Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
St000246: Permutations ⟶ ℤ (values match St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.)
Values
[1] => [] => [] => [] => 0
[2] => [] => [] => [] => 0
[1,1] => [1] => [1,0,1,0] => [1,2] => 1
[3] => [] => [] => [] => 0
[2,1] => [1] => [1,0,1,0] => [1,2] => 1
[1,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[4] => [] => [] => [] => 0
[3,1] => [1] => [1,0,1,0] => [1,2] => 1
[2,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[2,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[1,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[5] => [] => [] => [] => 0
[4,1] => [1] => [1,0,1,0] => [1,2] => 1
[3,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[3,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[2,2,1] => [2,1] => [1,0,1,0,1,0] => [1,2,3] => 3
[2,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[1,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 4
[6] => [] => [] => [] => 0
[5,1] => [1] => [1,0,1,0] => [1,2] => 1
[4,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[4,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[3,3] => [3] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 3
[3,2,1] => [2,1] => [1,0,1,0,1,0] => [1,2,3] => 3
[3,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[2,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 4
[2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 4
[2,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 4
[1,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 5
[7] => [] => [] => [] => 0
[6,1] => [1] => [1,0,1,0] => [1,2] => 1
[5,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[5,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[4,3] => [3] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 3
[4,2,1] => [2,1] => [1,0,1,0,1,0] => [1,2,3] => 3
[4,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[3,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 4
[3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 4
[3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 4
[3,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 4
[2,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 5
[2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 5
[2,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 5
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 6
[8] => [] => [] => [] => 0
[7,1] => [1] => [1,0,1,0] => [1,2] => 1
[6,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[6,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[5,3] => [3] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 3
[5,2,1] => [2,1] => [1,0,1,0,1,0] => [1,2,3] => 3
[5,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[4,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 4
[4,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 4
[4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 4
[4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 4
[4,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 4
[3,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 5
[3,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 5
[3,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 5
[3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 5
[3,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 5
[2,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 6
[2,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 6
[2,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 6
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 6
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 7
[9] => [] => [] => [] => 0
[8,1] => [1] => [1,0,1,0] => [1,2] => 1
[7,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[7,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[6,3] => [3] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 3
[6,2,1] => [2,1] => [1,0,1,0,1,0] => [1,2,3] => 3
[6,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[5,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 4
[5,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 4
[5,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 4
[5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 4
[5,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 4
[4,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 5
[4,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 5
[4,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 5
[4,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 5
[4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 5
[4,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 5
[3,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 6
[3,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 6
[3,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 6
[3,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 6
[3,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 6
[3,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 6
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 6
[2,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 7
[2,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => 7
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => 7
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 7
[1,1,1,1,1,1,1,1,1] => [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] => [1,9,8,7,6,5,4,3,2] => 8
[10] => [] => [] => [] => 0
[9,1] => [1] => [1,0,1,0] => [1,2] => 1
[8,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[8,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[7,3] => [3] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 3
>>> Load all 1089 entries. <<<[7,2,1] => [2,1] => [1,0,1,0,1,0] => [1,2,3] => 3
[7,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[6,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 4
[6,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 4
[6,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 4
[6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 4
[6,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 4
[5,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 5
[5,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 5
[5,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 5
[5,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 5
[5,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 5
[5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 5
[5,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 5
[4,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 6
[4,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 6
[4,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 6
[4,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 6
[4,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 6
[4,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 6
[4,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 6
[4,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 6
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 6
[3,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 7
[3,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 7
[3,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 7
[3,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => 7
[3,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 7
[3,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => 7
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => 7
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 7
[2,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 8
[2,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 8
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => 8
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => 8
[2,1,1,1,1,1,1,1,1] => [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] => [1,9,8,7,6,5,4,3,2] => 8
[1,1,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,7,6,5,4,3,2] => 9
[11] => [] => [] => [] => 0
[10,1] => [1] => [1,0,1,0] => [1,2] => 1
[9,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[9,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[8,3] => [3] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 3
[8,2,1] => [2,1] => [1,0,1,0,1,0] => [1,2,3] => 3
[8,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[7,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 4
[7,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 4
[7,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 4
[7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 4
[7,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 4
[6,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 5
[6,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 5
[6,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 5
[6,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 5
[6,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 5
[6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 5
[6,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 5
[5,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => 6
[5,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 6
[5,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 6
[5,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 6
[5,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 6
[5,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 6
[5,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 6
[5,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 6
[5,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 6
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 6
[4,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 7
[4,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 7
[4,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 7
[4,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 7
[4,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 7
[4,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 7
[4,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => 7
[4,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 7
[4,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => 7
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => 7
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 7
[3,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 8
[3,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 8
[3,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 8
[3,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => 8
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => 8
[3,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 8
[3,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 8
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => 8
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => 8
[3,1,1,1,1,1,1,1,1] => [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] => [1,9,8,7,6,5,4,3,2] => 8
[2,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 9
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => 9
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => 9
[2,2,1,1,1,1,1,1,1] => [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] => [1,9,8,7,5,6,4,3,2] => 9
[2,1,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,7,6,5,4,3,2] => 9
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 10
[12] => [] => [] => [] => 0
[11,1] => [1] => [1,0,1,0] => [1,2] => 1
[10,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[10,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[9,3] => [3] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 3
[9,2,1] => [2,1] => [1,0,1,0,1,0] => [1,2,3] => 3
[9,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[8,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 4
[8,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 4
[8,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 4
[8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 4
[8,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 4
[7,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 5
[7,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 5
[7,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 5
[7,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 5
[7,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 5
[7,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 5
[7,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 5
[6,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => 6
[6,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => 6
[6,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 6
[6,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 6
[6,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 6
[6,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 6
[6,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 6
[6,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 6
[6,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 6
[6,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 6
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 6
[5,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => 7
[5,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => 7
[5,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 7
[5,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 7
[5,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 7
[5,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 7
[5,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 7
[5,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 7
[5,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => 7
[5,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 7
[5,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => 7
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => 7
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 7
[4,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 8
[4,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 8
[4,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 8
[4,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 8
[4,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 8
[4,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 8
[4,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 8
[4,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 8
[4,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => 8
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => 8
[4,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 8
[4,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 8
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => 8
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => 8
[4,1,1,1,1,1,1,1,1] => [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] => [1,9,8,7,6,5,4,3,2] => 8
[3,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 9
[3,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 9
[3,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 9
[3,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => 9
[3,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => 9
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => 9
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => 9
[3,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 9
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => 9
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => 9
[3,2,1,1,1,1,1,1,1] => [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] => [1,9,8,7,5,6,4,3,2] => 9
[3,1,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,7,6,5,4,3,2] => 9
[2,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 10
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 10
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => 10
[2,2,2,1,1,1,1,1,1] => [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] => [1,9,8,5,7,6,4,3,2] => 10
[2,2,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,6,7,5,4,3,2] => 10
[2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 10
[13] => [] => [] => [] => 0
[12,1] => [1] => [1,0,1,0] => [1,2] => 1
[11,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[11,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[10,3] => [3] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 3
[10,2,1] => [2,1] => [1,0,1,0,1,0] => [1,2,3] => 3
[10,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[9,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 4
[9,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 4
[9,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 4
[9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 4
[9,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 4
[8,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 5
[8,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 5
[8,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 5
[8,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 5
[8,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 5
[8,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 5
[8,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 5
[7,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => 6
[7,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => 6
[7,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 6
[7,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 6
[7,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 6
[7,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 6
[7,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 6
[7,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 6
[7,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 6
[7,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 6
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 6
[6,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => 7
[6,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => 7
[6,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => 7
[6,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 7
[6,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 7
[6,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 7
[6,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 7
[6,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 7
[6,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 7
[6,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => 7
[6,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 7
[6,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => 7
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => 7
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 7
[5,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 8
[5,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => 8
[5,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 8
[5,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 8
[5,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 8
[5,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 8
[5,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 8
[5,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 8
[5,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 8
[5,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 8
[5,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 8
[5,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => 8
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => 8
[5,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 8
[5,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 8
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => 8
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => 8
[5,1,1,1,1,1,1,1,1] => [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] => [1,9,8,7,6,5,4,3,2] => 8
[4,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => 9
[4,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 9
[4,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 9
[4,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 9
[4,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 9
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => 9
[4,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 9
[4,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 9
[4,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 9
[4,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => 9
[4,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => 9
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => 9
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => 9
[4,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 9
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => 9
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => 9
[4,2,1,1,1,1,1,1,1] => [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] => [1,9,8,7,5,6,4,3,2] => 9
[4,1,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,7,6,5,4,3,2] => 9
[3,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 10
[3,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => 10
[3,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 10
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => 10
[3,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 10
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => 10
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => 10
[3,3,1,1,1,1,1,1,1] => [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] => [1,9,8,6,5,7,4,3,2] => 10
[3,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 10
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 10
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => 10
[3,2,2,1,1,1,1,1,1] => [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] => [1,9,8,5,7,6,4,3,2] => 10
[3,2,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,6,7,5,4,3,2] => 10
[3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 10
[14] => [] => [] => [] => 0
[13,1] => [1] => [1,0,1,0] => [1,2] => 1
[12,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[12,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[11,3] => [3] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 3
[11,2,1] => [2,1] => [1,0,1,0,1,0] => [1,2,3] => 3
[11,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[10,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 4
[10,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 4
[10,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 4
[10,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 4
[10,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 4
[9,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 5
[9,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 5
[9,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 5
[9,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 5
[9,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 5
[9,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 5
[9,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 5
[8,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => 6
[8,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => 6
[8,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 6
[8,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 6
[8,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 6
[8,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 6
[8,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 6
[8,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 6
[8,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 6
[8,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 6
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 6
[7,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => 7
[7,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => 7
[7,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => 7
[7,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => 7
[7,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 7
[7,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 7
[7,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 7
[7,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 7
[7,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 7
[7,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 7
[7,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => 7
[7,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 7
[7,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => 7
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => 7
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 7
[6,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => 8
[6,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => 8
[6,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 8
[6,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => 8
[6,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 8
[6,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 8
[6,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 8
[6,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 8
[6,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 8
[6,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 8
[6,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 8
[6,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 8
[6,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 8
[6,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => 8
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => 8
[6,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 8
[6,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 8
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => 8
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => 8
[6,1,1,1,1,1,1,1,1] => [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] => [1,9,8,7,6,5,4,3,2] => 8
[5,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 9
[5,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => 9
[5,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 9
[5,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => 9
[5,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 9
[5,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => 9
[5,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 9
[5,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 9
[5,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 9
[5,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 9
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => 9
[5,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 9
[5,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 9
[5,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 9
[5,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => 9
[5,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => 9
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => 9
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => 9
[5,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 9
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => 9
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => 9
[5,2,1,1,1,1,1,1,1] => [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] => [1,9,8,7,5,6,4,3,2] => 9
[5,1,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,7,6,5,4,3,2] => 9
[4,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => 10
[4,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => 10
[4,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => 10
[4,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 10
[4,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 10
[4,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => 10
[4,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 10
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => 10
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => 10
[4,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 10
[4,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => 10
[4,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 10
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => 10
[4,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 10
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => 10
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => 10
[4,3,1,1,1,1,1,1,1] => [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] => [1,9,8,6,5,7,4,3,2] => 10
[4,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 10
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 10
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => 10
[4,2,2,1,1,1,1,1,1] => [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] => [1,9,8,5,7,6,4,3,2] => 10
[4,2,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,6,7,5,4,3,2] => 10
[4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 10
[3,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 11
[3,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 11
[3,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => 11
[3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => 11
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 12
[15] => [] => [] => [] => 0
[14,1] => [1] => [1,0,1,0] => [1,2] => 1
[13,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[13,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[12,3] => [3] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 3
[12,2,1] => [2,1] => [1,0,1,0,1,0] => [1,2,3] => 3
[12,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[11,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 4
[11,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 4
[11,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 4
[11,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 4
[11,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 4
[10,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 5
[10,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 5
[10,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 5
[10,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 5
[10,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 5
[10,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 5
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 5
[9,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => 6
[9,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => 6
[9,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 6
[9,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 6
[9,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 6
[9,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 6
[9,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 6
[9,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 6
[9,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 6
[9,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 6
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 6
[8,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => 7
[8,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => 7
[8,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => 7
[8,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => 7
[8,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 7
[8,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 7
[8,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 7
[8,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 7
[8,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 7
[8,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 7
[8,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => 7
[8,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 7
[8,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => 7
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => 7
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 7
[7,7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => 8
[7,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => 8
[7,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => 8
[7,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 8
[7,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => 8
[7,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 8
[7,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 8
[7,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 8
[7,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 8
[7,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 8
[7,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 8
[7,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 8
[7,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 8
[7,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 8
[7,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => 8
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => 8
[7,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 8
[7,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 8
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => 8
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => 8
[7,1,1,1,1,1,1,1,1] => [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] => [1,9,8,7,6,5,4,3,2] => 8
[6,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => 9
[6,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => 9
[6,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => 9
[6,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 9
[6,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => 9
[6,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 9
[6,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => 9
[6,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 9
[6,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => 9
[6,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 9
[6,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 9
[6,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 9
[6,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 9
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => 9
[6,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 9
[6,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 9
[6,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 9
[6,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => 9
[6,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => 9
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => 9
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => 9
[6,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 9
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => 9
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => 9
[6,2,1,1,1,1,1,1,1] => [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] => [1,9,8,7,5,6,4,3,2] => 9
[6,1,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,7,6,5,4,3,2] => 9
[5,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 10
[5,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => 10
[5,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => 10
[5,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => 10
[5,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => 10
[5,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => 10
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => 10
[5,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => 10
[5,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => 10
[5,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => 10
[5,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 10
[5,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 10
[5,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => 10
[5,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 10
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => 10
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => 10
[5,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 10
[5,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => 10
[5,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 10
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => 10
[5,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 10
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => 10
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => 10
[5,3,1,1,1,1,1,1,1] => [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] => [1,9,8,6,5,7,4,3,2] => 10
[5,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 10
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 10
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => 10
[5,2,2,1,1,1,1,1,1] => [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] => [1,9,8,5,7,6,4,3,2] => 10
[5,2,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,6,7,5,4,3,2] => 10
[5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 10
[4,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 11
[4,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => 11
[4,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 11
[4,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => 11
[4,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => 11
[4,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 11
[4,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 11
[4,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 11
[4,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 11
[4,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => 11
[4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => 11
[3,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 12
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 12
[16] => [] => [] => [] => 0
[15,1] => [1] => [1,0,1,0] => [1,2] => 1
[14,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[14,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[13,3] => [3] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 3
[13,2,1] => [2,1] => [1,0,1,0,1,0] => [1,2,3] => 3
[13,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[12,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 4
[12,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 4
[12,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 4
[12,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 4
[12,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 4
[11,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 5
[11,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 5
[11,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 5
[11,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 5
[11,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 5
[11,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 5
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 5
[10,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => 6
[10,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => 6
[10,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 6
[10,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 6
[10,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 6
[10,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 6
[10,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 6
[10,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 6
[10,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 6
[10,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 6
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 6
[9,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => 7
[9,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => 7
[9,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => 7
[9,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => 7
[9,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 7
[9,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 7
[9,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 7
[9,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 7
[9,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 7
[9,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 7
[9,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => 7
[9,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 7
[9,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => 7
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => 7
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 7
[8,8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => 8
[8,7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => 8
[8,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => 8
[8,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => 8
[8,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 8
[8,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => 8
[8,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 8
[8,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 8
[8,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 8
[8,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 8
[8,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 8
[8,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 8
[8,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 8
[8,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 8
[8,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 8
[8,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => 8
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => 8
[8,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 8
[8,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 8
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => 8
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => 8
[8,1,1,1,1,1,1,1,1] => [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] => [1,9,8,7,6,5,4,3,2] => 8
[7,7,2] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => 9
[7,7,1,1] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => 9
[7,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => 9
[7,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => 9
[7,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => 9
[7,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 9
[7,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => 9
[7,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 9
[7,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => 9
[7,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 9
[7,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => 9
[7,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 9
[7,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 9
[7,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 9
[7,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 9
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => 9
[7,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 9
[7,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 9
[7,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 9
[7,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => 9
[7,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => 9
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => 9
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => 9
[7,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 9
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => 9
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => 9
[7,2,1,1,1,1,1,1,1] => [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] => [1,9,8,7,5,6,4,3,2] => 9
[7,1,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,7,6,5,4,3,2] => 9
[6,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => 10
[6,6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => 10
[6,6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => 10
[6,6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => 10
[6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => 10
[6,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 10
[6,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => 10
[6,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => 10
[6,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => 10
[6,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => 10
[6,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => 10
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => 10
[6,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => 10
[6,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => 10
[6,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => 10
[6,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 10
[6,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 10
[6,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => 10
[6,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 10
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => 10
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => 10
[6,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 10
[6,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => 10
[6,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 10
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => 10
[6,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 10
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => 10
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => 10
[6,3,1,1,1,1,1,1,1] => [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] => [1,9,8,6,5,7,4,3,2] => 10
[6,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 10
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 10
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => 10
[6,2,2,1,1,1,1,1,1] => [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] => [1,9,8,5,7,6,4,3,2] => 10
[6,2,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,6,7,5,4,3,2] => 10
[6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 10
[5,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => 11
[5,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => 11
[5,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 11
[5,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => 11
[5,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => 11
[5,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 11
[5,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => 11
[5,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 11
[5,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => 11
[5,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 11
[5,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => 11
[5,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => 11
[5,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 11
[5,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 11
[5,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 11
[5,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 11
[5,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => 11
[5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => 11
[4,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => 12
[4,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 12
[4,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => 12
[4,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => 12
[4,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => 12
[4,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 12
[4,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 12
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 12
[17] => [] => [] => [] => 0
[16,1] => [1] => [1,0,1,0] => [1,2] => 1
[15,2] => [2] => [1,1,0,0,1,0] => [2,1,3] => 2
[15,1,1] => [1,1] => [1,0,1,1,0,0] => [1,3,2] => 2
[14,3] => [3] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 3
[14,2,1] => [2,1] => [1,0,1,0,1,0] => [1,2,3] => 3
[14,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 3
[13,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 4
[13,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 4
[13,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 4
[13,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 4
[13,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 4
[12,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 5
[12,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 5
[12,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 5
[12,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 5
[12,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 5
[12,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 5
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 5
[11,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => 6
[11,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => 6
[11,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 6
[11,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 6
[11,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 6
[11,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 6
[11,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 6
[11,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 6
[11,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 6
[11,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => 6
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 6
[10,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => 7
[10,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => 7
[10,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => 7
[10,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => 7
[10,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 7
[10,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 7
[10,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 7
[10,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 7
[10,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 7
[10,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 7
[10,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => 7
[10,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 7
[10,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => 7
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => 7
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 7
[9,8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => 8
[9,7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => 8
[9,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => 8
[9,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => 8
[9,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 8
[9,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => 8
[9,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 8
[9,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 8
[9,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 8
[9,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 8
[9,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 8
[9,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 8
[9,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 8
[9,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 8
[9,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 8
[9,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => 8
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => 8
[9,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 8
[9,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 8
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => 8
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => 8
[9,1,1,1,1,1,1,1,1] => [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] => [1,9,8,7,6,5,4,3,2] => 8
[8,8,1] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,7,6,4,5,3,2,1,9] => 9
[8,7,2] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => 9
[8,7,1,1] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => 9
[8,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => 9
[8,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => 9
[8,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => 9
[8,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 9
[8,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => 9
[8,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 9
[8,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => 9
[8,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 9
[8,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => 9
[8,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 9
[8,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 9
[8,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 9
[8,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => 9
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => 9
[8,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 9
[8,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 9
[8,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 9
[8,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => 9
[8,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => 9
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => 9
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => 9
[8,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 9
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => 9
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => 9
[8,2,1,1,1,1,1,1,1] => [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] => [1,9,8,7,5,6,4,3,2] => 9
[8,1,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,7,6,5,4,3,2] => 9
[7,7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => 10
[7,7,2,1] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => 10
[7,7,1,1,1] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => 10
[7,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => 10
[7,6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => 10
[7,6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => 10
[7,6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => 10
[7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => 10
[7,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 10
[7,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => 10
[7,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => 10
[7,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => 10
[7,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => 10
[7,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => 10
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => 10
[7,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => 10
[7,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => 10
[7,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => 10
[7,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 10
[7,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 10
[7,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => 10
[7,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 10
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => 10
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => 10
[7,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 10
[7,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => 10
[7,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 10
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => 10
[7,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => 10
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => 10
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => 10
[7,3,1,1,1,1,1,1,1] => [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] => [1,9,8,6,5,7,4,3,2] => 10
[7,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 10
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 10
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => 10
[7,2,2,1,1,1,1,1,1] => [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] => [1,9,8,5,7,6,4,3,2] => 10
[7,2,1,1,1,1,1,1,1,1] => [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] => [1,10,9,8,6,7,5,4,3,2] => 10
[7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 10
[6,6,5] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => 11
[6,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => 11
[6,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => 11
[6,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 11
[6,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => 11
[6,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => 11
[6,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 11
[6,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => 11
[6,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 11
[6,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => 11
[6,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 11
[6,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => 11
[6,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => 11
[6,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 11
[6,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 11
[6,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 11
[6,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 11
[6,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => 11
[6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => 11
[5,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 12
[5,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => 12
[5,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 12
[5,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => 12
[5,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => 12
[5,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => 12
[5,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 12
[5,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => 12
[5,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 12
[5,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => 12
[5,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => 12
[5,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => 12
[5,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 12
[5,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 12
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 12
[4,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 13
[4,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 13
[4,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 13
[4,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 13
[6,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 15
[5,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 15
[6,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 14
[5,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 14
[4,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 14
[6,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 14
[5,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 14
[6,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 13
[5,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 13
[6,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 12
[6,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 14
[5,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 14
[6,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 13
[5,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 13
[6,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => 13
[5,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => 13
[6,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 12
[6,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 12
[6,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 14
[5,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 14
[6,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 13
[5,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 13
[6,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 13
[5,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 13
[6,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => 12
[6,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => 13
[5,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => 13
[6,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => 12
[6,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => 12
[6,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 12
[6,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 14
[5,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 14
[6,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 13
[5,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 13
[6,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 13
[5,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 13
[6,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => 12
[6,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 13
[5,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 13
[6,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 12
[6,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => 12
[6,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => 13
[5,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => 13
[6,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => 12
[6,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => 12
[6,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => 12
[6,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 12
[7,6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 21
[6,6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 21
[7,5,5,4,3,2,1] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 20
[6,5,5,4,3,2,1] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 20
[5,5,5,4,3,2,1] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 20
[7,6,4,4,3,2,1] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => 20
[6,6,4,4,3,2,1] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => 20
[7,6,5,4,3,1,1] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => 20
[6,6,5,4,3,1,1] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => 20
[7,6,5,4,3,2] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => 20
[6,6,5,4,3,2] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => 20
[7,6,5,4,3,1] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => 19
[6,6,5,4,3,1] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => 19
[7,6,5,4,2,1] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => 18
[5,5,5,4,2,1] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => 17
[7,6,5,3,2,1] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => 17
[6,6,5,3,2,1] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => 17
[5,5,5,3,2,1] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => 16
[7,6,4,3,2,1] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => 16
[6,6,4,3,2,1] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => 16
[7,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 15
[7,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 14
[7,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 13
[7,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 12
[7,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 11
[7,6,5,4,3] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => 18
[6,6,5,4,3] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => 18
[7,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 14
[7,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => 13
[7,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => 12
[7,6,5,4] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => 15
[7,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 12
[7,6,5] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => 11
[2,2,2,2,2,2,2,2,2] => [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] => [2,1,10,9,8,7,6,5,4,3] => 16
[3,3,3,3,3,3] => [3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 15
[4,3,3,3,3,3] => [3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 15
[4,4,4,4,4] => [4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 16
[5,5,5,5] => [5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 15
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 12
[6,6,6] => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 12
[7,6,6] => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 12
[10,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 8
[10,10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => 10
[6,6,6,6,6] => [6,6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 24
[11,7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => 10
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 12
[9,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => 9
[8,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => 10
[10,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => 10
[8,7,6] => [7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => 13
[9,8,7] => [8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => 15
[15,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 10
[8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => 28
[7,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => 28
[7,6,6,5,4,3,2,1] => [6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 27
[7,6,5,4,3,3,2,1] => [6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => 24
[9,8,7,6,5,4,3,2,1] => [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] => [1,2,3,4,5,6,7,8,9] => 36
[8,8,7,6,5,4,3,2,1] => [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] => [1,2,3,4,5,6,7,8,9] => 36
[6,6,6,5,4,3,2,1] => [6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 27
[8,7,7,6,5,4,3,2,1] => [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] => [1,2,3,4,5,6,7,9,8] => 35
[8,7,6,5,4,3,2] => [7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => 27
[8,7,6,5,3,2,1] => [7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => 24
[8,7,6,4,3,2,1] => [7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => 23
[8,7,5,4,3,2,1] => [7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => 22
[8,6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 21
[9,8,7,6,5,4,3,2] => [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] => [2,1,3,4,5,6,7,8,9] => 35
[8,7,6,5,4,3] => [7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => 25
[9,8,7,5,4,3,2,1] => [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] => [2,3,4,5,6,7,1,8,9] => 30
[8,5,5,4,3,2,1] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 20
[9,8,6,5,4,3,2,1] => [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] => [2,3,4,5,6,7,8,1,9] => 29
[9,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => 28
[9,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => 10
[10,7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => 10
[8,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => 11
[9,9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => 9
[8,8,8] => [8,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => 16
[4,4,4,4,4,4,4] => [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] => [4,3,2,1,10,9,8,7,6,5] => 24
[8,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 15
[8,6,5,4,3,2] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => 20
[7,7,6,5,4,3,2] => [7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => 27
[6,6,6,4,3,2,1] => [6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => 22
[6,5,5,5] => [5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 15
[5,4,4,4,4] => [4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 16
[7,6,6,5,4,3,2] => [6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => 26
[9,8,8,7,6,5,4,3,2,1] => [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] => [1,2,3,4,5,6,7,8,10,9] => 44
[7,7,6,5,4,3,1,1] => [7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => 27
[8,8,7,6,5,4,3,2] => [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] => [2,1,3,4,5,6,7,8,9] => 35
[9,9,8,7,6,5,4,3,2,1] => [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] => [1,2,3,4,5,6,7,8,9,10] => 45
[7,7,6,5,3,2,1] => [7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => 24
[9,8,7,6,5,4,3] => [8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => 33
[10,9,8,7,6,5,4,3,2] => [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] => [2,1,3,4,5,6,7,8,9,10] => 44
[8,6,6,5,4,3,2] => [6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => 26
[8,7,6,5] => [7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => 18
[8,7,6,5,4] => [7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => 22
[9,8,7,6] => [8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => 21
[9,8,7,6,5] => [8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => 26
[9,8,7,6,5,4] => [8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => 30
[7,7,5,5,4,3,2,1] => [7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => 27
[7,7,5,4,3,2,1] => [7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => 22
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,1,1 1,1,2,1 1,1,2,2,1 1,1,2,3,3,1 1,1,2,3,4,3,1 1,1,2,3,5,5,4,1 1,1,2,3,5,6,7,4,1 1,1,2,3,5,7,9,8,5,1 1,1,2,3,5,7,10,11,10,5,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + q + q^{2}$
$F_{4} = 1 + q + 2\ q^{2} + q^{3}$
$F_{5} = 1 + q + 2\ q^{2} + 2\ q^{3} + q^{4}$
$F_{6} = 1 + q + 2\ q^{2} + 3\ q^{3} + 3\ q^{4} + q^{5}$
$F_{7} = 1 + q + 2\ q^{2} + 3\ q^{3} + 4\ q^{4} + 3\ q^{5} + q^{6}$
$F_{8} = 1 + q + 2\ q^{2} + 3\ q^{3} + 5\ q^{4} + 5\ q^{5} + 4\ q^{6} + q^{7}$
$F_{9} = 1 + q + 2\ q^{2} + 3\ q^{3} + 5\ q^{4} + 6\ q^{5} + 7\ q^{6} + 4\ q^{7} + q^{8}$
$F_{10} = 1 + q + 2\ q^{2} + 3\ q^{3} + 5\ q^{4} + 7\ q^{5} + 9\ q^{6} + 8\ q^{7} + 5\ q^{8} + q^{9}$
$F_{11} = 1 + q + 2\ q^{2} + 3\ q^{3} + 5\ q^{4} + 7\ q^{5} + 10\ q^{6} + 11\ q^{7} + 10\ q^{8} + 5\ q^{9} + q^{10}$
Description
The number of non-inversions of a permutation.
For a permutation of $\{1,\ldots,n\}$, this is given by $\operatorname{noninv}(\pi) = \binom{n}{2}-\operatorname{inv}(\pi)$.
For a permutation of $\{1,\ldots,n\}$, this is given by $\operatorname{noninv}(\pi) = \binom{n}{2}-\operatorname{inv}(\pi)$.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
first row removal
Description
Removes the first entry of an integer partition
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