Loading [MathJax]/jax/output/HTML-CSS/jax.js

Identifier
Values
[2,1] => [1,0,1,0,1,0] => [1,1,1] => [3] => 1
[3,2] => [1,1,0,0,1,0,1,0] => [2,1,1] => [1,2] => 0
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,2,1] => [1,1,1] => 1
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,2] => [2,1] => 0
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1] => [4] => 1
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,2] => 0
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [1,1,1] => 1
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [2,1] => 0
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [3,1,1] => [1,2] => 0
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,1] => 0
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,3,1] => [1,1,1] => 1
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [1,1,1] => 1
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [1,2] => 0
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,3] => [2,1] => 0
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [1,2] => 0
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => [1,1,1] => 1
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [1,3] => 0
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [1,1,2] => 1
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [2,1,1] => 1
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [3,1] => 0
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => [2,1] => 0
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,1] => [1,2] => 0
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,1] => [1,1,1] => 1
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => [5] => 1
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => [2,1] => 0
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,1] => [1,2] => 0
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [4,1,1] => [1,2] => 0
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [1,1,1] => 1
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1] => [1,1,1] => 1
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => [1,1,1] => 1
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,4,1] => [1,1,1] => 1
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [1,1,1] => 1
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => [1,1,1] => 1
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => [2,1] => 0
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [1,1,1] => 1
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => [1,1,1] => 1
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,4] => [2,1] => 0
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => [2,1] => 0
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => [1,3] => 0
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1] => [1,2] => 0
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => [1,1,2] => 1
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [3,2,1] => [1,1,1] => 1
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1] => [1,1,1] => 1
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,4,1] => [1,1,1] => 1
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [2,1,1] => 1
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,2] => [1,1,1] => 1
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => [3] => 1
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2] => [1,1,1] => 1
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3] => [1,1,1] => 1
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3] => [1,1,1] => 1
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => [2,1] => 0
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => [3,1] => 0
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,5] => [2,1] => 0
[7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1] => [1,3] => 0
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => [2,2] => 1
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,1,1] => [1,1,2] => 1
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => [1,1,1,1] => 0
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => [1,2,1] => 2
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,3,1] => [2,1,1] => 1
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => [1,2,1] => 2
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [1,1,1,1] => 0
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => [2,2] => 1
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => [3,1] => 0
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5] => [2,1] => 0
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,5] => [2,1] => 0
[2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => [2,1] => 0
[7,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => [1,1,1] => 1
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => [1,1,1] => 1
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,1,1] => 1
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => [1,1,1] => 1
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => [1,4] => 0
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => [1,1,3] => 2
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => [2,1,2] => 3
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => [3,1,1] => 2
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,5] => [2,1] => 0
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => [4,1] => 0
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,5] => [2,1] => 0
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => [1,1,1] => 1
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => [1,1,1] => 1
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,5] => [2,1] => 0
[3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,6] => [2,1] => 0
[8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [1,2] => 0
[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] => [1,7,1] => [1,1,1] => 1
>>> Load all 447 entries. <<<
[7,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[7,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,3] => 0
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => [1,1,2] => 1
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [1,1,1] => 1
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [2,1] => 0
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,4,1] => [1,1,1] => 1
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => [2,1,1] => 1
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,1,1] => 1
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,2] => [1,1,1] => 1
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => [6] => 1
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,5] => [2,1] => 0
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [1,1,1] => 1
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => [1,2] => 0
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,5] => [2,1] => 0
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4] => [1,1,1] => 1
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4] => [1,1,1] => 1
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,5] => [2,1] => 0
[4,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,6] => [2,1] => 0
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => [3,1] => 0
[3,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,6] => [2,1] => 0
[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] => [1,1,7] => [2,1] => 0
[8,7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [1,2] => 0
[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] => [1,7,1] => [1,1,1] => 1
[7,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[7,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[7,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,3] => 0
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,1,1] => [1,1,2] => 1
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [1,1,1] => 1
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [1,1,1] => 1
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [2,1] => 0
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1] => [1,1,1] => 1
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [2,1] => 0
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1] => [1,1,1] => 1
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,4,1] => [2,1,1] => 1
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [1,1,1] => 1
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,1,1] => 1
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [1,2] => 0
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2] => [1,1,1] => 1
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => [1,1,1] => 1
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,4,2] => [1,1,1] => 1
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [1,1,1] => 1
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,3] => [1,2] => 0
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,5] => [2,1] => 0
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,4] => [1,1,1] => 1
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4] => [1,1,1] => 1
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,5] => [2,1] => 0
[5,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,6] => [2,1] => 0
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [1,1,1] => 1
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => [2,1] => 0
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,3] => [1,2] => 0
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,4] => [1,1,1] => 1
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4] => [1,1,1] => 1
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,5] => [2,1] => 0
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,4] => [3,1] => 0
[4,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,6] => [2,1] => 0
[3,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,6] => [2,1] => 0
[3,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,7] => [2,1] => 0
[9,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,1,1] => [1,2] => 0
[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] => [1,8,1] => [1,1,1] => 1
[8,7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => [1,2] => 0
[8,7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [1,2] => 0
[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] => [1,7,1] => [1,1,1] => 1
[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] => [1,7,1] => [1,1,1] => 1
[7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => 1
[7,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[7,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[7,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[7,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[7,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => [1,1,1] => 1
[7,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[6,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => 1
[6,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => 1
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,3] => 0
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,3] => 0
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [1,1,2] => 1
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => [1,2] => 0
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,1,1] => [1,1,2] => 1
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => [1,1,2] => 1
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,4,1,1] => [1,1,2] => 1
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [1,1,1,1] => 0
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [1,1,1] => 1
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => [1,1,1,1] => 0
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [2,1] => 0
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,4,1] => [1,1,1] => 1
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,5,1] => [1,1,1] => 1
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,4,1] => [2,1,1] => 1
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [1,1,1,1] => 0
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => [1,1,1,1] => 0
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,4,1] => [2,1,1] => 1
[6,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,6] => [2,1] => 0
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [1,2,1] => 2
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [1,1,1] => 1
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => [1,1,1,1] => 0
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [1,2] => 0
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,2] => [1,1,1] => 1
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,4,2] => [1,1,1] => 1
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => [2,1,1] => 1
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [1,1,1] => 1
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,3] => [2,1] => 0
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,3] => [1,2] => 0
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4] => [1,1,1] => 1
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4] => [1,1,1] => 1
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,5] => [2,1] => 0
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,4] => [3,1] => 0
[5,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,6] => [2,1] => 0
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [1,2,1] => 2
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => [1,1,1,1] => 0
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => [2,1,1] => 1
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,4] => [3,1] => 0
[4,4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,6] => [2,1] => 0
[4,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,6] => [2,1] => 0
[4,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,7] => [2,1] => 0
[3,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => [1,1,1] => 1
[3,3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => [1,1,1] => 1
[3,3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,6] => [2,1] => 0
[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] => [1,1,7] => [2,1] => 0
[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] => [1,1,8] => [2,1] => 0
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => [7] => 1
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => [5,1] => 0
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => [4,1,1] => 2
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,3] => [4,1] => 0
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => [4,1] => 0
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => [3,1,2] => 4
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => [3,2] => 1
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,3,1] => [3,1,1] => 2
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,4] => [3,1] => 0
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => [3,1,1] => 2
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => [2,1,3] => 4
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => [2,1,1,1] => 0
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => [2,2,1] => 4
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,3] => [2,1,1] => 1
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,3,1,1] => [2,1,2] => 3
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,3,2] => [2,1,1] => 1
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,4,1] => [2,1,1] => 1
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => [2,1,2] => 3
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [1,1,4] => 2
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => [1,1,2,1] => 1
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => [1,1,1,1,1] => 1
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,3] => [1,1,1,1] => 0
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => [1,2,2] => 4
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => [1,3] => 0
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,3,1] => [1,1,1,1] => 0
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [1,1,3] => 2
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,1,2] => [1,1,1,1] => 0
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,2,1] => [1,1,1,1] => 0
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,4,1,1] => [1,1,2] => 1
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [1,1,3] => 2
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [1,5] => 0
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [1,3,1] => 3
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [1,2,1,1] => 1
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,3] => [1,2,1] => 2
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [1,1,1,2] => 0
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [1,1,2] => 1
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,1] => [1,1,1,1] => 0
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [2,3] => 1
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => [2,1,1] => 1
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => [3,1] => 0
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,1] => [1,1,2] => 1
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,4] => 0
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [1,2,1] => 2
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [1,1,1,1] => 0
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [1,1,2] => 1
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,3] => 0
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,4] => 0
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => [8] => 1
[6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => [6,1] => 0
[7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => [5,1,1] => 3
[6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,3] => [5,1] => 0
[5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => [5,1] => 0
[7,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => [4,1,2] => 8
[6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => [4,2] => 2
[7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,3,1] => [4,1,1] => 2
[6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,4] => [4,1] => 0
[5,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,4] => [4,1] => 0
[7,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => [4,1,1] => 2
[6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,4] => [4,1] => 0
[5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,4] => [4,1] => 0
[4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => [4,1] => 0
[6,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => [3,1,1,1] => 2
[6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,5] => [3,1] => 0
[6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,5] => [3,1] => 0
[6,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,5] => [3,1] => 0
[5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,5] => [3,1] => 0
[6,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,5] => [3,1] => 0
[3,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => [3,1] => 0
[6,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [2,1,2,1] => 7
[6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,3] => [2,1,1,1] => 0
[6,5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,4] => [2,1,1] => 1
[6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,6] => [2,1] => 0
[5,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,6] => [2,1] => 0
[7,6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => [2,1,3] => 4
[6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,6] => [2,1] => 0
[6,5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,6] => [2,1] => 0
[6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,6] => [2,1] => 0
[5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,6] => [2,1] => 0
[6,5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,6] => [2,1] => 0
[7,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => [2,1,1] => 1
[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [1,1,5] => 3
[6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [1,1,3,1] => 4
[6,5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,3] => [1,1,2,1] => 1
[6,6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [1,1,2,1] => 1
[6,5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => [1,1,1,1] => 0
[4,4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [1,1,1] => 1
[7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [1,1,4] => 2
[6,5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => [1,1,1,1] => 0
[7,6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [1,1,3] => 2
[5,5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => [1,1,1] => 1
[7,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => 1
[7,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => 1
[6,6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => 1
[7,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => 1
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,6] => 0
[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [1,4,1] => 4
[7,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [1,3,1,1] => 4
[6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,3] => [1,3,1] => 3
[5,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [1,3,1] => 3
[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [1,2,1,2] => 7
[6,5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,4] => [1,2,1] => 2
[6,5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,5] => [1,1,1] => 1
[5,4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5] => [1,1,1] => 1
[4,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,5] => [1,1,1] => 1
[7,6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [1,1,3] => 2
[6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => [1,1,1] => 1
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,5] => 0
[6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,3,1] => 3
[6,5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [1,2,1] => 2
[4,4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => [1,1,1] => 1
[7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,4] => 0
[5,5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,1,1] => 1
[7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,3] => 0
[6,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => 1
[7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,3] => 0
[7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,4] => 0
[7,6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,5] => 0
[6,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,3,1] => 3
[6,5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [1,2,1] => 2
[5,4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4] => [1,1,1] => 1
[7,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [1,1,1] => 1
[7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,4] => 0
[7,6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,3] => 0
[7,6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,4] => 0
[7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,3] => 0
[6,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => 1
[7,6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,4] => 0
[6,5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,1,1] => 1
[7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,3] => 0
[7,6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [1,2] => 0
[7,6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,3] => 0
[7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,3] => 0
[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] => [2,6,1] => [1,1,1] => 1
[8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,3] => 0
[9,8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,1,1] => [1,3] => 0
[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] => [1,1,1,1,1,1,1,2] => [7,1] => 0
[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] => [1,1,1,1,1,1,3] => [6,1] => 0
[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] => [1,1,1,1,1,4] => [5,1] => 0
[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] => [1,1,1,1,5] => [4,1] => 0
[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] => [1,1,1,6] => [3,1] => 0
[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] => [1,1,7] => [2,1] => 0
[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] => [1,1,1,1,1,1,3] => [6,1] => 0
[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] => [1,1,1,1,1,1,1,3] => [7,1] => 0
[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] => [1,1,1,1,1,4] => [5,1] => 0
[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] => [1,1,1,1,1,1,4] => [6,1] => 0
[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] => [1,1,1,1,5] => [4,1] => 0
[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] => [1,1,1,1,1,5] => [5,1] => 0
[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] => [1,1,1,6] => [3,1] => 0
[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] => [1,1,1,1,6] => [4,1] => 0
[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] => [1,1,7] => [2,1] => 0
[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] => [1,1,1,7] => [3,1] => 0
[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] => [1,1,8] => [2,1] => 0
[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] => [2,1,1,1,1,1,1,1] => [1,7] => 0
[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] => [3,1,1,1,1,1,1] => [1,6] => 0
[8,7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [1,4] => 0
[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] => [7,1,1] => [1,2] => 0
[8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,6] => 0
[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] => [4,1,1,1,1,1] => [1,5] => 0
[8,7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [1,2] => 0
[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] => [1,6,2] => [1,1,1] => 1
[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] => [1,1,7] => [2,1] => 0
[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] => [1,1,2,1,4] => [2,1,1,1] => 0
[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] => [1,2,1,1,1,3] => [1,1,3,1] => 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] => [2,1,1,1,1,1,2] => [1,5,1] => 5
[6,5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,4] => [5,1] => 0
[6,5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,5] => [4,1] => 0
[6,5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,6] => [3,1] => 0
[6,5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,7] => [2,1] => 0
[8,7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,3] => 0
[8,7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [1,4] => 0
[8,7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [1,5] => 0
[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] => [2,1,1,1,1,3] => [1,4,1] => 4
[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] => [2,1,1,1,1,1,3] => [1,5,1] => 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] => [3,1,1,1,3] => [1,3,1] => 3
[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] => [3,1,1,1,1,2] => [1,4,1] => 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] => [1,2,1,1,1,1,2] => [1,1,4,1] => 7
[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] => [2,1,1,1,1,1,1,2] => [1,6,1] => 6
[8,7,6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => [1,1,4] => 2
[8,7,6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => [2,1,4] => 8
[8,7,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1] => [3,1,4] => 19
[9,8,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,3,1,1] => [5,1,2] => 11
[9,7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,4,1] => [5,1,1] => 3
[7,7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => [1,2,1] => 2
[8,7,6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,1,1,1] => [1,1,4] => 2
[8,7,6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1] => [1,2,4] => 10
[8,7,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1] => [2,1,5] => 11
[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] => [1,3,1,1,1,1,1] => [1,1,5] => 3
[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] => [3,1,1,1,1,1,1,1] => [1,7] => 0
[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] => [2,1,1,1,1,2,1] => [1,4,1,1] => 7
[8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [1,4] => 0
[8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [1,5] => 0
[8,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => [1,2] => 0
[9,8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1] => [1,4] => 0
[8,7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,3] => 0
[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] => [5,1,1,1,1,1] => [1,5] => 0
[8,7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [1,4] => 0
[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] => [4,1,1,1,1,1,1] => [1,6] => 0
[8,7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [1,5] => 0
[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] => [1,1,1,1,1,2,2] => [5,2] => 2
search for individual values
searching the database for the individual values of this statistic
Description
The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles.
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition C is the compositions composed of the lengths of consecutive runs of the same integer in C.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.