- FindStat

Identifier

Mp00080: Set partitions —to permutation⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
St000672: Permutations ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 573 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = 1$

$F_{2} = 1 + q$

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

$F_{4} = 1 + 2\ q + 11\ q^{2} + q^{3}$

$F_{5} = 10\ q + 15\ q^{2} + 26\ q^{3} + q^{4}$

$F_{6} = 1 + 6\ q + 66\ q^{2} + 72\ q^{3} + 57\ q^{4} + q^{5}$

Description

The number of minimal elements in Bruhat order not less than the permutation.
The minimal elements in question are biGrassmannian, that is

$1\dots r\ \ a+1\dots b\ \ r+1\dots a\ \ b+1\dots$
for some

$(r,a,b)$ .
This is also the size of Fulton's essential set of the reverse permutation, according to [ex.4.7, 2].

Map

to permutation

Description

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

Map

inverse first fundamental transformation

Description

Let

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

$\sigma$ to the permutation

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

Map

Kreweras complement

Description

Sends the permutation

$\pi \in \mathfrak{S}_n$ to the permutation

$\pi^{-1}c$ where

$c = (1,\ldots,n)$ is the long cycle.