edit this map or download as text // json
Identifier
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Images
=>
Cc0028;cc-rep-0Cc0029;cc-rep-1
[[1],[]]=>([],1) [[2],[]]=>([],1) [[1,1],[]]=>([],1) [[2,1],[1]]=>([(0,1)],2) [[3],[]]=>([],1) [[2,1],[]]=>([],1) [[3,1],[1]]=>([(0,1)],2) [[2,2],[1]]=>([],1) [[3,2],[2]]=>([(0,1)],2) [[1,1,1],[]]=>([],1) [[2,2,1],[1,1]]=>([(0,1)],2) [[2,1,1],[1]]=>([(0,1)],2) [[3,2,1],[2,1]]=>([(0,2),(2,1)],3) [[4],[]]=>([],1) [[3,1],[]]=>([],1) [[4,1],[1]]=>([(0,1)],2) [[2,2],[]]=>([],1) [[3,2],[1]]=>([(0,1)],2) [[4,2],[2]]=>([(0,2),(2,1)],3) [[2,1,1],[]]=>([],1) [[3,2,1],[1,1]]=>([(0,2),(2,1)],3) [[3,1,1],[1]]=>([(0,1)],2) [[4,2,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[3,3],[2]]=>([],1) [[4,3],[3]]=>([(0,1)],2) [[2,2,1],[1]]=>([(0,1)],2) [[3,3,1],[2,1]]=>([(0,2),(2,1)],3) [[3,2,1],[2]]=>([(0,2),(2,1)],3) [[4,3,1],[3,1]]=>([(0,3),(2,1),(3,2)],4) [[2,2,2],[1,1]]=>([],1) [[3,3,2],[2,2]]=>([(0,1)],2) [[3,2,2],[2,1]]=>([(0,2),(2,1)],3) [[4,3,2],[3,2]]=>([(0,3),(2,1),(3,2)],4) [[1,1,1,1],[]]=>([],1) [[2,2,2,1],[1,1,1]]=>([(0,1)],2) [[2,2,1,1],[1,1]]=>([(0,2),(2,1)],3) [[3,3,2,1],[2,2,1]]=>([(0,3),(2,1),(3,2)],4) [[2,1,1,1],[1]]=>([(0,1)],2) [[3,2,2,1],[2,1,1]]=>([(0,3),(2,1),(3,2)],4) [[3,2,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,3,2,1],[3,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5],[]]=>([],1) [[4,1],[]]=>([],1) [[5,1],[1]]=>([(0,1)],2) [[3,2],[]]=>([],1) [[4,2],[1]]=>([(0,1)],2) [[5,2],[2]]=>([(0,2),(2,1)],3) [[3,1,1],[]]=>([],1) [[4,2,1],[1,1]]=>([(0,2),(2,1)],3) [[4,1,1],[1]]=>([(0,1)],2) [[5,2,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[3,3],[1]]=>([],1) [[4,3],[2]]=>([(0,1)],2) [[5,3],[3]]=>([(0,2),(2,1)],3) [[2,2,1],[]]=>([],1) [[3,3,1],[1,1]]=>([(0,1)],2) [[3,2,1],[1]]=>([(0,2),(2,1)],3) [[4,3,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,2,1],[2]]=>([(0,3),(2,1),(3,2)],4) [[5,3,1],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[3,2,2],[1,1]]=>([(0,1)],2) [[4,3,2],[2,2]]=>([(0,3),(2,1),(3,2)],4) [[4,2,2],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[5,3,2],[3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[2,1,1,1],[]]=>([],1) [[3,2,2,1],[1,1,1]]=>([(0,2),(2,1)],3) [[3,2,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4) [[4,3,2,1],[2,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[3,1,1,1],[1]]=>([(0,1)],2) [[4,2,2,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,2,1,1],[2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,3,2,1],[3,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[4,4],[3]]=>([],1) [[5,4],[4]]=>([(0,1)],2) [[3,3,1],[2]]=>([(0,1)],2) [[4,4,1],[3,1]]=>([(0,2),(2,1)],3) [[4,3,1],[3]]=>([(0,2),(2,1)],3) [[5,4,1],[4,1]]=>([(0,3),(2,1),(3,2)],4) [[2,2,2],[1]]=>([],1) [[3,3,2],[2,1]]=>([(0,2),(2,1)],3) [[4,4,2],[3,2]]=>([(0,3),(2,1),(3,2)],4) [[3,2,2],[2]]=>([(0,1)],2) [[4,3,2],[3,1]]=>([(0,3),(2,1),(3,2)],4) [[5,4,2],[4,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[2,2,1,1],[1]]=>([(0,1)],2) [[3,3,2,1],[2,1,1]]=>([(0,3),(2,1),(3,2)],4) [[3,3,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,4,2,1],[3,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[3,2,1,1],[2]]=>([(0,2),(2,1)],3) [[4,3,2,1],[3,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,3,1,1],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,4,2,1],[4,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[3,3,3],[2,2]]=>([],1) [[4,4,3],[3,3]]=>([(0,1)],2) [[4,3,3],[3,2]]=>([(0,2),(2,1)],3) [[5,4,3],[4,3]]=>([(0,3),(2,1),(3,2)],4) [[2,2,2,1],[1,1]]=>([(0,1)],2) [[3,3,3,1],[2,2,1]]=>([(0,2),(2,1)],3) [[3,3,2,1],[2,2]]=>([(0,3),(2,1),(3,2)],4) [[4,4,3,1],[3,3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[3,2,2,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,3,3,1],[3,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,3,2,1],[3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,4,3,1],[4,3,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[2,2,2,2],[1,1,1]]=>([],1) [[3,3,3,2],[2,2,2]]=>([(0,1)],2) [[3,3,2,2],[2,2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,4,3,2],[3,3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[3,2,2,2],[2,1,1]]=>([(0,2),(2,1)],3) [[4,3,3,2],[3,2,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,3,2,2],[3,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,4,3,2],[4,3,2]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[1,1,1,1,1],[]]=>([],1) [[2,2,2,2,1],[1,1,1,1]]=>([(0,1)],2) [[2,2,2,1,1],[1,1,1]]=>([(0,2),(2,1)],3) [[3,3,3,2,1],[2,2,2,1]]=>([(0,3),(2,1),(3,2)],4) [[2,2,1,1,1],[1,1]]=>([(0,2),(2,1)],3) [[3,3,2,2,1],[2,2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[3,3,2,1,1],[2,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,4,3,2,1],[3,3,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[2,1,1,1,1],[1]]=>([(0,1)],2) [[3,2,2,2,1],[2,1,1,1]]=>([(0,3),(2,1),(3,2)],4) [[3,2,2,1,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,3,3,2,1],[3,2,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[3,2,1,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,3,2,2,1],[3,2,1,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[4,3,2,1,1],[3,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[5,4,3,2,1],[4,3,2,1]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[6],[]]=>([],1) [[5,1],[]]=>([],1) [[6,1],[1]]=>([(0,1)],2) [[4,2],[]]=>([],1) [[5,2],[1]]=>([(0,1)],2) [[6,2],[2]]=>([(0,2),(2,1)],3) [[4,1,1],[]]=>([],1) [[5,2,1],[1,1]]=>([(0,2),(2,1)],3) [[5,1,1],[1]]=>([(0,1)],2) [[6,2,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[3,3],[]]=>([],1) [[4,3],[1]]=>([(0,1)],2) [[5,3],[2]]=>([(0,2),(2,1)],3) [[6,3],[3]]=>([(0,3),(2,1),(3,2)],4) [[3,2,1],[]]=>([],1) [[4,3,1],[1,1]]=>([(0,2),(2,1)],3) [[4,2,1],[1]]=>([(0,2),(2,1)],3) [[5,3,1],[2,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[5,2,1],[2]]=>([(0,3),(2,1),(3,2)],4) [[6,3,1],[3,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[4,2,2],[1,1]]=>([(0,1)],2) [[5,3,2],[2,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[5,2,2],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[6,3,2],[3,2]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[3,1,1,1],[]]=>([],1) [[4,2,2,1],[1,1,1]]=>([(0,2),(2,1)],3) [[4,2,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4) [[5,3,2,1],[2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[4,1,1,1],[1]]=>([(0,1)],2) [[5,2,2,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,2,1,1],[2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[6,3,2,1],[3,2,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[4,4],[2]]=>([],1) [[5,4],[3]]=>([(0,1)],2) [[6,4],[4]]=>([(0,2),(2,1)],3) [[3,3,1],[1]]=>([(0,1)],2) [[4,4,1],[2,1]]=>([(0,2),(2,1)],3) [[4,3,1],[2]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[5,4,1],[3,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[5,3,1],[3]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[6,4,1],[4,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[2,2,2],[]]=>([],1) [[3,3,2],[1,1]]=>([(0,1)],2) [[4,4,2],[2,2]]=>([(0,2),(2,1)],3) [[3,2,2],[1]]=>([(0,1)],2) [[4,3,2],[2,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[5,4,2],[3,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[4,2,2],[2]]=>([(0,2),(2,1)],3) [[5,3,2],[3,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[6,4,2],[4,2]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[2,2,1,1],[]]=>([],1) [[3,3,2,1],[1,1,1]]=>([(0,2),(2,1)],3) [[3,3,1,1],[1,1]]=>([(0,2),(2,1)],3) [[4,4,2,1],[2,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[3,2,1,1],[1]]=>([(0,2),(2,1)],3) [[4,3,2,1],[2,1,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[4,3,1,1],[2,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[5,4,2,1],[3,2,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) [[4,2,1,1],[2]]=>([(0,3),(2,1),(3,2)],4) [[5,3,2,1],[3,1,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) [[5,3,1,1],[3,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[6,4,2,1],[4,2,1]]=>([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9) [[4,3,3],[2,2]]=>([(0,1)],2) [[5,4,3],[3,3]]=>([(0,3),(2,1),(3,2)],4) [[5,3,3],[3,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[6,4,3],[4,3]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[3,2,2,1],[1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[4,3,3,1],[2,2,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[4,3,2,1],[2,2]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[5,4,3,1],[3,3,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) [[4,2,2,1],[2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[5,3,3,1],[3,2,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) [[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) [[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) [[3,2,2,2],[1,1,1]]=>([(0,1)],2) [[4,3,3,2],[2,2,2]]=>([(0,3),(2,1),(3,2)],4) [[4,3,2,2],[2,2,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[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) [[4,2,2,2],[2,1,1]]=>([(0,3),(2,1),(3,2)],4) [[5,3,3,2],[3,2,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[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) [[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],[]]=>([],1) [[3,2,2,2,1],[1,1,1,1]]=>([(0,2),(2,1)],3) [[3,2,2,1,1],[1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[4,3,3,2,1],[2,2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[3,2,1,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4) [[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) [[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) [[5,4,3,2,1],[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) [[3,1,1,1,1],[1]]=>([(0,1)],2) [[4,2,2,2,1],[2,1,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,2,2,1,1],[2,1,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[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) [[4,2,1,1,1],[2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,3,2,2,1],[3,2,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) [[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) [[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) [[5,5],[4]]=>([],1) [[6,5],[5]]=>([(0,1)],2) [[4,4,1],[3]]=>([(0,1)],2) [[5,5,1],[4,1]]=>([(0,2),(2,1)],3) [[5,4,1],[4]]=>([(0,2),(2,1)],3) [[6,5,1],[5,1]]=>([(0,3),(2,1),(3,2)],4) [[3,3,2],[2]]=>([(0,1)],2) [[4,4,2],[3,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[5,5,2],[4,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[4,3,2],[3]]=>([(0,2),(2,1)],3) [[5,4,2],[4,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[6,5,2],[5,2]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[3,3,1,1],[2]]=>([(0,1)],2) [[4,4,2,1],[3,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[4,4,1,1],[3,1]]=>([(0,3),(2,1),(3,2)],4) [[5,5,2,1],[4,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[4,3,1,1],[3]]=>([(0,2),(2,1)],3) [[5,4,2,1],[4,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[5,4,1,1],[4,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[6,5,2,1],[5,2,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[3,3,3],[2,1]]=>([],1) [[4,4,3],[3,2]]=>([(0,2),(2,1)],3) [[5,5,3],[4,3]]=>([(0,3),(2,1),(3,2)],4) [[4,3,3],[3,1]]=>([(0,2),(2,1)],3) [[5,4,3],[4,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[6,5,3],[5,3]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[2,2,2,1],[1]]=>([(0,1)],2) [[3,3,3,1],[2,1,1]]=>([(0,2),(2,1)],3) [[3,3,2,1],[2,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[4,4,3,1],[3,2,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[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]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) [[3,2,2,1],[2]]=>([(0,2),(2,1)],3) [[4,3,3,1],[3,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,3,2,1],[3,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[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]]=>([(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]]=>([(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]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[4,4,3,2],[3,2,2]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[4,4,2,2],[3,2,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[5,5,3,2],[4,3,2]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) [[4,3,2,2],[3,1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[5,4,3,2],[4,2,2]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) [[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) [[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) [[2,2,1,1,1],[1]]=>([(0,1)],2) [[3,3,2,2,1],[2,1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[3,3,2,1,1],[2,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[4,4,3,2,1],[3,2,2,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) [[3,3,1,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,4,2,2,1],[3,2,1,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) [[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) [[5,5,3,2,1],[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) [[3,2,1,1,1],[2]]=>([(0,2),(2,1)],3) [[4,3,2,2,1],[3,1,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[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) [[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) [[4,3,1,1,1],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,4,2,2,1],[4,2,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) [[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) [[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) [[4,4,4],[3,3]]=>([],1) [[5,5,4],[4,4]]=>([(0,1)],2) [[5,4,4],[4,3]]=>([(0,2),(2,1)],3) [[6,5,4],[5,4]]=>([(0,3),(2,1),(3,2)],4) [[3,3,3,1],[2,2]]=>([(0,1)],2) [[4,4,4,1],[3,3,1]]=>([(0,2),(2,1)],3) [[4,4,3,1],[3,3]]=>([(0,3),(2,1),(3,2)],4) [[5,5,4,1],[4,4,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,3,3,1],[3,2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[5,4,4,1],[4,3,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[5,4,3,1],[4,3]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[6,5,4,1],[5,4,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[2,2,2,2],[1,1]]=>([],1) [[3,3,3,2],[2,2,1]]=>([(0,2),(2,1)],3) [[4,4,4,2],[3,3,2]]=>([(0,3),(2,1),(3,2)],4) [[3,3,2,2],[2,2]]=>([(0,2),(2,1)],3) [[4,4,3,2],[3,3,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[5,5,4,2],[4,4,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[3,2,2,2],[2,1]]=>([(0,2),(2,1)],3) [[4,3,3,2],[3,2,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[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) [[4,3,2,2],[3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,4,3,2],[4,3,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) [[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) [[2,2,2,1,1],[1,1]]=>([(0,2),(2,1)],3) [[3,3,3,2,1],[2,2,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[3,3,3,1,1],[2,2,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[4,4,4,2,1],[3,3,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[3,3,2,1,1],[2,2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[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) [[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]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) [[3,2,2,1,1],[2,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[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]]=>([(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]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) [[4,3,2,1,1],[3,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[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) [[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) [[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]]=>([],1) [[4,4,4,3],[3,3,3]]=>([(0,1)],2) [[4,4,3,3],[3,3,2]]=>([(0,3),(2,1),(3,2)],4) [[5,5,4,3],[4,4,3]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,3,3,3],[3,2,2]]=>([(0,2),(2,1)],3) [[5,4,4,3],[4,3,3]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,4,3,3],[4,3,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[6,5,4,3],[5,4,3]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[2,2,2,2,1],[1,1,1]]=>([(0,1)],2) [[3,3,3,3,1],[2,2,2,1]]=>([(0,2),(2,1)],3) [[3,3,3,2,1],[2,2,2]]=>([(0,3),(2,1),(3,2)],4) [[4,4,4,3,1],[3,3,3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[3,3,2,2,1],[2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[4,4,3,3,1],[3,3,2,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) [[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) [[5,5,4,3,1],[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) [[3,2,2,2,1],[2,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[4,3,3,3,1],[3,2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[4,3,3,2,1],[3,2,2]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) [[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) [[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) [[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) [[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) [[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) [[2,2,2,2,2],[1,1,1,1]]=>([],1) [[3,3,3,3,2],[2,2,2,2]]=>([(0,1)],2) [[3,3,3,2,2],[2,2,2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,4,4,3,2],[3,3,3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[3,3,2,2,2],[2,2,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[4,4,3,3,2],[3,3,2,2]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[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) [[5,5,4,3,2],[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) [[3,2,2,2,2],[2,1,1,1]]=>([(0,2),(2,1)],3) [[4,3,3,3,2],[3,2,2,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,3,3,2,2],[3,2,2,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) [[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) [[4,3,2,2,2],[3,2,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[5,4,3,3,2],[4,3,2,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9) [[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) [[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) [[1,1,1,1,1,1],[]]=>([],1) [[2,2,2,2,2,1],[1,1,1,1,1]]=>([(0,1)],2) [[2,2,2,2,1,1],[1,1,1,1]]=>([(0,2),(2,1)],3) [[3,3,3,3,2,1],[2,2,2,2,1]]=>([(0,3),(2,1),(3,2)],4) [[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]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[3,3,3,2,1,1],[2,2,2,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[4,4,4,3,2,1],[3,3,3,2,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[2,2,1,1,1,1],[1,1]]=>([(0,2),(2,1)],3) [[3,3,2,2,2,1],[2,2,1,1,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[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]]=>([(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]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[4,4,3,2,2,1],[3,3,2,1,1]]=>([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9) [[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]]=>([(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]]=>([(0,1)],2) [[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]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[4,3,3,3,2,1],[3,2,2,2,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[3,2,2,1,1,1],[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]]=>([(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]]=>([(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]]=>([(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]]=>([(0,3),(2,1),(3,2)],4) [[4,3,2,2,2,1],[3,2,1,1,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[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) [[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]]=>([(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]]=>([(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]]=>([(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]]=>([(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],[]]=>([],1) [[6,1],[]]=>([],1) [[7,1],[1]]=>([(0,1)],2) [[5,2],[]]=>([],1) [[6,2],[1]]=>([(0,1)],2) [[7,2],[2]]=>([(0,2),(2,1)],3) [[5,1,1],[]]=>([],1) [[6,2,1],[1,1]]=>([(0,2),(2,1)],3) [[6,1,1],[1]]=>([(0,1)],2) [[7,2,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,3],[]]=>([],1) [[5,3],[1]]=>([(0,1)],2) [[6,3],[2]]=>([(0,2),(2,1)],3) [[7,3],[3]]=>([(0,3),(2,1),(3,2)],4) [[4,2,1],[]]=>([],1) [[5,3,1],[1,1]]=>([(0,2),(2,1)],3) [[5,2,1],[1]]=>([(0,2),(2,1)],3) [[6,3,1],[2,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[6,2,1],[2]]=>([(0,3),(2,1),(3,2)],4) [[7,3,1],[3,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[5,2,2],[1,1]]=>([(0,1)],2) [[6,3,2],[2,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[6,2,2],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[7,3,2],[3,2]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[4,1,1,1],[]]=>([],1) [[5,2,2,1],[1,1,1]]=>([(0,2),(2,1)],3) [[5,2,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4) [[6,3,2,1],[2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[5,1,1,1],[1]]=>([(0,1)],2) [[6,2,2,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[6,2,1,1],[2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[7,3,2,1],[3,2,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[4,4],[1]]=>([],1) [[5,4],[2]]=>([(0,1)],2) [[6,4],[3]]=>([(0,2),(2,1)],3) [[7,4],[4]]=>([(0,3),(2,1),(3,2)],4) [[3,3,1],[]]=>([],1) [[4,4,1],[1,1]]=>([(0,1)],2) [[4,3,1],[1]]=>([(0,2),(2,1)],3) [[5,4,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[5,3,1],[2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[6,4,1],[3,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[6,3,1],[3]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[7,4,1],[4,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[3,2,2],[]]=>([],1) [[4,3,2],[1,1]]=>([(0,2),(2,1)],3) [[5,4,2],[2,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,2,2],[1]]=>([(0,1)],2) [[5,3,2],[2,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[6,4,2],[3,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[5,2,2],[2]]=>([(0,2),(2,1)],3) [[6,3,2],[3,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[7,4,2],[4,2]]=>([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) [[3,2,1,1],[]]=>([],1) [[4,3,2,1],[1,1,1]]=>([(0,3),(2,1),(3,2)],4) [[4,3,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4) [[5,4,2,1],[2,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[4,2,1,1],[1]]=>([(0,2),(2,1)],3) [[5,3,2,1],[2,1,1]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) [[5,3,1,1],[2,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[6,4,2,1],[3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[5,2,1,1],[2]]=>([(0,3),(2,1),(3,2)],4) [[6,3,2,1],[3,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[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) [[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) [[5,3,3],[2,2]]=>([(0,2),(2,1)],3) [[6,4,3],[3,3]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[6,3,3],[3,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[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]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[5,3,3,1],[2,2,1]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) [[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) [[6,4,3,1],[3,3,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[5,2,2,1],[2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[6,3,3,1],[3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[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) [[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) [[4,2,2,2],[1,1,1]]=>([(0,1)],2) [[5,3,3,2],[2,2,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[5,3,2,2],[2,2,1]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) [[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) [[5,2,2,2],[2,1,1]]=>([(0,3),(2,1),(3,2)],4) [[6,3,3,2],[3,2,2]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) [[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) [[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) [[3,1,1,1,1],[]]=>([],1) [[4,2,2,2,1],[1,1,1,1]]=>([(0,2),(2,1)],3) [[4,2,2,1,1],[1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[5,3,3,2,1],[2,2,2,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [[4,2,1,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4) [[5,3,2,2,1],[2,2,1,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) [[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) [[6,4,3,2,1],[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) [[4,1,1,1,1],[1]]=>([(0,1)],2) [[5,2,2,2,1],[2,1,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,2,2,1,1],[2,1,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[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) [[5,2,1,1,1],[2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[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) [[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) [[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) [[5,5],[3]]=>([],1) [[6,5],[4]]=>([(0,1)],2) [[7,5],[5]]=>([(0,2),(2,1)],3) [[4,4,1],[2]]=>([(0,1)],2) [[5,5,1],[3,1]]=>([(0,2),(2,1)],3) [[5,4,1],[3]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[6,5,1],[4,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[6,4,1],[4]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[7,5,1],[5,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[3,3,2],[1]]=>([(0,1)],2) [[4,4,2],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[5,5,2],[3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,3,2],[2]]=>([(0,3),(2,1),(3,2)],4) [[5,4,2],[3,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[6,5,2],[4,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[5,3,2],[3]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[6,4,2],[4,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[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]]=>([(0,1)],2) [[4,4,2,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,4,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[5,5,2,1],[3,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[4,3,1,1],[2]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[5,4,2,1],[3,1,1]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) [[5,4,1,1],[3,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[6,5,2,1],[4,2,1]]=>([(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]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[6,4,2,1],[4,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[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) [[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]]=>([],1) [[4,4,3],[2,2]]=>([(0,1)],2) [[5,5,3],[3,3]]=>([(0,2),(2,1)],3) [[4,3,3],[2,1]]=>([(0,2),(2,1)],3) [[5,4,3],[3,2]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[6,5,3],[4,3]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[5,3,3],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[6,4,3],[4,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[7,5,3],[5,3]]=>([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8) [[2,2,2,1],[]]=>([],1) [[3,3,3,1],[1,1,1]]=>([(0,1)],2) [[3,3,2,1],[1,1]]=>([(0,3),(2,1),(3,2)],4) [[4,4,3,1],[2,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,4,2,1],[2,2]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[5,5,3,1],[3,3,1]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[3,2,2,1],[1]]=>([(0,2),(2,1)],3) [[4,3,3,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,3,2,1],[2,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [[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) [[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) [[6,5,3,1],[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) [[4,2,2,1],[2]]=>([(0,3),(2,1),(3,2)],4) [[5,3,3,1],[3,1,1]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[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) [[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) [[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) [[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) [[3,3,2,2],[1,1,1]]=>([(0,1)],2) [[4,4,3,2],[2,2,2]]=>([(0,3),(2,1),(3,2)],4) [[4,4,2,2],[2,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[5,5,3,2],[3,3,2]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[4,3,2,2],[2,1,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [[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) [[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) [[6,5,3,2],[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) [[5,3,2,2],[3,1,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [[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) [[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) [[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) [[2,2,1,1,1],[]]=>([],1) [[3,3,2,2,1],[1,1,1,1]]=>([(0,2),(2,1)],3) [[3,3,2,1,1],[1,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,4,3,2,1],[2,2,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[3,3,1,1,1],[1,1]]=>([(0,2),(2,1)],3) [[4,4,2,2,1],[2,2,1,1]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[4,4,2,1,1],[2,2,1]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[5,5,3,2,1],[3,3,2,1]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) [[3,2,1,1,1],[1]]=>([(0,2),(2,1)],3) [[4,3,2,2,1],[2,1,1,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) [[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) [[5,4,3,2,1],[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) [[4,3,1,1,1],[2,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[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) [[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) [[6,5,3,2,1],[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) [[4,2,1,1,1],[2]]=>([(0,3),(2,1),(3,2)],4) [[5,3,2,2,1],[3,1,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) [[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) [[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) [[5,3,1,1,1],[3,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[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) [[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) [[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) [[5,4,4],[3,3]]=>([(0,1)],2) [[6,5,4],[4,4]]=>([(0,3),(2,1),(3,2)],4) [[6,4,4],[4,3]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[7,5,4],[5,4]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[4,3,3,1],[2,2]]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5) [[5,4,4,1],[3,3,1]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) [[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) [[6,5,4,1],[4,4,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[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) [[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) [[6,4,3,1],[4,3]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[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) [[3,2,2,2],[1,1]]=>([(0,1)],2) [[4,3,3,2],[2,2,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [[5,4,4,2],[3,3,2]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [[4,3,2,2],[2,2]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[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) [[6,5,4,2],[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) [[4,2,2,2],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[5,3,3,2],[3,2,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) [[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) [[5,3,2,2],[3,2]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[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) [[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) [[3,2,2,1,1],[1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[4,3,3,2,1],[2,2,1,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) [[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) [[5,4,4,2,1],[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) [[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) [[5,4,3,2,1],[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) [[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) [[6,5,4,2,1],[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) [[4,2,2,1,1],[2,1]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(0,1)],2) [[5,4,4,3],[3,3,3]]=>([(0,3),(2,1),(3,2)],4) [[5,4,3,3],[3,3,2]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) [[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) [[5,3,3,3],[3,2,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[6,4,4,3],[4,3,3]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8) [[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) [[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) [[3,2,2,2,1],[1,1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[4,3,3,3,1],[2,2,2,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[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) [[5,4,4,3,1],[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) [[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) [[5,4,3,3,1],[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) [[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) [[6,5,4,3,1],[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) [[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) [[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) [[5,3,3,2,1],[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) [[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) [[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) [[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) [[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) [[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) [[3,2,2,2,2],[1,1,1,1]]=>([(0,1)],2) [[4,3,3,3,2],[2,2,2,2]]=>([(0,3),(2,1),(3,2)],4) [[4,3,3,2,2],[2,2,2,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) [[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) [[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) [[5,4,3,3,2],[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) [[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]]=>([(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]]=>([(0,3),(2,1),(3,2)],4) [[5,3,3,3,2],[3,2,2,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[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) [[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) [[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) [[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) [[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) [[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],[]]=>([],1) [[3,2,2,2,2,1],[1,1,1,1,1]]=>([(0,2),(2,1)],3) [[3,2,2,2,1,1],[1,1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[4,3,3,3,2,1],[2,2,2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[3,2,2,1,1,1],[1,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[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) [[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) [[5,4,4,3,2,1],[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) [[3,2,1,1,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4) [[4,3,2,2,2,1],[2,2,1,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) [[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) [[5,4,3,3,2,1],[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) [[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) [[5,4,3,2,2,1],[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) [[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) [[6,5,4,3,2,1],[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) [[3,1,1,1,1,1],[1]]=>([(0,1)],2) [[4,2,2,2,2,1],[2,1,1,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,2,2,2,1,1],[2,1,1,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) [[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) [[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) [[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) [[5,3,3,2,1,1],[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) [[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) [[4,2,1,1,1,1],[2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[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) [[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) [[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) [[5,3,2,1,1,1],[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) [[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) [[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) [[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) [[6,6],[5]]=>([],1) [[7,6],[6]]=>([(0,1)],2) [[5,5,1],[4]]=>([(0,1)],2) [[6,6,1],[5,1]]=>([(0,2),(2,1)],3) [[6,5,1],[5]]=>([(0,2),(2,1)],3) [[7,6,1],[6,1]]=>([(0,3),(2,1),(3,2)],4) [[4,4,2],[3]]=>([(0,1)],2) [[5,5,2],[4,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[6,6,2],[5,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[5,4,2],[4]]=>([(0,2),(2,1)],3) [[6,5,2],[5,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[7,6,2],[6,2]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[4,4,1,1],[3]]=>([(0,1)],2) [[5,5,2,1],[4,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[5,5,1,1],[4,1]]=>([(0,3),(2,1),(3,2)],4) [[6,6,2,1],[5,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[5,4,1,1],[4]]=>([(0,2),(2,1)],3) [[6,5,2,1],[5,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[6,5,1,1],[5,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[7,6,2,1],[6,2,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[3,3,3],[2]]=>([],1) [[4,4,3],[3,1]]=>([(0,2),(2,1)],3) [[5,5,3],[4,2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[6,6,3],[5,3]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[4,3,3],[3]]=>([(0,1)],2) [[5,4,3],[4,1]]=>([(0,3),(2,1),(3,2)],4) [[6,5,3],[5,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[7,6,3],[6,3]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[3,3,2,1],[2]]=>([(0,2),(2,1)],3) [[4,4,3,1],[3,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,4,2,1],[3,1]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) [[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) [[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) [[6,6,3,1],[5,3,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[4,3,2,1],[3]]=>([(0,3),(2,1),(3,2)],4) [[5,4,3,1],[4,1,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[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) [[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) [[6,5,2,1],[5,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[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) [[4,4,2,2],[3,1,1]]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5) [[5,5,3,2],[4,2,2]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) [[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) [[6,6,3,2],[5,3,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[5,4,2,2],[4,1,1]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) [[6,5,3,2],[5,2,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[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) [[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) [[3,3,1,1,1],[2]]=>([(0,1)],2) [[4,4,2,2,1],[3,1,1,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [[4,4,2,1,1],[3,1,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [[5,5,3,2,1],[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) [[4,4,1,1,1],[3,1]]=>([(0,3),(2,1),(3,2)],4) [[5,5,2,2,1],[4,2,1,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) [[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) [[6,6,3,2,1],[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) [[4,3,1,1,1],[3]]=>([(0,2),(2,1)],3) [[5,4,2,2,1],[4,1,1,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [[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) [[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) [[5,4,1,1,1],[4,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[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) [[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) [[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) [[4,4,4],[3,2]]=>([],1) [[5,5,4],[4,3]]=>([(0,2),(2,1)],3) [[6,6,4],[5,4]]=>([(0,3),(2,1),(3,2)],4) [[5,4,4],[4,2]]=>([(0,2),(2,1)],3) [[6,5,4],[5,3]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[7,6,4],[6,4]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[3,3,3,1],[2,1]]=>([(0,2),(2,1)],3) [[4,4,4,1],[3,2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,4,3,1],[3,2]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) [[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) [[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) [[6,6,4,1],[5,4,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[4,3,3,1],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,4,4,1],[4,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[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) [[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) [[6,5,3,1],[5,3]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[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) [[2,2,2,2],[1]]=>([],1) [[3,3,3,2],[2,1,1]]=>([(0,2),(2,1)],3) [[4,4,4,2],[3,2,2]]=>([(0,3),(2,1),(3,2)],4) [[3,3,2,2],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,4,3,2],[3,2,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [[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) [[4,4,2,2],[3,2]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[5,5,3,2],[4,3,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) [[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) [[3,2,2,2],[2]]=>([(0,1)],2) [[4,3,3,2],[3,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,4,4,2],[4,2,2]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[4,3,2,2],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,4,3,2],[4,2,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) [[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) [[5,4,2,2],[4,2]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[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) [[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) [[2,2,2,1,1],[1]]=>([(0,1)],2) [[3,3,3,2,1],[2,1,1,1]]=>([(0,3),(2,1),(3,2)],4) [[3,3,3,1,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,4,4,2,1],[3,2,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[3,3,2,1,1],[2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[4,4,3,2,1],[3,2,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) [[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) [[5,5,4,2,1],[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) [[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) [[5,5,3,2,1],[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) [[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) [[6,6,4,2,1],[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) [[3,2,2,1,1],[2]]=>([(0,2),(2,1)],3) [[4,3,3,2,1],[3,1,1,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[4,3,3,1,1],[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]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) [[4,3,2,1,1],[3,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) [[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) [[5,4,3,1,1],[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) [[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) [[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) [[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) [[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) [[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) [[4,4,3,3],[3,2,2]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[5,5,4,3],[4,3,3]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[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) [[6,6,4,3],[5,4,3]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[5,4,3,3],[4,2,2]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) [[6,5,4,3],[5,3,3]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[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) [[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) [[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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[4,4,3,3,2],[3,2,2,2]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[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) [[5,5,4,3,2],[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) [[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) [[5,5,3,3,2],[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) [[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) [[6,6,4,3,2],[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) [[4,3,2,2,2],[3,1,1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[5,4,3,3,2],[4,2,2,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) [[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) [[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) [[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) [[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) [[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) [[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) [[2,2,1,1,1,1],[1]]=>([(0,1)],2) [[3,3,2,2,2,1],[2,1,1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[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) [[4,4,3,3,2,1],[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) [[3,3,2,1,1,1],[2,1,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[4,4,3,2,2,1],[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) [[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) [[5,5,4,3,2,1],[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) [[3,3,1,1,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,4,2,2,2,1],[3,2,1,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) [[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) [[5,5,3,3,2,1],[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) [[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) [[5,5,3,2,2,1],[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) [[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) [[6,6,4,3,2,1],[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) [[3,2,1,1,1,1],[2]]=>([(0,2),(2,1)],3) [[4,3,2,2,2,1],[3,1,1,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[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) [[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) [[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) [[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) [[5,4,3,2,1,1],[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) [[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) [[4,3,1,1,1,1],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[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) [[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) [[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) [[5,4,2,1,1,1],[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) [[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) [[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) [[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) [[5,5,5],[4,4]]=>([],1) [[6,6,5],[5,5]]=>([(0,1)],2) [[6,5,5],[5,4]]=>([(0,2),(2,1)],3) [[7,6,5],[6,5]]=>([(0,3),(2,1),(3,2)],4) [[4,4,4,1],[3,3]]=>([(0,1)],2) [[5,5,5,1],[4,4,1]]=>([(0,2),(2,1)],3) [[5,5,4,1],[4,4]]=>([(0,3),(2,1),(3,2)],4) [[6,6,5,1],[5,5,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,4,4,1],[4,3]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[6,5,5,1],[5,4,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[6,5,4,1],[5,4]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[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],[2,2]]=>([(0,1)],2) [[4,4,4,2],[3,3,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[5,5,5,2],[4,4,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[4,4,3,2],[3,3]]=>([(0,3),(2,1),(3,2)],4) [[5,5,4,2],[4,4,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[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) [[4,3,3,2],[3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,4,4,2],[4,3,1]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) [[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) [[5,4,3,2],[4,3]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[6,5,4,2],[5,4,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[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],[2,2]]=>([(0,2),(2,1)],3) [[4,4,4,2,1],[3,3,1,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [[4,4,4,1,1],[3,3,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[5,5,5,2,1],[4,4,2,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [[4,4,3,1,1],[3,3]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[5,5,4,2,1],[4,4,1,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) [[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]]=>([(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]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [[5,4,4,2,1],[4,3,1,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) [[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) [[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) [[5,4,3,1,1],[4,3]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [[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) [[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) [[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]]=>([],1) [[4,4,4,3],[3,3,2]]=>([(0,2),(2,1)],3) [[5,5,5,3],[4,4,3]]=>([(0,3),(2,1),(3,2)],4) [[4,4,3,3],[3,3,1]]=>([(0,3),(2,1),(3,2)],4) [[5,5,4,3],[4,4,2]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[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) [[4,3,3,3],[3,2,1]]=>([(0,3),(2,1),(3,2)],4) [[5,4,4,3],[4,3,2]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8) [[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) [[5,4,3,3],[4,3,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[6,5,4,3],[5,4,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9) [[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) [[2,2,2,2,1],[1,1]]=>([(0,1)],2) [[3,3,3,3,1],[2,2,1,1]]=>([(0,2),(2,1)],3) [[3,3,3,2,1],[2,2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[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) [[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) [[5,5,5,3,1],[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) [[3,3,2,2,1],[2,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,4,3,3,1],[3,3,1,1]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[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) [[5,5,4,3,1],[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) [[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) [[6,6,5,3,1],[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) [[3,2,2,2,1],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,3,3,3,1],[3,2,1,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[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) [[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) [[5,4,4,2,1],[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) [[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) [[4,3,2,2,1],[3,2]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[5,4,3,3,1],[4,3,1,1]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) [[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) [[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) [[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) [[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) [[3,3,3,2,2],[2,2,1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[4,4,4,3,2],[3,3,2,2]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[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) [[5,5,5,3,2],[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) [[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) [[5,5,4,3,2],[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) [[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) [[6,6,5,3,2],[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) [[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) [[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) [[5,4,4,2,2],[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) [[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) [[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) [[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) [[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) [[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) [[2,2,2,1,1,1],[1,1]]=>([(0,2),(2,1)],3) [[3,3,3,2,2,1],[2,2,1,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[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) [[4,4,4,3,2,1],[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) [[3,3,3,1,1,1],[2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[4,4,4,2,2,1],[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) [[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) [[5,5,5,3,2,1],[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) [[3,3,2,1,1,1],[2,2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[4,4,3,2,2,1],[3,3,1,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) [[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) [[5,5,4,3,2,1],[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) [[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) [[5,5,4,2,2,1],[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) [[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) [[6,6,5,3,2,1],[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) [[3,2,2,1,1,1],[2,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[4,3,3,2,2,1],[3,2,1,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) [[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) [[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) [[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) [[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) [[5,4,4,2,1,1],[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) [[6,5,5,3,2,1],[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) [[4,3,2,1,1,1],[3,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[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) [[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) [[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) [[5,4,3,1,1,1],[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) [[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) [[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) [[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) [[4,4,4,4],[3,3,3]]=>([],1) [[5,5,5,4],[4,4,4]]=>([(0,1)],2) [[5,5,4,4],[4,4,3]]=>([(0,3),(2,1),(3,2)],4) [[6,6,5,4],[5,5,4]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,4,4,4],[4,3,3]]=>([(0,2),(2,1)],3) [[6,5,5,4],[5,4,4]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[6,5,4,4],[5,4,3]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[7,6,5,4],[6,5,4]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[3,3,3,3,1],[2,2,2]]=>([(0,1)],2) [[4,4,4,4,1],[3,3,3,1]]=>([(0,2),(2,1)],3) [[4,4,4,3,1],[3,3,3]]=>([(0,3),(2,1),(3,2)],4) [[5,5,5,4,1],[4,4,4,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,4,3,3,1],[3,3,2]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [[5,5,4,4,1],[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) [[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) [[6,6,5,4,1],[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) [[4,3,3,3,1],[3,2,2]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [[5,4,4,4,1],[4,3,3,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [[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) [[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) [[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) [[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) [[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) [[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) [[2,2,2,2,2],[1,1,1]]=>([],1) [[3,3,3,3,2],[2,2,2,1]]=>([(0,2),(2,1)],3) [[4,4,4,4,2],[3,3,3,2]]=>([(0,3),(2,1),(3,2)],4) [[3,3,3,2,2],[2,2,2]]=>([(0,2),(2,1)],3) [[4,4,4,3,2],[3,3,3,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[5,5,5,4,2],[4,4,4,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[3,3,2,2,2],[2,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,4,3,3,2],[3,3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9) [[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) [[4,4,3,2,2],[3,3,2]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[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) [[6,6,5,4,2],[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) [[3,2,2,2,2],[2,1,1]]=>([(0,2),(2,1)],3) [[4,3,3,3,2],[3,2,2,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8) [[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) [[4,3,3,2,2],[3,2,2]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [[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) [[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) [[4,3,2,2,2],[3,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [[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) [[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) [[5,4,3,2,2],[4,3,2]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) [[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) [[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) [[2,2,2,2,1,1],[1,1,1]]=>([(0,2),(2,1)],3) [[3,3,3,3,2,1],[2,2,2,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[3,3,3,3,1,1],[2,2,2,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[4,4,4,4,2,1],[3,3,3,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[3,3,3,2,1,1],[2,2,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[4,4,4,3,2,1],[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) [[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) [[5,5,5,4,2,1],[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) [[3,3,2,2,1,1],[2,2,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[4,4,3,3,2,1],[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) [[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) [[5,5,4,4,2,1],[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) [[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) [[5,5,4,3,2,1],[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) [[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) [[6,6,5,4,2,1],[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) [[3,2,2,2,1,1],[2,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[4,3,3,3,2,1],[3,2,2,1,1]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([],1) [[4,4,4,4,3],[3,3,3,3]]=>([(0,1)],2) [[4,4,4,3,3],[3,3,3,2]]=>([(0,3),(2,1),(3,2)],4) [[5,5,5,4,3],[4,4,4,3]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[4,4,3,3,3],[3,3,2,2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[5,5,4,4,3],[4,4,3,3]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [[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) [[6,6,5,4,3],[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) [[4,3,3,3,3],[3,2,2,2]]=>([(0,2),(2,1)],3) [[5,4,4,4,3],[4,3,3,3]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[5,4,4,3,3],[4,3,3,2]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9) [[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) [[5,4,3,3,3],[4,3,2,2]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [[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) [[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) [[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) [[2,2,2,2,2,1],[1,1,1,1]]=>([(0,1)],2) [[3,3,3,3,3,1],[2,2,2,2,1]]=>([(0,2),(2,1)],3) [[3,3,3,3,2,1],[2,2,2,2]]=>([(0,3),(2,1),(3,2)],4) [[4,4,4,4,3,1],[3,3,3,3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[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) [[4,4,4,3,3,1],[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) [[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) [[5,5,5,4,3,1],[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) [[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) [[4,4,3,3,3,1],[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) [[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) [[5,5,4,4,3,1],[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) [[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) [[5,5,4,3,3,1],[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) [[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) [[6,6,5,4,3,1],[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) [[3,2,2,2,2,1],[2,1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[4,3,3,3,3,1],[3,2,2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[4,3,3,3,2,1],[3,2,2,2]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9) [[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) [[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) [[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) [[5,4,4,3,2,1],[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) [[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) [[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) [[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) [[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) [[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) [[5,4,3,2,2,1],[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) [[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) [[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) [[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) [[2,2,2,2,2,2],[1,1,1,1,1]]=>([],1) [[3,3,3,3,3,2],[2,2,2,2,2]]=>([(0,1)],2) [[3,3,3,3,2,2],[2,2,2,2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,4,4,4,3,2],[3,3,3,3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[3,3,3,2,2,2],[2,2,2,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[4,4,4,3,3,2],[3,3,3,2,2]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8) [[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) [[5,5,5,4,3,2],[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) [[3,3,2,2,2,2],[2,2,1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[4,4,3,3,3,2],[3,3,2,2,2]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(0,2),(2,1)],3) [[4,3,3,3,3,2],[3,2,2,2,2]]=>([(0,4),(2,3),(3,1),(4,2)],5) [[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) [[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) [[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) [[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) [[5,4,4,3,2,2],[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) [[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) [[4,3,2,2,2,2],[3,2,1,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [[5,4,3,3,3,2],[4,3,2,2,2]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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) [[2,2,2,2,2,2,1],[1,1,1,1,1,1]]=>([(0,1)],2) [[2,2,2,2,2,1,1],[1,1,1,1,1]]=>([(0,2),(2,1)],3) [[3,3,3,3,3,2,1],[2,2,2,2,2,1]]=>([(0,3),(2,1),(3,2)],4) [[2,2,2,2,1,1,1],[1,1,1,1]]=>([(0,3),(2,1),(3,2)],4) [[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) [[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) [[4,4,4,4,3,2,1],[3,3,3,3,2,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(0,2),(2,1)],3) [[3,3,2,2,2,2,1],[2,2,1,1,1,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(0,1)],2) [[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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(0,3),(2,1),(3,2)],4) [[4,3,2,2,2,2,1],[3,2,1,1,1,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [[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) [[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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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]]=>([(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],[]]=>([],1) [[7,1],[]]=>([],1) [[6,2],[]]=>([],1) [[6,1,1],[]]=>([],1) [[5,3],[]]=>([],1) [[5,2,1],[]]=>([],1) [[5,1,1,1],[]]=>([],1) [[4,4],[]]=>([],1) [[4,3,1],[]]=>([],1) [[4,2,2],[]]=>([],1) [[4,2,1,1],[]]=>([],1) [[4,1,1,1,1],[]]=>([],1) [[3,3,2],[]]=>([],1) [[3,3,1,1],[]]=>([],1) [[3,2,2,1],[]]=>([],1) [[3,2,1,1,1],[]]=>([],1) [[3,1,1,1,1,1],[]]=>([],1) [[2,2,2,2],[]]=>([],1) [[2,2,2,1,1],[]]=>([],1) [[2,2,1,1,1,1],[]]=>([],1) [[2,1,1,1,1,1,1],[]]=>([],1) [[1,1,1,1,1,1,1,1],[]]=>([],1) [[2,2,1,1,1,1,1],[1]]=>([(0,1)],2) [[2,2,2,1,1,1,1],[1,1]]=>([(0,2),(2,1)],3) [[3,2,1,1,1,1],[1]]=>([(0,2),(2,1)],3) [[2,2,2,2,1,1,1],[1,1,1]]=>([(0,3),(2,1),(3,2)],4) [[3,2,2,1,1,1],[1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[3,3,2,1,1,1],[2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[4,3,1,1,1],[2]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[2,2,2,2,2,1,1],[1,1,1,1]]=>([(0,2),(2,1)],3) [[3,2,2,2,1,1],[1,1,1]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[3,3,2,2,1,1],[2,1,1]]=>([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) [[3,3,3,2,1,1],[2,2,1]]=>([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) [[4,3,2,1,1],[2,1]]=>([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9) [[4,4,2,1,1],[3,1]]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) [[4,3,3,1,1],[2,2]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) [[4,4,3,1,1],[3,2]]=>([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) [[5,3,1,1],[2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[2,2,2,2,2,2,1],[1,1,1,1,1]]=>([(0,1)],2) [[3,2,2,2,2,1],[1,1,1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[3,3,2,2,2,1],[2,1,1,1]]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) [[3,3,3,2,2,1],[2,2,1,1]]=>([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) [[4,3,2,2,1],[2,1,1]]=>([(0,6),(1,9),(2,8),(3,7),(4,3),(4,8),(5,1),(5,7),(6,2),(6,4),(7,9),(8,5)],10) [[4,4,2,2,1],[3,1,1]]=>([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) [[3,3,3,3,2,1],[2,2,2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [[4,3,3,2,1],[2,2,1]]=>([(0,6),(1,9),(2,8),(3,7),(4,3),(4,8),(5,1),(5,7),(6,2),(6,4),(7,9),(8,5)],10) [[4,4,3,2,1],[3,2,1]]=>([(0,6),(1,10),(2,9),(3,8),(4,3),(4,9),(5,1),(5,8),(6,7),(7,2),(7,4),(8,10),(9,5)],11) [[5,3,2,1],[2,1]]=>([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9) [[4,4,4,2,1],[3,3,1]]=>([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) [[5,4,2,1],[3,1]]=>([(0,4),(0,6),(2,9),(3,8),(4,7),(5,2),(5,8),(6,3),(6,7),(7,5),(8,9),(9,1)],10) [[4,3,3,3,1],[2,2,2]]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5) [[4,4,3,3,1],[3,2,2]]=>([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) [[5,3,3,1],[2,2]]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) [[4,4,4,3,1],[3,3,2]]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) [[5,4,3,1],[3,2]]=>([(0,4),(0,6),(2,9),(3,8),(4,7),(5,2),(5,8),(6,3),(6,7),(7,5),(8,9),(9,1)],10) [[5,5,3,1],[4,2]]=>([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9) [[4,4,4,4,1],[3,3,3]]=>([(0,1)],2) [[5,4,4,1],[3,3]]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5) [[5,5,4,1],[4,3]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) [[6,4,1],[3]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[3,2,2,2,2,2],[1,1,1,1,1]]=>([(0,1)],2) [[3,3,2,2,2,2],[2,1,1,1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[3,3,3,2,2,2],[2,2,1,1,1]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[4,3,2,2,2],[2,1,1,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [[4,4,2,2,2],[3,1,1,1]]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5) [[3,3,3,3,2,2],[2,2,2,1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[4,3,3,2,2],[2,2,1,1]]=>([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9) [[4,4,3,2,2],[3,2,1,1]]=>([(0,6),(1,9),(2,8),(3,7),(4,3),(4,8),(5,1),(5,7),(6,2),(6,4),(7,9),(8,5)],10) [[5,3,2,2],[2,1,1]]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) [[4,4,4,2,2],[3,3,1,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) [[5,4,2,2],[3,1,1]]=>([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) [[3,3,3,3,3,2],[2,2,2,2,1]]=>([(0,2),(2,1)],3) [[4,3,3,3,2],[2,2,2,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [[4,4,3,3,2],[3,2,2,1]]=>([(0,6),(1,9),(2,8),(3,7),(4,3),(4,8),(5,1),(5,7),(6,2),(6,4),(7,9),(8,5)],10) [[5,3,3,2],[2,2,1]]=>([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) [[4,4,4,3,2],[3,3,2,1]]=>([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9) [[5,4,3,2],[3,2,1]]=>([(0,4),(0,7),(1,10),(3,8),(4,9),(5,2),(6,1),(6,8),(7,3),(7,9),(8,10),(9,6),(10,5)],11) [[5,5,3,2],[4,2,1]]=>([(0,4),(0,6),(2,9),(3,8),(4,7),(5,2),(5,8),(6,3),(6,7),(7,5),(8,9),(9,1)],10) [[4,4,4,4,2],[3,3,3,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[5,4,4,2],[3,3,1]]=>([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) [[5,5,4,2],[4,3,1]]=>([(0,4),(0,6),(2,9),(3,8),(4,7),(5,2),(5,8),(6,3),(6,7),(7,5),(8,9),(9,1)],10) [[6,4,2],[3,1]]=>([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) [[5,5,5,2],[4,4,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[6,5,2],[4,1]]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) [[4,4,3,3,3],[3,2,2,2]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[5,3,3,3],[2,2,2]]=>([(0,2),(2,1)],3) [[4,4,4,3,3],[3,3,2,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[5,4,3,3],[3,2,2]]=>([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) [[5,5,3,3],[4,2,2]]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) [[4,4,4,4,3],[3,3,3,2]]=>([(0,2),(2,1)],3) [[5,4,4,3],[3,3,2]]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) [[5,5,4,3],[4,3,2]]=>([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9) [[6,4,3],[3,2]]=>([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) [[5,5,5,3],[4,4,2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[6,5,3],[4,2]]=>([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) [[6,6,3],[5,2]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [[4,4,4,4,4],[3,3,3,3]]=>([],1) [[5,4,4,4],[3,3,3]]=>([(0,1)],2) [[5,5,4,4],[4,3,3]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[6,4,4],[3,3]]=>([(0,2),(2,1)],3) [[5,5,5,4],[4,4,3]]=>([(0,2),(2,1)],3) [[6,5,4],[4,3]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [[6,6,4],[5,3]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[7,4],[3]]=>([(0,3),(2,1),(3,2)],4) [[3,3,3],[1]]=>([],1) [[3,3,3,1],[1,1]]=>([(0,1)],2) [[4,4,1],[1]]=>([(0,1)],2) [[3,3,2,1],[1]]=>([(0,2),(2,1)],3) [[2,2,2,2,1],[1]]=>([(0,1)],2) [[3,3,3,1],[2]]=>([(0,1)],2) [[3,3,3,2],[1,1,1]]=>([(0,1)],2) [[4,4,2],[1,1]]=>([(0,1)],2) [[4,4,4],[2,2]]=>([],1) [[5,5],[2]]=>([],1) [[4,4,3],[2,1]]=>([(0,2),(2,1)],3) [[3,3,3,3],[2,1,1]]=>([],1) [[4,3,3],[1,1]]=>([(0,1)],2) [[4,4,4],[3,1]]=>([],1) [[5,4],[1]]=>([(0,1)],2) [[3,3,2,2],[1,1]]=>([(0,2),(2,1)],3) [[4,4,2],[2]]=>([(0,2),(2,1)],3) [[3,3,3,2],[2,1]]=>([(0,2),(2,1)],3) [[4,3,2],[1]]=>([(0,2),(2,1)],3) [[2,2,2,2,2],[1,1]]=>([],1) [[3,2,2,2],[1]]=>([(0,1)],2) [[3,3,2,2],[2]]=>([(0,1)],2) [[3,3,3,3],[2,2]]=>([],1) [[4,3,3],[2]]=>([(0,1)],2) [[4,4,3],[3]]=>([(0,1)],2) [[6,6],[4]]=>([],1) [[6,5],[3]]=>([(0,1)],2) [[6,4],[2]]=>([(0,2),(2,1)],3) [[6,3],[1]]=>([(0,1)],2) [[9],[]]=>([],1) [[8,1],[]]=>([],1) [[7,2],[]]=>([],1) [[7,1,1],[]]=>([],1) [[6,3],[]]=>([],1) [[6,2,1],[]]=>([],1) [[6,1,1,1],[]]=>([],1) [[5,4],[]]=>([],1) [[5,3,1],[]]=>([],1) [[5,2,2],[]]=>([],1) [[5,2,1,1],[]]=>([],1) [[5,1,1,1,1],[]]=>([],1) [[4,4,1],[]]=>([],1) [[4,3,2],[]]=>([],1) [[4,3,1,1],[]]=>([],1) [[4,2,2,1],[]]=>([],1) [[4,2,1,1,1],[]]=>([],1) [[4,1,1,1,1,1],[]]=>([],1) [[3,3,3],[]]=>([],1) [[3,3,2,1],[]]=>([],1) [[3,3,1,1,1],[]]=>([],1) [[3,2,2,2],[]]=>([],1) [[3,2,2,1,1],[]]=>([],1) [[3,2,1,1,1,1],[]]=>([],1) [[3,1,1,1,1,1,1],[]]=>([],1) [[2,2,2,2,1],[]]=>([],1) [[2,2,2,1,1,1],[]]=>([],1) [[2,2,1,1,1,1,1],[]]=>([],1) [[2,1,1,1,1,1,1,1],[]]=>([],1) [[1,1,1,1,1,1,1,1,1],[]]=>([],1) [[3,3,3,1],[1]]=>([(0,1)],2) [[3,3,3,3],[1,1,1]]=>([],1) [[4,4,3],[1,1]]=>([(0,1)],2) [[4,4,4],[2,1]]=>([],1) [[5,5],[1]]=>([],1) [[3,3,3,2],[1,1]]=>([(0,1)],2) [[4,4,2],[1]]=>([(0,1)],2) [[3,3,2,2],[1]]=>([(0,1)],2) [[2,2,2,2,2],[1]]=>([],1) [[3,3,3,2],[2]]=>([(0,1)],2) [[4,4,3],[2]]=>([(0,1)],2) [[3,3,3,3],[2,1]]=>([],1) [[4,3,3],[1]]=>([(0,1)],2) [[4,4,4],[3]]=>([],1) [[5,5,5],[3,3]]=>([],1) [[6,6],[3]]=>([],1) [[5,5,4],[3,2]]=>([(0,2),(2,1)],3) [[5,4,4],[2,2]]=>([(0,1)],2) [[6,5],[2]]=>([(0,1)],2) [[5,5,3],[3,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[5,4,3],[2,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [[5,3,3],[1,1]]=>([(0,1)],2) [[6,4],[1]]=>([(0,1)],2) [[5,5,2],[3]]=>([(0,2),(2,1)],3) [[5,4,2],[2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [[5,3,2],[1]]=>([(0,2),(2,1)],3) [[10],[]]=>([],1) [[9,1],[]]=>([],1) [[8,2],[]]=>([],1) [[8,1,1],[]]=>([],1) [[7,3],[]]=>([],1) [[7,2,1],[]]=>([],1) [[7,1,1,1],[]]=>([],1) [[6,4],[]]=>([],1) [[6,3,1],[]]=>([],1) [[6,2,2],[]]=>([],1) [[6,2,1,1],[]]=>([],1) [[6,1,1,1,1],[]]=>([],1) [[5,5],[]]=>([],1) [[5,4,1],[]]=>([],1) [[5,3,2],[]]=>([],1) [[5,3,1,1],[]]=>([],1) [[5,2,2,1],[]]=>([],1) [[5,2,1,1,1],[]]=>([],1) [[5,1,1,1,1,1],[]]=>([],1) [[4,4,2],[]]=>([],1) [[4,4,1,1],[]]=>([],1) [[4,3,3],[]]=>([],1) [[4,3,2,1],[]]=>([],1) [[4,3,1,1,1],[]]=>([],1) [[4,2,2,2],[]]=>([],1) [[4,2,2,1,1],[]]=>([],1) [[4,2,1,1,1,1],[]]=>([],1) [[4,1,1,1,1,1,1],[]]=>([],1) [[3,3,3,1],[]]=>([],1) [[3,3,2,2],[]]=>([],1) [[3,3,2,1,1],[]]=>([],1) [[3,3,1,1,1,1],[]]=>([],1) [[3,2,2,2,1],[]]=>([],1) [[3,2,2,1,1,1],[]]=>([],1) [[3,2,1,1,1,1,1],[]]=>([],1) [[3,1,1,1,1,1,1,1],[]]=>([],1) [[2,2,2,2,2],[]]=>([],1) [[2,2,2,2,1,1],[]]=>([],1) [[2,2,2,1,1,1,1],[]]=>([],1) [[2,2,1,1,1,1,1,1],[]]=>([],1) [[2,1,1,1,1,1,1,1,1],[]]=>([],1) [[1,1,1,1,1,1,1,1,1,1],[]]=>([],1) [[4,4,4],[1,1]]=>([],1) [[3,3,3,2],[1]]=>([(0,1)],2) [[3,3,3,3],[1,1]]=>([],1) [[4,4,3],[1]]=>([(0,1)],2) [[4,4,4],[2]]=>([],1) [[3,3,3,3],[2]]=>([],1) [[4,4,4,4],[2,2,2]]=>([],1) [[5,5,4],[2,2]]=>([(0,1)],2) [[5,5,5],[3,2]]=>([],1) [[6,6],[2]]=>([],1) [[4,4,4,3],[2,2,1]]=>([(0,2),(2,1)],3) [[5,5,3],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,4,3,3],[2,1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[4,3,3,3],[1,1,1]]=>([(0,1)],2) [[5,4,3],[1,1]]=>([(0,2),(2,1)],3) [[5,5,4],[3,1]]=>([(0,2),(2,1)],3) [[5,4,4],[2,1]]=>([(0,2),(2,1)],3) [[6,5],[1]]=>([(0,1)],2) [[4,4,4,2],[2,2]]=>([(0,2),(2,1)],3) [[5,5,2],[2]]=>([(0,2),(2,1)],3) [[4,4,3,2],[2,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [[4,3,3,2],[1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [[5,4,2],[1]]=>([(0,2),(2,1)],3) [[4,4,2,2],[2]]=>([(0,2),(2,1)],3) [[4,3,2,2],[1]]=>([(0,2),(2,1)],3) [[5,5,3],[3]]=>([(0,2),(2,1)],3) [[5,4,3],[2]]=>([(0,3),(2,1),(3,2)],4) [[5,3,3],[1]]=>([(0,1)],2) [[6,5],[]]=>([],1) [[5,5,1],[]]=>([],1) [[5,4,2],[]]=>([],1) [[5,3,3],[]]=>([],1) [[4,4,3],[]]=>([],1) [[4,4,2,1],[]]=>([],1) [[4,3,3,1],[]]=>([],1) [[4,3,2,2],[]]=>([],1) [[3,3,3,2],[]]=>([],1) [[3,2,2,2,2],[]]=>([],1) [[4,4,4],[1]]=>([],1) [[3,3,3,3],[1]]=>([],1) [[4,4,4,1],[1,1]]=>([(0,1)],2) [[4,4,3,1],[1]]=>([(0,2),(2,1)],3) [[4,4,4,1],[2]]=>([(0,1)],2) [[4,4,4,2],[1,1,1]]=>([(0,1)],2) [[5,5,5],[2,2]]=>([],1) [[3,3,3,3,3],[1,1,1,1]]=>([],1) [[4,4,3,3],[1,1,1]]=>([(0,1)],2) [[4,4,4,3],[2,1,1]]=>([(0,2),(2,1)],3) [[5,5,3],[1,1]]=>([(0,1)],2) [[4,4,4,4],[2,2,1]]=>([],1) [[5,5,4],[2,1]]=>([(0,2),(2,1)],3) [[5,5,5],[3,1]]=>([],1) [[6,6],[1]]=>([],1) [[4,4,4,4],[3,1,1]]=>([],1) [[5,4,4],[1,1]]=>([(0,1)],2) [[3,3,3,3,2],[1,1,1]]=>([(0,1)],2) [[4,4,3,2],[1,1]]=>([(0,3),(2,1),(3,2)],4) [[4,4,4,2],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[5,5,2],[1]]=>([(0,1)],2) [[3,3,3,2,2],[1,1]]=>([(0,2),(2,1)],3) [[4,4,2,2],[1]]=>([(0,1)],2) [[3,3,2,2,2],[1]]=>([(0,1)],2) [[4,4,3,2],[2]]=>([(0,3),(2,1),(3,2)],4) [[4,3,3,2],[1]]=>([(0,2),(2,1)],3) [[4,4,4,2],[3]]=>([(0,1)],2) [[4,4,4,3],[2,2]]=>([(0,1)],2) [[5,5,3],[2]]=>([(0,2),(2,1)],3) [[4,4,3,3],[2,1]]=>([(0,3),(2,1),(3,2)],4) [[4,3,3,3],[1,1]]=>([(0,1)],2) [[4,4,4,3],[3,1]]=>([(0,2),(2,1)],3) [[5,4,3],[1]]=>([(0,2),(2,1)],3) [[5,5,4],[3]]=>([(0,1)],2) [[4,4,4,4],[3,2]]=>([],1) [[5,4,4],[2]]=>([(0,1)],2) [[5,5,5],[4]]=>([],1) [[4,3,3,3],[2]]=>([(0,1)],2) [[4,4,3,3],[3]]=>([(0,1)],2) [[6,6],[]]=>([],1) [[5,5,2],[]]=>([],1) [[5,4,3],[]]=>([],1) [[4,4,4],[]]=>([],1) [[4,4,3,1],[]]=>([],1) [[4,4,2,2],[]]=>([],1) [[4,3,3,2],[]]=>([],1) [[3,3,3,3],[]]=>([],1) [[3,3,3,2,1],[]]=>([],1) [[3,3,2,2,2],[]]=>([],1) [[2,2,2,2,2,2],[]]=>([],1) [[4,4,4,1],[1]]=>([(0,1)],2) [[3,3,3,3,1],[1]]=>([(0,1)],2) [[4,4,4,3],[1,1,1]]=>([(0,1)],2) [[5,5,5],[2,1]]=>([],1) [[4,4,4,4],[2,1,1]]=>([],1) [[5,5,4],[1,1]]=>([(0,1)],2) [[4,4,4,2],[1,1]]=>([(0,1)],2) [[3,3,3,2,2],[1]]=>([(0,1)],2) [[3,3,3,3,2],[1,1]]=>([(0,1)],2) [[4,4,3,2],[1]]=>([(0,2),(2,1)],3) [[4,4,4,2],[2]]=>([(0,2),(2,1)],3) [[3,3,3,3,2],[2]]=>([(0,1)],2) [[3,3,3,3,3],[1,1,1]]=>([],1) [[4,4,3,3],[1,1]]=>([(0,2),(2,1)],3) [[4,4,4,3],[2,1]]=>([(0,2),(2,1)],3) [[5,5,3],[1]]=>([(0,1)],2) [[4,4,4,4],[2,2]]=>([],1) [[5,5,4],[2]]=>([(0,1)],2) [[5,5,5],[3]]=>([],1) [[4,4,4,4],[3,1]]=>([],1) [[5,4,4],[1]]=>([(0,1)],2) [[4,4,3,3],[2]]=>([(0,1)],2) [[3,3,3,3,3],[2,1]]=>([],1) [[4,3,3,3],[1]]=>([(0,1)],2) [[4,4,4,3],[3]]=>([(0,1)],2) [[5,5,3],[]]=>([],1) [[5,4,4],[]]=>([],1) [[4,4,4,1],[]]=>([],1) [[4,4,3,2],[]]=>([],1) [[4,3,3,3],[]]=>([],1) [[3,3,3,3,1],[]]=>([],1) [[3,3,3,2,2],[]]=>([],1) [[4,4,4,4],[1,1,1]]=>([],1) [[5,5,5],[1,1]]=>([],1) [[4,4,4,2],[1]]=>([(0,1)],2) [[3,3,3,3,2],[1]]=>([(0,1)],2) [[4,4,4,3],[1,1]]=>([(0,1)],2) [[5,5,5],[2]]=>([],1) [[4,4,4,4],[2,1]]=>([],1) [[5,5,4],[1]]=>([(0,1)],2) [[3,3,3,3,3],[1,1]]=>([],1) [[4,4,3,3],[1]]=>([(0,1)],2) [[4,4,4,3],[2]]=>([(0,1)],2) [[3,3,3,3,3],[2]]=>([],1) [[4,4,4,4],[3]]=>([],1) [[5,5,4],[]]=>([],1) [[4,4,4,2],[]]=>([],1) [[4,4,3,3],[]]=>([],1) [[3,3,3,3,2],[]]=>([],1) [[4,4,4,4],[1,1]]=>([],1) [[5,5,5],[1]]=>([],1) [[4,4,4,3],[1]]=>([(0,1)],2) [[3,3,3,3,3],[1]]=>([],1) [[4,4,4,4],[2]]=>([],1) [[5,5,5],[]]=>([],1) [[5,5,4,1],[]]=>([],1) [[4,4,4,3],[]]=>([],1) [[3,3,3,3,3],[]]=>([],1) [[4,4,4,4],[1]]=>([],1) [[5,5,5,1],[1]]=>([(0,1)],2) [[5,5,5,5],[4,1]]=>([],1) [[5,5,5,4],[4]]=>([(0,1)],2) [[5,5,5,1],[]]=>([],1) [[4,4,4,4],[]]=>([],1) [[4,4,4,3,1],[]]=>([],1) [[3,3,3,3,3,1],[]]=>([],1) [[4,4,4,4,1],[1]]=>([(0,1)],2) [[3,3,3,3,3,3],[2]]=>([],1) [[4,4,4,4,3],[3]]=>([(0,1)],2) [[4,4,4,4,4],[3,1]]=>([],1) [[5,5,5,5],[4]]=>([],1) [[4,4,4,4,1],[]]=>([],1) [[4,4,4,4,4],[3]]=>([],1) [[5,5,5,5,4],[4]]=>([(0,1)],2) [[5,5,5,5,5],[4,1]]=>([],1) [[5,5,5,4,1],[]]=>([],1) [[5,5,5,5,1],[1]]=>([(0,1)],2) [[5,5,5,5,5],[4]]=>([],1) [[5,5,5,5,1],[]]=>([],1) [[4,4,4,4,4,4],[3]]=>([],1) [[4,4,4,4,4,1],[]]=>([],1) [[6,6,6,6,6],[5]]=>([],1) [[6,6,6,6,1],[]]=>([],1) [[5,5,5,5,5,5],[4]]=>([],1) [[5,5,5,5,5,1],[]]=>([],1) [[6,6,6,6,6,6],[5]]=>([],1) [[6,6,6,6,6,1],[]]=>([],1)
click to show experimental identities (only identities of compositions of up to three maps are shown)
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.
References
[1] Azenhas, O. The admissible interval for the invariant factors of a product of matrices MathSciNet:1712853
Sage code
def mapping(la):
    support = SymmetricFunctions(QQ).s()(la).support()
    return LatticePoset((support, lambda mu, nu: mu.dominates(nu)))
Weight
26
Created
Sep 27, 2020 at 14:56 by Martin Rubey
Updated
Jun 08, 2022 at 17:02 by Martin Rubey