edit this map or download as text // json
Identifier
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Images
[] => []
[1] => [1,0,1,0]
[2] => [1,1,0,0,1,0]
[1,1] => [1,0,1,1,0,0]
[3] => [1,1,1,0,0,0,1,0]
[2,1] => [1,0,1,0,1,0]
[1,1,1] => [1,0,1,1,1,0,0,0]
[4] => [1,1,1,1,0,0,0,0,1,0]
[3,1] => [1,1,0,1,0,0,1,0]
[2,2] => [1,1,0,0,1,1,0,0]
[2,1,1] => [1,0,1,1,0,1,0,0]
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0]
[5] => [1,1,1,1,1,0,0,0,0,0,1,0]
[4,1] => [1,1,1,0,1,0,0,0,1,0]
[3,2] => [1,1,0,0,1,0,1,0]
[3,1,1] => [1,0,1,1,0,0,1,0]
[2,2,1] => [1,0,1,0,1,1,0,0]
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0]
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0]
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0]
[4,2] => [1,1,1,0,0,1,0,0,1,0]
[4,1,1] => [1,1,0,1,1,0,0,0,1,0]
[3,3] => [1,1,1,0,0,0,1,1,0,0]
[3,2,1] => [1,0,1,0,1,0,1,0]
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0]
[2,2,2] => [1,1,0,0,1,1,1,0,0,0]
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0]
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0]
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0]
[4,3] => [1,1,1,0,0,0,1,0,1,0]
[4,2,1] => [1,1,0,1,0,1,0,0,1,0]
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0]
[3,3,1] => [1,1,0,1,0,0,1,1,0,0]
[3,2,2] => [1,1,0,0,1,1,0,1,0,0]
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0]
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0]
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0]
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0]
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0]
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0]
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0]
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0]
[4,3,1] => [1,1,0,1,0,0,1,0,1,0]
[4,2,2] => [1,1,0,0,1,1,0,0,1,0]
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0]
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0]
[3,3,2] => [1,1,0,0,1,0,1,1,0,0]
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0]
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0]
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0]
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0]
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[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]
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0]
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0]
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0]
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0]
[4,3,2] => [1,1,0,0,1,0,1,0,1,0]
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0]
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0]
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0]
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0]
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0]
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0]
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[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]
[1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
[8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
>>> Load all 1544 entries. <<<
[7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0]
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0]
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0]
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0]
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0]
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0]
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0]
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0]
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0]
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0]
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[11] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[10,1] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[9,2] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[9,1,1] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]
[8,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[8,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]
[8,1,1,1] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]
[7,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[7,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[7,2,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[7,2,1,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[7,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0]
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0]
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0]
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0]
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0]
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0]
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0]
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0]
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0]
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0]
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0]
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0]
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0]
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[4,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0]
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0]
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0]
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[12] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[11,1] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,2] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]
[10,1,1] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,3] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]
[9,2,1] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[9,1,1,1] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,4] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]
[8,3,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]
[8,2,2] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]
[8,2,1,1] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]
[8,1,1,1,1] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[7,4,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[7,3,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[7,3,1,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[7,2,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[7,2,1,1,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[7,1,1,1,1,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[6,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0]
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0]
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0]
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0]
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[5,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[5,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0]
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0]
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0]
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0]
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[4,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[4,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0]
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[3,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[3,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[3,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[13] => [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[12,1] => [1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[11,2] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[11,1,1] => [1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,3] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,1,0]
[10,2,1] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]
[10,1,1,1] => [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,4] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]
[9,3,1] => [1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0]
[9,2,2] => [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,1,0]
[9,2,1,1] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0]
[9,1,1,1,1] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]
[8,4,1] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]
[8,3,2] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]
[8,3,1,1] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]
[8,2,2,1] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]
[8,2,1,1,1] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]
[8,1,1,1,1,1] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[7,5,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[7,4,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[7,4,1,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[7,3,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[7,3,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[7,3,1,1,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[7,2,2,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[7,2,2,1,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[7,2,1,1,1,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[6,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[6,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0]
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0]
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0]
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0]
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0]
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0]
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[5,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[5,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[5,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[5,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0]
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0]
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[4,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[4,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[4,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]
[4,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[3,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[3,3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
[3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[3,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[3,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]
[3,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[2,2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[14] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,1] => [1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[12,2] => [1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[12,1,1] => [1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[11,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
[11,2,1] => [1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[11,1,1,1] => [1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,1,0]
[10,3,1] => [1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,1,0]
[10,2,2] => [1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0]
[10,2,1,1] => [1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[10,1,1,1,1] => [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]
[9,4,1] => [1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,1,0]
[9,3,2] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]
[9,3,1,1] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,1,0]
[9,2,2,1] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0]
[9,2,1,1,1] => [1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[9,1,1,1,1,1] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]
[8,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,1,0]
[8,4,2] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]
[8,4,1,1] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0]
[8,3,3] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]
[8,3,2,1] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]
[8,3,1,1,1] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0]
[8,2,2,2] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,1,0]
[8,2,2,1,1] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]
[8,2,1,1,1,1] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[8,1,1,1,1,1,1] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[7,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[7,5,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[7,5,1,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[7,4,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[7,4,2,1] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[7,4,1,1,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[7,3,3,1] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[7,3,2,2] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[7,3,2,1,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[7,3,1,1,1,1] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[7,2,2,2,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[7,2,2,1,1,1] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[7,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[7,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[6,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[6,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[6,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[6,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[6,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0]
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0]
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0]
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[5,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0]
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[5,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[5,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[5,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[5,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[5,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]
[5,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0]
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[4,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[4,4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[4,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[4,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[4,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[4,3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]
[4,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[4,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[4,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[4,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]
[4,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[4,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[3,3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[3,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[3,3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[3,3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]
[3,3,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]
[3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[3,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[3,2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]
[3,2,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]
[3,2,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,2,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,2,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[15] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[14,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,2] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,1,1] => [1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[12,3] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[12,2,1] => [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[12,1,1,1] => [1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[11,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0]
[11,3,1] => [1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0]
[11,2,2] => [1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,1,0]
[11,2,1,1] => [1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[11,1,1,1,1] => [1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,1,0]
[10,4,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,1,0]
[10,3,2] => [1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,0]
[10,3,1,1] => [1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[10,2,2,1] => [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,1,0]
[10,2,1,1,1] => [1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[10,1,1,1,1,1] => [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]
[9,5,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,1,0]
[9,4,2] => [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,1,0]
[9,4,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,0]
[9,3,3] => [1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0]
[9,3,2,1] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]
[9,3,1,1,1] => [1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
[9,2,2,2] => [1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0]
[9,2,2,1,1] => [1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
[9,2,1,1,1,1] => [1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[9,1,1,1,1,1,1] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[8,6,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]
[8,5,2] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0]
[8,5,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0]
[8,4,3] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0]
[8,4,2,1] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]
[8,4,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]
[8,3,3,1] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0]
[8,3,2,2] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]
[8,3,2,1,1] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]
[8,3,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[8,2,2,2,1] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,1,0]
[8,2,2,1,1,1] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[8,2,1,1,1,1,1] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[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]
[7,7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]
[7,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[7,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[7,5,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[7,5,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[7,5,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[7,4,4] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[7,4,3,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[7,4,2,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[7,4,2,1,1] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[7,4,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[7,3,3,2] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[7,3,3,1,1] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[7,3,2,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[7,3,2,1,1,1] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[7,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[7,2,2,2,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[7,2,2,2,1,1] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[7,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[7,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[7,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[6,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[6,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[6,6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[6,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[6,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[6,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[6,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[6,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[6,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]
[6,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[5,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[5,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[5,4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[5,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[5,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[5,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[5,3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]
[5,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[5,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[5,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[5,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]
[5,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]
[5,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0]
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[4,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[4,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[4,4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[4,4,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[4,3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[4,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[4,3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[4,3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[4,3,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[4,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[4,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[4,2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]
[4,2,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0]
[4,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]
[3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[3,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[3,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[3,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[3,3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[3,3,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]
[3,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[3,3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[3,3,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
[3,3,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]
[3,3,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]
[3,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[3,2,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,2,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]
[3,2,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0]
[3,2,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0]
[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]
[2,2,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,2,2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,2,2,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[16] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[15,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[14,2] => [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[14,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,3] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[13,2,1] => [1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,1,1,1] => [1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[12,4] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
[12,3,1] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[12,2,2] => [1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[12,2,1,1] => [1,1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[12,1,1,1,1] => [1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[11,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0]
[11,4,1] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0]
[11,3,2] => [1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0]
[11,3,1,1] => [1,1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]
[11,2,2,1] => [1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]
[11,2,1,1,1] => [1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[11,1,1,1,1,1] => [1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0]
[10,5,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,1,0]
[10,4,2] => [1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,1,0]
[10,4,1,1] => [1,1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,0,1,0]
[10,3,3] => [1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,1,0]
[10,3,2,1] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[10,3,1,1,1] => [1,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[10,2,2,2] => [1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,1,0]
[10,2,2,1,1] => [1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]
[10,2,1,1,1,1] => [1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[10,1,1,1,1,1,1] => [1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]
[9,6,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,1,0]
[9,5,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]
[9,5,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,0,1,0]
[9,4,3] => [1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,0]
[9,4,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,1,0]
[9,4,1,1,1] => [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[9,3,3,1] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,1,0]
[9,3,2,2] => [1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,1,0]
[9,3,2,1,1] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,1,0]
[9,3,1,1,1,1] => [1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
[9,2,2,2,1] => [1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,1,0]
[9,2,2,1,1,1] => [1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
[9,2,1,1,1,1,1] => [1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[9,1,1,1,1,1,1,1] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[8,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[8,7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]
[8,6,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0]
[8,6,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0]
[8,5,3] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0]
[8,5,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]
[8,5,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0]
[8,4,4] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,0]
[8,4,3,1] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,1,0]
[8,4,2,2] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,1,0]
[8,4,2,1,1] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,0]
[8,4,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[8,3,3,2] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0]
[8,3,3,1,1] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0]
[8,3,2,2,1] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,1,0]
[8,3,2,1,1,1] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[8,3,1,1,1,1,1] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[8,2,2,2,2] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,1,0]
[8,2,2,2,1,1] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[8,2,2,1,1,1,1] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[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]
[8,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[7,7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]
[7,7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]
[7,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[7,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[7,6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[7,5,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[7,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[7,5,2,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[7,5,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[7,5,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[7,4,4,1] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[7,4,3,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[7,4,3,1,1] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[7,4,2,2,1] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[7,4,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[7,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[7,3,3,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[7,3,3,2,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[7,3,3,1,1,1] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[7,3,2,2,2] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[7,3,2,2,1,1] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[7,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[7,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[7,2,2,2,2,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[7,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[7,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[7,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]
[7,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[6,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[6,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[6,6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[6,6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[6,6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[6,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[6,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[6,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[6,4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[6,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[6,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[6,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[6,3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]
[6,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[6,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[6,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[6,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,0]
[6,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]
[6,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]
[5,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[5,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[5,5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[5,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[5,4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[5,4,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[5,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[5,3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[5,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[5,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[5,3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[5,3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[5,3,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]
[5,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[5,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[5,2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]
[5,2,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,0]
[5,2,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]
[5,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0]
[4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[4,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[4,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[4,4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[4,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[4,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[4,4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[4,4,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]
[4,4,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]
[4,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[4,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[4,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[4,3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[4,3,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]
[4,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[4,3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[4,3,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]
[4,3,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[4,3,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0]
[4,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[4,2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[4,2,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0,0]
[4,2,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0]
[4,2,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0]
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0]
[3,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[3,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[3,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[3,3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[3,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[3,3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[3,3,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]
[3,3,3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]
[3,3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[3,3,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,3,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]
[3,3,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0]
[3,3,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0]
[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]
[3,2,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,2,2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[3,2,2,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[3,2,2,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0]
[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]
[2,2,2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,2,2,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,2,2,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[17] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[16,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[15,2] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[15,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[14,3] => [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[14,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[14,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,4] => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[13,3,1] => [1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[13,2,2] => [1,1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,2,1,1] => [1,1,1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[13,1,1,1,1] => [1,1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
[12,5] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0]
[12,4,1] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,1,0]
[12,3,2] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[12,3,1,1] => [1,1,1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0]
[12,2,2,1] => [1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[12,2,1,1,1] => [1,1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]
[12,1,1,1,1,1] => [1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]
[11,6] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0]
[11,5,1] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0]
[11,4,2] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0]
[11,4,1,1] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,0,0,1,0]
[11,3,3] => [1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0]
[11,3,2,1] => [1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]
[11,3,1,1,1] => [1,1,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]
[11,2,2,2] => [1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[11,2,2,1,1] => [1,1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]
[11,2,1,1,1,1] => [1,1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]
[11,1,1,1,1,1,1] => [1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[10,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,1,0]
[10,6,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,1,0]
[10,5,2] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0,1,0]
[10,5,1,1] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,0,0,1,0]
[10,4,3] => [1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0]
[10,4,2,1] => [1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0,1,0]
[10,4,1,1,1] => [1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]
[10,3,3,1] => [1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0,1,0]
[10,3,2,2] => [1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0,1,0]
[10,3,2,1,1] => [1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[10,3,1,1,1,1] => [1,1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[10,2,2,2,1] => [1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]
[10,2,2,1,1,1] => [1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]
[10,2,1,1,1,1,1] => [1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[10,1,1,1,1,1,1,1] => [1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[9,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[9,7,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]
[9,6,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,1,0]
[9,6,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0,1,0]
[9,5,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0,1,0]
[9,5,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,1,0]
[9,5,1,1,1] => [1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0,1,0]
[9,4,4] => [1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,1,0]
[9,4,3,1] => [1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,1,0]
[9,4,2,2] => [1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0,1,0]
[9,4,2,1,1] => [1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0,1,0]
[9,4,1,1,1,1] => [1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[9,3,3,2] => [1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,1,0]
[9,3,3,1,1] => [1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0,1,0]
[9,3,2,2,1] => [1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,1,0]
[9,3,2,1,1,1] => [1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]
[9,3,1,1,1,1,1] => [1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
[9,2,2,2,2] => [1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,1,0]
[9,2,2,2,1,1] => [1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]
[9,2,2,1,1,1,1] => [1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]
[9,2,1,1,1,1,1,1] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[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]
[8,8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]
[8,7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]
[8,7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]
[8,6,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,1,0]
[8,6,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0]
[8,6,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,1,0]
[8,5,4] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]
[8,5,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]
[8,5,2,2] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0]
[8,5,2,1,1] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]
[8,5,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[8,4,4,1] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,1,0]
[8,4,3,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]
[8,4,3,1,1] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,1,0]
[8,4,2,2,1] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,1,0]
[8,4,2,1,1,1] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[8,4,1,1,1,1,1] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[8,3,3,3] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]
[8,3,3,2,1] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]
[8,3,3,1,1,1] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[8,3,2,2,2] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,1,0]
[8,3,2,2,1,1] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[8,3,2,1,1,1,1] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[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]
[8,2,2,2,2,1] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[8,2,2,2,1,1,1] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[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]
[8,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[8,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[7,7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]
[7,7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]
[7,7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[7,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[7,6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[7,6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[7,6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[7,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[7,5,4,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[7,5,3,2] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[7,5,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[7,5,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[7,5,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[7,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[7,4,4,2] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[7,4,4,1,1] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[7,4,3,3] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[7,4,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[7,4,2,2,2] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[7,4,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[7,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[7,4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[7,3,3,3,1] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[7,3,3,2,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[7,3,3,2,1,1] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[7,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[7,3,2,2,2,1] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[7,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[7,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[7,3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]
[7,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[7,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[7,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[7,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]
[7,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]
[7,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0]
[6,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[6,6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[6,6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[6,6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[6,6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[6,6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[6,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[6,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[6,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[6,5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[6,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[6,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[6,4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[6,4,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0]
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[6,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[6,3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[6,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[6,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[6,3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[6,3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]
[6,3,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,0]
[6,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[6,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[6,2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]
[6,2,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0,0,0]
[6,2,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0]
[6,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0]
[5,5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[5,5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[5,5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[5,5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[5,5,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[5,5,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]
[5,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[5,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[5,4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[5,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[5,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[5,4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[5,4,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]
[5,4,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0]
[5,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[5,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[5,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[5,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[5,3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[5,3,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]
[5,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[5,3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[5,3,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]
[5,3,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0,0]
[5,3,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0]
[5,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[5,2,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0,0]
[5,2,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]
[5,2,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,0,0]
[5,2,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0]
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0]
[4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[4,4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[4,4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[4,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[4,4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[4,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[4,4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[4,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[4,4,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]
[4,4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[4,4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[4,4,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]
[4,4,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]
[4,4,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0]
[4,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[4,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[4,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[4,3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[4,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[4,3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[4,3,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]
[4,3,3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0]
[4,3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[4,3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[4,3,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]
[4,3,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]
[4,3,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0]
[4,3,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0]
[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]
[4,2,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[4,2,2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[4,2,2,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[4,2,2,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0]
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[3,3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[3,3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[3,3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[3,3,3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
[3,3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,3,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[3,3,3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]
[3,3,3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]
[3,3,3,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0]
[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]
[3,3,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[3,3,2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
[3,3,2,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
[3,3,2,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
[3,2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,2,2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[3,2,2,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[3,2,2,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[3,2,2,2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]
[3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[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]
[2,2,2,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,2,2,2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[2,2,2,2,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[3,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[7,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[6,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[6,6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[7,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[4,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[7,4,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[5,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[4,4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[6,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[2,2,2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[6,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[10,4,4] => [1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0]
[9,6,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0]
[8,6,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0]
[9,9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]
[7,7,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[5,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[7,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[6,5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[4,4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[4,4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[7,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[6,6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[7,5,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[7,5,4,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[3,3,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,3,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[7,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]
[9,6,4] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,0,1,0]
[8,5,4,2] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0]
[8,5,5,1] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0,1,0]
[5,4,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[6,6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[6,5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[4,4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[5,5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[6,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[5,4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[4,4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[7,6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[5,4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[7,5,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[6,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[7,6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[6,5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[7,6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[7,6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[10,10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[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]
[8,6,4,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[10,6,4] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0]
[10,7,3] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0,0,1,0]
[9,7,4] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0,1,0]
[9,5,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0,0,1,0]
[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]
[5,4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[8,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]
[6,6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[6,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[6,5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[5,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[7,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[6,5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[5,5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[7,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[3,3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,4,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[11,7,3] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0]
[8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[7,7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[6,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]
[5,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]
[4,4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,5,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[6,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[5,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[5,5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[7,6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[9,6,4,3] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,0,1,0]
[6,5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[5,4,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[6,5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[7,6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[6,5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[6,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[7,6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[6,5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[7,6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[9,6,5,3] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0]
[8,6,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0]
[8,5,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[6,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[5,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[6,5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[6,5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[5,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[6,5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[7,6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[6,5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[6,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[3,3,3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[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]
[6,6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[9,8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[11,7,5,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0]
[9,7,5,3] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]
[8,8,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,0,0,0]
[6,5,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[7,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[5,4,4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[7,7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[6,5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[8,5,4,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[7,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[7,6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[6,5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[6,6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[15,5,5] => [1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[9,7,5,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[10,7,5,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0]
[5,5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[8,7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[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]
[8,7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]
[6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[6,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[6,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[7,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[9,7,5,4,1] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,0,1,0]
[5,5,5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[7,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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]
[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]
[8,7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[7,7,7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[7,6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[10,7,6,4,1] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0]
[9,7,6,4,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0]
[10,8,5,4,1] => [1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,1,0]
[4,4,4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[8,6,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[6,6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[6,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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]
[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]
[10,8,6,4,1] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]
[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]
[8,7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[8,7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]
[7,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[7,6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[6,6,6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[15,15] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0]
[5,5,5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[9,7,5,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[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]
[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]
[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]
[11,8,6,4,1] => [1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0]
[10,8,6,4,2] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[7,6,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[9,8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[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]
[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]
[11,8,6,5,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,1,0]
[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]
[8,7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[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]
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[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]
[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]
[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]
[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]
[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]
[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]
[8,7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[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]
[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]
[8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[12,9,7,5,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[13,9,7,5,1] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0,1,0]
[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]
[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]
[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]
[11,9,7,5,3,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[11,8,7,5,4,1] => [1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0,1,0,0,0,1,0]
[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]
[8,7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[9,7,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[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]
[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]
[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]
[10,10,10,10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[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]
[11,9,7,5,5,3] => [1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[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]
[9,8,7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[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]
[11,9,7,7,5,3,3] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]
[9,8,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[9,9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[10,9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[5,5,5,5,5,5,5,5,5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Properties
injective
Sage code
def mapping(elt):
    return elt.to_dyck_word()
Weight
26
Created
Jan 19, 2020 at 07:28 by FindStatCrew
Updated
Jan 19, 2020 at 07:28 by Martin Rubey