- FindStat

Identifier

Mp00080: Set partitions —to permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001203: Dyck paths ⟶ ℤ (values match St000306The bounce count of a Dyck path.)

Values

{{1}} => [1] => [1,0] => [1,0] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1155 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{1,4,6},{2,5,7},{3}} => [4,5,3,6,7,1,2] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4

{{1,4,6},{2,5},{3,7}} => [4,5,7,6,2,1,3] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5

{{1,4,6},{2,5},{3},{7}} => [4,5,3,6,2,1,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 4

{{1,4,7},{2,5,6},{3}} => [4,5,3,7,6,2,1] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4

{{1,4},{2,5,6,7},{3}} => [4,5,3,1,6,7,2] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 4

{{1,4},{2,5,6},{3,7}} => [4,5,7,1,6,2,3] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5

{{1,4},{2,5,6},{3},{7}} => [4,5,3,1,6,2,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 4

{{1,4,7},{2,5},{3,6}} => [4,5,6,7,2,3,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4

{{1,4},{2,5,7},{3,6}} => [4,5,6,1,7,3,2] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4

{{1,4},{2,5},{3,6,7}} => [4,5,6,1,2,7,3] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4

{{1,4},{2,5},{3,6},{7}} => [4,5,6,1,2,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4

{{1,4,7},{2,5},{3},{6}} => [4,5,3,7,2,6,1] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4

{{1,4},{2,5,7},{3},{6}} => [4,5,3,1,7,6,2] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4

{{1,4},{2,5},{3,7},{6}} => [4,5,7,1,2,6,3] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5

{{1,4},{2,5},{3},{6,7}} => [4,5,3,1,2,7,6] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4

{{1,4},{2,5},{3},{6},{7}} => [4,5,3,1,2,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 4

{{1,4,6,7},{2},{3,5}} => [4,2,5,6,3,7,1] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 4

{{1,4,6},{2,7},{3,5}} => [4,7,5,6,3,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6

{{1,4,6},{2},{3,5,7}} => [4,2,5,6,7,1,3] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4

{{1,4,6},{2},{3,5},{7}} => [4,2,5,6,3,1,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4

{{1,4,7},{2,6},{3,5}} => [4,6,5,7,3,2,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 5

{{1,4},{2,6,7},{3,5}} => [4,6,5,1,3,7,2] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 5

{{1,4},{2,6},{3,5,7}} => [4,6,5,1,7,2,3] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5

{{1,4},{2,6},{3,5},{7}} => [4,6,5,1,3,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5

{{1,4,7},{2},{3,5,6}} => [4,2,5,7,6,3,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

{{1,4},{2,7},{3,5,6}} => [4,7,5,1,6,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6

{{1,4},{2},{3,5,6,7}} => [4,2,5,1,6,7,3] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 4

{{1,4},{2},{3,5,6},{7}} => [4,2,5,1,6,3,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 4

{{1,4,7},{2},{3,5},{6}} => [4,2,5,7,3,6,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4

{{1,4},{2,7},{3,5},{6}} => [4,7,5,1,3,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6

{{1,4},{2},{3,5,7},{6}} => [4,2,5,1,7,6,3] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4

{{1,4},{2},{3,5},{6,7}} => [4,2,5,1,3,7,6] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4

{{1,4},{2},{3,5},{6},{7}} => [4,2,5,1,3,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 4

{{1,4,6,7},{2},{3},{5}} => [4,2,3,6,5,7,1] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4

{{1,4,6},{2,7},{3},{5}} => [4,7,3,6,5,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6

{{1,4,6},{2},{3,7},{5}} => [4,2,7,6,5,1,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

{{1,4,6},{2},{3},{5,7}} => [4,2,3,6,7,1,5] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4

{{1,4,6},{2},{3},{5},{7}} => [4,2,3,6,5,1,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 4

{{1,4,7},{2,6},{3},{5}} => [4,6,3,7,5,2,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 5

{{1,4},{2,6,7},{3},{5}} => [4,6,3,1,5,7,2] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 5

{{1,4},{2,6},{3,7},{5}} => [4,6,7,1,5,2,3] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5

{{1,4},{2,6},{3},{5,7}} => [4,6,3,1,7,2,5] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5

{{1,4},{2,6},{3},{5},{7}} => [4,6,3,1,5,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5

{{1,4,7},{2},{3,6},{5}} => [4,2,6,7,5,3,1] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4

{{1,4},{2,7},{3,6},{5}} => [4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6

{{1,4},{2},{3,6,7},{5}} => [4,2,6,1,5,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4

{{1,4},{2},{3,6},{5,7}} => [4,2,6,1,7,3,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4

{{1,4},{2},{3,6},{5},{7}} => [4,2,6,1,5,3,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4

{{1,4,7},{2},{3},{5,6}} => [4,2,3,7,6,5,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 4

{{1,4},{2,7},{3},{5,6}} => [4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6

{{1,4},{2},{3,7},{5,6}} => [4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

{{1,4},{2},{3},{5,6,7}} => [4,2,3,1,6,7,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4

{{1,4},{2},{3},{5,6},{7}} => [4,2,3,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4

{{1,4,7},{2},{3},{5},{6}} => [4,2,3,7,5,6,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 4

{{1,4},{2,7},{3},{5},{6}} => [4,7,3,1,5,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6

{{1,4},{2},{3,7},{5},{6}} => [4,2,7,1,5,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5

{{1,4},{2},{3},{5,7},{6}} => [4,2,3,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 4

{{1,4},{2},{3},{5},{6,7}} => [4,2,3,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4

{{1,4},{2},{3},{5},{6},{7}} => [4,2,3,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4

{{1,5,6,7},{2,4},{3}} => [5,4,3,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5

{{1,5,6},{2,4,7},{3}} => [5,4,3,7,6,1,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5

{{1,5,6},{2,4},{3,7}} => [5,4,7,2,6,1,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5

{{1,5,6},{2,4},{3},{7}} => [5,4,3,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5

{{1,5,7},{2,4,6},{3}} => [5,4,3,6,7,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5

{{1,5},{2,4,6,7},{3}} => [5,4,3,6,1,7,2] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5

{{1,5},{2,4,6},{3,7}} => [5,4,7,6,1,2,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5

{{1,5},{2,4,6},{3},{7}} => [5,4,3,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5

{{1,5,7},{2,4},{3,6}} => [5,4,6,2,7,3,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5

{{1,5},{2,4,7},{3,6}} => [5,4,6,7,1,3,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

{{1,5},{2,4},{3,6,7}} => [5,4,6,2,1,7,3] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 5

{{1,5},{2,4},{3,6},{7}} => [5,4,6,2,1,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5

{{1,5,7},{2,4},{3},{6}} => [5,4,3,2,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

{{1,5},{2,4,7},{3},{6}} => [5,4,3,7,1,6,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5

{{1,5},{2,4},{3,7},{6}} => [5,4,7,2,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5

{{1,5},{2,4},{3},{6,7}} => [5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5

{{1,5},{2,4},{3},{6},{7}} => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5

{{1,6,7},{2,4,5},{3}} => [6,4,3,5,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6

{{1,6},{2,4,5,7},{3}} => [6,4,3,5,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6

{{1,6},{2,4,5},{3,7}} => [6,4,7,5,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

{{1,6},{2,4,5},{3},{7}} => [6,4,3,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6

{{1,7},{2,4,5,6},{3}} => [7,4,3,5,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,4,5,6,7},{3}} => [1,4,3,5,6,7,2] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 3

{{1},{2,4,5,6},{3,7}} => [1,4,7,5,6,2,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5

{{1},{2,4,5,6},{3},{7}} => [1,4,3,5,6,2,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 3

{{1,7},{2,4,5},{3,6}} => [7,4,6,5,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,4,5,7},{3,6}} => [1,4,6,5,7,3,2] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 4

{{1},{2,4,5},{3,6,7}} => [1,4,6,5,2,7,3] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4

{{1},{2,4,5},{3,6},{7}} => [1,4,6,5,2,3,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4

{{1,7},{2,4,5},{3},{6}} => [7,4,3,5,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,4,5,7},{3},{6}} => [1,4,3,5,7,6,2] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 3

{{1},{2,4,5},{3,7},{6}} => [1,4,7,5,2,6,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5

{{1},{2,4,5},{3},{6,7}} => [1,4,3,5,2,7,6] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 3

{{1},{2,4,5},{3},{6},{7}} => [1,4,3,5,2,6,7] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 3

{{1,6,7},{2,4},{3,5}} => [6,4,5,2,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6

{{1,6},{2,4,7},{3,5}} => [6,4,5,7,3,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6

{{1,6},{2,4},{3,5,7}} => [6,4,5,2,7,1,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6

{{1,6},{2,4},{3,5},{7}} => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6

{{1,7},{2,4,6},{3,5}} => [7,4,5,6,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 3

{{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3

{{1},{2,4,6},{3,5},{7}} => [1,4,5,6,3,2,7] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 3

{{1,7},{2,4},{3,5,6}} => [7,4,5,2,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,4,7},{3,5,6}} => [1,4,5,7,6,3,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4

{{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 3

{{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 3

{{1,7},{2,4},{3,5},{6}} => [7,4,5,2,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,4,7},{3,5},{6}} => [1,4,5,7,3,6,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4

{{1},{2,4},{3,5,7},{6}} => [1,4,5,2,7,6,3] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3

{{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3

{{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 3

{{1,6,7},{2,4},{3},{5}} => [6,4,3,2,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6

{{1,6},{2,4,7},{3},{5}} => [6,4,3,7,5,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6

{{1,6},{2,4},{3,7},{5}} => [6,4,7,2,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

{{1,6},{2,4},{3},{5,7}} => [6,4,3,2,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6

{{1,6},{2,4},{3},{5},{7}} => [6,4,3,2,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6

{{1,7},{2,4,6},{3},{5}} => [7,4,3,6,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,4,6,7},{3},{5}} => [1,4,3,6,5,7,2] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3

{{1},{2,4,6},{3,7},{5}} => [1,4,7,6,5,2,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5

{{1},{2,4,6},{3},{5,7}} => [1,4,3,6,7,2,5] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3

{{1},{2,4,6},{3},{5},{7}} => [1,4,3,6,5,2,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3

{{1,7},{2,4},{3,6},{5}} => [7,4,6,2,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,4,7},{3,6},{5}} => [1,4,6,7,5,3,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 4

{{1},{2,4},{3,6,7},{5}} => [1,4,6,2,5,7,3] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4

{{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 4

{{1},{2,4},{3,6},{5},{7}} => [1,4,6,2,5,3,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4

{{1,7},{2,4},{3},{5,6}} => [7,4,3,2,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,4,7},{3},{5,6}} => [1,4,3,7,6,5,2] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4

{{1},{2,4},{3,7},{5,6}} => [1,4,7,2,6,5,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5

{{1},{2,4},{3},{5,6,7}} => [1,4,3,2,6,7,5] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 3

{{1},{2,4},{3},{5,6},{7}} => [1,4,3,2,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3

{{1,7},{2,4},{3},{5},{6}} => [7,4,3,2,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,4,7},{3},{5},{6}} => [1,4,3,7,5,6,2] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4

{{1},{2,4},{3,7},{5},{6}} => [1,4,7,2,5,6,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5

{{1},{2,4},{3},{5,7},{6}} => [1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3

{{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3

{{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3

{{1,5,6,7},{2},{3,4}} => [5,2,4,3,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5

{{1,5,6},{2,7},{3,4}} => [5,7,4,3,6,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6

{{1,5,6},{2},{3,4,7}} => [5,2,4,7,6,1,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5

{{1,5,6},{2},{3,4},{7}} => [5,2,4,3,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5

{{1,5,7},{2,6},{3,4}} => [5,6,4,3,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 5

{{1,5},{2,6,7},{3,4}} => [5,6,4,3,1,7,2] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 5

{{1,5},{2,6},{3,4,7}} => [5,6,4,7,1,2,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

{{1,5},{2,6},{3,4},{7}} => [5,6,4,3,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5

{{1,5,7},{2},{3,4,6}} => [5,2,4,6,7,3,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5

{{1,5},{2,7},{3,4,6}} => [5,7,4,6,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6

{{1,5},{2},{3,4,6,7}} => [5,2,4,6,1,7,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5

{{1,5},{2},{3,4,6},{7}} => [5,2,4,6,1,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5

{{1,5,7},{2},{3,4},{6}} => [5,2,4,3,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

{{1,5},{2,7},{3,4},{6}} => [5,7,4,3,1,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6

{{1,5},{2},{3,4,7},{6}} => [5,2,4,7,1,6,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5

{{1,5},{2},{3,4},{6,7}} => [5,2,4,3,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5

{{1,5},{2},{3,4},{6},{7}} => [5,2,4,3,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5

{{1,6,7},{2,5},{3,4}} => [6,5,4,3,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6

{{1,6},{2,5,7},{3,4}} => [6,5,4,3,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6

{{1,6},{2,5},{3,4,7}} => [6,5,4,7,2,1,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6

{{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6

{{1,7},{2,5,6},{3,4}} => [7,5,4,3,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,5,6,7},{3,4}} => [1,5,4,3,6,7,2] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 4

{{1},{2,5,6},{3,4,7}} => [1,5,4,7,6,2,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4

{{1},{2,5,6},{3,4},{7}} => [1,5,4,3,6,2,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4

{{1,7},{2,5},{3,4,6}} => [7,5,4,6,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,5,7},{3,4,6}} => [1,5,4,6,7,3,2] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 4

{{1},{2,5},{3,4,6,7}} => [1,5,4,6,2,7,3] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 4

{{1},{2,5},{3,4,6},{7}} => [1,5,4,6,2,3,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 4

{{1,7},{2,5},{3,4},{6}} => [7,5,4,3,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,5,7},{3,4},{6}} => [1,5,4,3,7,6,2] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4

{{1},{2,5},{3,4,7},{6}} => [1,5,4,7,2,6,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4

{{1},{2,5},{3,4},{6,7}} => [1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4

{{1},{2,5},{3,4},{6},{7}} => [1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4

{{1,6,7},{2},{3,4,5}} => [6,2,4,5,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6

{{1,6},{2,7},{3,4,5}} => [6,7,4,5,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

{{1,6},{2},{3,4,5,7}} => [6,2,4,5,7,1,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6

{{1,6},{2},{3,4,5},{7}} => [6,2,4,5,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6

{{1,7},{2,6},{3,4,5}} => [7,6,4,5,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,6,7},{3,4,5}} => [1,6,4,5,3,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 5

{{1},{2,6},{3,4,5,7}} => [1,6,4,5,7,2,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 5

{{1},{2,6},{3,4,5},{7}} => [1,6,4,5,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5

{{1,7},{2},{3,4,5,6}} => [7,2,4,5,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3,4,5,6}} => [1,7,4,5,6,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2

{{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 2

{{1,7},{2},{3,4,5},{6}} => [7,2,4,5,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3,4,5},{6}} => [1,7,4,5,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3

{{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2

{{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2

{{1,6,7},{2},{3,4},{5}} => [6,2,4,3,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6

{{1,6},{2,7},{3,4},{5}} => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

{{1,6},{2},{3,4,7},{5}} => [6,2,4,7,5,1,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6

{{1,6},{2},{3,4},{5,7}} => [6,2,4,3,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6

{{1,6},{2},{3,4},{5},{7}} => [6,2,4,3,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6

{{1,7},{2,6},{3,4},{5}} => [7,6,4,3,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,6,7},{3,4},{5}} => [1,6,4,3,5,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 5

{{1},{2,6},{3,4,7},{5}} => [1,6,4,7,5,2,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5

{{1},{2,6},{3,4},{5,7}} => [1,6,4,3,7,2,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 5

{{1},{2,6},{3,4},{5},{7}} => [1,6,4,3,5,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5

{{1,7},{2},{3,4,6},{5}} => [7,2,4,6,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3,4,6},{5}} => [1,7,4,6,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,4,6,7},{5}} => [1,2,4,6,5,7,3] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 3

{{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3

{{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3

{{1,7},{2},{3,4},{5,6}} => [7,2,4,3,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3,4},{5,6}} => [1,7,4,3,6,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,4,7},{5,6}} => [1,2,4,7,6,5,3] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4

{{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2

{{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2

{{1,7},{2},{3,4},{5},{6}} => [7,2,4,3,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3,4},{5},{6}} => [1,7,4,3,5,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,4,7},{5},{6}} => [1,2,4,7,5,6,3] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4

{{1},{2},{3,4},{5,7},{6}} => [1,2,4,3,7,6,5] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3

{{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2

{{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2

{{1,5,6,7},{2},{3},{4}} => [5,2,3,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5

{{1,5,6},{2,7},{3},{4}} => [5,7,3,4,6,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6

{{1,5,6},{2},{3,7},{4}} => [5,2,7,4,6,1,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5

{{1,5,6},{2},{3},{4,7}} => [5,2,3,7,6,1,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5

{{1,5,6},{2},{3},{4},{7}} => [5,2,3,4,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5

{{1,5,7},{2,6},{3},{4}} => [5,6,3,4,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 5

{{1,5},{2,6,7},{3},{4}} => [5,6,3,4,1,7,2] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 5

{{1,5},{2,6},{3,7},{4}} => [5,6,7,4,1,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5

{{1,5},{2,6},{3},{4,7}} => [5,6,3,7,1,2,4] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5

{{1,5},{2,6},{3},{4},{7}} => [5,6,3,4,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5

{{1,5,7},{2},{3,6},{4}} => [5,2,6,4,7,3,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5

{{1,5},{2,7},{3,6},{4}} => [5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6

{{1,5},{2},{3,6,7},{4}} => [5,2,6,4,1,7,3] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 5

{{1,5},{2},{3,6},{4,7}} => [5,2,6,7,1,3,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5

{{1,5},{2},{3,6},{4},{7}} => [5,2,6,4,1,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5

{{1,5,7},{2},{3},{4,6}} => [5,2,3,6,7,4,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5

{{1,5},{2,7},{3},{4,6}} => [5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6

{{1,5},{2},{3,7},{4,6}} => [5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5

{{1,5},{2},{3},{4,6,7}} => [5,2,3,6,1,7,4] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5

{{1,5},{2},{3},{4,6},{7}} => [5,2,3,6,1,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5

{{1,5,7},{2},{3},{4},{6}} => [5,2,3,4,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5

{{1,5},{2,7},{3},{4},{6}} => [5,7,3,4,1,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6

{{1,5},{2},{3,7},{4},{6}} => [5,2,7,4,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5

{{1,5},{2},{3},{4,7},{6}} => [5,2,3,7,1,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5

{{1,5},{2},{3},{4},{6,7}} => [5,2,3,4,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5

{{1,5},{2},{3},{4},{6},{7}} => [5,2,3,4,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5

{{1,6,7},{2,5},{3},{4}} => [6,5,3,4,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6

{{1,6},{2,5,7},{3},{4}} => [6,5,3,4,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6

{{1,6},{2,5},{3,7},{4}} => [6,5,7,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

{{1,6},{2,5},{3},{4,7}} => [6,5,3,7,2,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6

{{1,6},{2,5},{3},{4},{7}} => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6

{{1,7},{2,5,6},{3},{4}} => [7,5,3,4,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,5,6,7},{3},{4}} => [1,5,3,4,6,7,2] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 4

{{1},{2,5,6},{3,7},{4}} => [1,5,7,4,6,2,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5

{{1},{2,5,6},{3},{4,7}} => [1,5,3,7,6,2,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4

{{1},{2,5,6},{3},{4},{7}} => [1,5,3,4,6,2,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4

{{1,7},{2,5},{3,6},{4}} => [7,5,6,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,5,7},{3,6},{4}} => [1,5,6,4,7,3,2] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4

{{1},{2,5},{3,6,7},{4}} => [1,5,6,4,2,7,3] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4

{{1},{2,5},{3,6},{4,7}} => [1,5,6,7,2,3,4] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4

{{1},{2,5},{3,6},{4},{7}} => [1,5,6,4,2,3,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4

{{1,7},{2,5},{3},{4,6}} => [7,5,3,6,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,5,7},{3},{4,6}} => [1,5,3,6,7,4,2] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 4

{{1},{2,5},{3,7},{4,6}} => [1,5,7,6,2,4,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5

{{1},{2,5},{3},{4,6,7}} => [1,5,3,6,2,7,4] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 4

{{1},{2,5},{3},{4,6},{7}} => [1,5,3,6,2,4,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 4

{{1,7},{2,5},{3},{4},{6}} => [7,5,3,4,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,5,7},{3},{4},{6}} => [1,5,3,4,7,6,2] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4

{{1},{2,5},{3,7},{4},{6}} => [1,5,7,4,2,6,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5

{{1},{2,5},{3},{4,7},{6}} => [1,5,3,7,2,6,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4

{{1},{2,5},{3},{4},{6,7}} => [1,5,3,4,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4

{{1},{2,5},{3},{4},{6},{7}} => [1,5,3,4,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4

{{1,6,7},{2},{3,5},{4}} => [6,2,5,4,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6

{{1,6},{2,7},{3,5},{4}} => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

{{1,6},{2},{3,5,7},{4}} => [6,2,5,4,7,1,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6

{{1,6},{2},{3,5},{4,7}} => [6,2,5,7,3,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6

{{1,6},{2},{3,5},{4},{7}} => [6,2,5,4,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6

{{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,6,7},{3,5},{4}} => [1,6,5,4,3,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 5

{{1},{2,6},{3,5,7},{4}} => [1,6,5,4,7,2,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 5

{{1},{2,6},{3,5},{4,7}} => [1,6,5,7,3,2,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5

{{1},{2,6},{3,5},{4},{7}} => [1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5

{{1,7},{2},{3,5,6},{4}} => [7,2,5,4,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3,5,6},{4}} => [1,7,5,4,6,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,5,6,7},{4}} => [1,2,5,4,6,7,3] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 3

{{1},{2},{3,5,6},{4,7}} => [1,2,5,7,6,3,4] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4

{{1},{2},{3,5,6},{4},{7}} => [1,2,5,4,6,3,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3

{{1,7},{2},{3,5},{4,6}} => [7,2,5,6,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3,5},{4,6}} => [1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,5,7},{4,6}} => [1,2,5,6,7,4,3] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3

{{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 3

{{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 3

{{1,7},{2},{3,5},{4},{6}} => [7,2,5,4,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3,5},{4},{6}} => [1,7,5,4,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,5,7},{4},{6}} => [1,2,5,4,7,6,3] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3

{{1},{2},{3,5},{4,7},{6}} => [1,2,5,7,3,6,4] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4

{{1},{2},{3,5},{4},{6,7}} => [1,2,5,4,3,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3

{{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3

{{1,6,7},{2},{3},{4,5}} => [6,2,3,5,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6

{{1,6},{2,7},{3},{4,5}} => [6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

{{1,6},{2},{3,7},{4,5}} => [6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

{{1,6},{2},{3},{4,5,7}} => [6,2,3,5,7,1,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6

{{1,6},{2},{3},{4,5},{7}} => [6,2,3,5,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6

{{1,7},{2,6},{3},{4,5}} => [7,6,3,5,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,6,7},{3},{4,5}} => [1,6,3,5,4,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 5

{{1},{2,6},{3,7},{4,5}} => [1,6,7,5,4,2,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5

{{1},{2,6},{3},{4,5,7}} => [1,6,3,5,7,2,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 5

{{1},{2,6},{3},{4,5},{7}} => [1,6,3,5,4,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5

{{1,7},{2},{3,6},{4,5}} => [7,2,6,5,4,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,6,7},{4,5}} => [1,2,6,5,4,7,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4

{{1},{2},{3,6},{4,5,7}} => [1,2,6,5,7,3,4] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4

{{1},{2},{3,6},{4,5},{7}} => [1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4

{{1,7},{2},{3},{4,5,6}} => [7,2,3,5,6,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3},{4,5,6}} => [1,7,3,5,6,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,7},{4,5,6}} => [1,2,7,5,6,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

{{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2

{{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2

{{1,7},{2},{3},{4,5},{6}} => [7,2,3,5,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3},{4,5},{6}} => [1,7,3,5,4,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,7},{4,5},{6}} => [1,2,7,5,4,6,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

{{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3

{{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2

{{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2

{{1,6,7},{2},{3},{4},{5}} => [6,2,3,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6

{{1,6},{2,7},{3},{4},{5}} => [6,7,3,4,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6

{{1,6},{2},{3,7},{4},{5}} => [6,2,7,4,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6

{{1,6},{2},{3},{4,7},{5}} => [6,2,3,7,5,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6

{{1,6},{2},{3},{4},{5,7}} => [6,2,3,4,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6

{{1,6},{2},{3},{4},{5},{7}} => [6,2,3,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6

{{1,7},{2,6},{3},{4},{5}} => [7,6,3,4,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,6,7},{3},{4},{5}} => [1,6,3,4,5,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 5

{{1},{2,6},{3,7},{4},{5}} => [1,6,7,4,5,2,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5

{{1},{2,6},{3},{4,7},{5}} => [1,6,3,7,5,2,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5

{{1},{2,6},{3},{4},{5,7}} => [1,6,3,4,7,2,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 5

{{1},{2,6},{3},{4},{5},{7}} => [1,6,3,4,5,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5

{{1,7},{2},{3,6},{4},{5}} => [7,2,6,4,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3,6},{4},{5}} => [1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,6,7},{4},{5}} => [1,2,6,4,5,7,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4

{{1},{2},{3,6},{4,7},{5}} => [1,2,6,7,5,3,4] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4

{{1},{2},{3,6},{4},{5,7}} => [1,2,6,4,7,3,5] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4

{{1},{2},{3,6},{4},{5},{7}} => [1,2,6,4,5,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4

{{1,7},{2},{3},{4,6},{5}} => [7,2,3,6,5,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3},{4,6},{5}} => [1,7,3,6,5,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,7},{4,6},{5}} => [1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

{{1},{2},{3},{4,6,7},{5}} => [1,2,3,6,5,7,4] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 3

{{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3

{{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3

{{1,7},{2},{3},{4},{5,6}} => [7,2,3,4,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3},{4},{5,6}} => [1,7,3,4,6,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,7},{4},{5,6}} => [1,2,7,4,6,5,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

{{1},{2},{3},{4,7},{5,6}} => [1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

{{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2

{{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2

{{1,7},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7

{{1},{2,7},{3},{4},{5},{6}} => [1,7,3,4,5,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6

{{1},{2},{3,7},{4},{5},{6}} => [1,2,7,4,5,6,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5

{{1},{2},{3},{4,7},{5},{6}} => [1,2,3,7,5,6,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4

{{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3

{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2

{{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] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1

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Description

We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows:
In the list $L$ delete the first entry $c_0$ and substract from all other entries $n-1$ and then append the last element 1 (this was suggested by Christian Stump). The result is a Kupisch series of an LNakayama algebra.
Example:
[5,6,6,6,6] goes into [2,2,2,2,1].
Now associate to the CNakayama algebra with the above properties the Dyck path corresponding to the Kupisch series of the LNakayama algebra.
The statistic return the global dimension of the CNakayama algebra divided by 2.

Map

to permutation

Description

Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.

Map

zeta map

Description

The zeta map on Dyck paths.
The zeta map $\zeta$ is a bijection on Dyck paths of semilength $n$.
It was defined in [1, Theorem 1], see also [2, Theorem 3.15] and sends the bistatistic (area, dinv) to the bistatistic (bounce, area). It is defined by sending a Dyck path $D$ with corresponding area sequence $a=(a_1,\ldots,a_n)$ to a Dyck path as follows:

First, build an intermediate Dyck path consisting of $d_1$ north steps, followed by $d_1$ east steps, followed by $d_2$ north steps and $d_2$ east steps, and so on, where $d_i$ is the number of $i-1$'s within the sequence $a$.
For example, given $a=(0,1,2,2,2,3,1,2)$, we build the path
$$NE\ NNEE\ NNNNEEEE\ NE.$$
Next, the rectangles between two consecutive peaks are filled. Observe that such the rectangle between the $k$th and the $(k+1)$st peak must be filled by $d_k$ east steps and $d_{k+1}$ north steps. In the above example, the rectangle between the second and the third peak must be filled by $2$ east and $4$ north steps, the $2$ being the number of $1$'s in $a$, and $4$ being the number of $2$'s. To fill such a rectangle, scan through the sequence a from left to right, and add east or north steps whenever you see a $k-1$ or $k$, respectively. So to fill the $2\times 4$ rectangle, we look for $1$'s and $2$'s in the sequence and see $122212$, so this rectangle gets filled with $ENNNEN$.
The complete path we obtain in thus
$$NENNENNNENEEENEE.$$

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.