- FindStat

Identifier

Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Mp00191: Lattices —dual⟶ Lattices

Images

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

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

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

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

[[3],[]] => ([],1) => ([],1)

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

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

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

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

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

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

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

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

[[4],[]] => ([],1) => ([],1)

[[3,1],[]] => ([],1) => ([],1)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5],[]] => ([],1) => ([],1)

[[4,1],[]] => ([],1) => ([],1)

[[5,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

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

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

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

[[3,1,1],[]] => ([],1) => ([],1)

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

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

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

[[3,3],[1]] => ([],1) => ([],1)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1344 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[6],[]] => ([],1) => ([],1)

[[5,1],[]] => ([],1) => ([],1)

[[6,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

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

[[5,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

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

[[4,1,1],[]] => ([],1) => ([],1)

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

[[5,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

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

[[3,3],[]] => ([],1) => ([],1)

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

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

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

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

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

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

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

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

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

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

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

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

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

[[3,1,1,1],[]] => ([],1) => ([],1)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5,5],[4]] => ([],1) => ([],1)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[7],[]] => ([],1) => ([],1)

[[6,1],[]] => ([],1) => ([],1)

[[7,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,2],[]] => ([],1) => ([],1)

[[6,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[7,2],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,1,1],[]] => ([],1) => ([],1)

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

[[6,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

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

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

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

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

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

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

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

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

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

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

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

[[5,2,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

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

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

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

[[4,1,1,1],[]] => ([],1) => ([],1)

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

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

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

[[5,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

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

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

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

[[4,4],[1]] => ([],1) => ([],1)

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

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

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

[[3,3,1],[]] => ([],1) => ([],1)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[3,1,1,1,1],[]] => ([],1) => ([],1)

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

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

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

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

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

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

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

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

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

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

[[5,5],[3]] => ([],1) => ([],1)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[3,3,3],[1,1]] => ([],1) => ([],1)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[6,6],[5]] => ([],1) => ([],1)

[[7,6],[6]] => ([(0,1)],2) => ([(0,1)],2)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5,5,5],[4,4]] => ([],1) => ([],1)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5,5,5,4],[4,4,4]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,4,4],[4,4,3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[6,6,5,4],[5,5,4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)

[[5,4,4,4],[4,3,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[6,5,5,4],[5,4,4]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)

[[6,5,4,4],[5,4,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)

[[7,6,5,4],[6,5,4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)

[[3,3,3,3,1],[2,2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4,1],[3,3,3,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,4,3,1],[3,3,3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[5,5,5,4,1],[4,4,4,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)

[[4,4,3,3,1],[3,3,2]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)

[[5,5,4,4,1],[4,4,3,1]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)

[[5,5,4,3,1],[4,4,3]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)

[[4,3,3,3,1],[3,2,2]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)

[[5,4,4,4,1],[4,3,3,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)

[[5,4,4,3,1],[4,3,3]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)

[[5,4,3,3,1],[4,3,2]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)

[[2,2,2,2,2],[1,1,1]] => ([],1) => ([],1)

[[3,3,3,3,2],[2,2,2,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,4,4,2],[3,3,3,2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[3,3,3,2,2],[2,2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,4,3,2],[3,3,3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)

[[5,5,5,4,2],[4,4,4,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)

[[3,3,2,2,2],[2,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)

[[4,4,3,3,2],[3,3,2,1]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)

[[4,4,3,2,2],[3,3,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)

[[3,2,2,2,2],[2,1,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,3,3,3,2],[3,2,2,1]] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)

[[5,4,4,4,2],[4,3,3,2]] => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)

[[4,3,3,2,2],[3,2,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)

[[4,3,2,2,2],[3,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)

[[5,4,3,2,2],[4,3,2]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)

[[2,2,2,2,1,1],[1,1,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[3,3,3,3,2,1],[2,2,2,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[3,3,3,3,1,1],[2,2,2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[4,4,4,4,2,1],[3,3,3,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)

[[3,3,3,2,1,1],[2,2,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)

[[4,4,4,3,2,1],[3,3,3,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[4,4,4,3,1,1],[3,3,3,1]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)

[[3,3,2,2,1,1],[2,2,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)

[[4,4,3,2,1,1],[3,3,2]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[3,2,2,2,1,1],[2,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)

[[4,3,3,3,2,1],[3,2,2,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[4,3,3,3,1,1],[3,2,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[4,3,3,2,1,1],[3,2,2]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[4,3,2,2,1,1],[3,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[3,3,3,3,3],[2,2,2,2]] => ([],1) => ([],1)

[[4,4,4,4,3],[3,3,3,3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,3,3],[3,3,3,2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[5,5,5,4,3],[4,4,4,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)

[[4,4,3,3,3],[3,3,2,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[5,5,4,4,3],[4,4,3,3]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)

[[5,5,4,3,3],[4,4,3,2]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)

[[4,3,3,3,3],[3,2,2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,4,4,4,3],[4,3,3,3]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)

[[5,4,4,3,3],[4,3,3,2]] => ([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)

[[5,4,3,3,3],[4,3,2,2]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)

[[2,2,2,2,2,1],[1,1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,3,1],[2,2,2,2,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[3,3,3,3,2,1],[2,2,2,2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[4,4,4,4,3,1],[3,3,3,3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)

[[3,3,3,2,2,1],[2,2,2,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)

[[4,4,4,3,3,1],[3,3,3,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[4,4,4,3,2,1],[3,3,3,2]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[3,3,2,2,2,1],[2,2,1,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)

[[4,4,3,3,3,1],[3,3,2,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[3,2,2,2,2,1],[2,1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[4,3,3,3,3,1],[3,2,2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)

[[4,3,3,3,2,1],[3,2,2,2]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[4,3,2,2,2,1],[3,2,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[2,2,2,2,2,2],[1,1,1,1,1]] => ([],1) => ([],1)

[[3,3,3,3,3,2],[2,2,2,2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,2,2],[2,2,2,2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[4,4,4,4,3,2],[3,3,3,3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)

[[3,3,3,2,2,2],[2,2,2,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)

[[4,4,4,3,3,2],[3,3,3,2,2]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)

[[4,4,4,3,2,2],[3,3,3,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[3,3,2,2,2,2],[2,2,1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[4,4,3,3,3,2],[3,3,2,2,2]] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)

[[4,4,3,2,2,2],[3,3,2,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[3,2,2,2,2,2],[2,1,1,1,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,3,3,3,3,2],[3,2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)

[[4,3,3,3,2,2],[3,2,2,2,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[4,3,3,2,2,2],[3,2,2,1,1]] => ([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)

[[4,3,2,2,2,2],[3,2,1,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)

[[1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2,2,2,2,1,1],[1,1,1,1,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[2,2,2,2,1,1,1],[1,1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)

[[3,3,3,3,2,1,1],[2,2,2,2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)

[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)

[[2,2,2,1,1,1,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)

[[3,3,3,2,2,1,1],[2,2,2,1,1]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)

[[3,3,3,2,1,1,1],[2,2,2,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)

[[2,2,1,1,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)

[[3,3,2,2,2,1,1],[2,2,1,1,1]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)

[[3,3,2,2,1,1,1],[2,2,1,1]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)

[[3,3,2,1,1,1,1],[2,2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)

[[2,1,1,1,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[3,2,2,2,2,1,1],[2,1,1,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)

[[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)

[[3,2,2,2,1,1,1],[2,1,1,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)

[[3,2,2,1,1,1,1],[2,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)

[[3,2,1,1,1,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)

[[4,3,2,1,1,1,1],[3,2,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)

[[8],[]] => ([],1) => ([],1)

[[7,1],[]] => ([],1) => ([],1)

[[6,2],[]] => ([],1) => ([],1)

[[6,1,1],[]] => ([],1) => ([],1)

[[5,3],[]] => ([],1) => ([],1)

[[5,2,1],[]] => ([],1) => ([],1)

[[5,1,1,1],[]] => ([],1) => ([],1)

[[4,4],[]] => ([],1) => ([],1)

[[4,3,1],[]] => ([],1) => ([],1)

[[4,2,2],[]] => ([],1) => ([],1)

[[4,2,1,1],[]] => ([],1) => ([],1)

[[4,1,1,1,1],[]] => ([],1) => ([],1)

[[3,3,2],[]] => ([],1) => ([],1)

[[3,3,1,1],[]] => ([],1) => ([],1)

[[3,2,2,1],[]] => ([],1) => ([],1)

[[3,2,1,1,1],[]] => ([],1) => ([],1)

[[3,1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,2,2,2],[]] => ([],1) => ([],1)

[[2,2,2,1,1],[]] => ([],1) => ([],1)

[[2,2,1,1,1,1],[]] => ([],1) => ([],1)

[[2,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[1,1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[9],[]] => ([],1) => ([],1)

[[8,1],[]] => ([],1) => ([],1)

[[7,2],[]] => ([],1) => ([],1)

[[7,1,1],[]] => ([],1) => ([],1)

[[6,3],[]] => ([],1) => ([],1)

[[6,2,1],[]] => ([],1) => ([],1)

[[6,1,1,1],[]] => ([],1) => ([],1)

[[5,4],[]] => ([],1) => ([],1)

[[5,3,1],[]] => ([],1) => ([],1)

[[5,2,2],[]] => ([],1) => ([],1)

[[5,2,1,1],[]] => ([],1) => ([],1)

[[5,1,1,1,1],[]] => ([],1) => ([],1)

[[4,4,1],[]] => ([],1) => ([],1)

[[4,3,2],[]] => ([],1) => ([],1)

[[4,3,1,1],[]] => ([],1) => ([],1)

[[4,2,2,1],[]] => ([],1) => ([],1)

[[4,2,1,1,1],[]] => ([],1) => ([],1)

[[4,1,1,1,1,1],[]] => ([],1) => ([],1)

[[3,3,3],[]] => ([],1) => ([],1)

[[3,3,2,1],[]] => ([],1) => ([],1)

[[3,3,1,1,1],[]] => ([],1) => ([],1)

[[3,2,2,2],[]] => ([],1) => ([],1)

[[3,2,2,1,1],[]] => ([],1) => ([],1)

[[3,2,1,1,1,1],[]] => ([],1) => ([],1)

[[3,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,2,2,2,1],[]] => ([],1) => ([],1)

[[2,2,2,1,1,1],[]] => ([],1) => ([],1)

[[2,2,1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[1,1,1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[10],[]] => ([],1) => ([],1)

[[9,1],[]] => ([],1) => ([],1)

[[8,2],[]] => ([],1) => ([],1)

[[8,1,1],[]] => ([],1) => ([],1)

[[7,3],[]] => ([],1) => ([],1)

[[7,2,1],[]] => ([],1) => ([],1)

[[7,1,1,1],[]] => ([],1) => ([],1)

[[6,4],[]] => ([],1) => ([],1)

[[6,3,1],[]] => ([],1) => ([],1)

[[6,2,2],[]] => ([],1) => ([],1)

[[6,2,1,1],[]] => ([],1) => ([],1)

[[6,1,1,1,1],[]] => ([],1) => ([],1)

[[5,5],[]] => ([],1) => ([],1)

[[5,4,1],[]] => ([],1) => ([],1)

[[5,3,2],[]] => ([],1) => ([],1)

[[5,3,1,1],[]] => ([],1) => ([],1)

[[5,2,2,1],[]] => ([],1) => ([],1)

[[5,2,1,1,1],[]] => ([],1) => ([],1)

[[5,1,1,1,1,1],[]] => ([],1) => ([],1)

[[4,4,2],[]] => ([],1) => ([],1)

[[4,4,1,1],[]] => ([],1) => ([],1)

[[4,3,3],[]] => ([],1) => ([],1)

[[4,3,2,1],[]] => ([],1) => ([],1)

[[4,3,1,1,1],[]] => ([],1) => ([],1)

[[4,2,2,2],[]] => ([],1) => ([],1)

[[4,2,2,1,1],[]] => ([],1) => ([],1)

[[4,2,1,1,1,1],[]] => ([],1) => ([],1)

[[4,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[3,3,3,1],[]] => ([],1) => ([],1)

[[3,3,2,2],[]] => ([],1) => ([],1)

[[3,3,2,1,1],[]] => ([],1) => ([],1)

[[3,3,1,1,1,1],[]] => ([],1) => ([],1)

[[3,2,2,2,1],[]] => ([],1) => ([],1)

[[3,2,2,1,1,1],[]] => ([],1) => ([],1)

[[3,2,1,1,1,1,1],[]] => ([],1) => ([],1)

[[3,1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,2,2,2,2],[]] => ([],1) => ([],1)

[[2,2,2,2,1,1],[]] => ([],1) => ([],1)

[[2,2,2,1,1,1,1],[]] => ([],1) => ([],1)

[[2,2,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[2,1,1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[1,1,1,1,1,1,1,1,1,1],[]] => ([],1) => ([],1)

[[6,5],[]] => ([],1) => ([],1)

[[5,5,1],[]] => ([],1) => ([],1)

[[5,4,2],[]] => ([],1) => ([],1)

[[5,3,3],[]] => ([],1) => ([],1)

[[4,4,3],[]] => ([],1) => ([],1)

[[4,4,2,1],[]] => ([],1) => ([],1)

[[4,3,3,1],[]] => ([],1) => ([],1)

[[4,3,2,2],[]] => ([],1) => ([],1)

[[3,3,3,2],[]] => ([],1) => ([],1)

[[3,2,2,2,2],[]] => ([],1) => ([],1)

[[6,6],[]] => ([],1) => ([],1)

[[5,5,2],[]] => ([],1) => ([],1)

[[5,4,3],[]] => ([],1) => ([],1)

[[4,4,4],[]] => ([],1) => ([],1)

[[4,4,3,1],[]] => ([],1) => ([],1)

[[4,4,2,2],[]] => ([],1) => ([],1)

[[4,3,3,2],[]] => ([],1) => ([],1)

[[3,3,3,3],[]] => ([],1) => ([],1)

[[3,3,3,2,1],[]] => ([],1) => ([],1)

[[3,3,2,2,2],[]] => ([],1) => ([],1)

[[2,2,2,2,2,2],[]] => ([],1) => ([],1)

[[5,5,3],[]] => ([],1) => ([],1)

[[5,4,4],[]] => ([],1) => ([],1)

[[4,4,4,1],[]] => ([],1) => ([],1)

[[4,4,3,2],[]] => ([],1) => ([],1)

[[4,3,3,3],[]] => ([],1) => ([],1)

[[3,3,3,3,1],[]] => ([],1) => ([],1)

[[3,3,3,2,2],[]] => ([],1) => ([],1)

[[5,5,4],[]] => ([],1) => ([],1)

[[4,4,4,2],[]] => ([],1) => ([],1)

[[4,4,3,3],[]] => ([],1) => ([],1)

[[3,3,3,3,2],[]] => ([],1) => ([],1)

[[5,5,5],[]] => ([],1) => ([],1)

[[5,5,4,1],[]] => ([],1) => ([],1)

[[4,4,4,3],[]] => ([],1) => ([],1)

[[3,3,3,3,3],[]] => ([],1) => ([],1)

[[5,5,5,1],[]] => ([],1) => ([],1)

[[4,4,4,4],[]] => ([],1) => ([],1)

[[4,4,4,3,1],[]] => ([],1) => ([],1)

[[3,3,3,3,3,1],[]] => ([],1) => ([],1)

[[4,4,4,4,1],[]] => ([],1) => ([],1)

[[2,2,1,1,1,1,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2,2,1,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[3,2,1,1,1,1],[1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[2,2,2,2,1,1,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[3,2,2,1,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)

[[3,3,2,1,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)

[[4,3,1,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[2,2,2,2,2,1,1],[1,1,1,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[3,2,2,2,1,1],[1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)

[[3,3,2,2,1,1],[2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)

[[3,3,3,2,1,1],[2,2,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)

[[4,3,2,1,1],[2,1]] => ([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9) => ([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9)

[[4,4,2,1,1],[3,1]] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)

[[4,3,3,1,1],[2,2]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)

[[4,4,3,1,1],[3,2]] => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8)

[[5,3,1,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[2,2,2,2,2,2,1],[1,1,1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,2,2,2,2,1],[1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,2,2,2,1],[2,1,1,1]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)

[[3,3,3,2,2,1],[2,2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)

[[4,4,2,2,1],[3,1,1]] => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8)

[[3,3,3,3,2,1],[2,2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)

[[5,3,2,1],[2,1]] => ([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9) => ([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9)

[[4,4,4,2,1],[3,3,1]] => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8)

[[4,3,3,3,1],[2,2,2]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)

[[4,4,3,3,1],[3,2,2]] => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8)

[[5,3,3,1],[2,2]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)

[[4,4,4,3,1],[3,3,2]] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)

[[5,5,3,1],[4,2]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9) => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9)

[[4,4,4,4,1],[3,3,3]] => ([(0,1)],2) => ([(0,1)],2)

[[5,4,4,1],[3,3]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)

[[5,5,4,1],[4,3]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)

[[6,4,1],[3]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)

[[3,2,2,2,2,2],[1,1,1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,2,2,2],[2,1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,2,2,2],[2,2,1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)

[[4,3,2,2,2],[2,1,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)

[[4,4,2,2,2],[3,1,1,1]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)

[[3,3,3,3,2,2],[2,2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)

[[4,3,3,2,2],[2,2,1,1]] => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9) => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9)

[[5,3,2,2],[2,1,1]] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)

[[4,4,4,2,2],[3,3,1,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)

[[5,4,2,2],[3,1,1]] => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8)

[[3,3,3,3,3,2],[2,2,2,2,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,3,3,3,2],[2,2,2,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)

[[5,3,3,2],[2,2,1]] => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8)

[[4,4,4,3,2],[3,3,2,1]] => ([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9) => ([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9)

[[4,4,4,4,2],[3,3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,4,4,2],[3,3,1]] => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8)

[[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)

[[5,5,5,2],[4,4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,5,2],[4,1]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)

[[4,4,3,3,3],[3,2,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[5,3,3,3],[2,2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,4,3,3],[3,3,2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)

[[5,4,3,3],[3,2,2]] => ([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) => ([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8)

[[5,5,3,3],[4,2,2]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)

[[4,4,4,4,3],[3,3,3,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,4,4,3],[3,3,2]] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)

[[5,5,4,3],[4,3,2]] => ([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9) => ([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9)

[[6,4,3],[3,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)

[[5,5,5,3],[4,4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)

[[6,6,3],[5,2]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)

[[4,4,4,4,4],[3,3,3,3]] => ([],1) => ([],1)

[[5,4,4,4],[3,3,3]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,4,4],[4,3,3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[6,4,4],[3,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,5,5,4],[4,4,3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[6,5,4],[4,3]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)

[[6,6,4],[5,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[7,4],[3]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[3,3,3],[1]] => ([],1) => ([],1)

[[3,3,3,1],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,1],[1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[2,2,2,2,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,1],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,2],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4],[2,2]] => ([],1) => ([],1)

[[5,5],[2]] => ([],1) => ([],1)

[[4,4,3],[2,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[3,3,3,3],[2,1,1]] => ([],1) => ([],1)

[[4,3,3],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3],[1,1,1]] => ([],1) => ([],1)

[[4,4,3],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4],[3,1]] => ([],1) => ([],1)

[[5,4],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4],[2,1]] => ([],1) => ([],1)

[[5,5],[1]] => ([],1) => ([],1)

[[4,4,4],[1,1]] => ([],1) => ([],1)

[[3,3,2,2],[1,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,2],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[3,3,3,2],[2,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,3,2],[1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[3,3,3,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2,2,2,2],[1,1]] => ([],1) => ([],1)

[[3,2,2,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,2],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[2,2,2,2,2],[1]] => ([],1) => ([],1)

[[3,3,3,2],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3],[2,2]] => ([],1) => ([],1)

[[4,3,3],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3],[2,1]] => ([],1) => ([],1)

[[4,3,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3],[1,1]] => ([],1) => ([],1)

[[4,4,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4],[3]] => ([],1) => ([],1)

[[4,4,4],[2]] => ([],1) => ([],1)

[[4,4,4],[1]] => ([],1) => ([],1)

[[3,3,3,3],[2]] => ([],1) => ([],1)

[[3,3,3,3],[1]] => ([],1) => ([],1)

[[4,4,4,1],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,1],[1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,4,1],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,2],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[6,6],[4]] => ([],1) => ([],1)

[[6,5],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5],[3,3]] => ([],1) => ([],1)

[[6,6],[3]] => ([],1) => ([],1)

[[6,4],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,5,4],[3,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,4,4],[2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[2,2,2]] => ([],1) => ([],1)

[[5,5,4],[2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[6,5],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5],[3,2]] => ([],1) => ([],1)

[[6,6],[2]] => ([],1) => ([],1)

[[5,5,5],[2,2]] => ([],1) => ([],1)

[[6,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,3],[3,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)

[[5,4,3],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)

[[4,4,4,3],[2,2,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,5,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[5,3,3],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,3],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[4,3,3,3],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,3],[1,1,1,1]] => ([],1) => ([],1)

[[4,4,3,3],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,4,3],[1,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,4,3],[2,1,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,5,3],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,3],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[6,4],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,4],[3,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,4,4],[2,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,4,4],[2,2,1]] => ([],1) => ([],1)

[[5,5,4],[2,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[6,5],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5],[3,1]] => ([],1) => ([],1)

[[6,6],[1]] => ([],1) => ([],1)

[[5,5,5],[2,1]] => ([],1) => ([],1)

[[4,4,4,4],[3,1,1]] => ([],1) => ([],1)

[[5,4,4],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[2,1,1]] => ([],1) => ([],1)

[[5,5,4],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[1,1,1]] => ([],1) => ([],1)

[[5,5,5],[1,1]] => ([],1) => ([],1)

[[5,5,2],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,4,2],[2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)

[[4,4,4,2],[2,2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,5,2],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,3,2],[1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,3,2],[2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)

[[4,3,3,2],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4)

[[3,3,3,3,2],[1,1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,2],[1,1]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[5,4,2],[1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[5,5,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,2,2],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,3,2,2],[1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[3,3,3,2,2],[1,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,2,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,2,2,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,2,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[4,3,3,2],[1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[3,3,3,3,2],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,2],[1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,4,2],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,2],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,4,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,2],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,2],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,3],[3]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,4,3],[2]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[4,4,4,3],[2,2]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,3],[2]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,3,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,3],[2,1]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)

[[4,3,3,3],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,3],[1,1,1]] => ([],1) => ([],1)

[[4,4,3,3],[1,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,4,3],[3,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,4,3],[1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[4,4,4,3],[2,1]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)

[[5,5,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,3],[1,1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,4],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[3,2]] => ([],1) => ([],1)

[[5,4,4],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[2,2]] => ([],1) => ([],1)

[[5,5,4],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5],[4]] => ([],1) => ([],1)

[[5,5,5],[3]] => ([],1) => ([],1)

[[5,5,5],[2]] => ([],1) => ([],1)

[[4,4,4,4],[3,1]] => ([],1) => ([],1)

[[5,4,4],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[2,1]] => ([],1) => ([],1)

[[5,5,4],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4],[1,1]] => ([],1) => ([],1)

[[5,5,5],[1]] => ([],1) => ([],1)

[[4,3,3,3],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,3],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,3,3],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,3],[2,1]] => ([],1) => ([],1)

[[4,3,3,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,3],[1,1]] => ([],1) => ([],1)

[[4,4,3,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,3],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,3],[2]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,3],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[3,3,3,3,3],[2]] => ([],1) => ([],1)

[[3,3,3,3,3],[1]] => ([],1) => ([],1)

[[4,4,4,4],[3]] => ([],1) => ([],1)

[[4,4,4,4],[2]] => ([],1) => ([],1)

[[4,4,4,4],[1]] => ([],1) => ([],1)

[[5,5,5,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5,5],[4,1]] => ([],1) => ([],1)

[[3,3,3,3,3,3],[2]] => ([],1) => ([],1)

[[4,4,4,4,3],[3]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5,4],[4]] => ([(0,1)],2) => ([(0,1)],2)

[[4,4,4,4,4],[3,1]] => ([],1) => ([],1)

[[5,5,5,5],[4]] => ([],1) => ([],1)

[[4,4,4,4,4],[3]] => ([],1) => ([],1)

[[5,5,5,5,5],[4]] => ([],1) => ([],1)

[[5,5,5,5,1],[]] => ([],1) => ([],1)

[[5,5,5,5,5,5],[4]] => ([],1) => ([],1)

[[4,4,4,4,4,4],[3]] => ([],1) => ([],1)

[[4,4,4,4,4,1],[]] => ([],1) => ([],1)

[[5,5,5,5,5,1],[]] => ([],1) => ([],1)

[[6,6,6,6,6,6],[5]] => ([],1) => ([],1)

[[6,6,6,6,6],[5]] => ([],1) => ([],1)

[[5,5,5,5,4],[4]] => ([(0,1)],2) => ([(0,1)],2)

[[5,5,5,5,5],[4,1]] => ([],1) => ([],1)

[[5,5,5,4,1],[]] => ([],1) => ([],1)

[[5,5,5,5,1],[1]] => ([(0,1)],2) => ([(0,1)],2)

[[6,6,6,6,1],[]] => ([],1) => ([],1)

[[6,6,6,6,6,1],[]] => ([],1) => ([],1)

Map

dominating sublattice

Description

Return the sublattice of the dominance order induced by the support of the expansion of the skew Schur function into Schur functions.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the subposet of the dominance order whose elements are the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a lattice.
The example $\lambda = (5^2,4^2,1)$ and $\mu=(3,2)$ shows that this lattice is not a sublattice of the dominance order.

Map

dual

Description

Return the dual lattice.
The dual (or opposite) of a lattice $(\mathcal P,\leq)$ is the lattice $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.