Identifier
Mp00189:
Skew partitions
—rotate⟶
Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Images
[[1],[]] => [[1],[]] => ([],1)
[[2],[]] => [[2],[]] => ([],1)
[[1,1],[]] => [[1,1],[]] => ([],1)
[[2,1],[1]] => [[2,1],[1]] => ([(0,1)],2)
[[3],[]] => [[3],[]] => ([],1)
[[2,1],[]] => [[2,2],[1]] => ([],1)
[[3,1],[1]] => [[3,2],[2]] => ([(0,1)],2)
[[2,2],[1]] => [[2,1],[]] => ([],1)
[[3,2],[2]] => [[3,1],[1]] => ([(0,1)],2)
[[1,1,1],[]] => [[1,1,1],[]] => ([],1)
[[2,2,1],[1,1]] => [[2,1,1],[1]] => ([(0,1)],2)
[[2,1,1],[1]] => [[2,2,1],[1,1]] => ([(0,1)],2)
[[3,2,1],[2,1]] => [[3,2,1],[2,1]] => ([(0,2),(2,1)],3)
[[4],[]] => [[4],[]] => ([],1)
[[3,1],[]] => [[3,3],[2]] => ([],1)
[[4,1],[1]] => [[4,3],[3]] => ([(0,1)],2)
[[2,2],[]] => [[2,2],[]] => ([],1)
[[3,2],[1]] => [[3,2],[1]] => ([(0,1)],2)
[[4,2],[2]] => [[4,2],[2]] => ([(0,2),(2,1)],3)
[[2,1,1],[]] => [[2,2,2],[1,1]] => ([],1)
[[3,2,1],[1,1]] => [[3,2,2],[2,1]] => ([(0,2),(2,1)],3)
[[3,1,1],[1]] => [[3,3,2],[2,2]] => ([(0,1)],2)
[[4,2,1],[2,1]] => [[4,3,2],[3,2]] => ([(0,3),(2,1),(3,2)],4)
[[3,3],[2]] => [[3,1],[]] => ([],1)
[[4,3],[3]] => [[4,1],[1]] => ([(0,1)],2)
[[2,2,1],[1]] => [[2,2,1],[1]] => ([(0,1)],2)
[[3,3,1],[2,1]] => [[3,2,1],[2]] => ([(0,2),(2,1)],3)
[[3,2,1],[2]] => [[3,3,1],[2,1]] => ([(0,2),(2,1)],3)
[[4,3,1],[3,1]] => [[4,3,1],[3,1]] => ([(0,3),(2,1),(3,2)],4)
[[2,2,2],[1,1]] => [[2,1,1],[]] => ([],1)
[[3,3,2],[2,2]] => [[3,1,1],[1]] => ([(0,1)],2)
[[3,2,2],[2,1]] => [[3,2,1],[1,1]] => ([(0,2),(2,1)],3)
[[4,3,2],[3,2]] => [[4,2,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[1,1,1,1],[]] => [[1,1,1,1],[]] => ([],1)
[[2,2,2,1],[1,1,1]] => [[2,1,1,1],[1]] => ([(0,1)],2)
[[2,2,1,1],[1,1]] => [[2,2,1,1],[1,1]] => ([(0,2),(2,1)],3)
[[3,3,2,1],[2,2,1]] => [[3,2,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[2,1,1,1],[1]] => [[2,2,2,1],[1,1,1]] => ([(0,1)],2)
[[3,2,2,1],[2,1,1]] => [[3,2,2,1],[2,1,1]] => ([(0,3),(2,1),(3,2)],4)
[[3,2,1,1],[2,1]] => [[3,3,2,1],[2,2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,1],[3,2,1]] => [[4,3,2,1],[3,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5],[]] => [[5],[]] => ([],1)
[[4,1],[]] => [[4,4],[3]] => ([],1)
[[5,1],[1]] => [[5,4],[4]] => ([(0,1)],2)
[[3,2],[]] => [[3,3],[1]] => ([],1)
[[4,2],[1]] => [[4,3],[2]] => ([(0,1)],2)
[[5,2],[2]] => [[5,3],[3]] => ([(0,2),(2,1)],3)
[[3,1,1],[]] => [[3,3,3],[2,2]] => ([],1)
[[4,2,1],[1,1]] => [[4,3,3],[3,2]] => ([(0,2),(2,1)],3)
[[4,1,1],[1]] => [[4,4,3],[3,3]] => ([(0,1)],2)
[[5,2,1],[2,1]] => [[5,4,3],[4,3]] => ([(0,3),(2,1),(3,2)],4)
[[3,3],[1]] => [[3,2],[]] => ([],1)
[[4,3],[2]] => [[4,2],[1]] => ([(0,1)],2)
[[5,3],[3]] => [[5,2],[2]] => ([(0,2),(2,1)],3)
[[2,2,1],[]] => [[2,2,2],[1]] => ([],1)
[[3,3,1],[1,1]] => [[3,2,2],[2]] => ([(0,1)],2)
[[3,2,1],[1]] => [[3,3,2],[2,1]] => ([(0,2),(2,1)],3)
[[4,3,1],[2,1]] => [[4,3,2],[3,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,2,1],[2]] => [[4,4,2],[3,2]] => ([(0,3),(2,1),(3,2)],4)
[[5,3,1],[3,1]] => [[5,4,2],[4,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,2,2],[1,1]] => [[3,2,2],[1,1]] => ([(0,1)],2)
[[4,3,2],[2,2]] => [[4,2,2],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,2,2],[2,1]] => [[4,3,2],[2,2]] => ([(0,3),(2,1),(3,2)],4)
[[5,3,2],[3,2]] => [[5,3,2],[3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]] => ([],1)
[[3,2,2,1],[1,1,1]] => [[3,2,2,2],[2,1,1]] => ([(0,2),(2,1)],3)
[[3,2,1,1],[1,1]] => [[3,3,2,2],[2,2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,1],[2,2,1]] => [[4,3,2,2],[3,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,1,1,1],[1]] => [[3,3,3,2],[2,2,2]] => ([(0,1)],2)
[[4,2,2,1],[2,1,1]] => [[4,3,3,2],[3,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,2,1,1],[2,1]] => [[4,4,3,2],[3,3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,3,2,1],[3,2,1]] => [[5,4,3,2],[4,3,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,4],[3]] => [[4,1],[]] => ([],1)
[[5,4],[4]] => [[5,1],[1]] => ([(0,1)],2)
[[3,3,1],[2]] => [[3,3,1],[2]] => ([(0,1)],2)
[[4,4,1],[3,1]] => [[4,3,1],[3]] => ([(0,2),(2,1)],3)
[[4,3,1],[3]] => [[4,4,1],[3,1]] => ([(0,2),(2,1)],3)
[[5,4,1],[4,1]] => [[5,4,1],[4,1]] => ([(0,3),(2,1),(3,2)],4)
[[2,2,2],[1]] => [[2,2,1],[]] => ([],1)
[[3,3,2],[2,1]] => [[3,2,1],[1]] => ([(0,2),(2,1)],3)
[[4,4,2],[3,2]] => [[4,2,1],[2]] => ([(0,3),(2,1),(3,2)],4)
[[3,2,2],[2]] => [[3,3,1],[1,1]] => ([(0,1)],2)
[[4,3,2],[3,1]] => [[4,3,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,4,2],[4,2]] => [[5,3,1],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,1,1],[1]] => [[2,2,2,1],[1,1]] => ([(0,1)],2)
[[3,3,2,1],[2,1,1]] => [[3,2,2,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[3,3,1,1],[2,1]] => [[3,3,2,1],[2,2]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,2,1],[3,2,1]] => [[4,3,2,1],[3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,2,1,1],[2]] => [[3,3,3,1],[2,2,1]] => ([(0,2),(2,1)],3)
[[4,3,2,1],[3,1,1]] => [[4,3,3,1],[3,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,1,1],[3,1]] => [[4,4,3,1],[3,3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,2,1],[4,2,1]] => [[5,4,3,1],[4,3,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,3,3],[2,2]] => [[3,1,1],[]] => ([],1)
[[4,4,3],[3,3]] => [[4,1,1],[1]] => ([(0,1)],2)
[[4,3,3],[3,2]] => [[4,2,1],[1,1]] => ([(0,2),(2,1)],3)
[[5,4,3],[4,3]] => [[5,2,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[2,2,2,1],[1,1]] => [[2,2,1,1],[1]] => ([(0,1)],2)
[[3,3,3,1],[2,2,1]] => [[3,2,1,1],[2]] => ([(0,2),(2,1)],3)
[[3,3,2,1],[2,2]] => [[3,3,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,3,1],[3,3,1]] => [[4,3,1,1],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,2,2,1],[2,1]] => [[3,3,2,1],[2,1,1]] => ([(0,3),(2,1),(3,2)],4)
>>> Load all 1368 entries. <<<
[[4,3,3,1],[3,2,1]] => [[4,3,2,1],[3,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,2,1],[3,2]] => [[4,4,2,1],[3,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,1],[4,3,1]] => [[5,4,2,1],[4,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,2,2],[1,1,1]] => [[2,1,1,1],[]] => ([],1)
[[3,3,3,2],[2,2,2]] => [[3,1,1,1],[1]] => ([(0,1)],2)
[[3,3,2,2],[2,2,1]] => [[3,2,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,3,2],[3,3,2]] => [[4,2,1,1],[2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,2,2,2],[2,1,1]] => [[3,2,2,1],[1,1,1]] => ([(0,2),(2,1)],3)
[[4,3,3,2],[3,2,2]] => [[4,2,2,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,2,2],[3,2,1]] => [[4,3,2,1],[2,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,2],[4,3,2]] => [[5,3,2,1],[3,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,1,1],[]] => [[1,1,1,1,1],[]] => ([],1)
[[2,2,2,2,1],[1,1,1,1]] => [[2,1,1,1,1],[1]] => ([(0,1)],2)
[[2,2,2,1,1],[1,1,1]] => [[2,2,1,1,1],[1,1]] => ([(0,2),(2,1)],3)
[[3,3,3,2,1],[2,2,2,1]] => [[3,2,1,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[2,2,1,1,1],[1,1]] => [[2,2,2,1,1],[1,1,1]] => ([(0,2),(2,1)],3)
[[3,3,2,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,2,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,3,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,1,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1,1]] => ([(0,1)],2)
[[3,2,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1,1]] => ([(0,3),(2,1),(3,2)],4)
[[3,2,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,2,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,3,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,4,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[6],[]] => [[6],[]] => ([],1)
[[5,1],[]] => [[5,5],[4]] => ([],1)
[[6,1],[1]] => [[6,5],[5]] => ([(0,1)],2)
[[4,2],[]] => [[4,4],[2]] => ([],1)
[[5,2],[1]] => [[5,4],[3]] => ([(0,1)],2)
[[6,2],[2]] => [[6,4],[4]] => ([(0,2),(2,1)],3)
[[4,1,1],[]] => [[4,4,4],[3,3]] => ([],1)
[[5,2,1],[1,1]] => [[5,4,4],[4,3]] => ([(0,2),(2,1)],3)
[[5,1,1],[1]] => [[5,5,4],[4,4]] => ([(0,1)],2)
[[6,2,1],[2,1]] => [[6,5,4],[5,4]] => ([(0,3),(2,1),(3,2)],4)
[[3,3],[]] => [[3,3],[]] => ([],1)
[[4,3],[1]] => [[4,3],[1]] => ([(0,1)],2)
[[5,3],[2]] => [[5,3],[2]] => ([(0,2),(2,1)],3)
[[6,3],[3]] => [[6,3],[3]] => ([(0,3),(2,1),(3,2)],4)
[[3,2,1],[]] => [[3,3,3],[2,1]] => ([],1)
[[4,3,1],[1,1]] => [[4,3,3],[3,1]] => ([(0,2),(2,1)],3)
[[4,2,1],[1]] => [[4,4,3],[3,2]] => ([(0,2),(2,1)],3)
[[5,3,1],[2,1]] => [[5,4,3],[4,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,2,1],[2]] => [[5,5,3],[4,3]] => ([(0,3),(2,1),(3,2)],4)
[[6,3,1],[3,1]] => [[6,5,3],[5,3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,2,2],[1,1]] => [[4,3,3],[2,2]] => ([(0,1)],2)
[[5,3,2],[2,2]] => [[5,3,3],[3,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,2,2],[2,1]] => [[5,4,3],[3,3]] => ([(0,3),(2,1),(3,2)],4)
[[6,3,2],[3,2]] => [[6,4,3],[4,3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[3,1,1,1],[]] => [[3,3,3,3],[2,2,2]] => ([],1)
[[4,2,2,1],[1,1,1]] => [[4,3,3,3],[3,2,2]] => ([(0,2),(2,1)],3)
[[4,2,1,1],[1,1]] => [[4,4,3,3],[3,3,2]] => ([(0,3),(2,1),(3,2)],4)
[[5,3,2,1],[2,2,1]] => [[5,4,3,3],[4,3,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,1,1,1],[1]] => [[4,4,4,3],[3,3,3]] => ([(0,1)],2)
[[5,2,2,1],[2,1,1]] => [[5,4,4,3],[4,3,3]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,2,1,1],[2,1]] => [[5,5,4,3],[4,4,3]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,3,2,1],[3,2,1]] => [[6,5,4,3],[5,4,3]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4],[2]] => [[4,2],[]] => ([],1)
[[5,4],[3]] => [[5,2],[1]] => ([(0,1)],2)
[[6,4],[4]] => [[6,2],[2]] => ([(0,2),(2,1)],3)
[[3,3,1],[1]] => [[3,3,2],[2]] => ([(0,1)],2)
[[4,4,1],[2,1]] => [[4,3,2],[3]] => ([(0,2),(2,1)],3)
[[4,3,1],[2]] => [[4,4,2],[3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4)
[[5,4,1],[3,1]] => [[5,4,2],[4,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,3,1],[3]] => [[5,5,2],[4,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,4,1],[4,1]] => [[6,5,2],[5,2]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[2,2,2],[]] => [[2,2,2],[]] => ([],1)
[[3,3,2],[1,1]] => [[3,2,2],[1]] => ([(0,1)],2)
[[4,4,2],[2,2]] => [[4,2,2],[2]] => ([(0,2),(2,1)],3)
[[3,2,2],[1]] => [[3,3,2],[1,1]] => ([(0,1)],2)
[[4,3,2],[2,1]] => [[4,3,2],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,4,2],[3,2]] => [[5,3,2],[3,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,2,2],[2]] => [[4,4,2],[2,2]] => ([(0,2),(2,1)],3)
[[5,3,2],[3,1]] => [[5,4,2],[3,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,4,2],[4,2]] => [[6,4,2],[4,2]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[2,2,1,1],[]] => [[2,2,2,2],[1,1]] => ([],1)
[[3,3,2,1],[1,1,1]] => [[3,2,2,2],[2,1]] => ([(0,2),(2,1)],3)
[[3,3,1,1],[1,1]] => [[3,3,2,2],[2,2]] => ([(0,2),(2,1)],3)
[[4,4,2,1],[2,2,1]] => [[4,3,2,2],[3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,2,1,1],[1]] => [[3,3,3,2],[2,2,1]] => ([(0,2),(2,1)],3)
[[4,3,2,1],[2,1,1]] => [[4,3,3,2],[3,2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[4,3,1,1],[2,1]] => [[4,4,3,2],[3,3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[5,4,2,1],[3,2,1]] => [[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)
[[4,2,1,1],[2]] => [[4,4,4,2],[3,3,2]] => ([(0,3),(2,1),(3,2)],4)
[[5,3,2,1],[3,1,1]] => [[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)
[[5,3,1,1],[3,1]] => [[5,5,4,2],[4,4,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[6,4,2,1],[4,2,1]] => [[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)
[[4,3,3],[2,2]] => [[4,2,2],[1,1]] => ([(0,1)],2)
[[5,4,3],[3,3]] => [[5,2,2],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,3,3],[3,2]] => [[5,3,2],[2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,4,3],[4,3]] => [[6,3,2],[3,2]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[3,2,2,1],[1,1]] => [[3,3,2,2],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4)
[[4,3,3,1],[2,2,1]] => [[4,3,2,2],[3,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,3,2,1],[2,2]] => [[4,4,2,2],[3,2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,4,3,1],[3,3,1]] => [[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)
[[4,2,2,1],[2,1]] => [[4,4,3,2],[3,2,2]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[5,3,3,1],[3,2,1]] => [[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)
[[5,3,2,1],[3,2]] => [[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)
[[6,4,3,1],[4,3,1]] => [[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)
[[3,2,2,2],[1,1,1]] => [[3,2,2,2],[1,1,1]] => ([(0,1)],2)
[[4,3,3,2],[2,2,2]] => [[4,2,2,2],[2,1,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,2],[2,2,1]] => [[4,3,2,2],[2,2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,4,3,2],[3,3,2]] => [[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)
[[4,2,2,2],[2,1,1]] => [[4,3,3,2],[2,2,2]] => ([(0,3),(2,1),(3,2)],4)
[[5,3,3,2],[3,2,2]] => [[5,3,3,2],[3,2,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[5,3,2,2],[3,2,1]] => [[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)
[[6,4,3,2],[4,3,2]] => [[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)
[[2,1,1,1,1],[]] => [[2,2,2,2,2],[1,1,1,1]] => ([],1)
[[3,2,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1,1]] => ([(0,2),(2,1)],3)
[[3,2,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,3,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,2,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,2,1],[2,2,1,1]] => [[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)
[[4,3,2,1,1],[2,2,1]] => [[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)
[[5,4,3,2,1],[3,3,2,1]] => [[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)
[[3,1,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,2]] => ([(0,1)],2)
[[4,2,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,2,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,2]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[5,3,3,2,1],[3,2,2,1]] => [[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)
[[4,2,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,3,2,2,1],[3,2,1,1]] => [[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)
[[5,3,2,1,1],[3,2,1]] => [[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)
[[6,4,3,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,3,2]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10)
[[5,5],[4]] => [[5,1],[]] => ([],1)
[[6,5],[5]] => [[6,1],[1]] => ([(0,1)],2)
[[4,4,1],[3]] => [[4,4,1],[3]] => ([(0,1)],2)
[[5,5,1],[4,1]] => [[5,4,1],[4]] => ([(0,2),(2,1)],3)
[[5,4,1],[4]] => [[5,5,1],[4,1]] => ([(0,2),(2,1)],3)
[[6,5,1],[5,1]] => [[6,5,1],[5,1]] => ([(0,3),(2,1),(3,2)],4)
[[3,3,2],[2]] => [[3,3,1],[1]] => ([(0,1)],2)
[[4,4,2],[3,1]] => [[4,3,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4)
[[5,5,2],[4,2]] => [[5,3,1],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,3,2],[3]] => [[4,4,1],[2,1]] => ([(0,2),(2,1)],3)
[[5,4,2],[4,1]] => [[5,4,1],[3,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,5,2],[5,2]] => [[6,4,1],[4,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[3,3,1,1],[2]] => [[3,3,3,1],[2,2]] => ([(0,1)],2)
[[4,4,2,1],[3,1,1]] => [[4,3,3,1],[3,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,1,1],[3,1]] => [[4,4,3,1],[3,3]] => ([(0,3),(2,1),(3,2)],4)
[[5,5,2,1],[4,2,1]] => [[5,4,3,1],[4,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,1,1],[3]] => [[4,4,4,1],[3,3,1]] => ([(0,2),(2,1)],3)
[[5,4,2,1],[4,1,1]] => [[5,4,4,1],[4,3,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,1,1],[4,1]] => [[5,5,4,1],[4,4,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,5,2,1],[5,2,1]] => [[6,5,4,1],[5,4,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[3,3,3],[2,1]] => [[3,2,1],[]] => ([],1)
[[4,4,3],[3,2]] => [[4,2,1],[1]] => ([(0,2),(2,1)],3)
[[5,5,3],[4,3]] => [[5,2,1],[2]] => ([(0,3),(2,1),(3,2)],4)
[[4,3,3],[3,1]] => [[4,3,1],[1,1]] => ([(0,2),(2,1)],3)
[[5,4,3],[4,2]] => [[5,3,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,5,3],[5,3]] => [[6,3,1],[3,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[2,2,2,1],[1]] => [[2,2,2,1],[1]] => ([(0,1)],2)
[[3,3,3,1],[2,1,1]] => [[3,2,2,1],[2]] => ([(0,2),(2,1)],3)
[[3,3,2,1],[2,1]] => [[3,3,2,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,4,3,1],[3,2,1]] => [[4,3,2,1],[3,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[4,4,2,1],[3,2]] => [[4,4,2,1],[3,2]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,5,3,1],[4,3,1]] => [[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)
[[3,2,2,1],[2]] => [[3,3,3,1],[2,1,1]] => ([(0,2),(2,1)],3)
[[4,3,3,1],[3,1,1]] => [[4,3,3,1],[3,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,2,1],[3,1]] => [[4,4,3,1],[3,2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,4,3,1],[4,2,1]] => [[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)
[[5,4,2,1],[4,2]] => [[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)
[[6,5,3,1],[5,3,1]] => [[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)
[[3,3,2,2],[2,1,1]] => [[3,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4)
[[4,4,3,2],[3,2,2]] => [[4,2,2,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,4,2,2],[3,2,1]] => [[4,3,2,1],[2,2]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,5,3,2],[4,3,2]] => [[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)
[[4,3,2,2],[3,1,1]] => [[4,3,3,1],[2,2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,4,3,2],[4,2,2]] => [[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)
[[5,4,2,2],[4,2,1]] => [[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)
[[6,5,3,2],[5,3,2]] => [[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)
[[2,2,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1]] => ([(0,1)],2)
[[3,3,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,4,3,2,1],[3,2,2,1]] => [[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)
[[3,3,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,2,2,1],[3,2,1,1]] => [[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)
[[4,4,2,1,1],[3,2,1]] => [[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)
[[5,5,3,2,1],[4,3,2,1]] => [[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)
[[3,2,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2,1]] => ([(0,2),(2,1)],3)
[[4,3,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,2,1,1],[3,1,1]] => [[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)
[[5,4,3,2,1],[4,2,2,1]] => [[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)
[[4,3,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,2,2,1],[4,2,1,1]] => [[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)
[[5,4,2,1,1],[4,2,1]] => [[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)
[[6,5,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10)
[[4,4,4],[3,3]] => [[4,1,1],[]] => ([],1)
[[5,5,4],[4,4]] => [[5,1,1],[1]] => ([(0,1)],2)
[[5,4,4],[4,3]] => [[5,2,1],[1,1]] => ([(0,2),(2,1)],3)
[[6,5,4],[5,4]] => [[6,2,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,1],[2,2]] => [[3,3,1,1],[2]] => ([(0,1)],2)
[[4,4,4,1],[3,3,1]] => [[4,3,1,1],[3]] => ([(0,2),(2,1)],3)
[[4,4,3,1],[3,3]] => [[4,4,1,1],[3,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,5,4,1],[4,4,1]] => [[5,4,1,1],[4,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,3,1],[3,2]] => [[4,4,2,1],[3,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,4,4,1],[4,3,1]] => [[5,4,2,1],[4,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,3,1],[4,3]] => [[5,5,2,1],[4,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,5,4,1],[5,4,1]] => [[6,5,2,1],[5,2,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[2,2,2,2],[1,1]] => [[2,2,1,1],[]] => ([],1)
[[3,3,3,2],[2,2,1]] => [[3,2,1,1],[1]] => ([(0,2),(2,1)],3)
[[4,4,4,2],[3,3,2]] => [[4,2,1,1],[2]] => ([(0,3),(2,1),(3,2)],4)
[[3,3,2,2],[2,2]] => [[3,3,1,1],[1,1]] => ([(0,2),(2,1)],3)
[[4,4,3,2],[3,3,1]] => [[4,3,1,1],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[5,5,4,2],[4,4,2]] => [[5,3,1,1],[3,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[3,2,2,2],[2,1]] => [[3,3,2,1],[1,1,1]] => ([(0,2),(2,1)],3)
[[4,3,3,2],[3,2,1]] => [[4,3,2,1],[2,1,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[5,4,4,2],[4,3,2]] => [[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)
[[4,3,2,2],[3,2]] => [[4,4,2,1],[2,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,2],[4,3,1]] => [[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)
[[6,5,4,2],[5,4,2]] => [[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)
[[2,2,2,1,1],[1,1]] => [[2,2,2,1,1],[1,1]] => ([(0,2),(2,1)],3)
[[3,3,3,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,3,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,4,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,3,2,1,1],[2,2]] => [[3,3,3,1,1],[2,2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,3,2,1],[3,3,1,1]] => [[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)
[[4,4,3,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[5,5,4,2,1],[4,4,2,1]] => [[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)
[[3,2,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,3,3,2,1],[3,2,1,1]] => [[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)
[[4,3,3,1,1],[3,2,1]] => [[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)
[[5,4,4,2,1],[4,3,2,1]] => [[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)
[[4,3,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,3,2,1],[4,3,1,1]] => [[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)
[[5,4,3,1,1],[4,3,1]] => [[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)
[[6,5,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10)
[[3,3,3,3],[2,2,2]] => [[3,1,1,1],[]] => ([],1)
[[4,4,4,3],[3,3,3]] => [[4,1,1,1],[1]] => ([(0,1)],2)
[[4,4,3,3],[3,3,2]] => [[4,2,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,5,4,3],[4,4,3]] => [[5,2,1,1],[2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,3,3],[3,2,2]] => [[4,2,2,1],[1,1,1]] => ([(0,2),(2,1)],3)
[[5,4,4,3],[4,3,3]] => [[5,2,2,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,3],[4,3,2]] => [[5,3,2,1],[2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,5,4,3],[5,4,3]] => [[6,3,2,1],[3,2,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[2,2,2,2,1],[1,1,1]] => [[2,2,1,1,1],[1]] => ([(0,1)],2)
[[3,3,3,3,1],[2,2,2,1]] => [[3,2,1,1,1],[2]] => ([(0,2),(2,1)],3)
[[3,3,3,2,1],[2,2,2]] => [[3,3,1,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,4,3,1],[3,3,3,1]] => [[4,3,1,1,1],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,2,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,4,3,3,1],[3,3,2,1]] => [[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)
[[4,4,3,2,1],[3,3,2]] => [[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)
[[5,5,4,3,1],[4,4,3,1]] => [[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)
[[3,2,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,3,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,3,2,1],[3,2,2]] => [[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)
[[5,4,4,3,1],[4,3,3,1]] => [[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)
[[4,3,2,2,1],[3,2,1]] => [[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)
[[5,4,3,3,1],[4,3,2,1]] => [[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)
[[5,4,3,2,1],[4,3,2]] => [[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)
[[6,5,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10)
[[2,2,2,2,2],[1,1,1,1]] => [[2,1,1,1,1],[]] => ([],1)
[[3,3,3,3,2],[2,2,2,2]] => [[3,1,1,1,1],[1]] => ([(0,1)],2)
[[3,3,3,2,2],[2,2,2,1]] => [[3,2,1,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,4,3,2],[3,3,3,2]] => [[4,2,1,1,1],[2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,2,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,3,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4,3,2,2],[3,3,2,1]] => [[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)
[[5,5,4,3,2],[4,4,3,2]] => [[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)
[[3,2,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1,1]] => ([(0,2),(2,1)],3)
[[4,3,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,3,2,2],[3,2,2,1]] => [[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)
[[5,4,4,3,2],[4,3,3,2]] => [[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)
[[4,3,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,3,3,2],[4,3,2,2]] => [[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)
[[5,4,3,2,2],[4,3,2,1]] => [[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)
[[6,5,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(6,7),(7,1),(7,2),(8,5),(9,3),(9,4)],10)
[[1,1,1,1,1,1],[]] => [[1,1,1,1,1,1],[]] => ([],1)
[[2,2,2,2,2,1],[1,1,1,1,1]] => [[2,1,1,1,1,1],[1]] => ([(0,1)],2)
[[2,2,2,2,1,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1,1]] => ([(0,2),(2,1)],3)
[[3,3,3,3,2,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[2,2,2,1,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,2,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[3,3,3,2,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[4,4,4,3,2,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,2,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[2,2,1,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1,1]] => ([(0,2),(2,1)],3)
[[3,3,2,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[3,3,2,2,1,1],[2,2,1,1]] => [[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)
[[4,4,3,3,2,1],[3,3,2,2,1]] => [[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)
[[3,3,2,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[4,4,3,2,2,1],[3,3,2,1,1]] => [[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)
[[4,4,3,2,1,1],[3,3,2,1]] => [[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)
[[5,5,4,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2,1]] => ([(0,7),(1,9),(2,9),(4,8),(5,8),(6,3),(7,1),(7,2),(8,6),(9,4),(9,5)],10)
[[2,1,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1,1]] => ([(0,1)],2)
[[3,2,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1,1]] => ([(0,3),(2,1),(3,2)],4)
[[3,2,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[4,3,3,3,2,1],[3,2,2,2,1]] => [[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)
[[3,2,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[4,3,3,2,2,1],[3,2,2,1,1]] => [[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)
[[4,3,3,2,1,1],[3,2,2,1]] => [[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)
[[5,4,4,3,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1,1]] => ([(0,7),(1,9),(2,9),(4,8),(5,8),(6,3),(7,1),(7,2),(8,6),(9,4),(9,5)],10)
[[3,2,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,2,2,1],[3,2,1,1,1]] => [[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)
[[4,3,2,2,1,1],[3,2,1,1]] => [[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)
[[5,4,3,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,2,1]] => ([(0,7),(1,9),(2,9),(4,8),(5,8),(6,3),(7,1),(7,2),(8,6),(9,4),(9,5)],10)
[[4,3,2,1,1,1],[3,2,1]] => [[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)
[[5,4,3,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,2,1]] => ([(0,7),(1,9),(2,9),(4,8),(5,8),(6,3),(7,1),(7,2),(8,6),(9,4),(9,5)],10)
[[5,4,3,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,2,1]] => ([(0,7),(1,9),(2,9),(4,8),(5,8),(6,3),(7,1),(7,2),(8,6),(9,4),(9,5)],10)
[[6,5,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2,1]] => ([(0,7),(1,10),(2,10),(4,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,6),(10,4),(10,5)],11)
[[7],[]] => [[7],[]] => ([],1)
[[6,1],[]] => [[6,6],[5]] => ([],1)
[[7,1],[1]] => [[7,6],[6]] => ([(0,1)],2)
[[5,2],[]] => [[5,5],[3]] => ([],1)
[[6,2],[1]] => [[6,5],[4]] => ([(0,1)],2)
[[7,2],[2]] => [[7,5],[5]] => ([(0,2),(2,1)],3)
[[5,1,1],[]] => [[5,5,5],[4,4]] => ([],1)
[[6,2,1],[1,1]] => [[6,5,5],[5,4]] => ([(0,2),(2,1)],3)
[[6,1,1],[1]] => [[6,6,5],[5,5]] => ([(0,1)],2)
[[7,2,1],[2,1]] => [[7,6,5],[6,5]] => ([(0,3),(2,1),(3,2)],4)
[[4,3],[]] => [[4,4],[1]] => ([],1)
[[5,3],[1]] => [[5,4],[2]] => ([(0,1)],2)
[[6,3],[2]] => [[6,4],[3]] => ([(0,2),(2,1)],3)
[[7,3],[3]] => [[7,4],[4]] => ([(0,3),(2,1),(3,2)],4)
[[4,2,1],[]] => [[4,4,4],[3,2]] => ([],1)
[[5,3,1],[1,1]] => [[5,4,4],[4,2]] => ([(0,2),(2,1)],3)
[[5,2,1],[1]] => [[5,5,4],[4,3]] => ([(0,2),(2,1)],3)
[[6,3,1],[2,1]] => [[6,5,4],[5,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,2,1],[2]] => [[6,6,4],[5,4]] => ([(0,3),(2,1),(3,2)],4)
[[7,3,1],[3,1]] => [[7,6,4],[6,4]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[5,2,2],[1,1]] => [[5,4,4],[3,3]] => ([(0,1)],2)
[[6,3,2],[2,2]] => [[6,4,4],[4,3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,2,2],[2,1]] => [[6,5,4],[4,4]] => ([(0,3),(2,1),(3,2)],4)
[[7,3,2],[3,2]] => [[7,5,4],[5,4]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,1,1,1],[]] => [[4,4,4,4],[3,3,3]] => ([],1)
[[5,2,2,1],[1,1,1]] => [[5,4,4,4],[4,3,3]] => ([(0,2),(2,1)],3)
[[5,2,1,1],[1,1]] => [[5,5,4,4],[4,4,3]] => ([(0,3),(2,1),(3,2)],4)
[[6,3,2,1],[2,2,1]] => [[6,5,4,4],[5,4,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,1,1,1],[1]] => [[5,5,5,4],[4,4,4]] => ([(0,1)],2)
[[6,2,2,1],[2,1,1]] => [[6,5,5,4],[5,4,4]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,2,1,1],[2,1]] => [[6,6,5,4],[5,5,4]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[7,3,2,1],[3,2,1]] => [[7,6,5,4],[6,5,4]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4],[1]] => [[4,3],[]] => ([],1)
[[5,4],[2]] => [[5,3],[1]] => ([(0,1)],2)
[[6,4],[3]] => [[6,3],[2]] => ([(0,2),(2,1)],3)
[[7,4],[4]] => [[7,3],[3]] => ([(0,3),(2,1),(3,2)],4)
[[3,3,1],[]] => [[3,3,3],[2]] => ([],1)
[[4,4,1],[1,1]] => [[4,3,3],[3]] => ([(0,1)],2)
[[4,3,1],[1]] => [[4,4,3],[3,1]] => ([(0,2),(2,1)],3)
[[5,4,1],[2,1]] => [[5,4,3],[4,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,3,1],[2]] => [[5,5,3],[4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[6,4,1],[3,1]] => [[6,5,3],[5,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,3,1],[3]] => [[6,6,3],[5,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[7,4,1],[4,1]] => [[7,6,3],[6,3]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[3,2,2],[]] => [[3,3,3],[1,1]] => ([],1)
[[4,3,2],[1,1]] => [[4,3,3],[2,1]] => ([(0,2),(2,1)],3)
[[5,4,2],[2,2]] => [[5,3,3],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,2,2],[1]] => [[4,4,3],[2,2]] => ([(0,1)],2)
[[5,3,2],[2,1]] => [[5,4,3],[3,2]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[6,4,2],[3,2]] => [[6,4,3],[4,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[5,2,2],[2]] => [[5,5,3],[3,3]] => ([(0,2),(2,1)],3)
[[6,3,2],[3,1]] => [[6,5,3],[4,3]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[7,4,2],[4,2]] => [[7,5,3],[5,3]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
[[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]] => ([],1)
[[4,3,2,1],[1,1,1]] => [[4,3,3,3],[3,2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,3,1,1],[1,1]] => [[4,4,3,3],[3,3,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,4,2,1],[2,2,1]] => [[5,4,3,3],[4,3,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,2,1,1],[1]] => [[4,4,4,3],[3,3,2]] => ([(0,2),(2,1)],3)
[[5,3,2,1],[2,1,1]] => [[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)
[[5,3,1,1],[2,1]] => [[5,5,4,3],[4,4,2]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[6,4,2,1],[3,2,1]] => [[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)
[[5,2,1,1],[2]] => [[5,5,5,3],[4,4,3]] => ([(0,3),(2,1),(3,2)],4)
[[6,3,2,1],[3,1,1]] => [[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)
[[6,3,1,1],[3,1]] => [[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)
[[7,4,2,1],[4,2,1]] => [[7,6,5,3],[6,5,3]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[5,3,3],[2,2]] => [[5,3,3],[2,2]] => ([(0,2),(2,1)],3)
[[6,4,3],[3,3]] => [[6,3,3],[3,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,3,3],[3,2]] => [[6,4,3],[3,3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[7,4,3],[4,3]] => [[7,4,3],[4,3]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,2,2,1],[1,1]] => [[4,4,3,3],[3,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4)
[[5,3,3,1],[2,2,1]] => [[5,4,3,3],[4,2,2]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[5,3,2,1],[2,2]] => [[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)
[[6,4,3,1],[3,3,1]] => [[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)
[[5,2,2,1],[2,1]] => [[5,5,4,3],[4,3,3]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[6,3,3,1],[3,2,1]] => [[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)
[[6,3,2,1],[3,2]] => [[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)
[[7,4,3,1],[4,3,1]] => [[7,6,4,3],[6,4,3]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[4,2,2,2],[1,1,1]] => [[4,3,3,3],[2,2,2]] => ([(0,1)],2)
[[5,3,3,2],[2,2,2]] => [[5,3,3,3],[3,2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,3,2,2],[2,2,1]] => [[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)
[[6,4,3,2],[3,3,2]] => [[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)
[[5,2,2,2],[2,1,1]] => [[5,4,4,3],[3,3,3]] => ([(0,3),(2,1),(3,2)],4)
[[6,3,3,2],[3,2,2]] => [[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)
[[6,3,2,2],[3,2,1]] => [[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)
[[7,4,3,2],[4,3,2]] => [[7,5,4,3],[5,4,3]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,1,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,2]] => ([],1)
[[4,2,2,2,1],[1,1,1,1]] => [[4,3,3,3,3],[3,2,2,2]] => ([(0,2),(2,1)],3)
[[4,2,2,1,1],[1,1,1]] => [[4,4,3,3,3],[3,3,2,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,3,3,2,1],[2,2,2,1]] => [[5,4,3,3,3],[4,3,2,2]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[4,2,1,1,1],[1,1]] => [[4,4,4,3,3],[3,3,3,2]] => ([(0,3),(2,1),(3,2)],4)
[[5,3,2,2,1],[2,2,1,1]] => [[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)
[[5,3,2,1,1],[2,2,1]] => [[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)
[[6,4,3,2,1],[3,3,2,1]] => [[6,5,4,3,3],[5,4,3,2]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,1,1,1,1],[1]] => [[4,4,4,4,3],[3,3,3,3]] => ([(0,1)],2)
[[5,2,2,2,1],[2,1,1,1]] => [[5,4,4,4,3],[4,3,3,3]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,2,2,1,1],[2,1,1]] => [[5,5,4,4,3],[4,4,3,3]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[6,3,3,2,1],[3,2,2,1]] => [[6,5,4,4,3],[5,4,3,3]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,2,1,1,1],[2,1]] => [[5,5,5,4,3],[4,4,4,3]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,3,2,2,1],[3,2,1,1]] => [[6,5,5,4,3],[5,4,4,3]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,3,2,1,1],[3,2,1]] => [[6,6,5,4,3],[5,5,4,3]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,4,3,2,1],[4,3,2,1]] => [[7,6,5,4,3],[6,5,4,3]] => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[5,5],[3]] => [[5,2],[]] => ([],1)
[[6,5],[4]] => [[6,2],[1]] => ([(0,1)],2)
[[7,5],[5]] => [[7,2],[2]] => ([(0,2),(2,1)],3)
[[4,4,1],[2]] => [[4,4,2],[3]] => ([(0,1)],2)
[[5,5,1],[3,1]] => [[5,4,2],[4]] => ([(0,2),(2,1)],3)
[[5,4,1],[3]] => [[5,5,2],[4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4)
[[6,5,1],[4,1]] => [[6,5,2],[5,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,4,1],[4]] => [[6,6,2],[5,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[7,5,1],[5,1]] => [[7,6,2],[6,2]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[3,3,2],[1]] => [[3,3,2],[1]] => ([(0,1)],2)
[[4,4,2],[2,1]] => [[4,3,2],[2]] => ([(0,3),(2,1),(3,2)],4)
[[5,5,2],[3,2]] => [[5,3,2],[3]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,2],[2]] => [[4,4,2],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,4,2],[3,1]] => [[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[6,5,2],[4,2]] => [[6,4,2],[4,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[5,3,2],[3]] => [[5,5,2],[3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,4,2],[4,1]] => [[6,5,2],[4,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[7,5,2],[5,2]] => [[7,5,2],[5,2]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
[[3,3,1,1],[1]] => [[3,3,3,2],[2,2]] => ([(0,1)],2)
[[4,4,2,1],[2,1,1]] => [[4,3,3,2],[3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,1,1],[2,1]] => [[4,4,3,2],[3,3]] => ([(0,3),(2,1),(3,2)],4)
[[5,5,2,1],[3,2,1]] => [[5,4,3,2],[4,3]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,3,1,1],[2]] => [[4,4,4,2],[3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4)
[[5,4,2,1],[3,1,1]] => [[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)
[[5,4,1,1],[3,1]] => [[5,5,4,2],[4,4,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[6,5,2,1],[4,2,1]] => [[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)
[[5,3,1,1],[3]] => [[5,5,5,2],[4,4,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,4,2,1],[4,1,1]] => [[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)
[[6,4,1,1],[4,1]] => [[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)
[[7,5,2,1],[5,2,1]] => [[7,6,5,2],[6,5,2]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,3,3],[1,1]] => [[3,2,2],[]] => ([],1)
[[4,4,3],[2,2]] => [[4,2,2],[1]] => ([(0,1)],2)
[[5,5,3],[3,3]] => [[5,2,2],[2]] => ([(0,2),(2,1)],3)
[[4,3,3],[2,1]] => [[4,3,2],[1,1]] => ([(0,2),(2,1)],3)
[[5,4,3],[3,2]] => [[5,3,2],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[6,5,3],[4,3]] => [[6,3,2],[3,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[5,3,3],[3,1]] => [[5,4,2],[2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,4,3],[4,2]] => [[6,4,2],[3,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[7,5,3],[5,3]] => [[7,4,2],[4,2]] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
[[2,2,2,1],[]] => [[2,2,2,2],[1]] => ([],1)
[[3,3,3,1],[1,1,1]] => [[3,2,2,2],[2]] => ([(0,1)],2)
[[3,3,2,1],[1,1]] => [[3,3,2,2],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,3,1],[2,2,1]] => [[4,3,2,2],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,2,1],[2,2]] => [[4,4,2,2],[3,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,5,3,1],[3,3,1]] => [[5,4,2,2],[4,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[3,2,2,1],[1]] => [[3,3,3,2],[2,1,1]] => ([(0,2),(2,1)],3)
[[4,3,3,1],[2,1,1]] => [[4,3,3,2],[3,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,2,1],[2,1]] => [[4,4,3,2],[3,2,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[5,4,3,1],[3,2,1]] => [[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)
[[5,4,2,1],[3,2]] => [[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)
[[6,5,3,1],[4,3,1]] => [[6,5,3,2],[5,3,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,2,2,1],[2]] => [[4,4,4,2],[3,2,2]] => ([(0,3),(2,1),(3,2)],4)
[[5,3,3,1],[3,1,1]] => [[5,4,4,2],[4,2,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[5,3,2,1],[3,1]] => [[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)
[[6,4,3,1],[4,2,1]] => [[6,5,4,2],[5,3,2]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,4,2,1],[4,2]] => [[6,6,4,2],[5,4,2]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,5,3,1],[5,3,1]] => [[7,6,4,2],[6,4,2]] => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[3,3,2,2],[1,1,1]] => [[3,2,2,2],[1,1]] => ([(0,1)],2)
[[4,4,3,2],[2,2,2]] => [[4,2,2,2],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,2,2],[2,2,1]] => [[4,3,2,2],[2,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,5,3,2],[3,3,2]] => [[5,3,2,2],[3,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[4,3,2,2],[2,1,1]] => [[4,3,3,2],[2,2,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[5,4,3,2],[3,2,2]] => [[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)
[[5,4,2,2],[3,2,1]] => [[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)
[[6,5,3,2],[4,3,2]] => [[6,4,3,2],[4,3,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,3,2,2],[3,1,1]] => [[5,4,4,2],[3,3,2]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[6,4,3,2],[4,2,2]] => [[6,4,4,2],[4,3,2]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,4,2,2],[4,2,1]] => [[6,5,4,2],[4,4,2]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,5,3,2],[5,3,2]] => [[7,5,4,2],[5,4,2]] => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[2,2,1,1,1],[]] => [[2,2,2,2,2],[1,1,1]] => ([],1)
[[3,3,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1]] => ([(0,2),(2,1)],3)
[[3,3,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,3,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2]] => ([(0,2),(2,1)],3)
[[4,4,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[4,4,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[5,5,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[3,2,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,1]] => ([(0,2),(2,1)],3)
[[4,3,2,2,1],[2,1,1,1]] => [[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)
[[4,3,2,1,1],[2,1,1]] => [[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)
[[5,4,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[4,3,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[5,4,2,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,3,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,2,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,3,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,3,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,3,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,2,1,1,1],[2]] => [[4,4,4,4,2],[3,3,3,2]] => ([(0,3),(2,1),(3,2)],4)
[[5,3,2,2,1],[3,1,1,1]] => [[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)
[[5,3,2,1,1],[3,1,1]] => [[5,5,4,4,2],[4,4,3,2]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,4,3,2,1],[4,2,2,1]] => [[6,5,4,4,2],[5,4,3,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,3,1,1,1],[3,1]] => [[5,5,5,4,2],[4,4,4,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[6,4,2,2,1],[4,2,1,1]] => [[6,5,5,4,2],[5,4,4,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,4,2,1,1],[4,2,1]] => [[6,6,5,4,2],[5,5,4,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,5,3,2,1],[5,3,2,1]] => [[7,6,5,4,2],[6,5,4,2]] => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[5,4,4],[3,3]] => [[5,2,2],[1,1]] => ([(0,1)],2)
[[6,5,4],[4,4]] => [[6,2,2],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[6,4,4],[4,3]] => [[6,3,2],[2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[7,5,4],[5,4]] => [[7,3,2],[3,2]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,3,3,1],[2,2]] => [[4,4,2,2],[3,1,1]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[5,4,4,1],[3,3,1]] => [[5,4,2,2],[4,1,1]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[5,4,3,1],[3,3]] => [[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)
[[6,5,4,1],[4,4,1]] => [[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)
[[5,3,3,1],[3,2]] => [[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)
[[6,4,4,1],[4,3,1]] => [[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)
[[6,4,3,1],[4,3]] => [[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)
[[7,5,4,1],[5,4,1]] => [[7,6,3,2],[6,3,2]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,2,2,2],[1,1]] => [[3,3,2,2],[1,1,1]] => ([(0,1)],2)
[[4,3,3,2],[2,2,1]] => [[4,3,2,2],[2,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[5,4,4,2],[3,3,2]] => [[5,3,2,2],[3,1,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[4,3,2,2],[2,2]] => [[4,4,2,2],[2,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,4,3,2],[3,3,1]] => [[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)
[[6,5,4,2],[4,4,2]] => [[6,4,2,2],[4,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,2,2,2],[2,1]] => [[4,4,3,2],[2,2,2]] => ([(0,3),(2,1),(3,2)],4)
[[5,3,3,2],[3,2,1]] => [[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)
[[6,4,4,2],[4,3,2]] => [[6,4,3,2],[4,2,2]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,3,2,2],[3,2]] => [[5,5,3,2],[3,3,2]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[6,4,3,2],[4,3,1]] => [[6,5,3,2],[4,3,2]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,5,4,2],[5,4,2]] => [[7,5,3,2],[5,3,2]] => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[3,2,2,1,1],[1,1]] => [[3,3,3,2,2],[2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,3,3,2,1],[2,2,1,1]] => [[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)
[[4,3,3,1,1],[2,2,1]] => [[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)
[[5,4,4,2,1],[3,3,2,1]] => [[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)
[[4,3,2,1,1],[2,2]] => [[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)
[[5,4,3,2,1],[3,3,1,1]] => [[5,4,4,2,2],[4,3,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,3,1,1],[3,3,1]] => [[5,5,4,2,2],[4,4,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,2,1],[4,4,2,1]] => [[6,5,4,2,2],[5,4,2,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,2,2,1,1],[2,1]] => [[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)
[[5,3,3,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,2,2]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,3,3,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,2,2]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,4,4,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,2,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,3,2,1,1],[3,2]] => [[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)
[[6,4,3,2,1],[4,3,1,1]] => [[6,5,5,3,2],[5,4,3,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,4,3,1,1],[4,3,1]] => [[6,6,5,3,2],[5,5,3,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,5,4,2,1],[5,4,2,1]] => [[7,6,5,3,2],[6,5,3,2]] => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[4,3,3,3],[2,2,2]] => [[4,2,2,2],[1,1,1]] => ([(0,1)],2)
[[5,4,4,3],[3,3,3]] => [[5,2,2,2],[2,1,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,4,3,3],[3,3,2]] => [[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)
[[6,5,4,3],[4,4,3]] => [[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)
[[5,3,3,3],[3,2,2]] => [[5,3,3,2],[2,2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,4,4,3],[4,3,3]] => [[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)
[[6,4,3,3],[4,3,2]] => [[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)
[[7,5,4,3],[5,4,3]] => [[7,4,3,2],[4,3,2]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,2,2,2,1],[1,1,1]] => [[3,3,2,2,2],[2,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4)
[[4,3,3,3,1],[2,2,2,1]] => [[4,3,2,2,2],[3,1,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,3,3,2,1],[2,2,2]] => [[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)
[[5,4,4,3,1],[3,3,3,1]] => [[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)
[[4,3,2,2,1],[2,2,1]] => [[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)
[[5,4,3,3,1],[3,3,2,1]] => [[5,4,3,2,2],[4,2,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,3,2,1],[3,3,2]] => [[5,5,3,2,2],[4,3,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,3,1],[4,4,3,1]] => [[6,5,3,2,2],[5,3,2,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,2,2,2,1],[2,1,1]] => [[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)
[[5,3,3,3,1],[3,2,2,1]] => [[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)
[[5,3,3,2,1],[3,2,2]] => [[5,5,3,3,2],[4,3,2,2]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,4,4,3,1],[4,3,3,1]] => [[6,5,3,3,2],[5,3,2,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,3,2,2,1],[3,2,1]] => [[5,5,4,3,2],[4,3,3,2]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,4,3,3,1],[4,3,2,1]] => [[6,5,4,3,2],[5,3,3,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,4,3,2,1],[4,3,2]] => [[6,6,4,3,2],[5,4,3,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,5,4,3,1],[5,4,3,1]] => [[7,6,4,3,2],[6,4,3,2]] => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[3,2,2,2,2],[1,1,1,1]] => [[3,2,2,2,2],[1,1,1,1]] => ([(0,1)],2)
[[4,3,3,3,2],[2,2,2,2]] => [[4,2,2,2,2],[2,1,1,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,3,3,2,2],[2,2,2,1]] => [[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)
[[5,4,4,3,2],[3,3,3,2]] => [[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)
[[4,3,2,2,2],[2,2,1,1]] => [[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)
[[5,4,3,3,2],[3,3,2,2]] => [[5,3,3,2,2],[3,2,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,3,2,2],[3,3,2,1]] => [[5,4,3,2,2],[3,3,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,3,2],[4,4,3,2]] => [[6,4,3,2,2],[4,3,2,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,2,2,2,2],[2,1,1,1]] => [[4,3,3,3,2],[2,2,2,2]] => ([(0,3),(2,1),(3,2)],4)
[[5,3,3,3,2],[3,2,2,2]] => [[5,3,3,3,2],[3,2,2,2]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[5,3,3,2,2],[3,2,2,1]] => [[5,4,3,3,2],[3,3,2,2]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,4,4,3,2],[4,3,3,2]] => [[6,4,3,3,2],[4,3,2,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,3,2,2,2],[3,2,1,1]] => [[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)
[[6,4,3,3,2],[4,3,2,2]] => [[6,4,4,3,2],[4,3,3,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,4,3,2,2],[4,3,2,1]] => [[6,5,4,3,2],[4,4,3,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,5,4,3,2],[5,4,3,2]] => [[7,5,4,3,2],[5,4,3,2]] => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[2,1,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1,1]] => ([],1)
[[3,2,2,2,2,1],[1,1,1,1,1]] => [[3,2,2,2,2,2],[2,1,1,1,1]] => ([(0,2),(2,1)],3)
[[3,2,2,2,1,1],[1,1,1,1]] => [[3,3,2,2,2,2],[2,2,1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,3,3,3,2,1],[2,2,2,2,1]] => [[4,3,2,2,2,2],[3,2,1,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,2,2,1,1,1],[1,1,1]] => [[3,3,3,2,2,2],[2,2,2,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,3,2,2,1],[2,2,2,1,1]] => [[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)
[[4,3,3,2,1,1],[2,2,2,1]] => [[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)
[[5,4,4,3,2,1],[3,3,3,2,1]] => [[5,4,3,2,2,2],[4,3,2,1,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[3,2,1,1,1,1],[1,1]] => [[3,3,3,3,2,2],[2,2,2,2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,2,2,1],[2,2,1,1,1]] => [[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)
[[4,3,2,2,1,1],[2,2,1,1]] => [[4,4,3,3,2,2],[3,3,2,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,3,3,2,1],[3,3,2,2,1]] => [[5,4,3,3,2,2],[4,3,2,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,3,2,1,1,1],[2,2,1]] => [[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)
[[5,4,3,2,2,1],[3,3,2,1,1]] => [[5,4,4,3,2,2],[4,3,3,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,3,2,1,1],[3,3,2,1]] => [[5,5,4,3,2,2],[4,4,3,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,3,2,1],[4,4,3,2,1]] => [[6,5,4,3,2,2],[5,4,3,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[3,1,1,1,1,1],[1]] => [[3,3,3,3,3,2],[2,2,2,2,2]] => ([(0,1)],2)
[[4,2,2,2,2,1],[2,1,1,1,1]] => [[4,3,3,3,3,2],[3,2,2,2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,2,2,2,1,1],[2,1,1,1]] => [[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)
[[5,3,3,3,2,1],[3,2,2,2,1]] => [[5,4,3,3,3,2],[4,3,2,2,2]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,2,2,1,1,1],[2,1,1]] => [[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)
[[5,3,3,2,2,1],[3,2,2,1,1]] => [[5,4,4,3,3,2],[4,3,3,2,2]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,3,3,2,1,1],[3,2,2,1]] => [[5,5,4,3,3,2],[4,4,3,2,2]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,4,4,3,2,1],[4,3,3,2,1]] => [[6,5,4,3,3,2],[5,4,3,2,2]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[4,2,1,1,1,1],[2,1]] => [[4,4,4,4,3,2],[3,3,3,3,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,3,2,2,2,1],[3,2,1,1,1]] => [[5,4,4,4,3,2],[4,3,3,3,2]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,3,2,2,1,1],[3,2,1,1]] => [[5,5,4,4,3,2],[4,4,3,3,2]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,4,3,3,2,1],[4,3,2,2,1]] => [[6,5,4,4,3,2],[5,4,3,3,2]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[5,3,2,1,1,1],[3,2,1]] => [[5,5,5,4,3,2],[4,4,4,3,2]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[6,4,3,2,2,1],[4,3,2,1,1]] => [[6,5,5,4,3,2],[5,4,4,3,2]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[6,4,3,2,1,1],[4,3,2,1]] => [[6,6,5,4,3,2],[5,5,4,3,2]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[7,5,4,3,2,1],[5,4,3,2,1]] => [[7,6,5,4,3,2],[6,5,4,3,2]] => ([(0,9),(1,13),(2,11),(3,11),(4,12),(5,12),(7,13),(8,1),(9,10),(10,4),(10,5),(11,6),(12,7),(12,8),(13,2),(13,3)],14)
[[6,6],[5]] => [[6,1],[]] => ([],1)
[[7,6],[6]] => [[7,1],[1]] => ([(0,1)],2)
[[5,5,1],[4]] => [[5,5,1],[4]] => ([(0,1)],2)
[[6,6,1],[5,1]] => [[6,5,1],[5]] => ([(0,2),(2,1)],3)
[[6,5,1],[5]] => [[6,6,1],[5,1]] => ([(0,2),(2,1)],3)
[[7,6,1],[6,1]] => [[7,6,1],[6,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,2],[3]] => [[4,4,1],[2]] => ([(0,1)],2)
[[5,5,2],[4,1]] => [[5,4,1],[3]] => ([(0,1),(0,2),(1,3),(2,3)],4)
[[6,6,2],[5,2]] => [[6,4,1],[4]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,4,2],[4]] => [[5,5,1],[3,1]] => ([(0,2),(2,1)],3)
[[6,5,2],[5,1]] => [[6,5,1],[4,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[7,6,2],[6,2]] => [[7,5,1],[5,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,4,1,1],[3]] => [[4,4,4,1],[3,3]] => ([(0,1)],2)
[[5,5,2,1],[4,1,1]] => [[5,4,4,1],[4,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,5,1,1],[4,1]] => [[5,5,4,1],[4,4]] => ([(0,3),(2,1),(3,2)],4)
[[6,6,2,1],[5,2,1]] => [[6,5,4,1],[5,4]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,1,1],[4]] => [[5,5,5,1],[4,4,1]] => ([(0,2),(2,1)],3)
[[6,5,2,1],[5,1,1]] => [[6,5,5,1],[5,4,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,5,1,1],[5,1]] => [[6,6,5,1],[5,5,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[7,6,2,1],[6,2,1]] => [[7,6,5,1],[6,5,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[3,3,3],[2]] => [[3,3,1],[]] => ([],1)
[[4,4,3],[3,1]] => [[4,3,1],[1]] => ([(0,2),(2,1)],3)
[[5,5,3],[4,2]] => [[5,3,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[6,6,3],[5,3]] => [[6,3,1],[3]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,3],[3]] => [[4,4,1],[1,1]] => ([(0,1)],2)
[[5,4,3],[4,1]] => [[5,4,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[6,5,3],[5,2]] => [[6,4,1],[3,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[7,6,3],[6,3]] => [[7,4,1],[4,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[3,3,2,1],[2]] => [[3,3,3,1],[2,1]] => ([(0,2),(2,1)],3)
[[4,4,3,1],[3,1,1]] => [[4,3,3,1],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,2,1],[3,1]] => [[4,4,3,1],[3,2]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[5,5,3,1],[4,2,1]] => [[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)
[[5,5,2,1],[4,2]] => [[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)
[[6,6,3,1],[5,3,1]] => [[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)
[[4,3,2,1],[3]] => [[4,4,4,1],[3,2,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,4,3,1],[4,1,1]] => [[5,4,4,1],[4,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,4,2,1],[4,1]] => [[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)
[[6,5,3,1],[5,2,1]] => [[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)
[[6,5,2,1],[5,2]] => [[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)
[[7,6,3,1],[6,3,1]] => [[7,6,4,1],[6,4,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[4,4,2,2],[3,1,1]] => [[4,3,3,1],[2,2]] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[5,5,3,2],[4,2,2]] => [[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)
[[5,5,2,2],[4,2,1]] => [[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)
[[6,6,3,2],[5,3,2]] => [[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)
[[5,4,2,2],[4,1,1]] => [[5,4,4,1],[3,3,1]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[6,5,3,2],[5,2,2]] => [[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)
[[6,5,2,2],[5,2,1]] => [[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)
[[7,6,3,2],[6,3,2]] => [[7,5,4,1],[5,4,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,3,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2]] => ([(0,1)],2)
[[4,4,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[4,4,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[5,5,3,2,1],[4,2,2,1]] => [[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)
[[4,4,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3]] => ([(0,3),(2,1),(3,2)],4)
[[5,5,2,2,1],[4,2,1,1]] => [[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)
[[5,5,2,1,1],[4,2,1]] => [[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)
[[6,6,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,3,1,1,1],[3]] => [[4,4,4,4,1],[3,3,3,1]] => ([(0,2),(2,1)],3)
[[5,4,2,2,1],[4,1,1,1]] => [[5,4,4,4,1],[4,3,3,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[5,4,2,1,1],[4,1,1]] => [[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)
[[6,5,3,2,1],[5,2,2,1]] => [[6,5,4,4,1],[5,4,3,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,4,1,1,1],[4,1]] => [[5,5,5,4,1],[4,4,4,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,5,2,2,1],[5,2,1,1]] => [[6,5,5,4,1],[5,4,4,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,5,2,1,1],[5,2,1]] => [[6,6,5,4,1],[5,5,4,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,6,3,2,1],[6,3,2,1]] => [[7,6,5,4,1],[6,5,4,1]] => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[4,4,4],[3,2]] => [[4,2,1],[]] => ([],1)
[[5,5,4],[4,3]] => [[5,2,1],[1]] => ([(0,2),(2,1)],3)
[[6,6,4],[5,4]] => [[6,2,1],[2]] => ([(0,3),(2,1),(3,2)],4)
[[5,4,4],[4,2]] => [[5,3,1],[1,1]] => ([(0,2),(2,1)],3)
[[6,5,4],[5,3]] => [[6,3,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[7,6,4],[6,4]] => [[7,3,1],[3,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[3,3,3,1],[2,1]] => [[3,3,2,1],[2]] => ([(0,2),(2,1)],3)
[[4,4,4,1],[3,2,1]] => [[4,3,2,1],[3]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,3,1],[3,2]] => [[4,4,2,1],[3,1]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[5,5,4,1],[4,3,1]] => [[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)
[[5,5,3,1],[4,3]] => [[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)
[[6,6,4,1],[5,4,1]] => [[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)
[[4,3,3,1],[3,1]] => [[4,4,3,1],[3,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,4,1],[4,2,1]] => [[5,4,3,1],[4,1,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,4,3,1],[4,2]] => [[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)
[[6,5,4,1],[5,3,1]] => [[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)
[[6,5,3,1],[5,3]] => [[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)
[[7,6,4,1],[6,4,1]] => [[7,6,3,1],[6,3,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[2,2,2,2],[1]] => [[2,2,2,1],[]] => ([],1)
[[3,3,3,2],[2,1,1]] => [[3,2,2,1],[1]] => ([(0,2),(2,1)],3)
[[4,4,4,2],[3,2,2]] => [[4,2,2,1],[2]] => ([(0,3),(2,1),(3,2)],4)
[[3,3,2,2],[2,1]] => [[3,3,2,1],[1,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,3,2],[3,2,1]] => [[4,3,2,1],[2,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[5,5,4,2],[4,3,2]] => [[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)
[[4,4,2,2],[3,2]] => [[4,4,2,1],[2,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,5,3,2],[4,3,1]] => [[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)
[[6,6,4,2],[5,4,2]] => [[6,4,2,1],[4,2]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[3,2,2,2],[2]] => [[3,3,3,1],[1,1,1]] => ([(0,1)],2)
[[4,3,3,2],[3,1,1]] => [[4,3,3,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,4,2],[4,2,2]] => [[5,3,3,1],[3,1,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[4,3,2,2],[3,1]] => [[4,4,3,1],[2,2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,2],[4,2,1]] => [[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)
[[6,5,4,2],[5,3,2]] => [[6,4,3,1],[4,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,4,2,2],[4,2]] => [[5,5,3,1],[3,3,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[6,5,3,2],[5,3,1]] => [[6,5,3,1],[4,3,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,6,4,2],[6,4,2]] => [[7,5,3,1],[5,3,1]] => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[2,2,2,1,1],[1]] => [[2,2,2,2,1],[1,1]] => ([(0,1)],2)
[[3,3,3,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,4,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,3,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,4,3,2,1],[3,2,1,1]] => [[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)
[[4,4,3,1,1],[3,2,1]] => [[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)
[[5,5,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[4,4,2,1,1],[3,2]] => [[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)
[[5,5,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,5,3,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,2]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,6,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[3,2,2,1,1],[2]] => [[3,3,3,3,1],[2,2,1,1]] => ([(0,2),(2,1)],3)
[[4,3,3,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,1,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,3,3,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,1,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[5,4,4,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,1,1]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[4,3,2,1,1],[3,1]] => [[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)
[[5,4,3,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,3,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,2,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,4,2,1,1],[4,2]] => [[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)
[[6,5,3,2,1],[5,3,1,1]] => [[6,5,5,3,1],[5,4,3,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,5,3,1,1],[5,3,1]] => [[6,6,5,3,1],[5,5,3,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,6,4,2,1],[6,4,2,1]] => [[7,6,5,3,1],[6,5,3,1]] => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[4,4,3,3],[3,2,2]] => [[4,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4)
[[5,5,4,3],[4,3,3]] => [[5,2,2,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[5,5,3,3],[4,3,2]] => [[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)
[[6,6,4,3],[5,4,3]] => [[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)
[[5,4,3,3],[4,2,2]] => [[5,3,3,1],[2,2,1]] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[6,5,4,3],[5,3,3]] => [[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)
[[6,5,3,3],[5,3,2]] => [[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)
[[7,6,4,3],[6,4,3]] => [[7,4,3,1],[4,3,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,3,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,4,3,3,1],[3,2,2,1]] => [[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)
[[4,4,3,2,1],[3,2,2]] => [[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)
[[5,5,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[4,4,2,2,1],[3,2,1]] => [[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)
[[5,5,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,5,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,6,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,3,2,2,1],[3,1,1]] => [[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)
[[5,4,3,3,1],[4,2,2,1]] => [[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)
[[5,4,3,2,1],[4,2,2]] => [[5,5,3,3,1],[4,3,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,3,1],[5,3,3,1]] => [[6,5,3,3,1],[5,3,2,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,4,2,2,1],[4,2,1]] => [[5,5,4,3,1],[4,3,3,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,3,3,1],[5,3,2,1]] => [[6,5,4,3,1],[5,3,3,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,5,3,2,1],[5,3,2]] => [[6,6,4,3,1],[5,4,3,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,6,4,3,1],[6,4,3,1]] => [[7,6,4,3,1],[6,4,3,1]] => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[3,3,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4)
[[4,4,3,3,2],[3,2,2,2]] => [[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)
[[4,4,3,2,2],[3,2,2,1]] => [[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)
[[5,5,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[4,4,2,2,2],[3,2,1,1]] => [[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)
[[5,5,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,5,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,6,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,3,2,2,2],[3,1,1,1]] => [[4,3,3,3,1],[2,2,2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,4,3,3,2],[4,2,2,2]] => [[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)
[[5,4,3,2,2],[4,2,2,1]] => [[5,4,3,3,1],[3,3,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,3,2],[5,3,3,2]] => [[6,4,3,3,1],[4,3,2,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,4,2,2,2],[4,2,1,1]] => [[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)
[[6,5,3,3,2],[5,3,2,2]] => [[6,4,4,3,1],[4,3,3,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,5,3,2,2],[5,3,2,1]] => [[6,5,4,3,1],[4,4,3,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,6,4,3,2],[6,4,3,2]] => [[7,5,4,3,1],[5,4,3,1]] => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[2,2,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1]] => ([(0,1)],2)
[[3,3,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,2,2,1,1],[2,1,1,1]] => [[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)
[[4,4,3,3,2,1],[3,2,2,2,1]] => [[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)
[[3,3,2,1,1,1],[2,1,1]] => [[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)
[[4,4,3,2,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,4,3,2,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,4,3,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[3,3,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,2,2,2,1],[3,2,1,1,1]] => [[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)
[[4,4,2,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,2]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,3,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,2]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,4,2,1,1,1],[3,2,1]] => [[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)
[[5,5,3,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,2]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,5,3,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,2]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,6,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[3,2,1,1,1,1],[2]] => [[3,3,3,3,3,1],[2,2,2,2,1]] => ([(0,2),(2,1)],3)
[[4,3,2,2,2,1],[3,1,1,1,1]] => [[4,3,3,3,3,1],[3,2,2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,2,2,1,1],[3,1,1,1]] => [[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)
[[5,4,3,3,2,1],[4,2,2,2,1]] => [[5,4,3,3,3,1],[4,3,2,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,3,2,1,1,1],[3,1,1]] => [[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)
[[5,4,3,2,2,1],[4,2,2,1,1]] => [[5,4,4,3,3,1],[4,3,3,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,3,2,1,1],[4,2,2,1]] => [[5,5,4,3,3,1],[4,4,3,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,3,2,1],[5,3,3,2,1]] => [[6,5,4,3,3,1],[5,4,3,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[4,3,1,1,1,1],[3,1]] => [[4,4,4,4,3,1],[3,3,3,3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,2,2,2,1],[4,2,1,1,1]] => [[5,4,4,4,3,1],[4,3,3,3,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,2,2,1,1],[4,2,1,1]] => [[5,5,4,4,3,1],[4,4,3,3,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,3,3,2,1],[5,3,2,2,1]] => [[6,5,4,4,3,1],[5,4,3,3,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[5,4,2,1,1,1],[4,2,1]] => [[5,5,5,4,3,1],[4,4,4,3,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[6,5,3,2,2,1],[5,3,2,1,1]] => [[6,5,5,4,3,1],[5,4,4,3,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[6,5,3,2,1,1],[5,3,2,1]] => [[6,6,5,4,3,1],[5,5,4,3,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[7,6,4,3,2,1],[6,4,3,2,1]] => [[7,6,5,4,3,1],[6,5,4,3,1]] => ([(0,9),(1,13),(2,11),(3,11),(4,12),(5,12),(7,13),(8,1),(9,10),(10,4),(10,5),(11,6),(12,7),(12,8),(13,2),(13,3)],14)
[[5,5,5],[4,4]] => [[5,1,1],[]] => ([],1)
[[6,6,5],[5,5]] => [[6,1,1],[1]] => ([(0,1)],2)
[[6,5,5],[5,4]] => [[6,2,1],[1,1]] => ([(0,2),(2,1)],3)
[[7,6,5],[6,5]] => [[7,2,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,4,1],[3,3]] => [[4,4,1,1],[3]] => ([(0,1)],2)
[[5,5,5,1],[4,4,1]] => [[5,4,1,1],[4]] => ([(0,2),(2,1)],3)
[[5,5,4,1],[4,4]] => [[5,5,1,1],[4,1]] => ([(0,3),(2,1),(3,2)],4)
[[6,6,5,1],[5,5,1]] => [[6,5,1,1],[5,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,4,1],[4,3]] => [[5,5,2,1],[4,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[6,5,5,1],[5,4,1]] => [[6,5,2,1],[5,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[6,5,4,1],[5,4]] => [[6,6,2,1],[5,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[7,6,5,1],[6,5,1]] => [[7,6,2,1],[6,2,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[3,3,3,2],[2,2]] => [[3,3,1,1],[1]] => ([(0,1)],2)
[[4,4,4,2],[3,3,1]] => [[4,3,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4)
[[5,5,5,2],[4,4,2]] => [[5,3,1,1],[3]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,4,3,2],[3,3]] => [[4,4,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,5,4,2],[4,4,1]] => [[5,4,1,1],[3,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[6,6,5,2],[5,5,2]] => [[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)
[[4,3,3,2],[3,2]] => [[4,4,2,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,4,2],[4,3,1]] => [[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)
[[6,5,5,2],[5,4,2]] => [[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)
[[5,4,3,2],[4,3]] => [[5,5,2,1],[3,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[6,5,4,2],[5,4,1]] => [[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)
[[7,6,5,2],[6,5,2]] => [[7,5,2,1],[5,2,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[3,3,3,1,1],[2,2]] => [[3,3,3,1,1],[2,2]] => ([(0,2),(2,1)],3)
[[4,4,4,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[4,4,4,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,5,5,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[4,4,3,1,1],[3,3]] => [[4,4,4,1,1],[3,3,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,5,4,2,1],[4,4,1,1]] => [[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)
[[5,5,4,1,1],[4,4,1]] => [[5,5,4,1,1],[4,4,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[6,6,5,2,1],[5,5,2,1]] => [[6,5,4,1,1],[5,4,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,3,3,1,1],[3,2]] => [[4,4,4,2,1],[3,3,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[5,4,4,2,1],[4,3,1,1]] => [[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)
[[5,4,4,1,1],[4,3,1]] => [[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)
[[6,5,5,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,1,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,4,3,1,1],[4,3]] => [[5,5,5,2,1],[4,4,2,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[6,5,4,2,1],[5,4,1,1]] => [[6,5,5,2,1],[5,4,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,5,4,1,1],[5,4,1]] => [[6,6,5,2,1],[5,5,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,6,5,2,1],[6,5,2,1]] => [[7,6,5,2,1],[6,5,2,1]] => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[3,3,3,3],[2,2,1]] => [[3,2,1,1],[]] => ([],1)
[[4,4,4,3],[3,3,2]] => [[4,2,1,1],[1]] => ([(0,2),(2,1)],3)
[[5,5,5,3],[4,4,3]] => [[5,2,1,1],[2]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,3,3],[3,3,1]] => [[4,3,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,5,4,3],[4,4,2]] => [[5,3,1,1],[2,1]] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[6,6,5,3],[5,5,3]] => [[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)
[[4,3,3,3],[3,2,1]] => [[4,3,2,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,4,4,3],[4,3,2]] => [[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)
[[6,5,5,3],[5,4,3]] => [[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)
[[5,4,3,3],[4,3,1]] => [[5,4,2,1],[2,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[6,5,4,3],[5,4,2]] => [[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)
[[7,6,5,3],[6,5,3]] => [[7,4,2,1],[4,2,1]] => ([(0,6),(1,9),(2,9),(3,8),(4,8),(5,4),(6,7),(7,1),(7,2),(9,3),(9,5)],10)
[[2,2,2,2,1],[1,1]] => [[2,2,2,1,1],[1]] => ([(0,1)],2)
[[3,3,3,3,1],[2,2,1,1]] => [[3,2,2,1,1],[2]] => ([(0,2),(2,1)],3)
[[3,3,3,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[4,4,4,3,1],[3,3,2,1]] => [[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)
[[4,4,4,2,1],[3,3,2]] => [[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)
[[5,5,5,3,1],[4,4,3,1]] => [[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)
[[3,3,2,2,1],[2,2]] => [[3,3,3,1,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,3,3,1],[3,3,1,1]] => [[4,3,3,1,1],[3,1,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[4,4,3,2,1],[3,3,1]] => [[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)
[[5,5,4,3,1],[4,4,2,1]] => [[5,4,3,1,1],[4,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,5,4,2,1],[4,4,2]] => [[5,5,3,1,1],[4,3,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,6,5,3,1],[5,5,3,1]] => [[6,5,3,1,1],[5,3,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[3,2,2,2,1],[2,1]] => [[3,3,3,2,1],[2,1,1,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,3,3,3,1],[3,2,1,1]] => [[4,3,3,2,1],[3,1,1,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,3,3,2,1],[3,2,1]] => [[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)
[[5,4,4,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,1,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,4,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,1,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,5,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,1,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,3,2,2,1],[3,2]] => [[4,4,4,2,1],[3,2,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,4,3,3,1],[4,3,1,1]] => [[5,4,4,2,1],[4,2,2,1]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[5,4,3,2,1],[4,3,1]] => [[5,5,4,2,1],[4,3,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,3,1],[5,4,2,1]] => [[6,5,4,2,1],[5,3,2,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,5,4,2,1],[5,4,2]] => [[6,6,4,2,1],[5,4,2,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,6,5,3,1],[6,5,3,1]] => [[7,6,4,2,1],[6,4,2,1]] => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[3,3,3,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,4,4,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1]] => ([(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]] => [[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)
[[5,5,5,3,2],[4,4,3,2]] => [[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)
[[4,4,3,2,2],[3,3,1,1]] => [[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)
[[5,5,4,3,2],[4,4,2,2]] => [[5,3,3,1,1],[3,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,5,4,2,2],[4,4,2,1]] => [[5,4,3,1,1],[3,3,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,6,5,3,2],[5,5,3,2]] => [[6,4,3,1,1],[4,3,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,3,3,2,2],[3,2,1,1]] => [[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)
[[5,4,4,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,1,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[5,4,4,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,1,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,5,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,1,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,4,3,2,2],[4,3,1,1]] => [[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)
[[6,5,4,3,2],[5,4,2,2]] => [[6,4,4,2,1],[4,3,2,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[6,5,4,2,2],[5,4,2,1]] => [[6,5,4,2,1],[4,4,2,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,6,5,3,2],[6,5,3,2]] => [[7,5,4,2,1],[5,4,2,1]] => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[2,2,2,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1]] => ([(0,2),(2,1)],3)
[[3,3,3,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,3,3,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4,4,3,2,1],[3,3,2,2,1]] => [[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)
[[3,3,3,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,4,4,2,2,1],[3,3,2,1,1]] => [[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)
[[4,4,4,2,1,1],[3,3,2,1]] => [[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)
[[5,5,5,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[3,3,2,1,1,1],[2,2]] => [[3,3,3,3,1,1],[2,2,2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,3,2,2,1],[3,3,1,1,1]] => [[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)
[[4,4,3,2,1,1],[3,3,1,1]] => [[4,4,3,3,1,1],[3,3,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,4,3,2,1],[4,4,2,2,1]] => [[5,4,3,3,1,1],[4,3,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,4,3,1,1,1],[3,3,1]] => [[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)
[[5,5,4,2,2,1],[4,4,2,1,1]] => [[5,4,4,3,1,1],[4,3,3,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,5,4,2,1,1],[4,4,2,1]] => [[5,5,4,3,1,1],[4,4,3,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,6,5,3,2,1],[5,5,3,2,1]] => [[6,5,4,3,1,1],[5,4,3,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[3,2,2,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,3,3,2,2,1],[3,2,1,1,1]] => [[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)
[[4,3,3,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,1,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,4,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,1,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,3,3,1,1,1],[3,2,1]] => [[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)
[[5,4,4,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,1,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,4,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,1,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,5,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,1,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[4,3,2,1,1,1],[3,2]] => [[4,4,4,4,2,1],[3,3,3,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,3,2,2,1],[4,3,1,1,1]] => [[5,4,4,4,2,1],[4,3,3,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,3,2,1,1],[4,3,1,1]] => [[5,5,4,4,2,1],[4,4,3,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,3,2,1],[5,4,2,2,1]] => [[6,5,4,4,2,1],[5,4,3,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[5,4,3,1,1,1],[4,3,1]] => [[5,5,5,4,2,1],[4,4,4,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[6,5,4,2,2,1],[5,4,2,1,1]] => [[6,5,5,4,2,1],[5,4,4,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[6,5,4,2,1,1],[5,4,2,1]] => [[6,6,5,4,2,1],[5,5,4,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[7,6,5,3,2,1],[6,5,3,2,1]] => [[7,6,5,4,2,1],[6,5,4,2,1]] => ([(0,9),(1,13),(2,11),(3,11),(4,12),(5,12),(7,13),(8,1),(9,10),(10,4),(10,5),(11,6),(12,7),(12,8),(13,2),(13,3)],14)
[[4,4,4,4],[3,3,3]] => [[4,1,1,1],[]] => ([],1)
[[5,5,5,4],[4,4,4]] => [[5,1,1,1],[1]] => ([(0,1)],2)
[[5,5,4,4],[4,4,3]] => [[5,2,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4)
[[6,6,5,4],[5,5,4]] => [[6,2,1,1],[2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,4,4],[4,3,3]] => [[5,2,2,1],[1,1,1]] => ([(0,2),(2,1)],3)
[[6,5,5,4],[5,4,4]] => [[6,2,2,1],[2,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6,5,4,4],[5,4,3]] => [[6,3,2,1],[2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[7,6,5,4],[6,5,4]] => [[7,3,2,1],[3,2,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[3,3,3,3,1],[2,2,2]] => [[3,3,1,1,1],[2]] => ([(0,1)],2)
[[4,4,4,4,1],[3,3,3,1]] => [[4,3,1,1,1],[3]] => ([(0,2),(2,1)],3)
[[4,4,4,3,1],[3,3,3]] => [[4,4,1,1,1],[3,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,5,5,4,1],[4,4,4,1]] => [[5,4,1,1,1],[4,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,3,3,1],[3,3,2]] => [[4,4,2,1,1],[3,1,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[5,5,4,4,1],[4,4,3,1]] => [[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)
[[5,5,4,3,1],[4,4,3]] => [[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)
[[6,6,5,4,1],[5,5,4,1]] => [[6,5,2,1,1],[5,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,3,3,3,1],[3,2,2]] => [[4,4,2,2,1],[3,1,1,1]] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[5,4,4,4,1],[4,3,3,1]] => [[5,4,2,2,1],[4,1,1,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[5,4,4,3,1],[4,3,3]] => [[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)
[[6,5,5,4,1],[5,4,4,1]] => [[6,5,2,2,1],[5,2,1,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,4,3,3,1],[4,3,2]] => [[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)
[[6,5,4,4,1],[5,4,3,1]] => [[6,5,3,2,1],[5,2,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,5,4,3,1],[5,4,3]] => [[6,6,3,2,1],[5,3,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,6,5,4,1],[6,5,4,1]] => [[7,6,3,2,1],[6,3,2,1]] => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[2,2,2,2,2],[1,1,1]] => [[2,2,1,1,1],[]] => ([],1)
[[3,3,3,3,2],[2,2,2,1]] => [[3,2,1,1,1],[1]] => ([(0,2),(2,1)],3)
[[4,4,4,4,2],[3,3,3,2]] => [[4,2,1,1,1],[2]] => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,2,2],[2,2,2]] => [[3,3,1,1,1],[1,1]] => ([(0,2),(2,1)],3)
[[4,4,4,3,2],[3,3,3,1]] => [[4,3,1,1,1],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[5,5,5,4,2],[4,4,4,2]] => [[5,3,1,1,1],[3,1]] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[3,3,2,2,2],[2,2,1]] => [[3,3,2,1,1],[1,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,3,3,2],[3,3,2,1]] => [[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)
[[5,5,4,4,2],[4,4,3,2]] => [[5,3,2,1,1],[3,1,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[4,4,3,2,2],[3,3,2]] => [[4,4,2,1,1],[2,2,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[5,5,4,3,2],[4,4,3,1]] => [[5,4,2,1,1],[3,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,6,5,4,2],[5,5,4,2]] => [[6,4,2,1,1],[4,2,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[3,2,2,2,2],[2,1,1]] => [[3,3,2,2,1],[1,1,1,1]] => ([(0,2),(2,1)],3)
[[4,3,3,3,2],[3,2,2,1]] => [[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)
[[5,4,4,4,2],[4,3,3,2]] => [[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)
[[4,3,3,2,2],[3,2,2]] => [[4,4,2,2,1],[2,2,1,1]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[5,4,4,3,2],[4,3,3,1]] => [[5,4,2,2,1],[3,2,1,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,5,4,2],[5,4,4,2]] => [[6,4,2,2,1],[4,2,1,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[4,3,2,2,2],[3,2,1]] => [[4,4,3,2,1],[2,2,2,1]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,4,3,3,2],[4,3,2,1]] => [[5,4,3,2,1],[3,2,2,1]] => ([(0,5),(0,6),(1,10),(2,10),(3,8),(4,8),(5,9),(6,9),(7,2),(9,1),(9,7),(10,3),(10,4)],11)
[[6,5,4,4,2],[5,4,3,2]] => [[6,4,3,2,1],[4,2,2,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[5,4,3,2,2],[4,3,2]] => [[5,5,3,2,1],[3,3,2,1]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[6,5,4,3,2],[5,4,3,1]] => [[6,5,3,2,1],[4,3,2,1]] => ([(0,8),(1,11),(2,10),(3,10),(4,11),(5,9),(6,9),(7,4),(8,2),(8,3),(10,1),(10,7),(11,5),(11,6)],12)
[[7,6,5,4,2],[6,5,4,2]] => [[7,5,3,2,1],[5,3,2,1]] => ([(0,8),(1,12),(2,11),(3,11),(4,12),(5,10),(6,10),(7,4),(8,9),(9,2),(9,3),(11,1),(11,7),(12,5),(12,6)],13)
[[2,2,2,2,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1]] => ([(0,2),(2,1)],3)
[[3,3,3,3,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,3,3,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,4,4,2,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,2]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,3,3,2,1,1],[2,2,2]] => [[3,3,3,1,1,1],[2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,4,4,3,2,1],[3,3,3,1,1]] => [[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)
[[4,4,4,3,1,1],[3,3,3,1]] => [[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)
[[5,5,5,4,2,1],[4,4,4,2,1]] => [[5,4,3,1,1,1],[4,3,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[3,3,2,2,1,1],[2,2,1]] => [[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)
[[4,4,3,3,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,1,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,4,3,3,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,1,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,4,4,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,1,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,4,3,2,1,1],[3,3,2]] => [[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)
[[5,5,4,3,2,1],[4,4,3,1,1]] => [[5,4,4,2,1,1],[4,3,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,5,4,3,1,1],[4,4,3,1]] => [[5,5,4,2,1,1],[4,4,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,6,5,4,2,1],[5,5,4,2,1]] => [[6,5,4,2,1,1],[5,4,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[3,2,2,2,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,1,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,3,3,2,1],[3,2,2,1,1]] => [[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)
[[4,3,3,3,1,1],[3,2,2,1]] => [[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)
[[5,4,4,4,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,1,1,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,3,3,2,1,1],[3,2,2]] => [[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)
[[5,4,4,3,2,1],[4,3,3,1,1]] => [[5,4,4,2,2,1],[4,3,2,1,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,4,3,1,1],[4,3,3,1]] => [[5,5,4,2,2,1],[4,4,2,1,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,5,4,2,1],[5,4,4,2,1]] => [[6,5,4,2,2,1],[5,4,2,1,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[4,3,2,2,1,1],[3,2,1]] => [[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)
[[5,4,3,3,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,2,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,3,3,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,2,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,4,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,2,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[5,4,3,2,1,1],[4,3,2]] => [[5,5,5,3,2,1],[4,4,3,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[6,5,4,3,2,1],[5,4,3,1,1]] => [[6,5,5,3,2,1],[5,4,3,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[6,5,4,3,1,1],[5,4,3,1]] => [[6,6,5,3,2,1],[5,5,3,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[7,6,5,4,2,1],[6,5,4,2,1]] => [[7,6,5,3,2,1],[6,5,3,2,1]] => ([(0,9),(1,13),(2,11),(3,11),(4,12),(5,12),(7,13),(8,1),(9,10),(10,4),(10,5),(11,6),(12,7),(12,8),(13,2),(13,3)],14)
[[3,3,3,3,3],[2,2,2,2]] => [[3,1,1,1,1],[]] => ([],1)
[[4,4,4,4,3],[3,3,3,3]] => [[4,1,1,1,1],[1]] => ([(0,1)],2)
[[4,4,4,3,3],[3,3,3,2]] => [[4,2,1,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4)
[[5,5,5,4,3],[4,4,4,3]] => [[5,2,1,1,1],[2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,3,3,3],[3,3,2,2]] => [[4,2,2,1,1],[1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,5,4,4,3],[4,4,3,3]] => [[5,2,2,1,1],[2,1,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[5,5,4,3,3],[4,4,3,2]] => [[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)
[[6,6,5,4,3],[5,5,4,3]] => [[6,3,2,1,1],[3,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[4,3,3,3,3],[3,2,2,2]] => [[4,2,2,2,1],[1,1,1,1]] => ([(0,2),(2,1)],3)
[[5,4,4,4,3],[4,3,3,3]] => [[5,2,2,2,1],[2,1,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,4,3,3],[4,3,3,2]] => [[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)
[[6,5,5,4,3],[5,4,4,3]] => [[6,3,2,2,1],[3,2,1,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[5,4,3,3,3],[4,3,2,2]] => [[5,3,3,2,1],[2,2,2,1]] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[6,5,4,4,3],[5,4,3,3]] => [[6,3,3,2,1],[3,2,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[6,5,4,3,3],[5,4,3,2]] => [[6,4,3,2,1],[3,3,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(5,8),(6,3),(7,1),(7,2),(8,4),(9,5),(9,6)],10)
[[7,6,5,4,3],[6,5,4,3]] => [[7,4,3,2,1],[4,3,2,1]] => ([(0,7),(1,10),(2,10),(3,9),(5,9),(6,3),(7,8),(8,1),(8,2),(9,4),(10,5),(10,6)],11)
[[2,2,2,2,2,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1]] => ([(0,1)],2)
[[3,3,3,3,3,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2]] => ([(0,2),(2,1)],3)
[[3,3,3,3,2,1],[2,2,2,2]] => [[3,3,1,1,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,4,4,3,1],[3,3,3,3,1]] => [[4,3,1,1,1,1],[3,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,3,2,2,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,1,1]] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[4,4,4,3,3,1],[3,3,3,2,1]] => [[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)
[[4,4,4,3,2,1],[3,3,3,2]] => [[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)
[[5,5,5,4,3,1],[4,4,4,3,1]] => [[5,4,2,1,1,1],[4,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[3,3,2,2,2,1],[2,2,1,1]] => [[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)
[[4,4,3,3,3,1],[3,3,2,2,1]] => [[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)
[[4,4,3,3,2,1],[3,3,2,2]] => [[4,4,2,2,1,1],[3,2,1,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,4,4,3,1],[4,4,3,3,1]] => [[5,4,2,2,1,1],[4,2,1,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,4,3,2,2,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,2,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,4,3,3,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,2,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,5,4,3,2,1],[4,4,3,2]] => [[5,5,3,2,1,1],[4,3,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,6,5,4,3,1],[5,5,4,3,1]] => [[6,5,3,2,1,1],[5,3,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[3,2,2,2,2,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,1,1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,3,3,3,3,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,1,1,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,3,3,3,2,1],[3,2,2,2]] => [[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)
[[5,4,4,4,3,1],[4,3,3,3,1]] => [[5,4,2,2,2,1],[4,2,1,1,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,3,3,2,2,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,2,2,1,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,4,3,3,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,2,2,1,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,4,3,2,1],[4,3,3,2]] => [[5,5,3,2,2,1],[4,3,2,1,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,5,4,3,1],[5,4,4,3,1]] => [[6,5,3,2,2,1],[5,3,2,1,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[4,3,2,2,2,1],[3,2,1,1]] => [[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)
[[5,4,3,3,3,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,2,2,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,3,3,2,1],[4,3,2,2]] => [[5,5,3,3,2,1],[4,3,2,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,4,3,1],[5,4,3,3,1]] => [[6,5,3,3,2,1],[5,3,2,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[5,4,3,2,2,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,3,3,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,3,3,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,3,3,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[6,5,4,3,2,1],[5,4,3,2]] => [[6,6,4,3,2,1],[5,4,3,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[7,6,5,4,3,1],[6,5,4,3,1]] => [[7,6,4,3,2,1],[6,4,3,2,1]] => ([(0,9),(1,13),(2,11),(3,11),(4,12),(5,12),(7,13),(8,1),(9,10),(10,4),(10,5),(11,6),(12,7),(12,8),(13,2),(13,3)],14)
[[2,2,2,2,2,2],[1,1,1,1,1]] => [[2,1,1,1,1,1],[]] => ([],1)
[[3,3,3,3,3,2],[2,2,2,2,2]] => [[3,1,1,1,1,1],[1]] => ([(0,1)],2)
[[3,3,3,3,2,2],[2,2,2,2,1]] => [[3,2,1,1,1,1],[1,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,4,4,4,3,2],[3,3,3,3,2]] => [[4,2,1,1,1,1],[2,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,3,2,2,2],[2,2,2,1,1]] => [[3,2,2,1,1,1],[1,1,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[4,4,4,3,3,2],[3,3,3,2,2]] => [[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)
[[4,4,4,3,2,2],[3,3,3,2,1]] => [[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)
[[5,5,5,4,3,2],[4,4,4,3,2]] => [[5,3,2,1,1,1],[3,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[3,3,2,2,2,2],[2,2,1,1,1]] => [[3,2,2,2,1,1],[1,1,1,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,3,3,3,2],[3,3,2,2,2]] => [[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)
[[4,4,3,3,2,2],[3,3,2,2,1]] => [[4,3,2,2,1,1],[2,2,1,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,5,4,4,3,2],[4,4,3,3,2]] => [[5,3,2,2,1,1],[3,2,1,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[4,4,3,2,2,2],[3,3,2,1,1]] => [[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)
[[5,5,4,3,3,2],[4,4,3,2,2]] => [[5,3,3,2,1,1],[3,2,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,5,4,3,2,2],[4,4,3,2,1]] => [[5,4,3,2,1,1],[3,3,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,6,5,4,3,2],[5,5,4,3,2]] => [[6,4,3,2,1,1],[4,3,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[3,2,2,2,2,2],[2,1,1,1,1]] => [[3,2,2,2,2,1],[1,1,1,1,1]] => ([(0,2),(2,1)],3)
[[4,3,3,3,3,2],[3,2,2,2,2]] => [[4,2,2,2,2,1],[2,1,1,1,1]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,3,3,2,2],[3,2,2,2,1]] => [[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)
[[5,4,4,4,3,2],[4,3,3,3,2]] => [[5,3,2,2,2,1],[3,2,1,1,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[4,3,3,2,2,2],[3,2,2,1,1]] => [[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)
[[5,4,4,3,3,2],[4,3,3,2,2]] => [[5,3,3,2,2,1],[3,2,2,1,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[5,4,4,3,2,2],[4,3,3,2,1]] => [[5,4,3,2,2,1],[3,3,2,1,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,5,4,3,2],[5,4,4,3,2]] => [[6,4,3,2,2,1],[4,3,2,1,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[4,3,2,2,2,2],[3,2,1,1,1]] => [[4,3,3,3,2,1],[2,2,2,2,1]] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[5,4,3,3,3,2],[4,3,2,2,2]] => [[5,3,3,3,2,1],[3,2,2,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[5,4,3,3,2,2],[4,3,2,2,1]] => [[5,4,3,3,2,1],[3,3,2,2,1]] => ([(0,6),(0,7),(1,11),(2,9),(3,9),(5,11),(6,10),(7,10),(8,1),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
[[6,5,4,4,3,2],[5,4,3,3,2]] => [[6,4,3,3,2,1],[4,3,2,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[5,4,3,2,2,2],[4,3,2,1,1]] => [[5,4,4,3,2,1],[3,3,3,2,1]] => ([(0,7),(1,9),(2,9),(3,8),(4,8),(6,2),(7,1),(7,6),(8,5),(9,3),(9,4)],10)
[[6,5,4,3,3,2],[5,4,3,2,2]] => [[6,4,4,3,2,1],[4,3,3,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[6,5,4,3,2,2],[5,4,3,2,1]] => [[6,5,4,3,2,1],[4,4,3,2,1]] => ([(0,9),(1,12),(2,10),(3,10),(4,11),(5,11),(7,12),(8,1),(9,4),(9,5),(10,6),(11,7),(11,8),(12,2),(12,3)],13)
[[7,6,5,4,3,2],[6,5,4,3,2]] => [[7,5,4,3,2,1],[5,4,3,2,1]] => ([(0,9),(1,13),(2,11),(3,11),(4,12),(5,12),(7,13),(8,1),(9,10),(10,4),(10,5),(11,6),(12,7),(12,8),(13,2),(13,3)],14)
[[1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1],[]] => ([],1)
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [[2,1,1,1,1,1,1],[1]] => ([(0,1)],2)
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => [[2,2,1,1,1,1,1],[1,1]] => ([(0,2),(2,1)],3)
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [[3,2,1,1,1,1,1],[2,1]] => ([(0,3),(2,1),(3,2)],4)
[[2,2,2,2,1,1,1],[1,1,1,1]] => [[2,2,2,1,1,1,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [[3,2,2,1,1,1,1],[2,1,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => [[3,3,2,1,1,1,1],[2,2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [[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)
[[2,2,2,1,1,1,1],[1,1,1]] => [[2,2,2,2,1,1,1],[1,1,1,1]] => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [[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)
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => [[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)
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [[4,3,2,2,1,1,1],[3,2,1,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)
[[3,3,3,2,1,1,1],[2,2,2,1]] => [[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)
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [[4,3,3,2,1,1,1],[3,2,2,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)
[[4,4,4,3,2,1,1],[3,3,3,2,1]] => [[4,4,3,2,1,1,1],[3,3,2,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)
[[5,5,5,4,3,2,1],[4,4,4,3,2,1]] => [[5,4,3,2,1,1,1],[4,3,2,1]] => ([(0,8),(2,10),(3,10),(4,9),(5,9),(6,3),(7,1),(8,2),(8,6),(9,7),(10,4),(10,5)],11)
[[2,2,1,1,1,1,1],[1,1]] => [[2,2,2,2,2,1,1],[1,1,1,1,1]] => ([(0,2),(2,1)],3)
[[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => [[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)
[[3,3,2,2,2,1,1],[2,2,1,1,1]] => [[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)
[[4,4,3,3,3,2,1],[3,3,2,2,2,1]] => [[4,3,2,2,2,1,1],[3,2,1,1,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)
[[3,3,2,2,1,1,1],[2,2,1,1]] => [[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)
[[4,4,3,3,2,2,1],[3,3,2,2,1,1]] => [[4,3,3,2,2,1,1],[3,2,2,1,1]] => ([(0,8),(2,10),(3,10),(4,9),(5,9),(6,3),(7,1),(8,2),(8,6),(9,7),(10,4),(10,5)],11)
[[4,4,3,3,2,1,1],[3,3,2,2,1]] => [[4,4,3,2,2,1,1],[3,3,2,1,1]] => ([(0,8),(2,10),(3,10),(4,9),(5,9),(6,3),(7,1),(8,2),(8,6),(9,7),(10,4),(10,5)],11)
[[5,5,4,4,3,2,1],[4,4,3,3,2,1]] => [[5,4,3,2,2,1,1],[4,3,2,1,1]] => ([(0,6),(0,7),(2,12),(3,12),(4,10),(5,10),(6,11),(7,11),(8,3),(9,1),(10,9),(11,2),(11,8),(12,4),(12,5)],13)
[[3,3,2,1,1,1,1],[2,2,1]] => [[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)
[[4,4,3,2,2,2,1],[3,3,2,1,1,1]] => [[4,3,3,3,2,1,1],[3,2,2,2,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)
[[4,4,3,2,2,1,1],[3,3,2,1,1]] => [[4,4,3,3,2,1,1],[3,3,2,2,1]] => ([(0,8),(2,10),(3,10),(4,9),(5,9),(6,3),(7,1),(8,2),(8,6),(9,7),(10,4),(10,5)],11)
[[5,5,4,3,3,2,1],[4,4,3,2,2,1]] => [[5,4,3,3,2,1,1],[4,3,2,2,1]] => ([(0,6),(0,7),(2,12),(3,12),(4,10),(5,10),(6,11),(7,11),(8,3),(9,1),(10,9),(11,2),(11,8),(12,4),(12,5)],13)
[[4,4,3,2,1,1,1],[3,3,2,1]] => [[4,4,4,3,2,1,1],[3,3,3,2,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)
[[5,5,4,3,2,2,1],[4,4,3,2,1,1]] => [[5,4,4,3,2,1,1],[4,3,3,2,1]] => ([(0,6),(0,7),(2,12),(3,12),(4,10),(5,10),(6,11),(7,11),(8,3),(9,1),(10,9),(11,2),(11,8),(12,4),(12,5)],13)
[[5,5,4,3,2,1,1],[4,4,3,2,1]] => [[5,5,4,3,2,1,1],[4,4,3,2,1]] => ([(0,6),(0,7),(2,12),(3,12),(4,10),(5,10),(6,11),(7,11),(8,3),(9,1),(10,9),(11,2),(11,8),(12,4),(12,5)],13)
[[6,6,5,4,3,2,1],[5,5,4,3,2,1]] => [[6,5,4,3,2,1,1],[5,4,3,2,1]] => ([(0,10),(2,13),(3,12),(4,12),(5,13),(6,11),(7,11),(8,5),(9,1),(10,3),(10,4),(11,9),(12,2),(12,8),(13,6),(13,7)],14)
[[2,1,1,1,1,1,1],[1]] => [[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => ([(0,1)],2)
[[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => [[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => ([(0,3),(2,1),(3,2)],4)
[[3,2,2,2,2,1,1],[2,1,1,1,1]] => [[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)
[[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => [[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)
[[3,2,2,2,1,1,1],[2,1,1,1]] => [[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)
[[4,3,3,3,2,2,1],[3,2,2,2,1,1]] => [[4,3,3,2,2,2,1],[3,2,2,1,1,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)
[[4,3,3,3,2,1,1],[3,2,2,2,1]] => [[4,4,3,2,2,2,1],[3,3,2,1,1,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)
[[5,4,4,4,3,2,1],[4,3,3,3,2,1]] => [[5,4,3,2,2,2,1],[4,3,2,1,1,1]] => ([(0,8),(2,10),(3,10),(4,9),(5,9),(6,3),(7,1),(8,2),(8,6),(9,7),(10,4),(10,5)],11)
[[3,2,2,1,1,1,1],[2,1,1]] => [[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)
[[4,3,3,2,2,2,1],[3,2,2,1,1,1]] => [[4,3,3,3,2,2,1],[3,2,2,2,1,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)
[[4,3,3,2,2,1,1],[3,2,2,1,1]] => [[4,4,3,3,2,2,1],[3,3,2,2,1,1]] => ([(0,8),(2,10),(3,10),(4,9),(5,9),(6,3),(7,1),(8,2),(8,6),(9,7),(10,4),(10,5)],11)
[[5,4,4,3,3,2,1],[4,3,3,2,2,1]] => [[5,4,3,3,2,2,1],[4,3,2,2,1,1]] => ([(0,6),(0,7),(2,12),(3,12),(4,10),(5,10),(6,11),(7,11),(8,3),(9,1),(10,9),(11,2),(11,8),(12,4),(12,5)],13)
[[4,3,3,2,1,1,1],[3,2,2,1]] => [[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)
[[5,4,4,3,2,2,1],[4,3,3,2,1,1]] => [[5,4,4,3,2,2,1],[4,3,3,2,1,1]] => ([(0,6),(0,7),(2,12),(3,12),(4,10),(5,10),(6,11),(7,11),(8,3),(9,1),(10,9),(11,2),(11,8),(12,4),(12,5)],13)
[[5,4,4,3,2,1,1],[4,3,3,2,1]] => [[5,5,4,3,2,2,1],[4,4,3,2,1,1]] => ([(0,6),(0,7),(2,12),(3,12),(4,10),(5,10),(6,11),(7,11),(8,3),(9,1),(10,9),(11,2),(11,8),(12,4),(12,5)],13)
[[6,5,5,4,3,2,1],[5,4,4,3,2,1]] => [[6,5,4,3,2,2,1],[5,4,3,2,1,1]] => ([(0,10),(2,13),(3,12),(4,12),(5,13),(6,11),(7,11),(8,5),(9,1),(10,3),(10,4),(11,9),(12,2),(12,8),(13,6),(13,7)],14)
[[3,2,1,1,1,1,1],[2,1]] => [[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => ([(0,3),(2,1),(3,2)],4)
[[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => [[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)
[[4,3,2,2,2,1,1],[3,2,1,1,1]] => [[4,4,3,3,3,2,1],[3,3,2,2,2,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)
[[5,4,3,3,3,2,1],[4,3,2,2,2,1]] => [[5,4,3,3,3,2,1],[4,3,2,2,2,1]] => ([(0,8),(2,10),(3,10),(4,9),(5,9),(6,3),(7,1),(8,2),(8,6),(9,7),(10,4),(10,5)],11)
[[4,3,2,2,1,1,1],[3,2,1,1]] => [[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => ([(0,5),(0,7),(1,9),(3,8),(4,8),(5,9),(6,2),(7,1),(8,6),(9,3),(9,4)],10)
[[5,4,3,3,2,2,1],[4,3,2,2,1,1]] => [[5,4,4,3,3,2,1],[4,3,3,2,2,1]] => ([(0,6),(0,7),(2,12),(3,12),(4,10),(5,10),(6,11),(7,11),(8,3),(9,1),(10,9),(11,2),(11,8),(12,4),(12,5)],13)
[[5,4,3,3,2,1,1],[4,3,2,2,1]] => [[5,5,4,3,3,2,1],[4,4,3,2,2,1]] => ([(0,6),(0,7),(2,12),(3,12),(4,10),(5,10),(6,11),(7,11),(8,3),(9,1),(10,9),(11,2),(11,8),(12,4),(12,5)],13)
[[6,5,4,4,3,2,1],[5,4,3,3,2,1]] => [[6,5,4,3,3,2,1],[5,4,3,2,2,1]] => ([(0,10),(2,13),(3,12),(4,12),(5,13),(6,11),(7,11),(8,5),(9,1),(10,3),(10,4),(11,9),(12,2),(12,8),(13,6),(13,7)],14)
[[4,3,2,1,1,1,1],[3,2,1]] => [[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)
[[5,4,3,2,2,2,1],[4,3,2,1,1,1]] => [[5,4,4,4,3,2,1],[4,3,3,3,2,1]] => ([(0,8),(2,10),(3,10),(4,9),(5,9),(6,3),(7,1),(8,2),(8,6),(9,7),(10,4),(10,5)],11)
[[5,4,3,2,2,1,1],[4,3,2,1,1]] => [[5,5,4,4,3,2,1],[4,4,3,3,2,1]] => ([(0,6),(0,7),(2,12),(3,12),(4,10),(5,10),(6,11),(7,11),(8,3),(9,1),(10,9),(11,2),(11,8),(12,4),(12,5)],13)
[[6,5,4,3,3,2,1],[5,4,3,2,2,1]] => [[6,5,4,4,3,2,1],[5,4,3,3,2,1]] => ([(0,10),(2,13),(3,12),(4,12),(5,13),(6,11),(7,11),(8,5),(9,1),(10,3),(10,4),(11,9),(12,2),(12,8),(13,6),(13,7)],14)
[[5,4,3,2,1,1,1],[4,3,2,1]] => [[5,5,5,4,3,2,1],[4,4,4,3,2,1]] => ([(0,8),(2,10),(3,10),(4,9),(5,9),(6,3),(7,1),(8,2),(8,6),(9,7),(10,4),(10,5)],11)
[[6,5,4,3,2,2,1],[5,4,3,2,1,1]] => [[6,5,5,4,3,2,1],[5,4,4,3,2,1]] => ([(0,10),(2,13),(3,12),(4,12),(5,13),(6,11),(7,11),(8,5),(9,1),(10,3),(10,4),(11,9),(12,2),(12,8),(13,6),(13,7)],14)
[[6,5,4,3,2,1,1],[5,4,3,2,1]] => [[6,6,5,4,3,2,1],[5,5,4,3,2,1]] => ([(0,10),(2,13),(3,12),(4,12),(5,13),(6,11),(7,11),(8,5),(9,1),(10,3),(10,4),(11,9),(12,2),(12,8),(13,6),(13,7)],14)
[[7,6,5,4,3,2,1],[6,5,4,3,2,1]] => [[7,6,5,4,3,2,1],[6,5,4,3,2,1]] => ([(0,10),(2,14),(3,13),(4,13),(5,14),(6,12),(7,12),(8,5),(9,1),(10,11),(11,3),(11,4),(12,9),(13,2),(13,8),(14,6),(14,7)],15)
[[8],[]] => [[8],[]] => ([],1)
[[6,2],[]] => [[6,6],[4]] => ([],1)
[[5,3],[]] => [[5,5],[2]] => ([],1)
[[4,4],[]] => [[4,4],[]] => ([],1)
[[4,3,1],[]] => [[4,4,4],[3,1]] => ([],1)
[[4,2,2],[]] => [[4,4,4],[2,2]] => ([],1)
[[4,1,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,3]] => ([],1)
[[3,3,2],[]] => [[3,3,3],[1]] => ([],1)
[[3,3,1,1],[]] => [[3,3,3,3],[2,2]] => ([],1)
[[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]] => ([],1)
[[2,2,2,2],[]] => [[2,2,2,2],[]] => ([],1)
[[2,2,2,1,1],[]] => [[2,2,2,2,2],[1,1]] => ([],1)
[[1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1],[]] => ([],1)
[[9],[]] => [[9],[]] => ([],1)
[[6,3],[]] => [[6,6],[3]] => ([],1)
[[5,4],[]] => [[5,5],[1]] => ([],1)
[[5,2,2],[]] => [[5,5,5],[3,3]] => ([],1)
[[4,4,1],[]] => [[4,4,4],[3]] => ([],1)
[[4,3,2],[]] => [[4,4,4],[2,1]] => ([],1)
[[3,3,3],[]] => [[3,3,3],[]] => ([],1)
[[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => ([],1)
[[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]] => ([],1)
[[2,2,2,2,1],[]] => [[2,2,2,2,2],[1]] => ([],1)
[[1,1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1,1],[]] => ([],1)
[[10],[]] => [[10],[]] => ([],1)
[[6,4],[]] => [[6,6],[2]] => ([],1)
[[5,5],[]] => [[5,5],[]] => ([],1)
[[5,3,2],[]] => [[5,5,5],[3,2]] => ([],1)
[[4,4,2],[]] => [[4,4,4],[2]] => ([],1)
[[4,3,3],[]] => [[4,4,4],[1,1]] => ([],1)
[[4,2,2,2],[]] => [[4,4,4,4],[2,2,2]] => ([],1)
[[3,3,3,1],[]] => [[3,3,3,3],[2]] => ([],1)
[[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => ([],1)
[[2,2,2,2,2],[]] => [[2,2,2,2,2],[]] => ([],1)
[[1,1,1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1,1,1],[]] => ([],1)
[[6,5],[]] => [[6,6],[1]] => ([],1)
[[5,5,1],[]] => [[5,5,5],[4]] => ([],1)
[[5,4,2],[]] => [[5,5,5],[3,1]] => ([],1)
[[5,3,3],[]] => [[5,5,5],[2,2]] => ([],1)
[[4,4,3],[]] => [[4,4,4],[1]] => ([],1)
[[4,4,2,1],[]] => [[4,4,4,4],[3,2]] => ([],1)
[[4,3,3,1],[]] => [[4,4,4,4],[3,1,1]] => ([],1)
[[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]] => ([],1)
[[3,3,3,2],[]] => [[3,3,3,3],[1]] => ([],1)
[[3,2,2,2,2],[]] => [[3,3,3,3,3],[1,1,1,1]] => ([],1)
[[6,6],[]] => [[6,6],[]] => ([],1)
[[5,5,2],[]] => [[5,5,5],[3]] => ([],1)
[[5,4,3],[]] => [[5,5,5],[2,1]] => ([],1)
[[4,4,4],[]] => [[4,4,4],[]] => ([],1)
[[4,4,3,1],[]] => [[4,4,4,4],[3,1]] => ([],1)
[[4,4,2,2],[]] => [[4,4,4,4],[2,2]] => ([],1)
[[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]] => ([],1)
[[3,3,3,3],[]] => [[3,3,3,3],[]] => ([],1)
[[3,3,3,2,1],[]] => [[3,3,3,3,3],[2,1]] => ([],1)
[[3,3,2,2,2],[]] => [[3,3,3,3,3],[1,1,1]] => ([],1)
[[2,2,2,2,2,2],[]] => [[2,2,2,2,2,2],[]] => ([],1)
[[5,5,3],[]] => [[5,5,5],[2]] => ([],1)
[[5,4,4],[]] => [[5,5,5],[1,1]] => ([],1)
[[4,4,4,1],[]] => [[4,4,4,4],[3]] => ([],1)
[[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => ([],1)
[[4,3,3,3],[]] => [[4,4,4,4],[1,1,1]] => ([],1)
[[3,3,3,3,1],[]] => [[3,3,3,3,3],[2]] => ([],1)
[[3,3,3,2,2],[]] => [[3,3,3,3,3],[1,1]] => ([],1)
[[5,5,4],[]] => [[5,5,5],[1]] => ([],1)
[[4,4,4,2],[]] => [[4,4,4,4],[2]] => ([],1)
[[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => ([],1)
[[3,3,3,3,2],[]] => [[3,3,3,3,3],[1]] => ([],1)
[[5,5,5],[]] => [[5,5,5],[]] => ([],1)
[[4,4,4,3],[]] => [[4,4,4,4],[1]] => ([],1)
[[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => ([],1)
[[4,4,4,4],[]] => [[4,4,4,4],[]] => ([],1)
[[3,3,3],[1]] => [[3,3,2],[]] => ([],1)
[[3,3,3,1],[1,1]] => [[3,3,2,2],[2]] => ([(0,1)],2)
[[4,4,1],[1]] => [[4,4,3],[3]] => ([(0,1)],2)
[[3,3,2,1],[1]] => [[3,3,3,2],[2,1]] => ([(0,2),(2,1)],3)
[[2,2,2,2,1],[1]] => [[2,2,2,2,1],[1]] => ([(0,1)],2)
[[3,3,3,1],[2]] => [[3,3,3,1],[2]] => ([(0,1)],2)
[[3,3,3,1],[1]] => [[3,3,3,2],[2]] => ([(0,1)],2)
[[3,3,3,2],[1,1,1]] => [[3,2,2,2],[1]] => ([(0,1)],2)
[[4,4,2],[1,1]] => [[4,3,3],[2]] => ([(0,1)],2)
[[4,4,4],[2,2]] => [[4,2,2],[]] => ([],1)
[[5,5],[2]] => [[5,3],[]] => ([],1)
[[4,4,3],[2,1]] => [[4,3,2],[1]] => ([(0,2),(2,1)],3)
[[3,3,3,3],[2,1,1]] => [[3,2,2,1],[]] => ([],1)
[[4,3,3],[1,1]] => [[4,3,3],[1,1]] => ([(0,1)],2)
[[3,3,3,3],[1,1,1]] => [[3,2,2,2],[]] => ([],1)
[[4,4,3],[1,1]] => [[4,3,3],[1]] => ([(0,1)],2)
[[4,4,4],[3,1]] => [[4,3,1],[]] => ([],1)
[[5,4],[1]] => [[5,4],[1]] => ([(0,1)],2)
[[4,4,4],[2,1]] => [[4,3,2],[]] => ([],1)
[[5,5],[1]] => [[5,4],[]] => ([],1)
[[4,4,4],[1,1]] => [[4,3,3],[]] => ([],1)
[[3,3,2,2],[1,1]] => [[3,3,2,2],[1,1]] => ([(0,2),(2,1)],3)
[[4,4,2],[2]] => [[4,4,2],[2]] => ([(0,2),(2,1)],3)
[[3,3,3,2],[2,1]] => [[3,3,2,1],[1]] => ([(0,2),(2,1)],3)
[[4,3,2],[1]] => [[4,4,3],[2,1]] => ([(0,2),(2,1)],3)
[[3,3,3,2],[1,1]] => [[3,3,2,2],[1]] => ([(0,1)],2)
[[4,4,2],[1]] => [[4,4,3],[2]] => ([(0,1)],2)
[[2,2,2,2,2],[1,1]] => [[2,2,2,1,1],[]] => ([],1)
[[3,2,2,2],[1]] => [[3,3,3,2],[1,1,1]] => ([(0,1)],2)
[[3,3,2,2],[2]] => [[3,3,3,1],[1,1]] => ([(0,1)],2)
[[3,3,2,2],[1]] => [[3,3,3,2],[1,1]] => ([(0,1)],2)
[[2,2,2,2,2],[1]] => [[2,2,2,2,1],[]] => ([],1)
[[3,3,3,2],[2]] => [[3,3,3,1],[1]] => ([(0,1)],2)
[[3,3,3,2],[1]] => [[3,3,3,2],[1]] => ([(0,1)],2)
[[3,3,3,3],[2,2]] => [[3,3,1,1],[]] => ([],1)
[[4,3,3],[2]] => [[4,4,2],[1,1]] => ([(0,1)],2)
[[4,4,3],[3]] => [[4,4,1],[1]] => ([(0,1)],2)
[[4,4,3],[2]] => [[4,4,2],[1]] => ([(0,1)],2)
[[3,3,3,3],[2,1]] => [[3,3,2,1],[]] => ([],1)
[[4,3,3],[1]] => [[4,4,3],[1,1]] => ([(0,1)],2)
[[3,3,3,3],[1,1]] => [[3,3,2,2],[]] => ([],1)
[[4,4,3],[1]] => [[4,4,3],[1]] => ([(0,1)],2)
[[4,4,4],[3]] => [[4,4,1],[]] => ([],1)
[[4,4,4],[2]] => [[4,4,2],[]] => ([],1)
[[4,4,4],[1]] => [[4,4,3],[]] => ([],1)
[[3,3,3,3],[2]] => [[3,3,3,1],[]] => ([],1)
[[3,3,3,3],[1]] => [[3,3,3,2],[]] => ([],1)
Map
rotate
Description
The rotation of a skew partition.
This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition $\lambda/\mu$, its rotation $(\lambda/\mu)^\natural$ is the skew partition with cells $\{(a-i, b-j)| (i, j) \in \lambda/\mu\}$, where $b$ and $a$ are the first part and the number of parts of $\lambda$ respectively.
This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition $\lambda/\mu$, its rotation $(\lambda/\mu)^\natural$ is the skew partition with cells $\{(a-i, b-j)| (i, j) \in \lambda/\mu\}$, where $b$ and $a$ are the first part and the number of parts of $\lambda$ respectively.
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.
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.
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