- FindStat

Identifier

Mp00311: Plane partitions —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St000990: Permutations ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 473 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = q^{2}$

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

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

$F_{4} = 3\ q + 7\ q^{2} + 3\ q^{3}$

$F_{5} = 3\ q + 12\ q^{2} + 9\ q^{3}$

Description

The first ascent of a permutation.
For a permutation

$\pi$ , this is the smallest index such that

$\pi(i) < \pi(i+1)$ .
For the first descent, see St000654The first descent of a permutation..

Map

to Dyck path

Description

Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.

Map

to partition

Description

The underlying integer partition of a plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.

Map

to 132-avoiding permutation

Description

Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].