Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00124: Dyck paths —Adin-Bagno-Roichman transformation⟶ Dyck paths
Images
[1] => [1,0] => [1,0]
[1,1] => [1,0,1,0] => [1,0,1,0]
[2] => [1,1,0,0] => [1,1,0,0]
[1,1,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0]
[1,2] => [1,0,1,1,0,0] => [1,1,0,1,0,0]
[2,1] => [1,1,0,0,1,0] => [1,1,0,0,1,0]
[3] => [1,1,1,0,0,0] => [1,1,1,0,0,0]
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0]
[1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0]
[1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0]
[1,3] => [1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,0]
[2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0]
[2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0]
[3,1] => [1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0]
[4] => [1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0]
[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]
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0]
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0]
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0]
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0]
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0]
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0]
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0]
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0]
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0]
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0]
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0]
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0]
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,0]
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0]
[5] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0]
[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]
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0]
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0]
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0]
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0]
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0]
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0]
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0]
[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]
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0]
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0]
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0]
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0]
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0]
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0]
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0]
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [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] => [1,1,1,1,0,0,0,1,0,1,0,0]
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0]
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0]
[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]
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0]
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [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] => [1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0]
>>> Load all 526 entries. <<<
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [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] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [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] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [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] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [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] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [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] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [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] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [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] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [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] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [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] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[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] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[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] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[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] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[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] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[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] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[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] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[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] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[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] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,2,3] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]
[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] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,4,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[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] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[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] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,2,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,2,4] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]
[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] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,3,3] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]
[1,1,1,5,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]
[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] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[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] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,2,1,1,3] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]
[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] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,2,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0]
[1,1,2,4,1] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]
[1,1,2,5] => [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]
[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] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,4,1,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]
[1,1,5,1,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,5,2] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]
[1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]
[1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
[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] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[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] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[1,2,1,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]
[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] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[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] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[1,2,1,5] => [1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]
[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] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[1,2,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]
[1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]
[1,2,3,1,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,1,0]
[1,2,5,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]
[1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]
[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] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,3,2,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]
[1,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,4,1,3] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]
[1,4,2,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]
[1,4,4] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]
[1,5,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]
[1,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]
[1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]
[1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]
[1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
[1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
[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] => [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] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[2,1,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]
[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] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[2,1,1,1,2,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]
[2,1,1,1,3,1] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]
[2,1,1,1,4] => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]
[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] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[2,1,1,2,3] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]
[2,1,1,4,1] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]
[2,1,1,5] => [1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]
[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] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[2,1,5,1] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]
[2,1,6] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]
[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] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[2,2,1,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]
[2,2,2,1,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0]
[2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[2,2,2,3] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]
[2,2,3,1,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0]
[2,2,3,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0]
[2,2,5] => [1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]
[2,3,1,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0]
[2,3,3,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0]
[2,4,1,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0]
[2,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]
[2,5,1,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]
[2,5,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]
[2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
[2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
[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] => [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] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,1,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,1,0]
[3,1,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]
[3,1,2,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0]
[3,1,2,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0]
[3,1,4,1] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0]
[3,1,5] => [1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]
[3,2,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]
[3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]
[3,3,1,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]
[3,4,2] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]
[3,5,1] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]
[3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]
[4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [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] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[4,1,1,3] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0]
[4,1,3,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]
[4,1,4] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0]
[4,2,1,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]
[4,2,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0]
[4,2,3] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,0]
[4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]
[4,3,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]
[4,4,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]
[4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]
[5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [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] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[5,1,2,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,1,0]
[5,1,3] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]
[5,2,1,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]
[5,3,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]
[5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]
[6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [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] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]
[6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
[7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [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] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [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] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[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] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[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] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[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] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[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] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[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] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[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] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[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] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[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] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[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] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]
[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] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]
[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] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[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] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]
[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] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]
[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] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[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] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[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] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0]
[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] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0,1,0]
[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] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,7] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
[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] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]
[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] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,4,4] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0,0]
[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] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,6,2] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]
[1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]
[1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
[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] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[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] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]
[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] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,1,0,0]
[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] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[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] => [1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]
[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] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,1,0]
[1,2,7] => [1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]
[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] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]
[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] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[1,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]
[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] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]
[1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]
[1,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]
[1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]
[1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
[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] => [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] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[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] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[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] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[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] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[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] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]
[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] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]
[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] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,1,0,0]
[2,1,6,1] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]
[2,1,7] => [1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]
[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] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,1,0,0]
[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] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0]
[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] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[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] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]
[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] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0,1,0]
[2,2,3,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0]
[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] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[2,4,3,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,1,0]
[2,4,4] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0]
[2,6,1,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,1,0]
[2,6,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]
[2,7,1] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]
[2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
[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] => [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] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[3,1,5,1] => [1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,0]
[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] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[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] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]
[3,2,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0]
[3,3,2,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0]
[3,3,4] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0]
[3,4,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0,0]
[3,6,1] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]
[3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]
[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] => [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] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,1,1,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0,0]
[4,1,4,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,1,0]
[4,2,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0]
[4,2,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,0,0]
[4,3,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0,0]
[4,4,1,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0,1,0]
[4,4,2] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0,0]
[4,5,1] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]
[4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]
[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] => [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] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]
[5,1,3,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0,1,0]
[5,1,4] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0,0]
[5,2,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0,1,0]
[5,4,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]
[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] => [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] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]
[6,1,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,1,0]
[6,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0,0]
[6,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]
[6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]
[7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [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] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]
[7,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]
[7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
[8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [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] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [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] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
[10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[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] => [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
[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] => [1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[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] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]
[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] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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] => [1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
Adin-Bagno-Roichman transformation
Description
The Adin-Bagno-Roichman transformation of a Dyck path.
This is a bijection preserving the number of up steps before each peak and sending the number of returns to the number of up steps after the last double up step.