Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
St000042: Perfect matchings ⟶ ℤ
Values
[1,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[2,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[1,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[3,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[2,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[2,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[1,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[4,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[3,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[3,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[2,2,1] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[2,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[1,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[5,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[4,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[4,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[3,3] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 0
[3,2,1] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[3,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[2,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 0
[2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 0
[2,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[1,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 0
[6,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[5,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[5,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[4,3] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 0
[4,2,1] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[4,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[3,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 0
[3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 0
[3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 0
[3,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[2,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 0
[2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 0
[2,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 0
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 0
[7,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[6,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[6,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[5,3] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 0
[5,2,1] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[5,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[4,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 0
[4,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 0
[4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 0
[4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 0
[4,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[3,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 0
[3,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 0
[3,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 0
[3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 0
[3,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 0
[2,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 0
[2,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 0
[2,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 0
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 0
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[8,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[7,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[7,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[6,3] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 0
[6,2,1] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[6,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[5,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 0
[5,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 0
[5,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 0
[5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 0
[5,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[4,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 0
[4,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 0
[4,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 0
[4,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 0
[4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 0
[4,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 0
[3,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 0
[3,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 0
[3,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 0
[3,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 0
[3,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 0
[3,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 0
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 0
[2,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 0
[2,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => 0
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => 0
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)] => 0
[9,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[8,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[8,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[7,3] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 0
[7,2,1] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[7,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[6,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 0
[6,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 0
[6,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 0
[6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 0
[6,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[5,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => 0
[5,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 0
[5,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 0
>>> Load all 985 entries. <<<[5,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 0
[5,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 0
[5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 0
[5,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 0
[4,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 0
[4,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 0
[4,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 0
[4,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 0
[4,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 0
[4,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 0
[4,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 0
[4,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 0
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 0
[3,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 0
[3,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 0
[3,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 0
[3,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => 0
[3,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 0
[3,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => 0
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => 0
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[2,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => 0
[2,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => 0
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)] => 0
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)] => 0
[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)] => 0
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)] => 0
[10,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[9,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[9,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[8,3] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 0
[8,2,1] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[8,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[7,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 0
[7,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 0
[7,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 0
[7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 0
[7,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[6,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => 0
[6,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 0
[6,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 0
[6,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 0
[6,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 0
[6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 0
[6,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 0
[5,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => 0
[5,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 0
[5,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 0
[5,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 0
[5,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 0
[5,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 0
[5,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 0
[5,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 0
[5,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 0
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 0
[4,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 0
[4,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 0
[4,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 0
[4,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 0
[4,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 0
[4,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 0
[4,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => 0
[4,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 0
[4,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => 0
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => 0
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[3,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 0
[3,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 0
[3,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 0
[3,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => 0
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)] => 0
[3,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => 0
[3,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => 0
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)] => 0
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)] => 0
[3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)] => 0
[2,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 0
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)] => 0
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)] => 0
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,10),(11,12)] => 0
[2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)] => 0
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [(1,2),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13)] => 0
[11,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[10,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[10,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[9,3] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 0
[9,2,1] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[9,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[8,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 0
[8,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 0
[8,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 0
[8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 0
[8,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[7,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => 0
[7,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 0
[7,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 0
[7,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 0
[7,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 0
[7,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 0
[7,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 0
[6,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)] => 0
[6,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => 0
[6,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 0
[6,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 0
[6,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 0
[6,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 0
[6,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 0
[6,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 0
[6,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 0
[6,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 0
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 0
[5,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => 0
[5,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => 0
[5,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 0
[5,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 0
[5,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 0
[5,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 0
[5,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 0
[5,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 0
[5,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => 0
[5,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 0
[5,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => 0
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => 0
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[4,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => 0
[4,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 0
[4,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 0
[4,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 0
[4,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => 0
[4,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 0
[4,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 0
[4,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 0
[4,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => 0
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)] => 0
[4,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => 0
[4,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => 0
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)] => 0
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)] => 0
[4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)] => 0
[3,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => 0
[3,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 0
[3,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => 0
[3,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => 0
[3,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => 0
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)] => 0
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)] => 0
[3,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 0
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)] => 0
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)] => 0
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,10),(11,12)] => 0
[3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)] => 0
[2,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)] => 0
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)] => 0
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,9),(10,13),(11,12)] => 0
[2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,11),(12,13)] => 0
[2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [(1,2),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13)] => 0
[12,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[11,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[11,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[10,3] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 0
[10,2,1] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[10,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[9,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 0
[9,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 0
[9,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 0
[9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 0
[9,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[8,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => 0
[8,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 0
[8,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 0
[8,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 0
[8,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 0
[8,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 0
[8,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 0
[7,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)] => 0
[7,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => 0
[7,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 0
[7,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 0
[7,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 0
[7,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 0
[7,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 0
[7,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 0
[7,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 0
[7,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 0
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 0
[6,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)] => 0
[6,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => 0
[6,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => 0
[6,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 0
[6,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 0
[6,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 0
[6,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 0
[6,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 0
[6,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 0
[6,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => 0
[6,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 0
[6,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => 0
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => 0
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[5,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => 0
[5,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => 0
[5,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => 0
[5,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => 0
[5,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 0
[5,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 0
[5,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 0
[5,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => 0
[5,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 0
[5,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 0
[5,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 0
[5,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => 0
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)] => 0
[5,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => 0
[5,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => 0
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)] => 0
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)] => 0
[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)] => 0
[4,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => 0
[4,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 0
[4,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 0
[4,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 0
[4,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => 0
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,9),(7,8),(11,12)] => 0
[4,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => 0
[4,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 0
[4,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => 0
[4,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => 0
[4,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => 0
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)] => 0
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)] => 0
[4,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 0
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)] => 0
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)] => 0
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,10),(11,12)] => 0
[4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)] => 0
[3,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => 0
[3,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => 0
[3,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => 0
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)] => 0
[3,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 0
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,9),(10,11)] => 0
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,10),(11,12)] => 0
[3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,11),(9,10),(12,13)] => 0
[3,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)] => 0
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)] => 0
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,9),(10,13),(11,12)] => 0
[3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,11),(12,13)] => 0
[3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [(1,2),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13)] => 0
[13,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[12,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[12,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[11,3] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 0
[11,2,1] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[11,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[10,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 0
[10,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 0
[10,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 0
[10,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 0
[10,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[9,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => 0
[9,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 0
[9,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 0
[9,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 0
[9,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 0
[9,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 0
[9,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 0
[8,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)] => 0
[8,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => 0
[8,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 0
[8,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 0
[8,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 0
[8,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 0
[8,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 0
[8,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 0
[8,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 0
[8,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 0
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 0
[7,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)] => 0
[7,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)] => 0
[7,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => 0
[7,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => 0
[7,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 0
[7,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 0
[7,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 0
[7,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 0
[7,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 0
[7,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 0
[7,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => 0
[7,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 0
[7,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => 0
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => 0
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[6,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9),(13,14)] => 0
[6,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8),(13,14)] => 0
[6,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => 0
[6,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => 0
[6,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => 0
[6,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => 0
[6,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 0
[6,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 0
[6,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 0
[6,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => 0
[6,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 0
[6,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 0
[6,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 0
[6,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => 0
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)] => 0
[6,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => 0
[6,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => 0
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)] => 0
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)] => 0
[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)] => 0
[5,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => 0
[5,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => 0
[5,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => 0
[5,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => 0
[5,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => 0
[5,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => 0
[5,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 0
[5,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 0
[5,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 0
[5,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => 0
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,9),(7,8),(11,12)] => 0
[5,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => 0
[5,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 0
[5,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => 0
[5,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => 0
[5,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => 0
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)] => 0
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)] => 0
[5,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 0
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)] => 0
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)] => 0
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,10),(11,12)] => 0
[5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)] => 0
[4,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => 0
[4,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => 0
[4,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => 0
[4,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 0
[4,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => 0
[4,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => 0
[4,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => 0
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,7),(8,9),(11,12)] => 0
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,11),(7,10),(8,9),(12,13)] => 0
[4,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => 0
[4,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => 0
[4,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => 0
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)] => 0
[4,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 0
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,9),(10,11)] => 0
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,10),(11,12)] => 0
[4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,11),(9,10),(12,13)] => 0
[4,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)] => 0
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)] => 0
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,9),(10,13),(11,12)] => 0
[4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,11),(12,13)] => 0
[4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [(1,2),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13)] => 0
[3,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => 0
[3,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => 0
[3,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 0
[14,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[13,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[13,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[12,3] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 0
[12,2,1] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[12,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[11,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 0
[11,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 0
[11,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 0
[11,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 0
[11,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[10,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => 0
[10,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 0
[10,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 0
[10,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 0
[10,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 0
[10,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 0
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 0
[9,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)] => 0
[9,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => 0
[9,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 0
[9,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 0
[9,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 0
[9,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 0
[9,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 0
[9,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 0
[9,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 0
[9,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 0
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 0
[8,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)] => 0
[8,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)] => 0
[8,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => 0
[8,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => 0
[8,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 0
[8,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 0
[8,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 0
[8,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 0
[8,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 0
[8,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 0
[8,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => 0
[8,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 0
[8,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => 0
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => 0
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[7,7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9),(15,16)] => 0
[7,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9),(13,14)] => 0
[7,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8),(13,14)] => 0
[7,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => 0
[7,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => 0
[7,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => 0
[7,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => 0
[7,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 0
[7,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 0
[7,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 0
[7,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => 0
[7,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 0
[7,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 0
[7,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 0
[7,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => 0
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)] => 0
[7,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => 0
[7,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => 0
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)] => 0
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)] => 0
[7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)] => 0
[6,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10),(13,14)] => 0
[6,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9),(13,14)] => 0
[6,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8),(13,14)] => 0
[6,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => 0
[6,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => 0
[6,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => 0
[6,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => 0
[6,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => 0
[6,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => 0
[6,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 0
[6,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 0
[6,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 0
[6,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => 0
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,9),(7,8),(11,12)] => 0
[6,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => 0
[6,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 0
[6,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => 0
[6,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => 0
[6,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => 0
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)] => 0
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)] => 0
[6,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 0
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)] => 0
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)] => 0
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,10),(11,12)] => 0
[6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)] => 0
[5,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,14),(12,13)] => 0
[5,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => 0
[5,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => 0
[5,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => 0
[5,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => 0
[5,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => 0
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [(1,2),(3,14),(4,11),(5,10),(6,9),(7,8),(12,13)] => 0
[5,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => 0
[5,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => 0
[5,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => 0
[5,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 0
[5,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => 0
[5,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => 0
[5,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => 0
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,7),(8,9),(11,12)] => 0
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,11),(7,10),(8,9),(12,13)] => 0
[5,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => 0
[5,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => 0
[5,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => 0
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)] => 0
[5,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 0
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,9),(10,11)] => 0
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,10),(11,12)] => 0
[5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,11),(9,10),(12,13)] => 0
[5,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)] => 0
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)] => 0
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,9),(10,13),(11,12)] => 0
[5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,11),(12,13)] => 0
[5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [(1,2),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13)] => 0
[4,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => 0
[4,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => 0
[4,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => 0
[4,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => 0
[4,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => 0
[4,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => 0
[4,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => 0
[4,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => 0
[4,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => 0
[4,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 0
[3,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 0
[15,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[14,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[14,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[13,3] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 0
[13,2,1] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[13,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[12,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 0
[12,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 0
[12,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 0
[12,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 0
[12,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[11,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => 0
[11,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 0
[11,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 0
[11,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 0
[11,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 0
[11,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 0
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 0
[10,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)] => 0
[10,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => 0
[10,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 0
[10,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 0
[10,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 0
[10,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 0
[10,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 0
[10,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 0
[10,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 0
[10,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 0
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 0
[9,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)] => 0
[9,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)] => 0
[9,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => 0
[9,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => 0
[9,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 0
[9,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 0
[9,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 0
[9,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 0
[9,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 0
[9,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 0
[9,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => 0
[9,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 0
[9,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => 0
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => 0
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[8,8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9),(17,18)] => 0
[8,7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9),(15,16)] => 0
[8,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9),(13,14)] => 0
[8,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8),(13,14)] => 0
[8,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => 0
[8,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => 0
[8,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => 0
[8,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => 0
[8,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 0
[8,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 0
[8,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 0
[8,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => 0
[8,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 0
[8,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 0
[8,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 0
[8,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => 0
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)] => 0
[8,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => 0
[8,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => 0
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)] => 0
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)] => 0
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)] => 0
[7,7,2] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10),(15,16)] => 0
[7,7,1,1] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9),(15,16)] => 0
[7,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10),(13,14)] => 0
[7,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9),(13,14)] => 0
[7,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8),(13,14)] => 0
[7,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => 0
[7,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => 0
[7,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => 0
[7,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => 0
[7,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => 0
[7,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => 0
[7,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 0
[7,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 0
[7,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 0
[7,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => 0
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,9),(7,8),(11,12)] => 0
[7,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => 0
[7,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 0
[7,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => 0
[7,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => 0
[7,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => 0
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)] => 0
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)] => 0
[7,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 0
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)] => 0
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)] => 0
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,10),(11,12)] => 0
[7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)] => 0
[6,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11),(13,14)] => 0
[6,6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10),(13,14)] => 0
[6,6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9),(13,14)] => 0
[6,6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9),(13,14)] => 0
[6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8),(13,14)] => 0
[6,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,14),(12,13)] => 0
[6,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => 0
[6,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => 0
[6,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => 0
[6,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => 0
[6,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => 0
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [(1,2),(3,14),(4,11),(5,10),(6,9),(7,8),(12,13)] => 0
[6,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => 0
[6,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => 0
[6,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => 0
[6,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 0
[6,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => 0
[6,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => 0
[6,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => 0
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,7),(8,9),(11,12)] => 0
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,11),(7,10),(8,9),(12,13)] => 0
[6,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => 0
[6,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => 0
[6,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => 0
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)] => 0
[6,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 0
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,9),(10,11)] => 0
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,10),(11,12)] => 0
[6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,11),(9,10),(12,13)] => 0
[6,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)] => 0
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)] => 0
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,9),(10,13),(11,12)] => 0
[6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,11),(12,13)] => 0
[6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [(1,2),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13)] => 0
[5,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => 0
[5,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => 0
[5,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => 0
[5,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => 0
[5,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => 0
[5,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => 0
[5,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => 0
[5,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => 0
[5,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => 0
[5,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => 0
[5,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => 0
[5,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => 0
[5,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => 0
[5,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => 0
[5,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => 0
[5,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => 0
[5,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 0
[4,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => 0
[4,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => 0
[4,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => 0
[4,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => 0
[4,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => 0
[4,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 0
[4,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 0
[16,1] => [1] => [1,0,1,0] => [(1,2),(3,4)] => 0
[15,2] => [2] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 0
[15,1,1] => [1,1] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 0
[14,3] => [3] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 0
[14,2,1] => [2,1] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[14,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 0
[13,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 0
[13,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 0
[13,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 0
[13,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 0
[13,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[12,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => 0
[12,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 0
[12,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 0
[12,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 0
[12,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 0
[12,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 0
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 0
[11,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)] => 0
[11,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => 0
[11,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 0
[11,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 0
[11,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 0
[11,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 0
[11,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 0
[11,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 0
[11,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 0
[11,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 0
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 0
[10,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)] => 0
[10,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)] => 0
[10,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => 0
[10,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => 0
[10,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 0
[10,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 0
[10,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 0
[10,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 0
[10,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 0
[10,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 0
[10,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => 0
[10,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 0
[10,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => 0
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => 0
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[9,8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9),(17,18)] => 0
[9,7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9),(15,16)] => 0
[9,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9),(13,14)] => 0
[9,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8),(13,14)] => 0
[9,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => 0
[9,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => 0
[9,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => 0
[9,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => 0
[9,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 0
[9,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 0
[9,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 0
[9,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => 0
[9,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 0
[9,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 0
[9,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 0
[9,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => 0
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)] => 0
[9,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => 0
[9,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => 0
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)] => 0
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)] => 0
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)] => 0
[8,8,1] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10),(17,18)] => 0
[8,7,2] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10),(15,16)] => 0
[8,7,1,1] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9),(15,16)] => 0
[8,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10),(13,14)] => 0
[8,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9),(13,14)] => 0
[8,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8),(13,14)] => 0
[8,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => 0
[8,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => 0
[8,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => 0
[8,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => 0
[8,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => 0
[8,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => 0
[8,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 0
[8,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 0
[8,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 0
[8,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => 0
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,9),(7,8),(11,12)] => 0
[8,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => 0
[8,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 0
[8,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => 0
[8,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => 0
[8,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => 0
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)] => 0
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)] => 0
[8,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 0
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)] => 0
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)] => 0
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,10),(11,12)] => 0
[8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)] => 0
[7,7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11),(15,16)] => 0
[7,7,2,1] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,8),(9,10),(15,16)] => 0
[7,7,1,1,1] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9),(15,16)] => 0
[7,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11),(13,14)] => 0
[7,6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10),(13,14)] => 0
[7,6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9),(13,14)] => 0
[7,6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9),(13,14)] => 0
[7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8),(13,14)] => 0
[7,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,14),(12,13)] => 0
[7,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => 0
[7,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => 0
[7,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => 0
[7,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => 0
[7,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => 0
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [(1,2),(3,14),(4,11),(5,10),(6,9),(7,8),(12,13)] => 0
[7,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => 0
[7,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => 0
[7,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => 0
[7,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 0
[7,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => 0
[7,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => 0
[7,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => 0
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,7),(8,9),(11,12)] => 0
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,11),(7,10),(8,9),(12,13)] => 0
[7,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => 0
[7,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => 0
[7,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => 0
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)] => 0
[7,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 0
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,9),(10,11)] => 0
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,10),(11,12)] => 0
[7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,11),(9,10),(12,13)] => 0
[7,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)] => 0
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)] => 0
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)] => 0
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,9),(10,13),(11,12)] => 0
[7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,11),(12,13)] => 0
[7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [(1,2),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13)] => 0
[6,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => 0
[6,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => 0
[6,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => 0
[6,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => 0
[6,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => 0
[6,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => 0
[6,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => 0
[6,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => 0
[6,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => 0
[6,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => 0
[6,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => 0
[6,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => 0
[6,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => 0
[6,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => 0
[6,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => 0
[6,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => 0
[6,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 0
[5,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => 0
[5,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => 0
[5,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => 0
[5,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => 0
[5,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => 0
[5,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => 0
[5,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => 0
[5,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => 0
[5,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => 0
[5,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => 0
[5,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => 0
[5,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => 0
[5,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 0
[5,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 0
[4,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => 0
[4,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => 0
[4,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => 0
[4,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 0
[6,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 0
[5,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 0
[6,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 0
[5,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 0
[4,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 0
[6,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => 0
[5,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => 0
[6,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 0
[5,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 0
[6,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 0
[6,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => 0
[5,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => 0
[6,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => 0
[5,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => 0
[6,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => 0
[5,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => 0
[6,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 0
[6,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => 0
[6,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => 0
[5,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => 0
[6,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => 0
[5,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => 0
[6,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => 0
[5,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => 0
[6,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => 0
[6,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => 0
[5,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => 0
[6,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => 0
[6,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => 0
[6,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => 0
[6,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => 0
[5,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => 0
[6,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => 0
[5,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => 0
[6,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => 0
[5,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => 0
[6,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => 0
[6,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => 0
[5,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => 0
[6,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => 0
[6,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => 0
[6,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => 0
[5,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => 0
[6,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => 0
[6,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => 0
[6,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => 0
[6,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => 0
[7,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 0
[7,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 0
[7,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 0
[7,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 0
[7,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => 0
[7,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => 0
[7,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => 0
[7,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => 0
[7,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => 0
[10,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => 0
[10,10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [(1,20),(2,19),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11),(21,22)] => 0
[11,7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11),(15,16)] => 0
[9,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10),(13,14)] => 0
[8,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11),(13,14)] => 0
[10,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11),(13,14)] => 0
[15,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,14),(12,13)] => 0
[9,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11),(13,14)] => 0
[10,7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11),(15,16)] => 0
[8,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => 0
[9,9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [(1,18),(2,17),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10),(19,20)] => 0
[8,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 0
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searching the database for the individual values of this statistic
Description
The number of crossings of a perfect matching.
This is the number of pairs of edges $((a,b),(c,d))$ such that $a\le c\le b\le d$, i.e., the edges $(a,b)$ and $(c,d)$ cross when drawing the perfect matching as a chord diagram.
The generating function for perfect matchings $M$ of $\{1,\dots,2n\}$ according to the number of crossings $\textrm{cr}(M)$ is given by the Touchard-Riordan formula ([2], [4], a bijective proof is given in [7]):
$$ \sum_{M} q^{\textrm{cr}(M)} = \frac{1}{(1-q)^n} \sum_{k=0}^n\left(\binom{2n}{n-k}-\binom{2n}{n-k-1}\right)(-1)^k q^{\binom{k+1}{2}} $$
This is the number of pairs of edges $((a,b),(c,d))$ such that $a\le c\le b\le d$, i.e., the edges $(a,b)$ and $(c,d)$ cross when drawing the perfect matching as a chord diagram.
The generating function for perfect matchings $M$ of $\{1,\dots,2n\}$ according to the number of crossings $\textrm{cr}(M)$ is given by the Touchard-Riordan formula ([2], [4], a bijective proof is given in [7]):
$$ \sum_{M} q^{\textrm{cr}(M)} = \frac{1}{(1-q)^n} \sum_{k=0}^n\left(\binom{2n}{n-k}-\binom{2n}{n-k-1}\right)(-1)^k q^{\binom{k+1}{2}} $$
Map
first row removal
Description
Removes the first entry of an integer partition
Map
to tunnel matching
Description
Sends a Dyck path of semilength n to the noncrossing perfect matching given by matching an up-step with the corresponding down-step.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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