Identifier
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Images
[1,0] => [[1],[]] => ([],1) => ([],1)
[1,0,1,0] => [[1,1],[]] => ([(0,1)],2) => ([(0,1)],2)
[1,1,0,0] => [[2],[]] => ([(0,1)],2) => ([(0,1)],2)
[1,0,1,0,1,0] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3)
[1,0,1,1,0,0] => [[2,1],[]] => ([(0,1),(0,2)],3) => ([(0,2),(1,2)],3)
[1,1,0,0,1,0] => [[2,2],[1]] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3)
[1,1,0,1,0,0] => [[3],[]] => ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3)
[1,1,1,0,0,0] => [[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4)
[1,0,1,0,1,0,1,0] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(1,2),(2,3)],4)
[1,0,1,0,1,1,0,0] => [[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => ([(0,3),(1,2),(2,3)],4)
[1,0,1,1,0,0,1,0] => [[2,2,1],[1]] => ([(0,3),(1,2),(1,3)],4) => ([(0,3),(1,2),(2,3)],4)
[1,0,1,1,0,1,0,0] => [[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => ([(0,3),(1,2),(2,3)],4)
[1,0,1,1,1,0,0,0] => [[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
[1,1,0,0,1,0,1,0] => [[2,2,2],[1,1]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4)
[1,1,0,0,1,1,0,0] => [[3,2],[1]] => ([(0,3),(1,2),(1,3)],4) => ([(0,3),(1,2),(2,3)],4)
[1,1,0,1,0,0,1,0] => [[3,3],[2]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4)
[1,1,0,1,0,1,0,0] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(1,2),(2,3)],4)
[1,1,0,1,1,0,0,0] => [[3,3],[1]] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
[1,1,1,0,0,0,1,0] => [[2,2,2],[1]] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
[1,1,1,0,0,1,0,0] => [[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
[1,1,1,0,1,0,0,0] => [[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
[1,1,1,1,0,0,0,0] => [[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,0,1,1,0,1,0,0] => [[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
[1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1],[1,1]] => ([(0,3),(1,2),(1,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,1,0,0,1,1,0,0] => [[3,2,1],[1]] => ([(0,3),(0,4),(1,2),(1,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,1,0,1,0,0,1,0] => [[3,3,1],[2]] => ([(0,4),(1,2),(1,3),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,1,0,1,0,1,0,0] => [[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,1,0,1,1,0,0,0] => [[3,3,1],[1]] => ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1],[1]] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
[1,0,1,1,1,0,0,1,0,0] => [[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
[1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,0,0] => [[3,3,1],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2],[1,1,1]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,0,1,0,1,1,0,0] => [[3,2,2],[1,1]] => ([(0,4),(1,2),(1,3),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,0,1,1,0,0,1,0] => [[3,3,2],[2,1]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,0,1,1,0,1,0,0] => [[4,2],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,0,1,1,1,0,0,0] => [[3,3,2],[1,1]] => ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
[1,1,0,1,0,0,1,0,1,0] => [[3,3,3],[2,2]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,0,1,1,0,0] => [[4,3],[2]] => ([(0,3),(1,2),(1,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,1,0,0,1,0] => [[4,4],[3]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,1,0,1,0,0] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,1,1,0,0,0] => [[4,4],[2]] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
[1,1,0,1,1,0,0,0,1,0] => [[3,3,3],[2,1]] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,1,1,0,0,1,0,0] => [[4,3],[1]] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
[1,1,0,1,1,0,1,0,0,0] => [[3,3,3],[1,1]] => ([(0,2),(0,3),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,0,0,0,0] => [[4,4],[1]] => ([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2],[1,1]] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
[1,1,1,0,0,0,1,1,0,0] => [[3,2,2],[1]] => ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
[1,1,1,0,0,1,0,0,1,0] => [[3,3,2],[2]] => ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
[1,1,1,0,0,1,0,1,0,0] => [[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
[1,1,1,0,0,1,1,0,0,0] => [[3,3,2],[1]] => ([(0,3),(0,6),(1,2),(1,6),(2,4),(3,5),(6,4),(6,5)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
[1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2],[1]] => ([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,0,1,0,0] => [[3,2,2],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,0,0,0] => [[3,3,2],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8) => ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,0] => [[3,3,3],[2]] => ([(0,2),(0,3),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,0,1,0,0] => [[4,3],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,1,0,0,0] => [[3,3,3],[1]] => ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(5,4),(6,4),(7,5),(7,6)],8) => ([(0,3),(0,7),(1,2),(1,7),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,0,0] => [[4,4],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,0,0] => [[3,3,3],[]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,8),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1],[1]] => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1],[1,1]] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1],[1]] => ([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1],[2]] => ([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1],[1]] => ([(0,3),(0,6),(1,4),(1,6),(3,5),(4,2),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1],[1]] => ([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1],[1,1,1]] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1],[1,1]] => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1],[1]] => ([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1],[1,1]] => ([(0,4),(0,6),(1,2),(1,3),(2,5),(3,5),(3,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1],[2,2]] => ([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1],[2]] => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1],[3]] => ([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1],[2]] => ([(0,4),(0,6),(1,2),(1,3),(3,6),(4,5),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(4,6),(5,6)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1],[1]] => ([(0,3),(0,6),(1,4),(1,6),(4,2),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,0,1,1,0,1,1,0,1,0,0,0] => [[3,3,3,1],[1,1]] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(3,5),(3,7),(5,6),(7,6)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,0,0] => [[4,4,1],[1]] => ([(0,3),(0,7),(1,4),(1,7),(2,6),(4,2),(4,5),(5,6),(7,5)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1],[1,1]] => ([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1],[1]] => ([(0,3),(0,6),(1,4),(1,6),(4,2),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1],[2]] => ([(0,6),(1,3),(1,4),(3,5),(3,6),(4,2),(4,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,0,1,1,1,0,0,1,1,0,0,0] => [[3,3,2,1],[1]] => ([(0,3),(0,7),(1,4),(1,7),(3,5),(4,2),(4,6),(7,5),(7,6)],8) => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2,1],[1]] => ([(0,7),(1,4),(1,7),(3,2),(3,6),(4,3),(4,5),(5,6),(7,5)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
[1,0,1,1,1,0,1,1,0,0,0,0] => [[3,3,2,1],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
>>> Load all 347 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[3,3,3,1],[2]] => ([(0,7),(1,3),(1,4),(3,5),(3,7),(4,2),(4,5),(5,6),(7,6)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,0] => [[3,3,3,1],[1]] => ([(0,3),(0,8),(1,4),(1,8),(3,6),(4,2),(4,7),(6,5),(7,5),(8,6),(8,7)],9) => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,1,0,0,0,0] => [[4,4,1],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
[1,0,1,1,1,1,1,0,0,0,0,0] => [[3,3,3,1],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10) => ([(0,8),(1,5),(1,7),(2,4),(2,6),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,9),(7,9)],10)
[1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1,1]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1,1]] => ([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1,1]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2],[1,1]] => ([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1,1]] => ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2],[3,1]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2],[1]] => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(3,6),(5,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1,1]] => ([(0,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2],[1,1]] => ([(0,6),(1,3),(1,4),(3,5),(3,6),(4,2),(4,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,1,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1,1]] => ([(0,7),(1,3),(1,4),(2,6),(2,7),(3,5),(4,2),(4,5),(5,6)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,0] => [[4,4,2],[1,1]] => ([(0,7),(1,3),(1,4),(2,6),(3,5),(3,7),(4,2),(4,5),(5,6)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3],[2,2]] => ([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3],[2]] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(3,6),(4,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4],[3]] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5],[4]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,1,0,1,0,0] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5],[3]] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4],[3,2]] => ([(0,4),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4],[2]] => ([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,1,0,1,0,1,1,0,1,0,0,0] => [[4,4,4],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,0,0,0] => [[5,5],[2]] => ([(0,3),(1,4),(1,7),(2,6),(3,7),(4,2),(4,5),(5,6),(7,5)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2,1]] => ([(0,4),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(4,6),(5,6)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3],[3,1]] => ([(0,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3],[1]] => ([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
[1,1,0,1,1,0,0,1,1,0,0,0] => [[4,4,3],[2,1]] => ([(0,6),(1,3),(1,7),(2,6),(2,7),(3,5),(6,4),(7,4),(7,5)],8) => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1,1]] => ([(0,7),(1,6),(2,3),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,0] => [[4,3,3],[1,1]] => ([(0,7),(1,3),(1,4),(3,5),(3,7),(4,2),(4,5),(5,6),(7,6)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1,1]] => ([(0,2),(0,3),(1,7),(2,8),(3,4),(3,8),(4,6),(4,7),(6,5),(7,5),(8,6)],9) => ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,0,1,1,0,1,1,0,0,0,0] => [[4,4,3],[1,1]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,8),(4,7),(4,8),(7,5),(8,5),(8,6)],9) => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,0,0,0,1,0] => [[4,4,4],[3,1]] => ([(0,7),(1,6),(2,3),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,0] => [[5,4],[1]] => ([(0,7),(1,4),(1,7),(3,2),(3,6),(4,3),(4,5),(5,6),(7,5)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,0,1,0,0,0] => [[4,4,4],[2,1]] => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,6),(5,4),(6,4),(7,5),(8,5),(8,6)],9) => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,0,0,0,0] => [[5,5],[1]] => ([(0,8),(1,4),(1,8),(2,3),(2,7),(3,5),(4,2),(4,6),(6,7),(7,5),(8,6)],9) => ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4],[1,1]] => ([(0,3),(0,4),(1,7),(2,8),(3,2),(3,9),(4,7),(4,9),(6,5),(7,6),(8,5),(9,6),(9,8)],10) => ([(0,8),(1,5),(1,7),(2,4),(2,6),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,9),(7,9)],10)
[1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1]] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1]] => ([(0,4),(0,6),(1,2),(1,3),(3,6),(4,5),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(3,6),(5,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2],[1]] => ([(0,3),(0,6),(1,4),(1,6),(3,5),(4,2),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1]] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(3,5),(3,7),(4,6),(7,6)],8) => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(3,6),(4,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2],[2]] => ([(0,4),(0,6),(1,2),(1,3),(2,5),(3,5),(3,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2],[3]] => ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,1,1,0,0,0] => [[4,4,2],[2]] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(3,5),(3,7),(4,6),(7,6)],8) => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1]] => ([(0,6),(1,3),(1,7),(2,6),(2,7),(3,5),(6,4),(7,4),(7,5)],8) => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,0] => [[4,3,2],[1]] => ([(0,3),(0,7),(1,4),(1,7),(3,5),(4,2),(4,6),(7,5),(7,6)],8) => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1]] => ([(0,3),(0,4),(1,2),(1,8),(2,6),(3,7),(4,7),(4,8),(7,5),(8,5),(8,6)],9) => ([(0,1),(0,2),(1,8),(2,8),(3,4),(3,6),(4,7),(5,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,0,0] => [[4,4,2],[1]] => ([(0,3),(0,8),(1,4),(1,8),(2,5),(3,6),(4,2),(4,7),(7,5),(8,6),(8,7)],9) => ([(0,1),(0,2),(1,8),(2,8),(3,4),(3,6),(4,7),(5,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2],[1,1]] => ([(0,3),(1,4),(1,7),(2,6),(3,7),(4,2),(4,5),(5,6),(7,5)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2],[1]] => ([(0,3),(0,7),(1,4),(1,7),(2,6),(4,2),(4,5),(5,6),(7,5)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,0,1,0] => [[3,3,2,2],[2]] => ([(0,7),(1,3),(1,4),(2,6),(3,5),(3,7),(4,2),(4,5),(5,6)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2],[1]] => ([(0,3),(0,8),(1,4),(1,8),(2,5),(3,6),(4,2),(4,7),(7,5),(8,6),(8,7)],9) => ([(0,1),(0,2),(1,8),(2,8),(3,4),(3,6),(4,7),(5,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2],[1]] => ([(0,8),(1,4),(1,8),(2,3),(2,7),(3,5),(4,2),(4,6),(6,7),(7,5),(8,6)],9) => ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2],[]] => ([(0,4),(0,5),(2,7),(3,2),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(8,7)],9) => ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2],[]] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
[1,1,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2],[]] => ([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(9,7)],10) => ([(0,3),(0,9),(1,2),(1,6),(2,8),(3,5),(4,5),(4,7),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[1,1,1,0,1,1,0,0,0,0,1,0] => [[3,3,3,2],[2]] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,8),(4,7),(4,8),(7,5),(8,5),(8,6)],9) => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,1,0,0,0,1,0,0] => [[4,3,2],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9) => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2],[1]] => ([(0,3),(0,9),(1,4),(1,9),(2,5),(3,2),(3,8),(4,7),(7,6),(8,5),(8,6),(9,7),(9,8)],10) => ([(0,3),(0,9),(1,2),(1,8),(2,6),(3,7),(4,7),(4,8),(5,6),(5,9),(6,8),(7,9),(8,9)],10)
[1,1,1,0,1,1,0,1,0,0,0,0] => [[4,4,2],[]] => ([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(9,7)],10) => ([(0,3),(0,9),(1,2),(1,6),(2,8),(3,5),(4,5),(4,7),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[1,1,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2],[]] => ([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(8,10),(9,7),(9,10)],11) => ([(0,1),(0,9),(1,8),(2,5),(2,9),(3,5),(3,6),(4,6),(4,7),(5,10),(6,10),(7,8),(7,10),(8,9),(9,10)],11)
[1,1,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,0,0] => [[4,3,3],[2]] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(3,5),(3,7),(5,6),(7,6)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,0,1,0] => [[4,4,3],[3]] => ([(0,7),(1,3),(1,4),(2,6),(2,7),(3,5),(4,2),(4,5),(5,6)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,0,0] => [[4,4,3],[2]] => ([(0,3),(0,4),(1,2),(1,8),(2,6),(3,7),(4,7),(4,8),(7,5),(8,5),(8,6)],9) => ([(0,1),(0,2),(1,8),(2,8),(3,4),(3,6),(4,7),(5,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1]] => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,6),(5,4),(6,4),(7,5),(8,5),(8,6)],9) => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,0,1,0,0] => [[4,3,3],[1]] => ([(0,3),(0,8),(1,4),(1,8),(3,6),(4,2),(4,7),(6,5),(7,5),(8,6),(8,7)],9) => ([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1]] => ([(0,3),(0,4),(1,2),(1,9),(2,8),(3,7),(4,7),(4,9),(6,5),(7,6),(8,5),(9,6),(9,8)],10) => ([(0,3),(0,9),(1,2),(1,6),(2,8),(3,5),(4,5),(4,7),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3],[1]] => ([(0,3),(0,9),(1,4),(1,9),(2,5),(3,2),(3,8),(4,7),(7,6),(8,5),(8,6),(9,7),(9,8)],10) => ([(0,3),(0,9),(1,2),(1,8),(2,6),(3,7),(4,7),(4,8),(5,6),(5,9),(6,8),(7,9),(8,9)],10)
[1,1,1,1,0,1,0,0,0,0,1,0] => [[4,4,4],[3]] => ([(0,2),(0,3),(1,7),(2,8),(3,4),(3,8),(4,6),(4,7),(6,5),(7,5),(8,6)],9) => ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,1,1,0,1,0,0,0,1,0,0] => [[5,4],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,8),(4,1),(4,7),(5,3),(5,6),(6,8),(8,7)],9) => ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,1,1,0,1,0,0,1,0,0,0] => [[4,4,4],[2]] => ([(0,3),(0,4),(1,2),(1,9),(2,8),(3,7),(4,7),(4,9),(6,5),(7,6),(8,5),(9,6),(9,8)],10) => ([(0,3),(0,9),(1,2),(1,6),(2,8),(3,5),(4,5),(4,7),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[1,1,1,1,0,1,0,1,0,0,0,0] => [[5,5],[]] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,0,1,1,0,0,0,0,0] => [[4,4,4],[1]] => ([(0,3),(0,10),(1,4),(1,10),(2,7),(3,8),(4,2),(4,9),(6,5),(7,5),(8,6),(9,6),(9,7),(10,8),(10,9)],11) => ([(0,1),(0,9),(1,8),(2,5),(2,9),(3,5),(3,6),(4,6),(4,7),(5,10),(6,10),(7,8),(7,10),(8,9),(9,10)],11)
[1,1,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3],[2]] => ([(0,3),(0,4),(1,7),(2,8),(3,2),(3,9),(4,7),(4,9),(6,5),(7,6),(8,5),(9,6),(9,8)],10) => ([(0,8),(1,5),(1,7),(2,4),(2,6),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,9),(7,9)],10)
[1,1,1,1,1,0,0,0,0,1,0,0] => [[4,3,3],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10) => ([(0,8),(1,5),(1,7),(2,4),(2,6),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,9),(7,9)],10)
[1,1,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3],[1]] => ([(0,3),(0,10),(1,4),(1,10),(2,7),(3,8),(4,2),(4,9),(6,5),(7,5),(8,6),(9,6),(9,7),(10,8),(10,9)],11) => ([(0,1),(0,9),(1,8),(2,5),(2,9),(3,5),(3,6),(4,6),(4,7),(5,10),(6,10),(7,8),(7,10),(8,9),(9,10)],11)
[1,1,1,1,1,0,0,1,0,0,0,0] => [[4,4,3],[]] => ([(0,4),(0,5),(1,8),(2,7),(3,2),(3,9),(4,3),(4,6),(5,1),(5,6),(6,8),(6,9),(8,10),(9,7),(9,10)],11) => ([(0,1),(0,9),(1,8),(2,5),(2,9),(3,5),(3,6),(4,6),(4,7),(5,10),(6,10),(7,8),(7,10),(8,9),(9,10)],11)
[1,1,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3],[]] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
[1,1,1,1,1,1,0,0,0,0,0,0] => [[4,4,4],[]] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => ([(0,5),(0,9),(1,4),(1,9),(2,6),(2,8),(3,7),(3,8),(4,6),(4,10),(5,7),(5,10),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1],[1]] => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,7),(4,7),(5,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1],[1,1]] => ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1],[1]] => ([(0,5),(0,6),(1,3),(1,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1,1],[2]] => ([(0,6),(1,3),(1,5),(3,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => ([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1,1],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9) => ([(0,5),(1,2),(1,6),(2,8),(3,5),(3,7),(4,6),(4,7),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1,1],[]] => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9) => ([(0,5),(1,2),(1,6),(2,8),(3,5),(3,7),(4,6),(4,7),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1,1]] => ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1],[1,1]] => ([(0,5),(0,6),(1,3),(1,4),(4,6),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1],[2,1]] => ([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1,1],[1]] => ([(0,5),(0,6),(1,4),(1,6),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1],[2,2]] => ([(0,4),(1,3),(1,5),(3,6),(4,6),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1],[2]] => ([(0,4),(0,6),(1,3),(1,5),(3,6),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1,1],[3]] => ([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8) => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1,1],[]] => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9) => ([(0,8),(1,4),(2,6),(2,7),(3,5),(3,8),(4,7),(5,6),(5,7),(6,8)],9)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2,1,1],[]] => ([(0,2),(0,6),(2,7),(3,1),(4,3),(4,8),(5,4),(5,9),(6,5),(6,7),(7,9),(9,8)],10) => ([(0,4),(1,6),(1,7),(2,3),(2,8),(3,9),(4,7),(5,6),(5,7),(5,8),(6,9),(8,9)],10)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[3,3,2,1,1],[]] => ([(0,5),(0,6),(2,9),(3,1),(4,3),(4,8),(5,4),(5,7),(6,2),(6,7),(7,8),(7,9)],10) => ([(0,5),(1,2),(1,9),(2,6),(3,7),(3,9),(4,6),(4,8),(5,7),(6,9),(7,8),(8,9)],10)
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1,1],[]] => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9) => ([(0,8),(1,4),(2,6),(2,7),(3,5),(3,8),(4,7),(5,6),(5,7),(6,8)],9)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[4,4,1,1],[]] => ([(0,5),(0,6),(2,8),(3,1),(4,2),(4,9),(5,3),(5,7),(6,4),(6,7),(7,9),(9,8)],10) => ([(0,4),(1,6),(1,7),(2,3),(2,8),(3,9),(4,7),(5,6),(5,7),(5,8),(6,9),(8,9)],10)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1,1]] => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1,1]] => ([(0,4),(0,6),(1,2),(1,5),(3,6),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1,1]] => ([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1],[1,1]] => ([(0,4),(0,6),(1,3),(1,5),(3,6),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2,1]] => ([(0,5),(0,6),(1,4),(2,3),(2,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1],[2,1]] => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1],[3,1]] => ([(0,6),(1,3),(1,5),(2,4),(2,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1],[1]] => ([(0,5),(0,6),(1,3),(1,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,1],[2,2,2]] => ([(0,5),(1,2),(1,4),(3,6),(4,6),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1],[2,2]] => ([(0,3),(0,5),(1,2),(1,4),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1],[3,2]] => ([(0,5),(1,5),(1,6),(2,3),(2,4),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1],[2]] => ([(0,5),(0,6),(1,3),(1,4),(4,6),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,1],[3,3]] => ([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4,1],[3]] => ([(0,4),(0,6),(1,2),(1,5),(3,6),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5,1],[4]] => ([(0,6),(1,2),(1,5),(3,6),(4,3),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => ([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,1],[]] => ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9) => ([(0,8),(1,4),(2,6),(2,7),(3,5),(3,8),(4,7),(5,6),(5,7),(6,8)],9)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,1],[]] => ([(0,5),(0,6),(3,4),(3,9),(4,2),(4,8),(5,3),(5,7),(6,1),(6,7),(7,9),(9,8)],10) => ([(0,9),(1,8),(2,6),(2,8),(3,7),(3,9),(4,6),(4,7),(4,8),(5,6),(5,7),(5,9)],10)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[4,3,2,1],[]] => ([(0,5),(0,6),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9)],10) => ([(0,8),(1,7),(2,5),(2,6),(3,7),(3,9),(4,8),(4,9),(5,7),(5,9),(6,8),(6,9)],10)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3,1],[]] => ([(0,5),(0,6),(3,4),(3,8),(4,2),(5,3),(5,7),(6,1),(6,7),(7,8)],9) => ([(0,8),(1,4),(2,6),(2,7),(3,5),(3,8),(4,7),(5,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[5,4,1],[]] => ([(0,5),(0,6),(3,4),(3,9),(4,2),(4,8),(5,3),(5,7),(6,1),(6,7),(7,9),(9,8)],10) => ([(0,9),(1,8),(2,6),(2,8),(3,7),(3,9),(4,6),(4,7),(4,8),(5,6),(5,7),(5,9)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1,1]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1,1,1]] => ([(0,6),(1,2),(1,5),(3,6),(4,3),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1,1]] => ([(0,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1,1]] => ([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1,1]] => ([(0,6),(1,3),(2,4),(2,5),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1,1]] => ([(0,6),(1,3),(1,5),(2,4),(2,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1,1]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1,1]] => ([(0,6),(1,3),(1,5),(3,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2,1]] => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2,1]] => ([(0,5),(1,5),(1,6),(2,3),(2,4),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2,1]] => ([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2,1]] => ([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3,1]] => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3,1]] => ([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4,1]] => ([(0,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[6,2],[1]] => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,2]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,2]] => ([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,2]] => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3],[2,2]] => ([(0,4),(1,3),(1,5),(3,6),(4,6),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,2]] => ([(0,5),(0,6),(1,4),(2,3),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3],[3,2]] => ([(0,5),(0,6),(1,4),(2,3),(2,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3],[4,2]] => ([(0,6),(1,3),(2,4),(2,5),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[6,3],[2]] => ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4],[3,3,3]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4],[3,3]] => ([(0,5),(1,2),(1,4),(3,6),(4,6),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4],[4,3]] => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4],[3]] => ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5],[4,4]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[6,5],[4]] => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[6,6],[5]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2,1]] => ([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10) => ([(0,8),(1,7),(2,5),(2,6),(3,7),(3,9),(4,8),(4,9),(5,7),(5,9),(6,8),(6,9)],10)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(5,1),(6,4),(6,7)],8) => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,7),(4,7),(5,7)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[5,2,2],[]] => ([(0,5),(0,6),(2,8),(3,4),(4,1),(5,3),(5,7),(6,2),(6,7),(7,8)],9) => ([(0,5),(1,2),(1,6),(2,8),(3,5),(3,7),(4,6),(4,7),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,2],[]] => ([(0,5),(0,6),(2,8),(3,1),(4,2),(4,9),(5,3),(5,7),(6,4),(6,7),(7,9),(9,8)],10) => ([(0,4),(1,6),(1,7),(2,3),(2,8),(3,9),(4,7),(5,6),(5,7),(5,8),(6,9),(8,9)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,2],[]] => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12) => ([(0,3),(0,11),(1,2),(1,8),(2,9),(3,10),(4,5),(4,6),(4,8),(5,7),(5,9),(6,7),(6,10),(7,11),(8,9),(10,11)],12)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[5,3,2],[]] => ([(0,5),(0,6),(2,9),(3,1),(4,3),(4,8),(5,4),(5,7),(6,2),(6,7),(7,8),(7,9)],10) => ([(0,5),(1,2),(1,9),(2,6),(3,7),(3,9),(4,6),(4,8),(5,7),(6,9),(7,8),(8,9)],10)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[6,3],[]] => ([(0,2),(0,6),(2,7),(3,5),(4,3),(4,8),(5,1),(6,4),(6,7),(7,8)],9) => ([(0,5),(1,2),(1,6),(2,8),(3,5),(3,7),(4,6),(4,7),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[6,4],[]] => ([(0,2),(0,6),(2,7),(3,1),(4,3),(4,8),(5,4),(5,9),(6,5),(6,7),(7,9),(9,8)],10) => ([(0,4),(1,6),(1,7),(2,3),(2,8),(3,9),(4,7),(5,6),(5,7),(5,8),(6,9),(8,9)],10)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[6,6],[]] => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12) => ([(0,3),(0,11),(1,2),(1,8),(2,9),(3,10),(4,5),(4,6),(4,8),(5,7),(5,9),(6,7),(6,10),(7,11),(8,9),(10,11)],12)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[3,3,3,3,3],[]] => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15) => ([(0,7),(0,11),(1,6),(1,10),(2,8),(2,10),(3,9),(3,11),(4,8),(4,9),(4,14),(5,6),(5,7),(5,14),(6,12),(7,13),(8,12),(9,13),(10,12),(11,13),(12,14),(13,14)],15)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[5,5,5],[]] => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15) => ([(0,7),(0,11),(1,6),(1,10),(2,8),(2,10),(3,9),(3,11),(4,8),(4,9),(4,14),(5,6),(5,7),(5,14),(6,12),(7,13),(8,12),(9,13),(10,12),(11,13),(12,14),(13,14)],15)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[4,4,4,4],[]] => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16) => ([(0,10),(0,11),(1,6),(1,7),(2,5),(2,9),(3,4),(3,8),(4,6),(4,13),(5,7),(5,14),(6,12),(7,12),(8,10),(8,13),(9,11),(9,14),(10,15),(11,15),(12,13),(12,14),(13,15),(14,15)],16)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1,1],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1,1],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9) => ([(0,7),(1,3),(1,4),(2,5),(2,6),(3,7),(4,8),(5,8),(6,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1,1],[1,1]] => ([(0,3),(1,6),(1,7),(3,7),(4,5),(5,2),(6,4)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1,1],[1]] => ([(0,6),(0,7),(1,3),(1,7),(4,5),(5,2),(6,4)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9) => ([(0,8),(1,6),(2,3),(2,6),(3,7),(4,7),(4,8),(5,7),(5,8)],9)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1,1,1],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(5,9),(6,1),(7,5),(7,8),(8,9)],10) => ([(0,6),(1,4),(1,6),(2,3),(2,7),(3,9),(4,8),(5,7),(5,8),(7,9),(8,9)],10)
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1,1,1],[]] => ([(0,6),(0,7),(2,9),(3,5),(4,3),(5,1),(6,4),(6,8),(7,2),(7,8),(8,9)],10) => ([(0,6),(1,4),(1,6),(2,3),(2,7),(3,9),(4,8),(5,7),(5,8),(7,9),(8,9)],10)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9) => ([(0,6),(1,5),(2,5),(2,8),(3,7),(3,8),(4,7),(4,8),(6,7)],9)
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(4,9),(5,2),(6,4),(6,8),(7,1),(7,8),(8,9)],10) => ([(0,9),(1,5),(2,8),(2,9),(3,5),(3,6),(4,6),(4,7),(6,8),(7,8),(7,9)],10)
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(5,9),(6,5),(6,8),(7,3),(7,8),(8,9)],10) => ([(0,9),(1,5),(2,8),(2,9),(3,5),(3,6),(4,6),(4,7),(6,8),(7,8),(7,9)],10)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1,1],[1,1,1,1]] => ([(0,5),(1,6),(1,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8)],9) => ([(0,6),(1,5),(2,5),(2,8),(3,7),(3,8),(4,7),(4,8),(6,7)],9)
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,1,1],[]] => ([(0,6),(0,7),(3,4),(3,9),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8),(8,9)],10) => ([(0,5),(1,4),(2,6),(2,9),(3,7),(3,8),(4,6),(5,7),(6,8),(7,9),(8,9)],10)
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3,1,1],[]] => ([(0,6),(0,7),(3,4),(3,9),(4,1),(5,2),(6,5),(6,8),(7,3),(7,8),(8,9)],10) => ([(0,5),(1,4),(2,6),(2,9),(3,7),(3,8),(4,6),(5,7),(6,8),(7,9),(8,9)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(6,8),(7,1),(7,8)],9) => ([(0,8),(1,6),(2,3),(2,6),(3,7),(4,7),(4,8),(5,7),(5,8)],9)
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[5,2,2,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(5,9),(6,5),(6,8),(7,3),(7,8),(8,9)],10) => ([(0,9),(1,5),(2,8),(2,9),(3,5),(3,6),(4,6),(4,7),(6,8),(7,8),(7,9)],10)
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[6,3,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(4,9),(5,2),(6,4),(6,8),(7,1),(7,8),(8,9)],10) => ([(0,9),(1,5),(2,8),(2,9),(3,5),(3,6),(4,6),(4,7),(6,8),(7,8),(7,9)],10)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,2],[2,2,2,2,1]] => ([(0,3),(1,6),(2,6),(2,7),(3,5),(4,7),(5,4)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3,2],[3,2,2,1]] => ([(0,5),(1,6),(2,5),(2,7),(3,4),(3,6),(4,7)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4,2],[4,3,1]] => ([(0,5),(1,6),(2,5),(2,7),(3,4),(3,6),(4,7)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[5,3,3,3],[2,2,2]] => ([(0,4),(1,5),(1,6),(3,7),(4,7),(5,2),(6,3)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[4,4,4,4,4],[3,3,3,3]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[5,5,5,5],[4,4,4]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,2],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(6,1),(7,5),(7,8)],9) => ([(0,7),(1,3),(1,4),(2,5),(2,6),(3,7),(4,8),(5,8),(6,8)],9)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,2],[]] => ([(0,6),(0,7),(2,9),(3,5),(4,3),(5,1),(6,4),(6,8),(7,2),(7,8),(8,9)],10) => ([(0,6),(1,4),(1,6),(2,3),(2,7),(3,9),(4,8),(5,7),(5,8),(7,9),(8,9)],10)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[7,3],[]] => ([(0,2),(0,7),(2,8),(3,4),(4,6),(5,3),(5,9),(6,1),(7,5),(7,8),(8,9)],10) => ([(0,6),(1,4),(1,6),(2,3),(2,7),(3,9),(4,8),(5,7),(5,8),(7,9),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[9],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,2],[]] => ([(0,2),(0,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6),(8,9)],10) => ([(0,8),(1,2),(1,4),(2,7),(3,5),(3,6),(4,8),(5,9),(6,9),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1,1,1],[]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1,1],[]] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9) => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9) => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9) => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1,1],[]] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,1],[]] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1,1,1,1],[]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1,1,1],[]] => ([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1,1,1],[]] => ([(0,2),(0,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6),(8,9)],10) => ([(0,8),(1,2),(1,4),(2,7),(3,5),(3,6),(4,8),(5,9),(6,9),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1,1,1],[]] => ([(0,8),(0,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,1)],10) => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1,1,1],[]] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(7,9),(8,1),(8,9)],10) => ([(0,9),(1,7),(2,3),(2,4),(3,7),(4,8),(5,8),(5,9),(6,8),(6,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1,1,1],[]] => ([(0,8),(0,9),(3,4),(4,6),(5,3),(6,2),(7,1),(8,7),(9,5)],10) => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(7,9),(8,4),(8,9)],10) => ([(0,7),(1,6),(2,3),(2,6),(3,9),(4,8),(4,9),(5,8),(5,9),(7,8)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1,1,1],[]] => ([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10) => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1,1,1],[]] => ([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(7,9),(8,4),(8,9)],10) => ([(0,7),(1,6),(2,6),(2,8),(3,7),(3,9),(4,8),(4,9),(5,8),(5,9)],10)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1,1,1],[]] => ([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10) => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,1,1],[]] => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(7,9),(8,4),(8,9)],10) => ([(0,7),(1,6),(2,3),(2,6),(3,9),(4,8),(4,9),(5,8),(5,9),(7,8)],10)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1,1,1],[]] => ([(0,8),(0,9),(3,4),(4,6),(5,3),(6,2),(7,1),(8,7),(9,5)],10) => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,2,1],[]] => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(7,9),(8,1),(8,9)],10) => ([(0,9),(1,7),(2,3),(2,4),(3,7),(4,8),(5,8),(5,9),(6,8),(6,9)],10)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,1,1],[]] => ([(0,8),(0,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,1)],10) => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[9,1],[]] => ([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[10],[]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
Map
skew partition
Description
The parallelogram polyomino corresponding to a Dyck path, interpreted as a skew partition.
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.
This map returns the skew partition definded by the diagram of $\gamma(D)$.
Map
cell poset
Description
The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell $d$ is greater than a cell $c$ if the entry in $d$ must be larger than the entry of $c$ in any standard Young tableau on the skew partition.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.