- FindStat

Identifier

Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
St000185: Integer partitions ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 984 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[] => [] => [] => [] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[6,5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,8,7] => [4,4] => 4

[6,6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [4,4] => 4

[6,5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,7,3,4,8,6] => [4,4] => 4

[4,4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [4,4] => 4

[6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,8] => [5,3] => 3

[5,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6,8] => [5,3] => 3

[7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,6,3,7,4,8,5] => [4,4] => 4

[6,5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,6,1,7,3,4,8,5] => [4,4] => 4

[6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5,8] => [5,3] => 3

[7,6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,8,4,5,7] => [5,3] => 3

[5,5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,6,8,1,3,4,5,7] => [5,3] => 3

[6,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,8,5,7] => [5,3] => 3

[7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,8,7] => [5,3] => 3

[7,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,8,7] => [5,3] => 3

[6,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,8,7] => [5,3] => 3

[6,5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,7,4,8,5,6] => [5,3] => 3

[6,6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6,8] => [6,2] => 2

[7,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,8,3,4,5,6,7] => [6,2] => 2

[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7] => [4,4] => 4

[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [4,4] => 4

[7,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,8,7] => [4,4] => 4

[6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,8,7] => [4,4] => 4

[5,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,8,7] => [4,4] => 4

[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,8,5,7] => [4,4] => 4

[6,5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,8,5,7] => [4,4] => 4

[6,5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5,8] => [5,3] => 3

[5,4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [3,4,6,1,7,2,8,5] => [5,3] => 3

[4,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,4,6,7,1,8,2,5] => [5,3] => 3

[6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6,8] => [5,3] => 3

[4,4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6,8] => [5,3] => 3

[7,6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,2,8,5,6,7] => [5,3] => 3

[6,5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,2,8,6,7] => [5,3] => 3

[5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,8,7] => [5,3] => 3

[6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8] => [6,2] => 2

[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7] => [4,4] => 4

[6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,8,7] => [4,4] => 4

[6,5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,8,7] => [4,4] => 4

[4,4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [4,4] => 4

[7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6] => [4,4] => 4

[5,5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,7,1,2,4,8,6] => [4,4] => 4

[4,4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [4,4] => 4

[7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6,8] => [5,3] => 3

[6,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6,8] => [5,3] => 3

[5,5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6,8] => [5,3] => 3

[7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,8] => [5,3] => 3

[6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [5,3] => 3

[7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => [5,3] => 3

[7,6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [5,3] => 3

[7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5] => [4,4] => 4

[7,6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,8,7] => [5,3] => 3

[7,4,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,8,7] => [5,3] => 3

[7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7] => [4,4] => 4

[6,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => [4,4] => 4

[6,5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,8,7] => [4,4] => 4

[5,4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [4,4] => 4

[5,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5,6,1,7,2,8,3] => [5,3] => 3

[7,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,1,5,6,7,8,2,3] => [5,3] => 3

[7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,7,3,8,6] => [4,4] => 4

[4,4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [4,4] => 4

[7,6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6,8] => [5,3] => 3

[7,6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6,8] => [5,3] => 3

[7,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6,8] => [5,3] => 3

[7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5] => [4,4] => 4

[7,5,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5,8] => [5,3] => 3

[7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,8,3,5,7] => [5,3] => 3

[6,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,8,3,5,7] => [5,3] => 3

[7,6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,8,5,7] => [5,3] => 3

[7,5,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [5,3] => 3

[7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,8,7] => [5,3] => 3

[6,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,8,7] => [5,3] => 3

[7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4] => [4,4] => 4

[6,5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [5,6,1,7,2,3,8,4] => [4,4] => 4

[7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4,8] => [5,3] => 3

[7,6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4,8] => [5,3] => 3

[7,5,4,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4,8] => [5,3] => 3

[7,6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,6,2,8,3,4,7] => [5,3] => 3

[7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,7,2,8,3,4,5] => [5,3] => 3

[3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [6,3] => 3

[3,3,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,5,6,7,8,9,1,2,4] => [6,3] => 3

[3,3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [7,3] => 3

[3,3,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,7,8,9,1,2,6] => [6,3] => 3

[4,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,5,6,7,8,1,9,2,3] => [6,3] => 3

[4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [5,4] => 4

[4,4,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => [6,3] => 3

[4,4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [6,4] => 4

[5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [5,4] => 4

[6,6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [6,4] => 4

[6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [6,3] => 3

[7,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,8,1,9,2,3,4,5,6] => [6,3] => 3

[8,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,2] => [7,2] => 2

[8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,8,2,9,3,4,5,6] => [6,3] => 3

[9,8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [8,1,9,2,10,3,4,5,6,7] => [7,3] => 3

[7,7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [7,3] => 3

[8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9] => [5,4] => 4

[7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7,9] => [5,4] => 4

[7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7,9] => [5,4] => 4

[7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7,9] => [5,4] => 4

[7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7] => [5,4] => 4

[7,6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,9,8] => [5,4] => 4

[7,6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,9,8] => [5,4] => 4

[7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,9,8] => [5,4] => 4

[9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [5,5] => 5

[8,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7,10,9] => [5,5] => 5

[6,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,8,7,9] => [5,4] => 4

[8,7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7,10,9] => [5,5] => 5

[7,5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,8,3,5,7,9] => [5,4] => 4

[8,7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7,10,9] => [5,5] => 5

[7,6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,8,9,5,7] => [5,4] => 4

[8,7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => [5,5] => 5

[7,6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,8,9] => [6,3] => 3

[8,7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7,10] => [6,4] => 4

[7,6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,8,6,9,7] => [5,4] => 4

[8,7,6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,9,8,10] => [6,4] => 4

[7,6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5,9,8] => [5,4] => 4

[8,7,6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,9,8,10] => [6,4] => 4

[8,7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,9,8,10] => [6,4] => 4

[8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,9] => [5,4] => 4

[8,7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7,9] => [5,4] => 4

[8,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,9,8] => [5,4] => 4

[8,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => [5,4] => 4

[9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [5,5] => 5

[8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7,9] => [5,4] => 4

[8,7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5,9] => [5,4] => 4

[9,7,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8,10] => [6,4] => 4

[5,5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [5,5] => 5

[7,7,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [4,9,1,2,3,5,6,7,8] => [7,2] => 2

[8,5,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7,9] => [6,3] => 3

[8,7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,8,7,9] => [6,3] => 3

[7,7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,9,1,3,4,5,6,7,8] => [7,2] => 2

[5,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6,9,8] => [6,3] => 3

[6,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,8,7,9] => [6,3] => 3

[5,4,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,7,10,9] => [7,3] => 3

[6,5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,7,5,8,6,9] => [6,3] => 3

[6,5,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6,9,8,10] => [7,3] => 3

[7,6,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,8,7,10,9] => [6,4] => 4

[8,6,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6,9,8] => [5,4] => 4

[7,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,8,7,9] => [6,3] => 3

[7,6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,8,7,9] => [6,3] => 3

[7,6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,7,3,8,5,6,9] => [5,4] => 4

[7,6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,8,7,9] => [5,4] => 4

[7,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7,9] => [5,4] => 4

[6,6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6,9,8] => [5,4] => 4

[5,5,5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,7,9,1,2,4,6,8] => [5,4] => 4

[5,4,4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5,7,8,1,9,2,4,6] => [5,4] => 4

[5,4,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,8,2,9,4] => [6,3] => 3

[5,4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2,9,8] => [6,3] => 3

[6,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [6,7,8,1,9,2,3,4,5] => [5,4] => 4

[5,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,6,7,8,1,9,2,3,4] => [5,4] => 4

[8,7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,8,3,5,7,9] => [6,3] => 3

[8,7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,8,3,9,5,7] => [5,4] => 4

[8,7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5,9] => [5,4] => 4

[7,6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,8,7,9] => [5,4] => 4

[9,8,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7,10,9,11] => [6,5] => 5

[8,7,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,8,7,10,9] => [5,5] => 5

[7,6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,8,7,9] => [5,4] => 4

[7,7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,8,7,9] => [5,4] => 4

[7,7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,8,7,9] => [5,4] => 4

[8,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7,10,9] => [5,5] => 5

[9,9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7,10,9,11] => [6,5] => 5

[8,7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,6,3,7,4,8,5,9] => [5,4] => 4

[9,8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7,10,9] => [5,5] => 5

[10,9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,10,9,11] => [6,5] => 5

[8,6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,8,7,9] => [5,4] => 4

[8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,7,2,8,3,9,4,5] => [5,4] => 4

[8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4,9] => [5,4] => 4

[8,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [7,1,8,2,3,9,4,5,6] => [6,3] => 3

[9,8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [7,1,8,2,9,3,10,4,5,6] => [6,4] => 4

[8,7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [6,1,7,2,8,3,4,9,5] => [5,4] => 4

[9,8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [5,5] => 5

[8,7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,9,4,8] => [5,4] => 4

[9,8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4,10,9] => [5,5] => 5

[8,7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,7,3,8,6,9] => [5,4] => 4

[4,4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,6,7,8,9,1,2,3,5] => [5,4] => 4

[5,5,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,7,8,9,1,2,3,4,6] => [5,4] => 4

[6,6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,8,9,1,2,3,4,5,7] => [6,3] => 3

[7,7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,8,5,7,9] => [5,4] => 4

[7,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6,9,8] => [5,4] => 4

[6,6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,8,9,1,2,3,4,6,7] => [6,3] => 3

[7,7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,8,7,9] => [6,3] => 3

[6,5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,8,7,9] => [6,3] => 3

[8,5,4,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,8,7,9] => [6,3] => 3

[6,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6,9,8] => [5,4] => 4

[7,6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6,9,8] => [5,4] => 4

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Description

The weighted size of a partition.
Let $\lambda = (\lambda_0\geq\lambda_1 \geq \dots\geq\lambda_m)$ be an integer partition. Then the weighted size of $\lambda$ is
$$\sum_{i=0}^m i \cdot \lambda_i.$$
This is also the sum of the leg lengths of the cells in $\lambda$, or
$$ \sum_i \binom{\lambda^{\prime}_i}{2} $$
where $\lambda^{\prime}$ is the conjugate partition of $\lambda$.
This is the minimal number of inversions a permutation with the given shape can have, see [1, cor.2.2].
This is also the smallest possible sum of the entries of a semistandard tableau (allowing 0 as a part) of shape $\lambda=(\lambda_0,\lambda_1,\ldots,\lambda_m)$, obtained uniquely by placing $i-1$ in all the cells of the $i$th row of $\lambda$, see [2, eq.7.103].

Map

Robinson-Schensted tableau shape

Description

Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.

Map

to 321-avoiding permutation

Description

Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.

Map

to Dyck path

Description

Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.