- FindStat

Identifier

Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
Mp00137: Dyck paths —to symmetric ASM⟶ Alternating sign matrices
Mp00098: Alternating sign matrices —link pattern⟶ Perfect matchings
Mp00150: Perfect matchings —to Dyck path⟶ Dyck paths

Images

[1,0] => [1,0] => [[1]] => [(1,2)] => [1,0]

[1,0,1,0] => [1,1,0,0] => [[0,1],[1,0]] => [(1,2),(3,4)] => [1,0,1,0]

[1,1,0,0] => [1,0,1,0] => [[1,0],[0,1]] => [(1,4),(2,3)] => [1,1,0,0]

[1,0,1,0,1,0] => [1,1,0,1,0,0] => [[0,1,0],[1,-1,1],[0,1,0]] => [(1,2),(3,6),(4,5)] => [1,0,1,1,0,0]

[1,0,1,1,0,0] => [1,1,0,0,1,0] => [[0,1,0],[1,0,0],[0,0,1]] => [(1,2),(3,4),(5,6)] => [1,0,1,0,1,0]

[1,1,0,0,1,0] => [1,0,1,1,0,0] => [[1,0,0],[0,0,1],[0,1,0]] => [(1,6),(2,3),(4,5)] => [1,1,0,1,0,0]

[1,1,0,1,0,0] => [1,1,1,0,0,0] => [[0,0,1],[0,1,0],[1,0,0]] => [(1,4),(2,3),(5,6)] => [1,1,0,0,1,0]

[1,1,1,0,0,0] => [1,0,1,0,1,0] => [[1,0,0],[0,1,0],[0,0,1]] => [(1,6),(2,5),(3,4)] => [1,1,1,0,0,0]

[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]] => [(1,2),(3,8),(4,7),(5,6)] => [1,0,1,1,1,0,0,0]

[1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]] => [(1,2),(3,8),(4,5),(6,7)] => [1,0,1,1,0,1,0,0]

[1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]] => [(1,2),(3,4),(5,6),(7,8)] => [1,0,1,0,1,0,1,0]

[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]] => [(1,2),(3,4),(5,8),(6,7)] => [1,0,1,0,1,1,0,0]

[1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]] => [(1,2),(3,6),(4,5),(7,8)] => [1,0,1,1,0,0,1,0]

[1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]] => [(1,8),(2,3),(4,7),(5,6)] => [1,1,0,1,1,0,0,0]

[1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]] => [(1,8),(2,3),(4,5),(6,7)] => [1,1,0,1,0,1,0,0]

[1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]] => [(1,4),(2,3),(5,6),(7,8)] => [1,1,0,0,1,0,1,0]

[1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0] => [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]] => [(1,4),(2,3),(5,8),(6,7)] => [1,1,0,0,1,1,0,0]

[1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => [[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]] => [(1,6),(2,3),(4,5),(7,8)] => [1,1,0,1,0,0,1,0]

[1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]] => [(1,8),(2,7),(3,4),(5,6)] => [1,1,1,0,1,0,0,0]

[1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]] => [(1,8),(2,5),(3,4),(6,7)] => [1,1,1,0,0,1,0,0]

[1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => [[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]] => [(1,6),(2,5),(3,4),(7,8)] => [1,1,1,0,0,0,1,0]

[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]] => [(1,8),(2,7),(3,6),(4,5)] => [1,1,1,1,0,0,0,0]

[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => [1,0,1,1,1,1,0,0,0,0]

[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => [1,0,1,1,1,0,1,0,0,0]

[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => [1,0,1,1,0,1,0,1,0,0]

[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => [1,0,1,1,0,1,1,0,0,0]

[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => [1,0,1,1,1,0,0,1,0,0]

[1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => [1,0,1,0,1,1,0,0,1,0]

[1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => [1,0,1,0,1,0,1,0,1,0]

[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => [1,0,1,0,1,1,0,1,0,0]

[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => [[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => [1,0,1,0,1,1,1,0,0,0]

[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0] => [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => [1,0,1,0,1,0,1,1,0,0]

[1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => [1,0,1,1,0,1,0,0,1,0]

[1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => [1,0,1,1,0,0,1,0,1,0]

[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => [1,0,1,1,0,0,1,1,0,0]

[1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => [1,0,1,1,1,0,0,0,1,0]

[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => [1,1,0,1,1,1,0,0,0,0]

[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]] => [(1,10),(2,3),(4,9),(5,6),(7,8)] => [1,1,0,1,1,0,1,0,0,0]

[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [(1,10),(2,3),(4,5),(6,7),(8,9)] => [1,1,0,1,0,1,0,1,0,0]

[1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [(1,10),(2,3),(4,5),(6,9),(7,8)] => [1,1,0,1,0,1,1,0,0,0]

[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [(1,10),(2,3),(4,7),(5,6),(8,9)] => [1,1,0,1,1,0,0,1,0,0]

[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => [1,1,0,0,1,1,0,0,1,0]

[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => [1,1,0,0,1,0,1,0,1,0]

[1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,-1,1],[0,0,0,1,0]] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => [1,1,0,0,1,1,0,1,0,0]

[1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => [[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => [1,1,0,0,1,1,1,0,0,0]

[1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => [1,1,0,0,1,0,1,1,0,0]

[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => [1,1,0,1,0,1,0,0,1,0]

[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0]

[1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,0,-1,1,0],[0,0,1,0,0]] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0]

[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => [1,1,0,1,1,0,0,0,1,0]

[1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => [1,1,1,0,1,1,0,0,0,0]

[1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]] => [(1,10),(2,9),(3,4),(5,6),(7,8)] => [1,1,1,0,1,0,1,0,0,0]

[1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]] => [(1,10),(2,5),(3,4),(6,7),(8,9)] => [1,1,1,0,0,1,0,1,0,0]

[1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0]

[1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => [(1,10),(2,7),(3,4),(5,6),(8,9)] => [1,1,1,0,1,0,0,1,0,0]

[1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0]

[1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0] => [[0,0,1,0,0],[0,1,-1,0,1],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0]

[1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0]

[1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0]

[1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => [1,1,1,1,0,1,0,0,0,0]

[1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => [1,1,1,1,0,0,1,0,0,0]

[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => [1,1,1,1,0,0,0,1,0,0]

[1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0]

[1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => [1,1,1,1,1,0,0,0,0,0]

[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [1,0,1,1,1,1,1,0,0,0,0,0]

[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [1,0,1,1,1,1,0,1,0,0,0,0]

[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [1,0,1,1,1,0,1,0,1,0,0,0]

[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [1,0,1,1,1,0,1,1,0,0,0,0]

[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [1,0,1,1,1,1,0,0,1,0,0,0]

[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [1,0,1,1,0,1,1,0,0,1,0,0]

[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [1,0,1,1,0,1,0,1,0,1,0,0]

[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [1,0,1,1,0,1,1,0,1,0,0,0]

[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [1,0,1,1,0,1,1,1,0,0,0,0]

[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [1,0,1,1,0,1,0,1,1,0,0,0]

[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [1,0,1,1,1,0,1,0,0,1,0,0]

[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [1,0,1,1,1,0,0,1,0,1,0,0]

[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [1,0,1,1,1,0,0,1,1,0,0,0]

[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [1,0,1,1,1,1,0,0,0,1,0,0]

[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [1,0,1,0,1,1,1,0,0,0,1,0]

[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [1,0,1,0,1,1,0,1,0,0,1,0]

[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [1,0,1,0,1,0,1,0,1,0,1,0]

[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [1,0,1,0,1,0,1,1,0,0,1,0]

[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [1,0,1,0,1,1,0,0,1,0,1,0]

[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [1,0,1,0,1,1,1,0,0,1,0,0]

[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [1,0,1,0,1,1,0,1,0,1,0,0]

[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [1,0,1,0,1,1,1,0,1,0,0,0]

[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [1,0,1,0,1,1,1,1,0,0,0,0]

[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [1,0,1,0,1,1,0,1,1,0,0,0]

[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [1,0,1,0,1,0,1,0,1,1,0,0]

[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [1,0,1,0,1,0,1,1,0,1,0,0]

[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [1,0,1,0,1,0,1,1,1,0,0,0]

[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [1,0,1,0,1,1,0,0,1,1,0,0]

[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [1,0,1,1,0,1,1,0,0,0,1,0]

[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [1,0,1,1,0,1,0,1,0,0,1,0]

[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [1,0,1,1,0,0,1,0,1,0,1,0]

[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [1,0,1,1,0,0,1,1,0,0,1,0]

[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [1,0,1,1,0,1,0,0,1,0,1,0]

[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [1,0,1,1,0,0,1,0,1,1,0,0]

[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [1,0,1,1,0,0,1,1,0,1,0,0]

[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [1,0,1,1,0,0,1,1,1,0,0,0]

[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [1,0,1,1,0,1,0,0,1,1,0,0]

>>> Load all 196 entries. <<<

[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [1,0,1,1,1,0,1,0,0,0,1,0]

[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [1,0,1,1,1,0,0,1,0,0,1,0]

[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [1,0,1,1,1,0,0,0,1,0,1,0]

[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [1,0,1,1,1,0,0,0,1,1,0,0]

[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [1,0,1,1,1,1,0,0,0,0,1,0]

[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [1,1,0,1,1,1,1,0,0,0,0,0]

[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [1,1,0,1,1,1,0,1,0,0,0,0]

[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => [1,1,0,1,1,0,1,0,1,0,0,0]

[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [1,1,0,1,1,0,1,1,0,0,0,0]

[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [1,1,0,1,1,1,0,0,1,0,0,0]

[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [1,1,0,1,0,1,1,0,0,1,0,0]

[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [1,1,0,1,0,1,0,1,0,1,0,0]

[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [1,1,0,1,0,1,1,0,1,0,0,0]

[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [1,1,0,1,0,1,1,1,0,0,0,0]

[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [1,1,0,1,0,1,0,1,1,0,0,0]

[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [1,1,0,1,1,0,1,0,0,1,0,0]

[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [1,1,0,1,1,0,0,1,0,1,0,0]

[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [1,1,0,1,1,0,0,1,1,0,0,0]

[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [1,1,0,1,1,1,0,0,0,1,0,0]

[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [1,1,0,0,1,1,1,0,0,0,1,0]

[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [1,1,0,0,1,1,0,1,0,0,1,0]

[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [1,1,0,0,1,0,1,0,1,0,1,0]

[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [1,1,0,0,1,0,1,1,0,0,1,0]

[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [1,1,0,0,1,1,0,0,1,0,1,0]

[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [1,1,0,0,1,1,1,0,0,1,0,0]

[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [1,1,0,0,1,1,0,1,0,1,0,0]

[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]] => [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [1,1,0,0,1,1,1,0,1,0,0,0]

[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [1,1,0,0,1,1,1,1,0,0,0,0]

[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [1,1,0,0,1,1,0,1,1,0,0,0]

[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [1,1,0,0,1,0,1,0,1,1,0,0]

[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [1,1,0,0,1,0,1,1,0,1,0,0]

[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]] => [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [1,1,0,0,1,0,1,1,1,0,0,0]

[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [1,1,0,0,1,1,0,0,1,1,0,0]

[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [1,1,0,1,0,1,1,0,0,0,1,0]

[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [1,1,0,1,0,1,0,1,0,0,1,0]

[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [1,1,0,1,0,0,1,0,1,0,1,0]

[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [1,1,0,1,0,0,1,1,0,0,1,0]

[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [1,1,0,1,0,1,0,0,1,0,1,0]

[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [1,1,0,1,0,0,1,0,1,1,0,0]

[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [1,1,0,1,0,0,1,1,0,1,0,0]

[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [1,1,0,1,0,0,1,1,1,0,0,0]

[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [1,1,0,1,0,1,0,0,1,1,0,0]

[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [1,1,0,1,1,0,1,0,0,0,1,0]

[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [1,1,0,1,1,0,0,1,0,0,1,0]

[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [1,1,0,1,1,0,0,0,1,0,1,0]

[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [1,1,0,1,1,0,0,0,1,1,0,0]

[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [1,1,0,1,1,1,0,0,0,0,1,0]

[1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [1,1,1,0,1,1,1,0,0,0,0,0]

[1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [1,1,1,0,1,1,0,1,0,0,0,0]

[1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [1,1,1,0,1,0,1,0,1,0,0,0]

[1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [1,1,1,0,1,0,1,1,0,0,0,0]

[1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [1,1,1,0,1,1,0,0,1,0,0,0]

[1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [1,1,1,0,0,1,1,0,0,1,0,0]

[1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [1,1,1,0,0,1,0,1,0,1,0,0]

[1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]] => [(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [1,1,1,0,0,1,1,0,1,0,0,0]

[1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]] => [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [1,1,1,0,0,1,1,1,0,0,0,0]

[1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => [(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [1,1,1,0,0,1,0,1,1,0,0,0]

[1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [1,1,1,0,1,0,1,0,0,1,0,0]

[1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [1,1,1,0,1,0,0,1,0,1,0,0]

[1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]] => [(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [1,1,1,0,1,0,0,1,1,0,0,0]

[1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [1,1,1,0,1,1,0,0,0,1,0,0]

[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [1,1,1,0,0,1,1,0,0,0,1,0]

[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [1,1,1,0,0,1,0,1,0,0,1,0]

[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]] => [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [1,1,1,0,0,0,1,0,1,0,1,0]

[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]] => [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [1,1,1,0,0,0,1,1,0,0,1,0]

[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [1,1,1,0,0,1,0,0,1,0,1,0]

[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,-1,1],[0,0,0,0,1,0]] => [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [1,1,1,0,0,0,1,0,1,1,0,0]

[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0]] => [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [1,1,1,0,0,0,1,1,0,1,0,0]

[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]] => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [1,1,1,0,0,0,1,1,1,0,0,0]

[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [1,1,1,0,0,1,0,0,1,1,0,0]

[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [1,1,1,0,1,0,1,0,0,0,1,0]

[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [1,1,1,0,1,0,0,1,0,0,1,0]

[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]] => [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [1,1,1,0,1,0,0,0,1,0,1,0]

[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[1,0,0,-1,1,0],[0,0,0,1,0,0]] => [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [1,1,1,0,1,0,0,0,1,1,0,0]

[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [1,1,1,0,1,1,0,0,0,0,1,0]

[1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [1,1,1,1,0,1,1,0,0,0,0,0]

[1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [1,1,1,1,0,1,0,1,0,0,0,0]

[1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [1,1,1,1,0,0,1,0,1,0,0,0]

[1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [1,1,1,1,0,0,1,1,0,0,0,0]

[1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [1,1,1,1,0,1,0,0,1,0,0,0]

[1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [1,1,1,1,0,0,1,0,0,1,0,0]

[1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [1,1,1,1,0,0,0,1,0,1,0,0]

[1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => [(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [1,1,1,1,0,0,0,1,1,0,0,0]

[1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [1,1,1,1,0,1,0,0,0,1,0,0]

[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [1,1,1,1,0,0,1,0,0,0,1,0]

[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [1,1,1,1,0,0,0,1,0,0,1,0]

[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [[0,0,1,0,0,0],[0,1,-1,0,0,1],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [1,1,1,1,0,0,0,0,1,0,1,0]

[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0]] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [1,1,1,1,0,0,0,0,1,1,0,0]

[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [1,1,1,1,0,1,0,0,0,0,1,0]

[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [1,1,1,1,1,0,1,0,0,0,0,0]

[1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [1,1,1,1,1,0,0,1,0,0,0,0]

[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [1,1,1,1,1,0,0,0,1,0,0,0]

[1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [1,1,1,1,1,0,0,0,0,1,0,0]

[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [1,1,1,1,1,0,0,0,0,0,1,0]

[1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [1,1,1,1,1,1,0,0,0,0,0,0]

Map

Delest-Viennot

Description

Return the Dyck path corresponding to the parallelogram polyomino obtained by applying Delest-Viennot's bijection.
Let

$D$ be a Dyck path of semilength

$n$ . The parallelogram polyomino

$\gamma(D)$ is defined as follows: let

$\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to

$D$ . Then, the upper path of

$\gamma(D)$ corresponds to the sequence of steps of

$\tilde D$ with even indices, and the lower path of

$\gamma(D)$ corresponds to the sequence of steps of

$\tilde D$ with odd indices.
The Delest-Viennot bijection

$\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path

$(\gamma^{(-1)}\circ\beta)(D)$ .

Map

to symmetric ASM

Description

The diagonally symmetric alternating sign matrix corresponding to a Dyck path.

Map

link pattern

Description

Sends an alternating sign matrix to the link pattern of the corresponding fully packed loop configuration.

Map

to Dyck path

Description

The Dyck path corresponding to the opener-closer sequence of the perfect matching.