6,8},{7}} => [1,2,4,5,6,8,7,3] => [1,2,7,8,3,4,5,6] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10
{{1},{2},{3,4,5,6,7,8}} => [1,2,4,5,6,7,8,3] => [1,2,8,3,4,5,6,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
{{1},{2,3},{4},{5},{6,7},{8}} => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
{{1},{2,3},{4},{5,8},{6,7}} => [1,3,2,4,8,7,6,5] => [1,3,2,4,7,6,8,5] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 15
{{1},{2,3},{4},{5,6,7,8}} => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,5,6,7] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
{{1},{2,3},{4,5},{6,7},{8}} => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
{{1},{2,3},{4,5},{6,8},{7}} => [1,3,2,5,4,8,7,6] => [1,3,2,5,4,7,8,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 16
{{1},{2,3},{4,5},{6,7,8}} => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,6,7] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
{{1},{2,3},{4,6,7},{5},{8}} => [1,3,2,6,5,7,4,8] => [1,3,2,5,7,4,6,8] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 16
{{1},{2,3},{4,6,8},{5},{7}} => [1,3,2,6,5,8,7,4] => [1,3,2,5,7,8,4,6] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 16
{{1},{2,3},{4,6,7,8},{5}} => [1,3,2,6,5,7,8,4] => [1,3,2,5,8,4,6,7] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 9
{{1},{2,3},{4,7},{5,6},{8}} => [1,3,2,7,6,5,4,8] => [1,3,2,6,5,7,4,8] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 17
{{1},{2,3},{4,8},{5,6},{7}} => [1,3,2,8,6,5,7,4] => [1,3,2,6,5,7,8,4] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 17
{{1},{2,3},{4,7,8},{5,6}} => [1,3,2,7,6,5,8,4] => [1,3,2,6,5,8,4,7] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 10
{{1},{2,3},{4,8},{5,7},{6}} => [1,3,2,8,7,6,5,4] => [1,3,2,6,7,5,8,4] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 17
{{1},{2,3},{4,5,8},{6},{7}} => [1,3,2,5,8,6,7,4] => [1,3,2,6,7,8,4,5] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 17
{{1},{2,3},{4,8},{5,6,7}} => [1,3,2,8,6,7,5,4] => [1,3,2,7,5,6,8,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 11
{{1},{2,3},{4,5,8},{6,7}} => [1,3,2,5,8,7,6,4] => [1,3,2,7,6,8,4,5] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 11
{{1},{2,3},{4,5,6,7,8}} => [1,3,2,5,6,7,8,4] => [1,3,2,8,4,5,6,7] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
{{1},{2,4},{3},{5},{6},{7,8}} => [1,4,3,2,5,6,8,7] => [1,3,4,2,5,6,8,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 19
{{1},{2,4},{3},{5},{6,8},{7}} => [1,4,3,2,5,8,7,6] => [1,3,4,2,5,7,8,6] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 20
{{1},{2,4},{3},{5},{6,7,8}} => [1,4,3,2,5,7,8,6] => [1,3,4,2,5,8,6,7] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 13
{{1},{2,4},{3},{5,6},{7,8}} => [1,4,3,2,6,5,8,7] => [1,3,4,2,6,5,8,7] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 14
{{1},{2,4},{3},{5,7},{6},{8}} => [1,4,3,2,7,6,5,8] => [1,3,4,2,6,7,5,8] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 21
{{1},{2,4},{3},{5,8},{6,7}} => [1,4,3,2,8,7,6,5] => [1,3,4,2,7,6,8,5] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 15
{{1},{2,4},{3},{5,6,7,8}} => [1,4,3,2,6,7,8,5] => [1,3,4,2,8,5,6,7] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 8
{{1},{2,5},{3},{4},{6,8},{7}} => [1,5,3,4,2,8,7,6] => [1,3,4,5,2,7,8,6] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 20
{{1},{2,8},{3},{4},{5},{6},{7}} => [1,8,3,4,5,6,7,2] => [1,3,4,5,6,7,8,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 26
{{1},{2,5,6,7,8},{3},{4}} => [1,5,3,4,6,7,8,2] => [1,3,4,8,2,5,6,7] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 8
{{1},{2,4,5},{3},{6,7},{8}} => [1,4,3,5,2,7,6,8] => [1,3,5,2,4,7,6,8] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 16
{{1},{2,4,5},{3},{6,8},{7}} => [1,4,3,5,2,8,7,6] => [1,3,5,2,4,7,8,6] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 16
{{1},{2,4,5},{3},{6,7,8}} => [1,4,3,5,2,7,8,6] => [1,3,5,2,4,8,6,7] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 9
{{1},{2,6,8},{3},{4,5},{7}} => [1,6,3,5,4,8,7,2] => [1,3,5,4,7,8,2,6] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 16
{{1},{2,6,7,8},{3},{4,5}} => [1,6,3,5,4,7,8,2] => [1,3,5,4,8,2,6,7] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 9
{{1},{2,4,8},{3},{5},{6},{7}} => [1,4,3,8,5,6,7,2] => [1,3,5,6,7,8,2,4] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 22
{{1},{2,4,6,7},{3},{5},{8}} => [1,4,3,6,5,7,2,8] => [1,3,5,7,2,4,6,8] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 16
{{1},{2,8},{3},{4,6,7},{5}} => [1,8,3,6,5,7,4,2] => [1,3,5,7,4,6,8,2] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 16
{{1},{2,4,8},{3},{5},{6,7}} => [1,4,3,8,5,7,6,2] => [1,3,5,7,6,8,2,4] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 16
{{1},{2,4,6,8},{3},{5},{7}} => [1,4,3,6,5,8,7,2] => [1,3,5,7,8,2,4,6] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 16
{{1},{2,4,6,7,8},{3},{5}} => [1,4,3,6,5,7,8,2] => [1,3,5,8,2,4,6,7] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 9
{{1},{2,7,8},{3},{4,5,6}} => [1,7,3,5,6,4,8,2] => [1,3,6,4,5,8,2,7] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
{{1},{2,4,7},{3},{5,6},{8}} => [1,4,3,7,6,5,2,8] => [1,3,6,5,7,2,4,8] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 17
{{1},{2,8},{3},{4,7},{5,6}} => [1,8,3,7,6,5,4,2] => [1,3,6,5,7,4,8,2] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 17
{{1},{2,4,8},{3},{5,6},{7}} => [1,4,3,8,6,5,7,2] => [1,3,6,5,7,8,2,4] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 17
{{1},{2,4,8},{3},{5,7},{6}} => [1,4,3,8,7,6,5,2] => [1,3,6,7,5,8,2,4] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 17
{{1},{2,4,8},{3},{5,6,7}} => [1,4,3,8,6,7,5,2] => [1,3,7,5,6,8,2,4] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
{{1},{2,4,5,6,8},{3},{7}} => [1,4,3,5,6,8,7,2] => [1,3,7,8,2,4,5,6] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 11
{{1},{2,4,5,6,7,8},{3}} => [1,4,3,5,6,7,8,2] => [1,3,8,2,4,5,6,7] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 4
{{1},{2,3,4},{5},{6,7,8}} => [1,3,4,2,5,7,8,6] => [1,4,2,3,5,8,6,7] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
{{1},{2,3,4},{5,6},{7,8}} => [1,3,4,2,6,5,8,7] => [1,4,2,3,6,5,8,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
{{1},{2,3,4},{5,6,7},{8}} => [1,3,4,2,6,7,5,8] => [1,4,2,3,7,5,6,8] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
{{1},{2,3,4},{5,8},{6,7}} => [1,3,4,2,8,7,6,5] => [1,4,2,3,7,6,8,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 12
{{1},{2,3,4},{5,6,8},{7}} => [1,3,4,2,6,8,7,5] => [1,4,2,3,7,8,5,6] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 12
{{1},{2,5},{3,4},{6,7},{8}} => [1,5,4,3,2,7,6,8] => [1,4,3,5,2,7,6,8] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 17
{{1},{2,5},{3,4},{6,8},{7}} => [1,5,4,3,2,8,7,6] => [1,4,3,5,2,7,8,6] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 17
{{1},{2,5},{3,4},{6,7,8}} => [1,5,4,3,2,7,8,6] => [1,4,3,5,2,8,6,7] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 10
{{1},{2,6,8},{3,4},{5},{7}} => [1,6,4,3,5,8,7,2] => [1,4,3,5,7,8,2,6] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 17
{{1},{2,7},{3,4},{5,6},{8}} => [1,7,4,3,6,5,2,8] => [1,4,3,6,5,7,2,8] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 18
{{1},{2,8},{3,4},{5,6},{7}} => [1,8,4,3,6,5,7,2] => [1,4,3,6,5,7,8,2] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 18
{{1},{2,7,8},{3,4},{5,6}} => [1,7,4,3,6,5,8,2] => [1,4,3,6,5,8,2,7] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 11
{{1},{2,8},{3,4},{5,7},{6}} => [1,8,4,3,7,6,5,2] => [1,4,3,6,7,5,8,2] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 18
{{1},{2,5,8},{3,4},{6,7}} => [1,5,4,3,8,7,6,2] => [1,4,3,7,6,8,2,5] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 12
{{1},{2,5,6,7,8},{3,4}} => [1,5,4,3,6,7,8,2] => [1,4,3,8,2,5,6,7] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 5
{{1},{2,3,5},{4},{6,7,8}} => [1,3,5,4,2,7,8,6] => [1,4,5,2,3,8,6,7] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 10
{{1},{2,6,7},{3,5},{4},{8}} => [1,6,5,4,3,7,2,8] => [1,4,5,3,7,2,6,8] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 17
{{1},{2,6,8},{3,5},{4},{7}} => [1,6,5,4,3,8,7,2] => [1,4,5,3,7,8,2,6] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 17
{{1},{2,6,7,8},{3,5},{4}} => [1,6,5,4,3,7,8,2] => [1,4,5,3,8,2,6,7] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 10
{{1},{2,3,8},{4},{5},{6},{7}} => [1,3,8,4,5,6,7,2] => [1,4,5,6,7,8,2,3] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 23
{{1},{2,3,7,8},{4},{5},{6}} => [1,3,7,4,5,6,8,2] => [1,4,5,6,8,2,3,7] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 16
{{1},{2,3,6,7},{4},{5},{8}} => [1,3,6,4,5,7,2,8] => [1,4,5,7,2,3,6,8] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 17
{{1},{2,3,6,8},{4},{5},{7}} => [1,3,6,4,5,8,7,2] => [1,4,5,7,8,2,3,6] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 17
{{1},{2,8},{3,5,6},{4},{7}} => [1,8,5,4,6,3,7,2] => [1,4,6,3,5,7,8,2] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 18
{{1},{2,3,7},{4},{5,6},{8}} => [1,3,7,4,6,5,2,8] => [1,4,6,5,7,2,3,8] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 18
{{1},{2,8},{3,7},{4},{5,6}} => [1,8,7,4,6,5,3,2] => [1,4,6,5,7,3,8,2] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 18
{{1},{2,3,5,7},{4},{6},{8}} => [1,3,5,4,7,6,2,8] => [1,4,6,7,2,3,5,8] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 18
{{1},{2,8},{3,5,7},{4},{6}} => [1,8,5,4,7,6,3,2] => [1,4,6,7,3,5,8,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 18
{{1},{2,3,5,7,8},{4},{6}} => [1,3,5,4,7,6,8,2] => [1,4,6,8,2,3,5,7] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 11
{{1},{2,3,5,6,7},{4},{8}} => [1,3,5,4,6,7,2,8] => [1,4,7,2,3,5,6,8] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 12
{{1},{2,8},{3,5,6,7},{4}} => [1,8,5,4,6,7,3,2] => [1,4,7,3,5,6,8,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 12
{{1},{2,3,8},{4},{5,6,7}} => [1,3,8,4,6,7,5,2] => [1,4,7,5,6,8,2,3] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 12
{{1},{2,3,5,8},{4},{6,7}} => [1,3,5,4,8,7,6,2] => [1,4,7,6,8,2,3,5] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 12
{{1},{2,3,5,6,8},{4},{7}} => [1,3,5,4,6,8,7,2] => [1,4,7,8,2,3,5,6] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 12
{{1},{2,3,5,6,7,8},{4}} => [1,3,5,4,6,7,8,2] => [1,4,8,2,3,5,6,7] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 5
{{1},{2,6,8},{3,4,5},{7}} => [1,6,4,5,3,8,7,2] => [1,5,3,4,7,8,2,6] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 13
{{1},{2,7},{3,6},{4,5},{8}} => [1,7,6,5,4,3,2,8] => [1,5,4,6,3,7,2,8] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 19
{{1},{2,8},{3,6},{4,5},{7}} => [1,8,6,5,4,3,7,2] => [1,5,4,6,3,7,8,2] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 19
{{1},{2,7,8},{3,6},{4,5}} => [1,7,6,5,4,3,8,2] => [1,5,4,6,3,8,2,7] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 12
{{1},{2,8},{3,7},{4,5},{6}} => [1,8,7,5,4,6,3,2] => [1,5,4,6,7,3,8,2] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 19
{{1},{2,3,8},{4,5},{6},{7}} => [1,3,8,5,4,6,7,2] => [1,5,4,6,7,8,2,3] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 19
{{1},{2,8},{3,6,7},{4,5}} => [1,8,6,5,4,7,3,2] => [1,5,4,7,3,6,8,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 13
{{1},{2,3,8},{4,5},{6,7}} => [1,3,8,5,4,7,6,2] => [1,5,4,7,6,8,2,3] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
{{1},{2,3,4,6},{5},{7,8}} => [1,3,4,6,5,2,8,7] => [1,5,6,2,3,4,8,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 12
{{1},{2,8},{3,4,6},{5},{7}} => [1,8,4,6,5,3,7,2] => [1,5,6,3,4,7,8,2] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 19
{{1},{2,7,8},{3,4,6},{5}} => [1,7,4,6,5,3,8,2] => [1,5,6,3,4,8,2,7] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 12
{{1},{2,8},{3,7},{4,6},{5}} => [1,8,7,6,5,4,3,2] => [1,5,6,4,7,3,8,2] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 19
{{1},{2,3,4,8},{5},{6},{7}} => [1,3,4,8,5,6,7,2] => [1,5,6,7,8,2,3,4] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 19
{{1},{2,3,4,7,8},{5},{6}} => [1,3,4,7,5,6,8,2] => [1,5,6,8,2,3,4,7] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 12
{{1},{2,8},{3,4,6,7},{5}} => [1,8,4,6,5,7,3,2] => [1,5,7,3,4,6,8,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 13
{{1},{2,3,4,6,8},{5},{7}} => [1,3,4,6,5,8,7,2] => [1,5,7,8,2,3,4,6] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 13
{{1},{2,8},{3,7},{4,5,6}} => [1,8,7,5,6,4,3,2] => [1,6,4,5,7,3,8,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 14
{{1},{2,3,8},{4,5,6},{7}} => [1,3,8,5,6,4,7,2] => [1,6,4,5,7,8,2,3] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14
{{1},{2,8},{3,4,7},{5,6}} => [1,8,4,7,6,5,3,2] => [1,6,5,7,3,4,8,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
{{1},{2,3,4,8},{5,6},{7}} => [1,3,4,8,6,5,7,2] => [1,6,5,7,8,2,3,4] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 14
{{1},{2,3,4,5,7},{6},{8}} => [1,3,4,5,7,6,2,8] => [1,6,7,2,3,4,5,8] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
{{1},{2,8},{3,4,5,7},{6}} => [1,8,4,5,7,6,3,2] => [1,6,7,3,4,5,8,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 14
{{1},{2,3,4,8},{5,7},{6}} => [1,3,4,8,7,6,5,2] => [1,6,7,5,8,2,3,4] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 14
{{1},{2,3,4,5,8},{6},{7}} => [1,3,4,5,8,6,7,2] => [1,6,7,8,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 14
{{1},{2,3,4,5,7,8},{6}} => [1,3,4,5,7,6,8,2] => [1,6,8,2,3,4,5,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 7
{{1},{2,8},{3,4,5,6,7}} => [1,8,4,5,6,7,3,2] => [1,7,3,4,5,6,8,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 8
{{1},{2,3,4,5,8},{6,7}} => [1,3,4,5,8,7,6,2] => [1,7,6,8,2,3,4,5] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 8
{{1},{2,3,4,5,6,8},{7}} => [1,3,4,5,6,8,7,2] => [1,7,8,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 8
{{1},{2,3,4,5,6,7,8}} => [1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
{{1,2},{3},{4},{5},{6},{7},{8}} => [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] => 27
{{1,2},{3},{4},{5},{6},{7,8}} => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 20
{{1,2},{3},{4},{5,6},{7},{8}} => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 22
{{1,2},{3},{4},{5,8},{6,7}} => [2,1,3,4,8,7,6,5] => [2,1,3,4,7,6,8,5] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 16
{{1,2},{3},{4},{5,6,7,8}} => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,5,6,7] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
{{1,2},{3},{4,5},{6},{7},{8}} => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 23
{{1,2},{3},{4,6,7,8},{5}} => [2,1,3,6,5,7,8,4] => [2,1,3,5,8,4,6,7] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 10
{{1,2},{3},{4,5,6},{7,8}} => [2,1,3,5,6,4,8,7] => [2,1,3,6,4,5,8,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
{{1,2},{3},{4,5,6,8},{7}} => [2,1,3,5,6,8,7,4] => [2,1,3,7,8,4,5,6] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 12
{{1,2},{3,4},{5},{6},{7},{8}} => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 24
{{1,2},{3,4},{5},{6,7,8}} => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,6,7] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
{{1,2},{3,4},{5,6},{7},{8}} => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
{{1,2},{3,4},{5,7,8},{6}} => [2,1,4,3,7,6,8,5] => [2,1,4,3,6,8,5,7] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 12
{{1,2},{3,4},{5,6,8},{7}} => [2,1,4,3,6,8,7,5] => [2,1,4,3,7,8,5,6] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 13
{{1,2},{3,4},{5,6,7,8}} => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,5,6,7] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
{{1,2},{3,5},{4},{6},{7},{8}} => [2,1,5,4,3,6,7,8] => [2,1,4,5,3,6,7,8] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 24
{{1,2},{3,6,7,8},{4},{5}} => [2,1,6,4,5,7,8,3] => [2,1,4,5,8,3,6,7] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 11
{{1,2},{3,5,6},{4},{7,8}} => [2,1,5,4,6,3,8,7] => [2,1,4,6,3,5,8,7] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 12
{{1,2},{3,7,8},{4},{5,6}} => [2,1,7,4,6,5,8,3] => [2,1,4,6,5,8,3,7] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 12
{{1,2},{3,5,7,8},{4},{6}} => [2,1,5,4,7,6,8,3] => [2,1,4,6,8,3,5,7] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 12
{{1,2},{3,5,6,8},{4},{7}} => [2,1,5,4,6,8,7,3] => [2,1,4,7,8,3,5,6] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 13
{{1,2},{3,5,6,7,8},{4}} => [2,1,5,4,6,7,8,3] => [2,1,4,8,3,5,6,7] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 6
{{1,2},{3,4,5},{6},{7},{8}} => [2,1,4,5,3,6,7,8] => [2,1,5,3,4,6,7,8] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 20
{{1,2},{3,7,8},{4,5},{6}} => [2,1,7,5,4,6,8,3] => [2,1,5,4,6,8,3,7] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 13
{{1,2},{3,6,7,8},{4,5}} => [2,1,6,5,4,7,8,3] => [2,1,5,4,8,3,6,7] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 7
{{1,2},{3,4,6},{5},{7,8}} => [2,1,4,6,5,3,8,7] => [2,1,5,6,3,4,8,7] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 13
{{1,2},{3,7,8},{4,6},{5}} => [2,1,7,6,5,4,8,3] => [2,1,5,6,4,8,3,7] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 13
{{1,2},{3,4,7,8},{5},{6}} => [2,1,4,7,5,6,8,3] => [2,1,5,6,8,3,4,7] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 13
{{1,2},{3,8},{4,6,7},{5}} => [2,1,8,6,5,7,4,3] => [2,1,5,7,4,6,8,3] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 14
{{1,2},{3,4,6,8},{5},{7}} => [2,1,4,6,5,8,7,3] => [2,1,5,7,8,3,4,6] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 14
{{1,2},{3,4,6,7,8},{5}} => [2,1,4,6,5,7,8,3] => [2,1,5,8,3,4,6,7] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 7
{{1,2},{3,4,5,6},{7,8}} => [2,1,4,5,6,3,8,7] => [2,1,6,3,4,5,8,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
{{1,2},{3,8},{4,5,6},{7}} => [2,1,8,5,6,4,7,3] => [2,1,6,4,5,7,8,3] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 15
{{1,2},{3,4,8},{5,6},{7}} => [2,1,4,8,6,5,7,3] => [2,1,6,5,7,8,3,4] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 15
{{1,2},{3,4,8},{5,7},{6}} => [2,1,4,8,7,6,5,3] => [2,1,6,7,5,8,3,4] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 15
{{1,2},{3,4,5,8},{6},{7}} => [2,1,4,5,8,6,7,3] => [2,1,6,7,8,3,4,5] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 15
{{1,2},{3,4,5,7,8},{6}} => [2,1,4,5,7,6,8,3] => [2,1,6,8,3,4,5,7] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
{{1,2},{3,4,8},{5,6,7}} => [2,1,4,8,6,7,5,3] => [2,1,7,5,6,8,3,4] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 9
{{1,2},{3,4,5,8},{6,7}} => [2,1,4,5,8,7,6,3] => [2,1,7,6,8,3,4,5] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 9
{{1,2},{3,4,5,6,8},{7}} => [2,1,4,5,6,8,7,3] => [2,1,7,8,3,4,5,6] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 9
{{1,2},{3,4,5,6,7,8}} => [2,1,4,5,6,7,8,3] => [2,1,8,3,4,5,6,7] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
{{1,3},{2},{4},{5},{6},{7},{8}} => [3,2,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 27
{{1,3},{2},{4},{5},{6},{7,8}} => [3,2,1,4,5,6,8,7] => [2,3,1,4,5,6,8,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 20
{{1,3},{2},{4},{5},{6,8},{7}} => [3,2,1,4,5,8,7,6] => [2,3,1,4,5,7,8,6] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 21
{{1,3},{2},{4},{5},{6,7,8}} => [3,2,1,4,5,7,8,6] => [2,3,1,4,5,8,6,7] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 14
{{1,3},{2},{4},{5,8},{6,7}} => [3,2,1,4,8,7,6,5] => [2,3,1,4,7,6,8,5] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 16
{{1,3},{2},{4},{5,6,7,8}} => [3,2,1,4,6,7,8,5] => [2,3,1,4,8,5,6,7] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 9
{{1},{2,3,5,8},{4,6},{7}} => [1,3,5,6,8,4,7,2] => [1,6,4,7,8,2,3,5] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 14
{{1},{2,3,5,7},{4},{6,8}} => [1,3,5,4,7,8,2,6] => [1,4,7,2,3,5,8,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 12
{{1},{2,6},{3,4,7},{5,8}} => [1,6,4,7,8,2,3,5] => [1,6,2,7,3,4,8,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
{{1,2},{3,6,7},{4,8},{5}} => [2,1,6,8,5,7,3,4] => [2,1,5,7,3,6,8,4] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 14
{{1,2},{3,7},{4,6,8},{5}} => [2,1,7,6,5,8,3,4] => [2,1,5,7,3,8,4,6] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 14
{{1,2},{3,5,8},{4,7},{6}} => [2,1,5,7,8,6,4,3] => [2,1,6,7,4,8,3,5] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 15
{{1},{2,5},{3,4,8},{6,7}} => [1,5,4,8,2,7,6,3] => [1,5,2,7,6,8,3,4] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
{{1},{2,4},{3,5,8},{6,7}} => [1,4,5,2,8,7,6,3] => [1,4,2,7,6,8,3,5] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 12
{{1},{2,4},{3,7},{5,6,8}} => [1,4,7,2,6,8,3,5] => [1,4,2,7,3,8,5,6] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 12
{{1},{2,4},{3,6},{5,7,8}} => [1,4,6,2,7,3,8,5] => [1,4,2,6,3,8,5,7] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 11
{{1},{2,4},{3,6,7},{5,8}} => [1,4,6,2,8,7,3,5] => [1,4,2,7,3,6,8,5] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 12
{{1},{2,4,6},{3,7},{5,8}} => [1,4,7,6,8,2,3,5] => [1,6,2,4,7,3,8,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 14
{{1},{2,4,6},{3,8},{5,7}} => [1,4,8,6,7,2,5,3] => [1,6,2,4,7,5,8,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 14
{{1},{2,5,7},{3,4},{6,8}} => [1,5,4,3,7,8,2,6] => [1,4,3,7,2,5,8,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 12
{{1,2},{3,6,8},{4,7},{5}} => [2,1,6,7,5,8,4,3] => [2,1,5,7,4,8,3,6] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 14
{{1,2},{3,7},{4,5,8},{6}} => [2,1,7,5,8,6,3,4] => [2,1,6,7,3,8,4,5] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 15
{{1},{2,4,6,8},{3},{5,7}} => [1,4,3,6,7,8,5,2] => [1,3,7,5,8,2,4,6] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 11
{{1},{2,5,8},{3,7},{4,6}} => [1,5,7,6,8,4,3,2] => [1,6,4,7,3,8,2,5] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 14
{{1},{2,4,8},{3,6},{5,7}} => [1,4,6,8,7,3,5,2] => [1,6,3,7,5,8,2,4] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 14
{{1},{2,4,6,8},{3,5},{7}} => [1,4,5,6,3,8,7,2] => [1,5,3,7,8,2,4,6] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 13
{{1},{2,6,8},{3,5,7},{4}} => [1,6,5,4,7,8,3,2] => [1,4,7,3,5,8,2,6] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 12
{{1},{2,6,8},{3,5},{4,7}} => [1,6,5,7,3,8,4,2] => [1,5,3,7,4,8,2,6] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
{{1,2},{3,4,6},{5,8},{7}} => [2,1,4,6,8,3,7,5] => [2,1,6,3,4,7,8,5] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 15
{{1,2},{3,6},{4,5,8},{7}} => [2,1,6,5,8,3,7,4] => [2,1,6,3,7,8,4,5] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 15
{{1,2},{3,5,6},{4,8},{7}} => [2,1,5,8,6,3,7,4] => [2,1,6,3,5,7,8,4] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 15
{{1,2},{3,4,5,7},{6,8}} => [2,1,4,5,7,8,3,6] => [2,1,7,3,4,5,8,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 9
{{1,2},{3,4,6,7},{5,8}} => [2,1,4,6,8,7,3,5] => [2,1,7,3,4,6,8,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 9
{{1,2},{3,5},{4,6,7,8}} => [2,1,5,6,3,7,8,4] => [2,1,5,3,8,4,6,7] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 7
{{1,2},{3,6},{4,5,7,8}} => [2,1,6,5,7,3,8,4] => [2,1,6,3,8,4,5,7] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
{{1,2},{3,5,6,8},{4,7}} => [2,1,5,7,6,8,4,3] => [2,1,7,4,8,3,5,6] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 9
{{1,2},{3,6},{4},{5,7,8}} => [2,1,6,4,7,3,8,5] => [2,1,4,6,3,8,5,7] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 12
{{1,2},{3,6,7},{4},{5,8}} => [2,1,6,4,8,7,3,5] => [2,1,4,7,3,6,8,5] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 13
{{1},{2,5,6},{3,7},{4,8}} => [1,5,7,8,6,2,3,4] => [1,6,2,5,7,3,8,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 14
{{1},{2,5,6},{3},{4,7,8}} => [1,5,3,7,6,2,8,4] => [1,3,6,2,5,8,4,7] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
{{1},{2,5},{3,7},{4,6,8}} => [1,5,7,6,2,8,3,4] => [1,5,2,7,3,8,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
{{1},{2},{3,6,7},{4,5,8}} => [1,2,6,5,8,7,3,4] => [1,2,7,3,6,8,4,5] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10
{{1},{2,3,6,7},{4},{5,8}} => [1,3,6,4,8,7,2,5] => [1,4,7,2,3,6,8,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 12
{{1},{2,3,6},{4,8},{5,7}} => [1,3,6,8,7,2,5,4] => [1,6,2,3,7,5,8,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 14
{{1},{2},{3,4,6,8},{5,7}} => [1,2,4,6,7,8,5,3] => [1,2,7,5,8,3,4,6] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10
{{1},{2},{3,6},{4,5,7,8}} => [1,2,6,5,7,3,8,4] => [1,2,6,3,8,4,5,7] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 9
{{1},{2,5},{3},{4,6,7,8}} => [1,5,3,6,2,7,8,4] => [1,3,5,2,8,4,6,7] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 9
{{1},{2,5},{3,6},{4,7,8}} => [1,5,6,7,2,3,8,4] => [1,5,2,6,3,8,4,7] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 12
{{1},{2},{3,5},{4,6,7,8}} => [1,2,5,6,3,7,8,4] => [1,2,5,3,8,4,6,7] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
{{1},{2,4,8},{3,5},{6,7}} => [1,4,5,8,3,7,6,2] => [1,5,3,7,6,8,2,4] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
{{1},{2,4},{3,6,8},{5,7}} => [1,4,6,2,7,8,5,3] => [1,4,2,7,5,8,3,6] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 12
{{1},{2,4,7},{3,6},{5,8}} => [1,4,6,7,8,3,2,5] => [1,6,3,7,2,4,8,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
{{1},{2,4,7},{3},{5,6,8}} => [1,4,3,7,6,8,2,5] => [1,3,7,2,4,8,5,6] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
{{1},{2,3,7},{4,8},{5,6}} => [1,3,7,8,6,5,2,4] => [1,6,5,7,2,3,8,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
{{1},{2},{3,7},{4,5,6,8}} => [1,2,7,5,6,8,3,4] => [1,2,7,3,8,4,5,6] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10
{{1},{2},{3,5,7},{4,6,8}} => [1,2,5,6,7,8,3,4] => [1,2,7,3,5,8,4,6] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10
{{1},{2,6},{3,7},{4,5,8}} => [1,6,7,5,8,2,3,4] => [1,6,2,7,3,8,4,5] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 14
{{1,2},{3,5,7},{4},{6,8}} => [2,1,5,4,7,8,3,6] => [2,1,4,7,3,5,8,6] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 13
{{1,2},{3,4,7},{5},{6,8}} => [2,1,4,7,5,8,3,6] => [2,1,5,7,3,4,8,6] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 14
{{1,2},{3,4,7},{5,8},{6}} => [2,1,4,7,8,6,3,5] => [2,1,6,7,3,4,8,5] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 15
{{1,2},{3,5},{4,6,8},{7}} => [2,1,5,6,3,8,7,4] => [2,1,5,3,7,8,4,6] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 14
{{1,2},{3,5,8},{4,6},{7}} => [2,1,5,6,8,4,7,3] => [2,1,6,4,7,8,3,5] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 15
{{1},{2,3,4,7},{5},{6,8}} => [1,3,4,7,5,8,2,6] => [1,5,7,2,3,4,8,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 13
{{1},{2,3,4},{5,7},{6,8}} => [1,3,4,2,7,8,5,6] => [1,4,2,3,7,5,8,6] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 12
{{1},{2,4,5},{3,7},{6,8}} => [1,4,7,5,2,8,3,6] => [1,5,2,4,7,3,8,6] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 13
{{1},{2,3,5},{4,7},{6,8}} => [1,3,5,7,2,8,4,6] => [1,5,2,3,7,4,8,6] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 13
{{1},{2,3,5},{4,6},{7,8}} => [1,3,5,6,2,4,8,7] => [1,5,2,3,6,4,8,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 12
{{1},{2,4,7},{3},{5,8},{6}} => [1,4,3,7,8,6,2,5] => [1,3,6,7,2,4,8,5] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 17
{{1},{2,7},{3,4,5,8},{6}} => [1,7,4,5,8,6,2,3] => [1,6,7,2,8,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 14
{{1},{2,5,8},{3,7},{4},{6}} => [1,5,7,4,8,6,3,2] => [1,4,6,7,3,8,2,5] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 18
{{1},{2,7},{3,5,8},{4,6}} => [1,7,5,6,8,4,2,3] => [1,6,4,7,2,8,3,5] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 14
{{1},{2,8},{3,6},{4,5,7}} => [1,8,6,5,7,3,4,2] => [1,6,3,7,4,5,8,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
{{1},{2,5},{3,6,8},{4},{7}} => [1,5,6,4,2,8,7,3] => [1,4,5,2,7,8,3,6] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 17
{{1},{2,5,6,7},{3,8},{4}} => [1,5,8,4,6,7,2,3] => [1,4,7,2,5,6,8,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 12
{{1},{2,6},{3,7},{4},{5},{8}} => [1,6,7,4,5,2,3,8] => [1,4,5,6,2,7,3,8] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 23
{{1},{2,5,6},{3,4,7},{8}} => [1,5,4,7,6,2,3,8] => [1,6,2,5,7,3,4,8] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 14
{{1},{2,4,6},{3,5,7},{8}} => [1,4,5,6,7,2,3,8] => [1,6,2,4,7,3,5,8] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 14
{{1},{2,3,5},{4,6,7},{8}} => [1,3,5,6,2,7,4,8] => [1,5,2,3,7,4,6,8] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 13
{{1},{2},{3,5},{4,6},{7},{8}} => [1,2,5,6,3,4,7,8] => [1,2,5,3,6,4,7,8] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 21
{{1},{2,5},{3},{4,7},{6},{8}} => [1,5,3,7,2,6,4,8] => [1,3,5,2,6,7,4,8] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 22
{{1},{2,4,8},{3,7},{5,6}} => [1,4,7,8,6,5,3,2] => [1,6,5,7,3,8,2,4] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 14
{{1},{2,4},{3,7,8},{5,6}} => [1,4,7,2,6,5,8,3] => [1,4,2,6,5,8,3,7] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 11
{{1},{2,6,8},{3,4},{5,7}} => [1,6,4,3,7,8,5,2] => [1,4,3,7,5,8,2,6] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 12
{{1},{2,6},{3,4,8},{5,7}} => [1,6,4,8,7,2,5,3] => [1,6,2,7,5,8,3,4] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 14
{{1},{2,3},{4,6,8},{5,7}} => [1,3,2,6,7,8,5,4] => [1,3,2,7,5,8,4,6] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 11
{{1},{2,3,5,7},{4,8},{6}} => [1,3,5,8,7,6,2,4] => [1,6,7,2,3,5,8,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 14
{{1},{2,3,7},{4,6},{5,8}} => [1,3,7,6,8,4,2,5] => [1,6,4,7,2,3,8,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
{{1},{2,3,6},{4,7},{5,8}} => [1,3,6,7,8,2,4,5] => [1,6,2,3,7,4,8,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 14
{{1},{2,4,8},{3,5,6},{7}} => [1,4,5,8,6,3,7,2] => [1,6,3,5,7,8,2,4] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14
{{1},{2,7},{3,5,6},{4,8}} => [1,7,5,8,6,3,2,4] => [1,6,3,5,7,2,8,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 14
{{1},{2,6,8},{3,4,7},{5}} => [1,6,4,7,5,8,3,2] => [1,5,7,3,4,8,2,6] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 13
{{1},{2,6},{3,8},{4},{5,7}} => [1,6,8,4,7,2,5,3] => [1,4,6,2,7,5,8,3] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 18
{{1},{2,5,6,7},{3,4,8}} => [1,5,4,8,6,7,2,3] => [1,7,2,5,6,8,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 8
{{1},{2,3,5},{4,8},{6,7}} => [1,3,5,8,2,7,6,4] => [1,5,2,3,7,6,8,4] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 13
{{1},{2},{3,5},{4,8},{6,7}} => [1,2,5,8,3,7,6,4] => [1,2,5,3,7,6,8,4] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 15
{{1},{2,5},{3},{4,8},{6,7}} => [1,5,3,8,2,7,6,4] => [1,3,5,2,7,6,8,4] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 16
{{1},{2,7},{3,8},{4,5,6}} => [1,7,8,5,6,4,2,3] => [1,6,4,5,7,2,8,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 14
{{1},{2,5},{3,8},{4,6,7}} => [1,5,8,6,2,7,4,3] => [1,5,2,7,4,6,8,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 13
{{1},{2,3,7},{4,8},{5},{6}} => [1,3,7,8,5,6,2,4] => [1,5,6,7,2,3,8,4] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 19
{{1},{2,4},{3,7,8},{5},{6}} => [1,4,7,2,5,6,8,3] => [1,4,2,5,6,8,3,7] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 16
{{1},{2,5,7},{3,4,8},{6}} => [1,5,4,8,7,6,2,3] => [1,6,7,2,5,8,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 14
{{1},{2,4},{3,5},{6,7},{8}} => [1,4,5,2,3,7,6,8] => [1,4,2,5,3,7,6,8] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 17
{{1},{2,4,8},{3,5},{6},{7}} => [1,4,5,8,3,6,7,2] => [1,5,3,6,7,8,2,4] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 19
{{1},{2,5},{3,6},{4},{7,8}} => [1,5,6,4,2,3,8,7] => [1,4,5,2,6,3,8,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 16
{{1},{2,5,7},{3,8},{4,6}} => [1,5,8,6,7,4,2,3] => [1,6,4,7,2,5,8,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
{{1},{2,5},{3,6},{4,7},{8}} => [1,5,6,7,2,3,4,8] => [1,5,2,6,3,7,4,8] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 19
{{1},{2,3,6,7},{4,8},{5}} => [1,3,6,8,5,7,2,4] => [1,5,7,2,3,6,8,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 13
{{1,2},{3},{4,6},{5,7,8}} => [2,1,3,6,7,4,8,5] => [2,1,3,6,4,8,5,7] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 11
{{1},{2,5,6,8},{3},{4,7}} => [1,5,3,7,6,8,4,2] => [1,3,7,4,8,2,5,6] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 11
{{1},{2},{3,5,6,8},{4,7}} => [1,2,5,7,6,8,4,3] => [1,2,7,4,8,3,5,6] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10
{{1},{2,6},{3,7,8},{4,5}} => [1,6,7,5,4,2,8,3] => [1,5,4,6,2,8,3,7] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 12
{{1},{2,6,7},{3,5},{4,8}} => [1,6,5,8,3,7,2,4] => [1,5,3,7,2,6,8,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 13
{{1},{2},{3,6,8},{4,5,7}} => [1,2,6,5,7,8,4,3] => [1,2,7,4,5,8,3,6] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10
{{1},{2,3},{4,7},{5,6,8}} => [1,3,2,7,6,8,4,5] => [1,3,2,7,4,8,5,6] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 11
{{1},{2,5},{3,7,8},{4,6}} => [1,5,7,6,2,4,8,3] => [1,5,2,6,4,8,3,7] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 12
{{1},{2,8},{3,5,6},{4,7}} => [1,8,5,7,6,3,4,2] => [1,6,3,5,7,4,8,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 14
{{1},{2,5,6,7},{3},{4,8}} => [1,5,3,8,6,7,2,4] => [1,3,7,2,5,6,8,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 11
{{1},{2,6,8},{3,7},{4,5}} => [1,6,7,5,4,8,3,2] => [1,5,4,7,3,8,2,6] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
{{1},{2,4,5},{3,7,8},{6}} => [1,4,7,5,2,6,8,3] => [1,5,2,4,6,8,3,7] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 12
{{1},{2,6},{3,8},{4,5,7}} => [1,6,8,5,7,2,4,3] => [1,6,2,7,4,5,8,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 14
{{1},{2,4,6,7},{3,8},{5}} => [1,4,8,6,5,7,2,3] => [1,5,7,2,4,6,8,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 13
{{1,2},{3,5},{4,7,8},{6}} => [2,1,5,7,3,6,8,4] => [2,1,5,3,6,8,4,7] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 13
{{1},{2,3,4,7},{5,8},{6}} => [1,3,4,7,8,6,2,5] => [1,6,7,2,3,4,8,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 14
{{1},{2,3,4,6},{5,8},{7}} => [1,3,4,6,8,2,7,5] => [1,6,2,3,4,7,8,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 14
{{1},{2,4,5,8},{3,6},{7}} => [1,4,6,5,8,3,7,2] => [1,6,3,7,8,2,4,5] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 14
{{1},{2,6},{3,5},{4,8},{7}} => [1,6,5,8,3,2,7,4] => [1,5,3,6,2,7,8,4] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 19
{{1},{2,6},{3,5,7,8},{4}} => [1,6,5,4,7,2,8,3] => [1,4,6,2,8,3,5,7] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 11
{{1},{2,4},{3,6,7,8},{5}} => [1,4,6,2,5,7,8,3] => [1,4,2,5,8,3,6,7] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 10
{{1},{2,4,7},{3,6,8},{5}} => [1,4,6,7,5,8,2,3] => [1,5,7,2,4,8,3,6] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 13
{{1},{2,5,8},{3,4,6},{7}} => [1,5,4,6,8,3,7,2] => [1,6,3,4,7,8,2,5] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14
{{1},{2,3,6},{4,5,7},{8}} => [1,3,6,5,7,2,4,8] => [1,6,2,3,7,4,5,8] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 14
{{1},{2,3,6},{4,5,8},{7}} => [1,3,6,5,8,2,7,4] => [1,6,2,3,7,8,4,5] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 14
{{1},{2,3,7},{4,6,8},{5}} => [1,3,7,6,5,8,2,4] => [1,5,7,2,3,8,4,6] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 13
{{1},{2,3,7},{4,5,8},{6}} => [1,3,7,5,8,6,2,4] => [1,6,7,2,3,8,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 14
{{1,2},{3,6,8},{4},{5,7}} => [2,1,6,4,7,8,5,3] => [2,1,4,7,5,8,3,6] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 13
{{1},{2,3,7},{4},{5,6,8}} => [1,3,7,4,6,8,2,5] => [1,4,7,2,3,8,5,6] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 12
{{1},{2,3,6},{4},{5,7,8}} => [1,3,6,4,7,2,8,5] => [1,4,6,2,3,8,5,7] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11
{{1},{2,3},{4,6,7},{5,8}} => [1,3,2,6,8,7,4,5] => [1,3,2,7,4,6,8,5] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 11
{{1},{2,3},{4,6},{5,7,8}} => [1,3,2,6,7,4,8,5] => [1,3,2,6,4,8,5,7] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 10
{{1},{2,3,5,6},{4,8},{7}} => [1,3,5,8,6,2,7,4] => [1,6,2,3,5,7,8,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 14
{{1},{2,3,5},{4,7,8},{6}} => [1,3,5,7,2,6,8,4] => [1,5,2,3,6,8,4,7] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 12
{{1},{2,5},{3,4,7,8},{6}} => [1,5,4,7,2,6,8,3] => [1,5,2,6,8,3,4,7] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 12
{{1},{2,4,8},{3,6,7},{5}} => [1,4,6,8,5,7,3,2] => [1,5,7,3,6,8,2,4] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 13
{{1},{2,3,6},{4,7,8},{5}} => [1,3,6,7,5,2,8,4] => [1,5,6,2,3,8,4,7] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 12
{{1},{2,5},{3,4,7},{6,8}} => [1,5,4,7,2,8,3,6] => [1,5,2,7,3,4,8,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 13
{{1},{2,7},{3,6},{4,5,8}} => [1,7,6,5,8,3,2,4] => [1,6,3,7,2,8,4,5] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 14
{{1},{2,4,5,7},{3,6},{8}} => [1,4,6,5,7,3,2,8] => [1,6,3,7,2,4,5,8] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 14
{{1},{2,6},{3,4,5,7},{8}} => [1,6,4,5,7,2,3,8] => [1,6,2,7,3,4,5,8] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 14
{{1},{2,7},{3,6,8},{4,5}} => [1,7,6,5,4,8,2,3] => [1,5,4,7,2,8,3,6] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
{{1},{2,6,8},{3},{4,7},{5}} => [1,6,3,7,5,8,4,2] => [1,3,5,7,4,8,2,6] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 16
{{1},{2,7},{3,5},{4},{6,8}} => [1,7,5,4,3,8,2,6] => [1,4,5,3,7,2,8,6] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 17
{{1},{2,7},{3,5,6,8},{4}} => [1,7,5,4,6,8,2,3] => [1,4,7,2,8,3,5,6] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 12
{{1},{2,8},{3,6},{4},{5,7}} => [1,8,6,4,7,3,5,2] => [1,4,6,3,7,5,8,2] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 18
{{1},{2,7},{3,4,6,8},{5}} => [1,7,4,6,5,8,2,3] => [1,5,7,2,8,3,4,6] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 13
{{1},{2,6},{3,5,8},{4,7}} => [1,6,5,7,8,2,4,3] => [1,6,2,7,4,8,3,5] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 14
{{1},{2,5},{3,4,6,8},{7}} => [1,5,4,6,2,8,7,3] => [1,5,2,7,8,3,4,6] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 13
{{1},{2,5,6,8},{3,7},{4}} => [1,5,7,4,6,8,3,2] => [1,4,7,3,8,2,5,6] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 12
{{1},{2,7},{3,5},{4,6,8}} => [1,7,5,6,3,8,2,4] => [1,5,3,7,2,8,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
{{1},{2,4},{3,5,7},{6,8}} => [1,4,5,2,7,8,3,6] => [1,4,2,7,3,5,8,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 12
{{1},{2,4},{3,5,7},{6},{8}} => [1,4,5,2,7,6,3,8] => [1,4,2,6,7,3,5,8] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 18
{{1},{2,4},{3,5,8},{6},{7}} => [1,4,5,2,8,6,7,3] => [1,4,2,6,7,8,3,5] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 18
{{1},{2,4,5},{3,8},{6,7}} => [1,4,8,5,2,7,6,3] => [1,5,2,4,7,6,8,3] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 13
{{1},{2,4,5,7},{3},{6,8}} => [1,4,3,5,7,8,2,6] => [1,3,7,2,4,5,8,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 11
{{1},{2,4,7},{3,5,8},{6}} => [1,4,5,7,8,6,2,3] => [1,6,7,2,4,8,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 14
{{1},{2},{3,5,8},{4,6,7}} => [1,2,5,6,8,7,4,3] => [1,2,7,4,6,8,3,5] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10
{{1},{2,5,7,8},{3},{4,6}} => [1,5,3,6,7,4,8,2] => [1,3,6,4,8,2,5,7] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 10
{{1},{2,3,5},{4,6,7,8}} => [1,3,5,6,2,7,8,4] => [1,5,2,3,8,4,6,7] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 6
{{1},{2,3,5},{4,6,8},{7}} => [1,3,5,6,2,8,7,4] => [1,5,2,3,7,8,4,6] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 13
{{1},{2},{3,4,6},{5,7,8}} => [1,2,4,6,7,3,8,5] => [1,2,6,3,4,8,5,7] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 9
{{1},{2},{3,4,7},{5,6,8}} => [1,2,4,7,6,8,3,5] => [1,2,7,3,4,8,5,6] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10
{{1,2},{3},{4,6,8},{5,7}} => [2,1,3,6,7,8,5,4] => [2,1,3,7,5,8,4,6] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 12
{{1},{2,6,8},{3},{4,5,7}} => [1,6,3,5,7,8,4,2] => [1,3,7,4,5,8,2,6] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
{{1},{2,6,7},{3,8},{4,5}} => [1,6,8,5,4,7,2,3] => [1,5,4,7,2,6,8,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 13
{{1},{2,5,8},{3},{4,6,7}} => [1,5,3,6,8,7,4,2] => [1,3,7,4,6,8,2,5] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
{{1},{2,5,6},{3,7,8},{4}} => [1,5,7,4,6,2,8,3] => [1,4,6,2,5,8,3,7] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11
{{1},{2,4},{3,5,6},{7,8}} => [1,4,5,2,6,3,8,7] => [1,4,2,6,3,5,8,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 11
{{1},{2,4,6,7,8},{3,5}} => [1,4,5,6,3,7,8,2] => [1,5,3,8,2,4,6,7] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 6
{{1},{2,3,5,8},{4,7},{6}} => [1,3,5,7,8,6,4,2] => [1,6,7,4,8,2,3,5] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 14
{{1},{2},{3},{4},{5,7},{6,8}} => [1,2,3,4,7,8,5,6] => [1,2,3,4,7,5,8,6] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 17
{{1},{2},{3},{4,6},{5,8},{7}} => [1,2,3,6,8,4,7,5] => [1,2,3,6,4,7,8,5] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 19
{{1},{2},{3,5},{4,8},{6},{7}} => [1,2,5,8,3,6,7,4] => [1,2,5,3,6,7,8,4] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 21
{{1},{2,4},{3,8},{5},{6},{7}} => [1,4,8,2,5,6,7,3] => [1,4,2,5,6,7,8,3] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 23
{{1},{2},{3},{4,7},{5,8},{6}} => [1,2,3,7,8,6,4,5] => [1,2,3,6,7,4,8,5] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 19
{{1},{2},{3,6},{4,8},{5},{7}} => [1,2,6,8,5,3,7,4] => [1,2,5,6,3,7,8,4] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 21
{{1},{2},{3},{4,6,7},{5,8}} => [1,2,3,6,8,7,4,5] => [1,2,3,7,4,6,8,5] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 13
{{1},{2,5},{3,8},{4},{6},{7}} => [1,5,8,4,2,6,7,3] => [1,4,5,2,6,7,8,3] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 23
{{1},{2,4,5},{3,8},{6},{7}} => [1,4,8,5,2,6,7,3] => [1,5,2,4,6,7,8,3] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 19
{{1},{2,3,5,7,8},{4,6}} => [1,3,5,6,7,4,8,2] => [1,6,4,8,2,3,5,7] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 7
{{1},{2,3,5,7},{4,6,8}} => [1,3,5,6,7,8,2,4] => [1,7,2,3,5,8,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 8
{{1},{2,3,4,5,7},{6,8}} => [1,3,4,5,7,8,2,6] => [1,7,2,3,4,5,8,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 8
{{1},{2,4,7,8},{3,5},{6}} => [1,4,5,7,3,6,8,2] => [1,5,3,6,8,2,4,7] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 12
{{1},{2,4,7,8},{3,6},{5}} => [1,4,6,7,5,3,8,2] => [1,5,6,3,8,2,4,7] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 12
{{1},{2,3,4,6,8},{5,7}} => [1,3,4,6,7,8,5,2] => [1,7,5,8,2,3,4,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 8
{{1,2},{3,4,6},{5,7,8}} => [2,1,4,6,7,3,8,5] => [2,1,6,3,4,8,5,7] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
{{1},{2,3,6},{4,5,7,8}} => [1,3,6,5,7,2,8,4] => [1,6,2,3,8,4,5,7] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 7
{{1},{2,4},{3,5,6,7,8}} => [1,4,5,2,6,7,8,3] => [1,4,2,8,3,5,6,7] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 5
{{1},{2},{3,7},{4,8},{5},{6}} => [1,2,7,8,5,6,3,4] => [1,2,5,6,7,3,8,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 21
{{1},{2,5},{3,6},{4},{7},{8}} => [1,5,6,4,2,3,7,8] => [1,4,5,2,6,3,7,8] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 23
{{1},{2,6},{3},{4,8},{5},{7}} => [1,6,3,8,5,2,7,4] => [1,3,5,6,2,7,8,4] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 22
{{1,2},{3,6,8},{4,5,7}} => [2,1,6,5,7,8,4,3] => [2,1,7,4,5,8,3,6] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 9
{{1},{2,5},{3,4,6,7,8}} => [1,5,4,6,2,7,8,3] => [1,5,2,8,3,4,6,7] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 6
{{1},{2,3,4,6},{5,7,8}} => [1,3,4,6,7,2,8,5] => [1,6,2,3,4,8,5,7] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 7
{{1},{2,4,6},{3},{5,7,8}} => [1,4,3,6,7,2,8,5] => [1,3,6,2,4,8,5,7] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
{{1},{2,5,7},{3},{4,6,8}} => [1,5,3,6,7,8,2,4] => [1,3,7,2,5,8,4,6] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
{{1,2},{3,5,7},{4,6,8}} => [2,1,5,6,7,8,3,4] => [2,1,7,3,5,8,4,6] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 9
{{1},{2,7},{3,8},{4},{5},{6}} => [1,7,8,4,5,6,2,3] => [1,4,5,6,7,2,8,3] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 23
{{1},{2},{3},{4,6,8},{5,7}} => [1,2,3,6,7,8,5,4] => [1,2,3,7,5,8,4,6] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 13
{{1},{2},{3,5,8},{4,6},{7}} => [1,2,5,6,8,4,7,3] => [1,2,6,4,7,8,3,5] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 16
{{1},{2,4,8},{3,5,6,7}} => [1,4,5,8,6,7,3,2] => [1,7,3,5,6,8,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 8
{{1},{2,7},{3,6},{4},{5,8}} => [1,7,6,4,8,3,2,5] => [1,4,6,3,7,2,8,5] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 18
{{1},{2,7},{3},{4,5,6,8}} => [1,7,3,5,6,8,2,4] => [1,3,7,2,8,4,5,6] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 11
{{1},{2,5},{3},{4,7},{6,8}} => [1,5,3,7,2,8,4,6] => [1,3,5,2,7,4,8,6] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 16
{{1,2},{3,4,7},{5,6,8}} => [2,1,4,7,6,8,3,5] => [2,1,7,3,4,8,5,6] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 9
{{1,2},{3,5,7,8},{4,6}} => [2,1,5,6,7,4,8,3] => [2,1,6,4,8,3,5,7] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
{{1},{2,4},{3,5},{6,7,8}} => [1,4,5,2,3,7,8,6] => [1,4,2,5,3,8,6,7] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 10
{{1,2},{3,5,6},{4,7,8}} => [2,1,5,7,6,3,8,4] => [2,1,6,3,5,8,4,7] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
{{1,2},{3,7},{4,5,6,8}} => [2,1,7,5,6,8,3,4] => [2,1,7,3,8,4,5,6] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 9
{{1},{2},{3,4,5,7},{6,8}} => [1,2,4,5,7,8,3,6] => [1,2,7,3,4,5,8,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10
{{1},{2,5},{3,4,6,7},{8}} => [1,5,4,6,2,7,3,8] => [1,5,2,7,3,4,6,8] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 13
{{1},{2,3,6},{4},{5,8},{7}} => [1,3,6,4,8,2,7,5] => [1,4,6,2,3,7,8,5] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 18
{{1},{2,4},{3,7},{5},{6,8}} => [1,4,7,2,5,8,3,6] => [1,4,2,5,7,3,8,6] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 17
{{1},{2,5},{3},{4,6,8},{7}} => [1,5,3,6,2,8,7,4] => [1,3,5,2,7,8,4,6] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 16
{{1},{2,5},{3},{4,6,7},{8}} => [1,5,3,6,2,7,4,8] => [1,3,5,2,7,4,6,8] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 16
{{1,2},{3,4,6,8},{5,7}} => [2,1,4,6,7,8,5,3] => [2,1,7,5,8,3,4,6] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 9
{{1,2},{3,6,7},{4,5,8}} => [2,1,6,5,8,7,3,4] => [2,1,7,3,6,8,4,5] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 9
{{1},{2,4},{3,5,6,8},{7}} => [1,4,5,2,6,8,7,3] => [1,4,2,7,8,3,5,6] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 12
{{1},{2,5},{3,4,6},{7,8}} => [1,5,4,6,2,3,8,7] => [1,5,2,6,3,4,8,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 12
{{1},{2,3,6,8},{4,7},{5}} => [1,3,6,7,5,8,4,2] => [1,5,7,4,8,2,3,6] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 13
{{1},{2,4,7},{3,5,6,8}} => [1,4,5,7,6,8,2,3] => [1,7,2,4,8,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 8
{{1},{2,5,7},{3},{4,8},{6}} => [1,5,3,8,7,6,2,4] => [1,3,6,7,2,5,8,4] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 17
{{1},{2,4,6,7},{3,5},{8}} => [1,4,5,6,3,7,2,8] => [1,5,3,7,2,4,6,8] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 13
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,1,2,1 1,1,2,5,2,3,1 1,1,2,5,10,7,7,11,3,4,1 1,1,2,5,10,23,15,23,25,37,18,14,19,4,5,1 1,1,2,5,10,23,47,39,49,81,84,129,74,78,70,87,33,23,29,5,6,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + q + 2\ q^{2} + q^{3}$
$F_{4} = 1 + q + 2\ q^{2} + 5\ q^{3} + 2\ q^{4} + 3\ q^{5} + q^{6}$
$F_{5} = 1 + q + 2\ q^{2} + 5\ q^{3} + 10\ q^{4} + 7\ q^{5} + 7\ q^{6} + 11\ q^{7} + 3\ q^{8} + 4\ q^{9} + q^{10}$
$F_{6} = 1 + q + 2\ q^{2} + 5\ q^{3} + 10\ q^{4} + 23\ q^{5} + 15\ q^{6} + 23\ q^{7} + 25\ q^{8} + 37\ q^{9} + 18\ q^{10} + 14\ q^{11} + 19\ q^{12} + 4\ q^{13} + 5\ q^{14} + q^{15}$
$F_{7} = 1 + q + 2\ q^{2} + 5\ q^{3} + 10\ q^{4} + 23\ q^{5} + 47\ q^{6} + 39\ q^{7} + 49\ q^{8} + 81\ q^{9} + 84\ q^{10} + 129\ q^{11} + 74\ q^{12} + 78\ q^{13} + 70\ q^{14} + 87\ q^{15} + 33\ q^{16} + 23\ q^{17} + 29\ q^{18} + 5\ q^{19} + 6\ q^{20} + q^{21}$
Description
The major index north count of a Dyck path.
The descent set $\operatorname{des}(D)$ of a Dyck path $D = D_1 \cdots D_{2n}$ with $D_i \in \{N,E\}$ is given by all indices $i$ such that $D_i = E$ and $D_{i+1} = N$. This is, the positions of the valleys of $D$.
The major index of a Dyck path is then the sum of the positions of the valleys, $\sum_{i \in \operatorname{des}(D)} i$, see St000027The major index of a Dyck path..
The major index north count is given by $\sum_{i \in \operatorname{des}(D)} \#\{ j \leq i \mid D_j = N\}$.
The descent set $\operatorname{des}(D)$ of a Dyck path $D = D_1 \cdots D_{2n}$ with $D_i \in \{N,E\}$ is given by all indices $i$ such that $D_i = E$ and $D_{i+1} = N$. This is, the positions of the valleys of $D$.
The major index of a Dyck path is then the sum of the positions of the valleys, $\sum_{i \in \operatorname{des}(D)} i$, see St000027The major index of a Dyck path..
The major index north count is given by $\sum_{i \in \operatorname{des}(D)} \#\{ j \leq i \mid D_j = N\}$.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
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.
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.
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