edit this map or download as text // json
Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Images
[1] => [1,0]
[1,1] => [1,0,1,0]
[2] => [1,1,0,0]
[1,1,1] => [1,0,1,0,1,0]
[1,2] => [1,0,1,1,0,0]
[2,1] => [1,1,0,0,1,0]
[3] => [1,1,1,0,0,0]
[1,1,1,1] => [1,0,1,0,1,0,1,0]
[1,1,2] => [1,0,1,0,1,1,0,0]
[1,2,1] => [1,0,1,1,0,0,1,0]
[1,3] => [1,0,1,1,1,0,0,0]
[2,1,1] => [1,1,0,0,1,0,1,0]
[2,2] => [1,1,0,0,1,1,0,0]
[3,1] => [1,1,1,0,0,0,1,0]
[4] => [1,1,1,1,0,0,0,0]
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
[1,1,3] => [1,0,1,0,1,1,1,0,0,0]
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
[1,2,2] => [1,0,1,1,0,0,1,1,0,0]
[1,3,1] => [1,0,1,1,1,0,0,0,1,0]
[1,4] => [1,0,1,1,1,1,0,0,0,0]
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
[2,1,2] => [1,1,0,0,1,0,1,1,0,0]
[2,2,1] => [1,1,0,0,1,1,0,0,1,0]
[2,3] => [1,1,0,0,1,1,1,0,0,0]
[3,1,1] => [1,1,1,0,0,0,1,0,1,0]
[3,2] => [1,1,1,0,0,0,1,1,0,0]
[4,1] => [1,1,1,1,0,0,0,0,1,0]
[5] => [1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0]
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0]
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0]
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
[6] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
>>> Load all 1477 entries. <<<
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,2,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,2,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,2,3] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,3,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,4,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,2,1,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,2,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,2,1,3] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,2,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,2,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,2,3,1] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,2,4] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,3,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,3,1,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,3,3] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,4,1,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,4,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,5,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,2,1,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,2,1,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,2,1,1,3] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,2,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,2,1,2,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,2,1,3,1] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,2,1,4] => [1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,2,1,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,2,2,1,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,2,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,2,2,3] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,3,1,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,2,3,2] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,2,4,1] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,2,5] => [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,3,1,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,3,1,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,3,1,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,3,1,3] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,3,2,1,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,3,2,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,3,3,1] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,3,4] => [1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,4,1,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,4,1,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,4,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,5,1,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,5,2] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,1,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,1,1,2,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,1,1,2,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,2,1,1,3,1] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,1,1,4] => [1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,1,2,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,2,1,2,3] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,1,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,1,3,2] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,1,4,1] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,1,5] => [1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,2,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,2,1,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,2,1,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,2,2,1,3] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,2,3,1] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,2,2,4] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,3,1,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,2,3,1,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,2,3,2,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,2,3,3] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,4,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,2,4,2] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,5,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,3,1,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,1,3] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,3,1,2,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,3,1,2,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,3,1,3,1] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,3,1,4] => [1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,3,2,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,3,2,1,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,3,2,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,3,2,3] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,3,3,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,3,3,2] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,3,4,1] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,3,5] => [1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,4,1,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,4,1,2,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,4,1,3] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,4,2,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,4,2,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,4,3,1] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,4,4] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,5,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,5,1,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,5,2,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,1,1,2,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,1,1,3,1] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[2,1,1,1,4] => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,1,1,2,1,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,1,2,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[2,1,1,2,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[2,1,1,2,3] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[2,1,1,3,1,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[2,1,1,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[2,1,1,4,1] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[2,1,1,5] => [1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,2,1,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,2,1,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[2,1,2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[2,1,2,1,3] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[2,1,2,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[2,1,2,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,2,3,1] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[2,1,2,4] => [1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,3,1,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[2,1,3,1,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[2,1,3,2,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[2,1,3,3] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,1,4,1,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[2,1,4,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,5,1] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,1,6] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[2,2,1,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[2,2,1,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[2,2,1,1,3] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[2,2,1,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[2,2,1,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[2,2,1,3,1] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[2,2,1,4] => [1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[2,2,2,1,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[2,2,2,3] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[2,2,3,1,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[2,2,3,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[2,2,4,1] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,2,5] => [1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,3,1,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[2,3,1,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[2,3,1,2,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[2,3,1,3] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[2,3,2,1,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[2,3,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[2,3,3,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[2,3,4] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,4,1,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[2,4,1,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[2,4,2,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[2,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[2,5,1,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[2,5,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[3,1,1,2,1,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,1,2,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,1,3,1] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[3,1,1,4] => [1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[3,1,2,1,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,2,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,2,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,2,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[3,1,3,1,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[3,1,3,2] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[3,1,4,1] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[3,1,5] => [1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[3,2,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,1,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[3,2,1,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[3,2,1,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[3,2,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,2,3,1] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[3,2,4] => [1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[3,3,1,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[3,3,1,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[3,3,2,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[3,4,1,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[3,4,2] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[3,5,1] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[4,1,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]
[4,1,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,0]
[4,1,1,3] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]
[4,1,2,1,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,1,0]
[4,1,2,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0]
[4,1,3,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]
[4,1,4] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]
[4,2,1,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]
[4,2,1,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0]
[4,2,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[4,2,3] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]
[4,3,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[4,4,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[5,1,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]
[5,1,2,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]
[5,1,3] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]
[5,2,1,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]
[5,2,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[5,3,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]
[5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]
[6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]
[6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,2,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,1,2,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,2,3] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,1,3,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,1,4,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,2,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,2,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,2,1,3] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,2,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,2,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,2,3,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,2,4] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,3,1,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,3,1,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,3,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,4,1,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,4,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,5,1] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,6] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,2,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,2,1,1,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,2,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,2,1,1,3] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,2,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,2,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,2,1,3,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,2,1,4] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,2,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,2,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,2,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,2,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,2,3,1,1] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,2,3,2] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,2,4,1] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,2,5] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,3,1,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,3,1,1,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,3,1,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,3,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,3,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,3,2,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,3,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,3,4] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,4,1,1,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,4,1,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,4,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,4,3] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,5,1,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,5,2] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,6,1] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,7] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,2,1,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,2,1,1,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,2,1,1,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,2,1,1,1,3] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,2,1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,2,1,1,2,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,2,1,1,3,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,2,1,1,4] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,2,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,2,1,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,2,1,2,3] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,1,3,1,1] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,2,1,3,2] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,2,1,4,1] => [1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,2,1,5] => [1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,2,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,2,2,1,1,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,2,2,1,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,2,2,1,3] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,2,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,2,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,2,2,3,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,2,2,4] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,2,3,1,1,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,2,3,1,2] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,2,3,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,2,3,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,2,4,1,1] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,2,4,2] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,2,5,1] => [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,2,6] => [1,0,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,3,1,1,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,3,1,1,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,3,1,1,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,3,1,1,3] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,3,1,2,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,3,1,2,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,3,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,3,1,4] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,3,2,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,3,2,1,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,3,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,3,2,3] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,3,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,3,4,1] => [1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,3,5] => [1,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,4,1,1,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,4,1,1,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,4,1,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,4,1,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,4,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,4,3,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,4,4] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,5,1,1,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,5,1,2] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,5,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,5,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,6,1,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,6,2] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,2,1,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,1,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,1,1,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,1,1,1,2,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,1,1,1,2,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,2,1,1,1,3,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,1,1,1,4] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,1,1,2,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,1,1,2,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,2,1,1,2,3] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,1,1,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,1,1,3,2] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,1,1,4,1] => [1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,1,1,5] => [1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,2,1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,1,2,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,2,1,2,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,1,2,3,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,2,1,2,4] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,1,3,1,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,2,1,3,1,2] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,2,1,3,2,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,2,1,3,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,1,4,1,1] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,2,1,4,2] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,1,5,1] => [1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,2,1,6] => [1,0,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,2,1,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,2,2,1,1,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,2,2,1,1,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,2,2,1,1,3] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,2,2,1,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,2,2,1,2,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,2,2,1,3,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,2,2,1,4] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,2,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,2,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,2,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,2,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,2,2,3,2] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,2,4,1] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,2,2,5] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,2,3,1,1,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,2,3,1,1,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,2,3,1,2,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,2,3,1,3] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,2,3,2,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,2,3,2,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,2,3,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,2,3,4] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,2,4,1,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,2,4,1,2] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,2,4,2,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,2,4,3] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,2,5,1,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,2,5,2] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,2,6,1] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,2,7] => [1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,3,1,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,1,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,1,1,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,1,1,3] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,3,1,1,2,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,1,1,2,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,3,1,1,3,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,3,1,1,4] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,3,1,2,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,1,2,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,3,1,2,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,1,2,3] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,3,1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,3,1,3,2] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,3,1,4,1] => [1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,3,1,5] => [1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,3,2,1,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,2,1,1,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,3,2,1,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,2,1,3] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,3,2,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,2,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,2,3,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,3,2,4] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,3,3,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,3,3,1,2] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,3,3,2,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,3,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,3,4,1,1] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,3,4,2] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,3,5,1] => [1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,3,6] => [1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,4,1,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,4,1,1,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,4,1,1,2,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,4,1,1,3] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,4,1,2,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,4,1,2,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,4,1,3,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,4,1,4] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,4,2,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,4,2,1,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,4,2,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,4,2,3] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,4,3,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,4,3,2] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,4,4,1] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,4,5] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,5,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,5,1,1,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]
[1,5,1,2,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]
[1,5,1,3] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]
[1,5,2,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]
[1,5,2,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[1,5,3,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]
[1,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[1,6,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,6,1,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]
[1,6,2,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]
[1,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[1,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,1,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,1,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,1,1,1,2,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,1,1,1,3,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[2,1,1,1,1,4] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,1,1,1,2,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,1,1,2,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[2,1,1,1,2,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[2,1,1,1,2,3] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[2,1,1,1,3,1,1] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[2,1,1,1,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[2,1,1,1,4,1] => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[2,1,1,1,5] => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,1,2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,1,2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[2,1,1,2,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[2,1,1,2,1,3] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[2,1,1,2,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[2,1,1,2,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,1,2,3,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[2,1,1,2,4] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,1,3,1,1,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[2,1,1,3,1,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[2,1,1,3,2,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[2,1,1,3,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,1,1,4,1,1] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[2,1,1,4,2] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,1,1,5,1] => [1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,1,1,6] => [1,1,0,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,1,2,1,1,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[2,1,2,1,1,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[2,1,2,1,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[2,1,2,1,1,3] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[2,1,2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[2,1,2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[2,1,2,1,3,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[2,1,2,1,4] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[2,1,2,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[2,1,2,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[2,1,2,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[2,1,2,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[2,1,2,3,1,1] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[2,1,2,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[2,1,2,4,1] => [1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,1,2,5] => [1,1,0,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[2,1,3,1,1,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[2,1,3,1,1,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[2,1,3,1,2,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[2,1,3,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[2,1,3,2,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[2,1,3,2,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,3,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[2,1,3,4] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,1,4,1,1,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[2,1,4,1,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[2,1,4,2,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[2,1,4,3] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[2,1,5,1,1] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[2,1,5,2] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,1,6,1] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[2,1,7] => [1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,2,1,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,2,1,1,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,2,1,1,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[2,2,1,1,1,3] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,1,1,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[2,2,1,1,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[2,2,1,1,3,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[2,2,1,1,4] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,2,1,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[2,2,1,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[2,2,1,2,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[2,2,1,2,3] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[2,2,1,3,1,1] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[2,2,1,3,2] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[2,2,1,4,1] => [1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[2,2,1,5] => [1,1,0,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[2,2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[2,2,2,1,3] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[2,2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[2,2,2,4] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,2,3,1,1,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[2,2,3,1,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[2,2,3,2,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[2,2,3,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,2,4,1,1] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[2,2,4,2] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,2,5,1] => [1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,2,6] => [1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[2,3,1,1,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[2,3,1,1,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[2,3,1,1,2,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[2,3,1,1,3] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[2,3,1,2,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[2,3,1,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[2,3,1,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[2,3,1,4] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[2,3,2,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[2,3,2,1,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[2,3,2,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[2,3,2,3] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[2,3,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[2,3,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[2,3,4,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[2,3,5] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[2,4,1,1,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[2,4,1,1,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[2,4,1,2,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[2,4,1,3] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[2,4,2,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[2,4,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,4,3,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[2,4,4] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[2,5,1,1,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[2,5,1,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[2,5,2,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[2,5,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[2,6,1,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[2,6,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[2,7,1] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,1,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,1,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,1,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[3,1,1,1,2,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,1,1,2,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,1,1,3,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[3,1,1,1,4] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[3,1,1,2,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,1,2,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,1,2,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,1,2,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[3,1,1,3,1,1] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[3,1,1,3,2] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[3,1,1,4,1] => [1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[3,1,1,5] => [1,1,1,0,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[3,1,2,1,1,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,2,1,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,2,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,2,1,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[3,1,2,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,2,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,2,3,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[3,1,2,4] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[3,1,3,1,1,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[3,1,3,1,2] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[3,1,3,2,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[3,1,3,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[3,1,4,1,1] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[3,1,4,2] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[3,1,5,1] => [1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[3,1,6] => [1,1,1,0,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[3,2,1,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[3,2,1,1,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[3,2,1,1,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[3,2,1,1,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[3,2,1,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[3,2,1,2,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[3,2,1,3,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[3,2,1,4] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[3,2,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[3,2,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[3,2,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[3,2,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[3,2,3,1,1] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[3,2,3,2] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[3,2,4,1] => [1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[3,2,5] => [1,1,1,0,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[3,3,1,1,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[3,3,1,1,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[3,3,1,2,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[3,3,1,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[3,3,2,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[3,3,2,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[3,3,4] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,4,1,1,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[3,4,1,2] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[3,4,2,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[3,4,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[3,5,1,1] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[3,5,2] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[3,6,1] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,1,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[4,1,1,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,1,1,3] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[4,1,1,2,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,1,2,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[4,1,1,3,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[4,1,1,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[4,1,2,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,2,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[4,1,2,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[4,1,2,3] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[4,1,3,1,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,3,2] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[4,1,4,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[4,1,5] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[4,2,1,1,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,1,1,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[4,2,1,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[4,2,1,3] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[4,2,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[4,2,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[4,2,3,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[4,2,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[4,3,1,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[4,3,1,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[4,3,2,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[4,3,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[4,4,1,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[4,4,2] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[4,5,1] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[5,1,1,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]
[5,1,1,2,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0,1,0]
[5,1,1,3] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,1,0,0,0]
[5,1,2,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0,1,0]
[5,1,2,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,1,0,0]
[5,1,3,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0]
[5,1,4] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0]
[5,2,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0,1,0]
[5,2,1,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,1,0,0]
[5,2,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[5,2,3] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[5,3,1,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0,1,0]
[5,3,2] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[5,4,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[6,1,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]
[6,1,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0]
[6,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]
[6,2,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0,1,0]
[6,2,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[6,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]
[6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[7,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]
[7,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]
[7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,8,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[1,7,2,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]
[1,6,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]
[1,5,4,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,4,5,1] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,3,6,1] => [1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,2,7,1] => [1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,8,1] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[1,8,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]
[1,7,1,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]
[1,6,1,1,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]
[1,5,1,1,1,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,4,1,1,1,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,1,1,1,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,1,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]
[1,6,2,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]
[1,5,2,1,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,4,2,1,1,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,3,2,1,1,1,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,2,2,1,1,1,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,2,1,1,1,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,2,2,1,3] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,2,1,3,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,2,1,2,3] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,2,1,1,4] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,3,2,2] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,2,1,3,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,2,1,2,3,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,1,2,2,3] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,1,4,2] => [1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,1,1,3,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,1,1,2,4] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,1,1,1,5] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,3,2,2,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,3,2,1,3] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,3,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,3,1,2,3] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,1,1,4] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,3,2,2] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,2,3,1,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,2,2,3,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,2,2,2,3] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,2,1,4] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,1,4,2] => [1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,2,1,3,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,2,1,2,4] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,2,1,1,5] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,4,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,4,1,3] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,3,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,3,2,3] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,3,1,4] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,2,4,2] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,2,3,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,2,2,4] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,2,1,5] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,5,2] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,4,3] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,3,4] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,2,5] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,6] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,1,2,2,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,1,2,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,3,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,2,2,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,2,2,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,2,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,2,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,2,1,2,3] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,3,3,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,3,2,1,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,3,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,4,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,2,2,1,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,2,2,1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,2,2,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,2,2,2,1,1,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,2,2,3,3] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,2,1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,2,1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,2,1,1,1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,2,1,1,1,1,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,2,1,1,1,2,3] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,1,2,3,1,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,2,1,2,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,2,1,2,1,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,2,1,3,4] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,3,3,1,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,3,3,2,2] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,3,2,1,2,1,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,3,2,1,1,1,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,3,2,2,3] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,3,1,1,2,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,3,1,1,1,1,3] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,3,1,2,4] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,4,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,4,3,1,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,4,2,1,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,4,1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,5,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[2,2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,2,1,1,1,1,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[2,2,1,1,2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,1,1,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[2,2,1,1,3,3] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,2,2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,2,2,1,1,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[2,2,2,1,1,1,1,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,2,2,1,2,3] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[2,2,3,3,1,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[2,2,3,2,1,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[2,2,3,1,1,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[2,2,4,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[2,1,1,2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,1,2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,1,2,2,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[2,1,1,2,2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[2,1,1,2,3,3] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,1,1,1,1,2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,1,1,1,2,2,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,1,1,1,1,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,1,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,1,1,1,1,2,3] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[2,1,1,1,2,3,1,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[2,1,1,1,2,2,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[2,1,1,1,2,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[2,1,1,1,3,4] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,1,2,3,1,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[2,1,2,3,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[2,1,2,2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[2,1,2,2,1,1,1,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[2,1,2,2,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[2,1,2,1,1,3,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[2,1,2,1,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[2,1,2,1,1,1,1,3] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,2,1,2,4] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,1,3,4,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[2,1,3,3,1,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[2,1,3,2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[2,1,3,1,1,4] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[2,1,4,5] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[3,3,1,1,2,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[3,3,2,2,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[3,3,2,1,1,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[3,2,1,2,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,1,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,2,1,1,1,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,1,1,1,1,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[3,2,1,1,2,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[3,2,2,3,1,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[3,2,2,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[3,2,2,1,1,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[3,2,3,4] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[3,1,1,3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[3,1,1,3,2,2] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,1,1,2,1,2,1,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[3,1,1,2,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[3,1,1,2,2,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[3,1,1,1,1,3,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[3,1,1,1,1,2,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,1,1,1,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[3,1,1,1,2,4] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[3,1,2,4,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[3,1,2,3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[3,1,2,2,1,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[3,1,2,1,1,4] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[3,1,3,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[4,4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[4,4,2,2] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[4,3,1,2,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[4,3,1,1,1,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[4,3,2,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[4,2,1,3,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[4,2,1,2,1,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[4,2,1,1,1,3] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[4,2,2,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[4,1,1,4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[4,1,1,3,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[4,1,1,2,1,3] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[4,1,1,1,1,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[4,1,2,5] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[5,5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[5,4,1,2] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[5,3,1,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[5,2,1,4] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[5,1,1,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,2,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,2,2,2,3,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,2,3,3,1] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,2,2,3,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,2,2,4,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,2,3,3,2,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,2,3,4,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,3,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,2,3,2,2,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,3,3,3] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,4,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,2,4,3,2] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,4,2,3] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,5,4] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[1,3,3,2,2,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,3,3,3,2] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,3,4,3,1] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,3,4,2,2] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,3,5,3] => [1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,3,2,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,3,2,4,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,3,2,2,3,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,3,2,2,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,2,3,3] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,3,3,4,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,3,3,2,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,3,4,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,4,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,4,5,2] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,4,3,3,1] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,4,3,2,2] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,4,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,4,2,4,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,4,2,3,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,4,2,2,3] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,4,3,4] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,5,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,5,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,5,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[2,3,2,2,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[2,3,2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[2,3,3,3,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[2,3,3,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[2,3,4,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[2,4,3,2,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[2,4,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,4,2,3,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[2,4,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[2,4,3,3] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,5,4,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[2,5,3,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[2,5,2,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[2,6,4] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
[2,2,3,2,2,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[2,2,3,3,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[2,2,4,3,1] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[2,2,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[2,2,5,3] => [1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[2,2,2,3,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[2,2,2,4,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[2,2,2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[2,2,2,3,3] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[2,2,3,4,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[2,2,3,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[2,3,4,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[2,3,5,2] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[2,3,2,4,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[2,3,2,2,3] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[2,3,3,4] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[2,4,5,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[2,4,2,4] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[2,5,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[3,4,2,2,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]
[3,4,3,2] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[3,5,3,1] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]
[3,5,2,2] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[3,6,3] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[3,3,3,2,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[3,3,4,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[3,3,2,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[3,3,2,2,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[3,4,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]
[3,4,2,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[3,5,4] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[3,2,4,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[3,2,5,2] => [1,1,1,0,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[3,2,3,3,1] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[3,2,3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[3,2,4,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[3,2,2,4,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[3,2,2,3,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[3,2,2,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[3,3,5,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[3,3,2,4] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[3,4,5] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[4,5,2,1] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[4,6,2] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[4,4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[4,5,3] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[4,3,4,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[4,3,3,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[4,2,5,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[4,2,4,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[4,2,3,3] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[4,3,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[5,6,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[5,5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[5,4,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[5,3,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[5,2,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,11] => [1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,9,2] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]
[1,8,1,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,1,0,0]
[1,7,1,1,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,1,0,0]
[1,6,1,1,1,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,5,1,1,1,1,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,1,1,1,1,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,1,1,1,1,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,1,1,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,2,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,2,2,2,1,3] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,2,2,1,3,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,2,2,1,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,2,2,1,1,4] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,2,1,3,2,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,2,2,1,3,1,3] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,2,2,1,2,3,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,2,1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,2,1,2,1,4] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,2,2,1,1,4,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,2,1,1,3,3] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,2,1,1,2,4] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,2,1,1,1,5] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,1,3,2,2,2] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,2,1,3,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,1,3,1,3,2] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,1,3,1,2,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,2,1,3,1,1,4] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,2,3,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,2,1,2,3,1,3] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,2,1,2,2,3,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,1,2,2,2,3] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,1,2,2,1,4] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,2,1,4,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,1,2,1,3,3] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,1,2,1,2,4] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,1,2,1,1,5] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,1,1,4,2,2] => [1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,2,1,1,4,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,2,1,1,3,3,2] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,2,1,1,3,2,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,2,1,1,3,1,4] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,2,1,1,2,4,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,2,1,1,2,3,3] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,2,1,1,2,2,4] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,2,1,1,2,1,5] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,1,1,1,5,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,2,1,1,1,4,3] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,2,1,1,1,3,4] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,2,1,1,1,2,5] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,2,1,1,1,1,6] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,3,2,2,2,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,3,2,2,1,3] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,3,2,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,3,2,1,2,3] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,2,1,1,4] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,3,1,3,2,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,3,1,3,1,3] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,3,1,2,3,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,3,1,2,2,3] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,1,2,1,4] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,3,1,1,4,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,3,1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,3,1,1,2,4] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,3,1,1,1,5] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,2,3,2,2,2] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,2,3,2,1,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,2,3,1,3,2] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,2,3,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,3,1,1,4] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,2,3,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,2,2,3,1,3] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,2,2,2,3,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,2,2,2,2,3] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,2,2,1,4] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,2,1,4,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,2,2,1,3,3] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,2,2,1,2,4] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,2,2,1,1,5] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,2,1,4,2,2] => [1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,2,1,4,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,2,1,3,3,2] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,2,1,3,2,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,2,1,3,1,4] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,1,2,4,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,2,1,2,3,3] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,2,1,2,2,4] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,2,1,2,1,5] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,2,1,1,5,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,2,1,1,4,3] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,2,1,1,3,4] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,2,1,1,2,5] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,2,1,1,1,6] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,4,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,4,2,1,3] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,4,1,3,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,4,1,2,3] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,4,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,3,3,2,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,3,3,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,3,2,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,3,2,2,3] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,3,2,1,4] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,3,1,4,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,3,1,3,3] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,3,1,2,4] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,3,1,1,5] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,2,4,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,2,4,1,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,2,3,3,2] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,2,3,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,2,3,1,4] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,2,2,4,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,2,2,3,3] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,2,2,2,4] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,2,2,1,5] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,2,1,5,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,2,1,4,3] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,2,1,3,4] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,2,1,2,5] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,2,1,1,6] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,5,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,5,1,3] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,4,3,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,4,2,3] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,4,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,3,4,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,3,3,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,3,2,4] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,3,1,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,2,5,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,2,4,3] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,2,3,4] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,2,2,5] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,2,1,6] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,6,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,5,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,4,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,3,5] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,1,2,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
The bounce path determined by an integer composition.
Properties
injective, graded
Sage code
def mapping(c):
    return DyckWord(sum([[1]*a + [0]*a for a in c], []))
Weight
40
Created
May 11, 2021 at 15:03 by Martin Rubey
Updated
May 11, 2021 at 15:03 by Martin Rubey