Identifier
Mp00187:
Skew partitions
—conjugate⟶
Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Mp00263: Lattices —join irreducibles⟶ Posets
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Mp00263: Lattices —join irreducibles⟶ Posets
Images
=>
Cc0028;cc-rep-0Cc0028;cc-rep-1Cc0029;cc-rep-2Cc0014;cc-rep-3
[[1],[]]=>[[1],[]]=>([],1)=>([],0)
[[2],[]]=>[[1,1],[]]=>([],1)=>([],0)
[[1,1],[]]=>[[2],[]]=>([],1)=>([],0)
[[2,1],[1]]=>[[2,1],[1]]=>([(0,1)],2)=>([],1)
[[3],[]]=>[[1,1,1],[]]=>([],1)=>([],0)
[[2,1],[]]=>[[2,1],[]]=>([],1)=>([],0)
[[3,1],[1]]=>[[2,1,1],[1]]=>([(0,1)],2)=>([],1)
[[2,2],[1]]=>[[2,2],[1]]=>([],1)=>([],0)
[[3,2],[2]]=>[[2,2,1],[1,1]]=>([(0,1)],2)=>([],1)
[[1,1,1],[]]=>[[3],[]]=>([],1)=>([],0)
[[2,2,1],[1,1]]=>[[3,2],[2]]=>([(0,1)],2)=>([],1)
[[2,1,1],[1]]=>[[3,1],[1]]=>([(0,1)],2)=>([],1)
[[3,2,1],[2,1]]=>[[3,2,1],[2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4],[]]=>[[1,1,1,1],[]]=>([],1)=>([],0)
[[3,1],[]]=>[[2,1,1],[]]=>([],1)=>([],0)
[[4,1],[1]]=>[[2,1,1,1],[1]]=>([(0,1)],2)=>([],1)
[[2,2],[]]=>[[2,2],[]]=>([],1)=>([],0)
[[3,2],[1]]=>[[2,2,1],[1]]=>([(0,1)],2)=>([],1)
[[4,2],[2]]=>[[2,2,1,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[2,1,1],[]]=>[[3,1],[]]=>([],1)=>([],0)
[[3,2,1],[1,1]]=>[[3,2,1],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,1,1],[1]]=>[[3,1,1],[1]]=>([(0,1)],2)=>([],1)
[[4,2,1],[2,1]]=>[[3,2,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3],[2]]=>[[2,2,2],[1,1]]=>([],1)=>([],0)
[[4,3],[3]]=>[[2,2,2,1],[1,1,1]]=>([(0,1)],2)=>([],1)
[[2,2,1],[1]]=>[[3,2],[1]]=>([(0,1)],2)=>([],1)
[[3,3,1],[2,1]]=>[[3,2,2],[2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,2,1],[2]]=>[[3,2,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,1],[3,1]]=>[[3,2,2,1],[2,1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[2,2,2],[1,1]]=>[[3,3],[2]]=>([],1)=>([],0)
[[3,3,2],[2,2]]=>[[3,3,2],[2,2]]=>([(0,1)],2)=>([],1)
[[3,2,2],[2,1]]=>[[3,3,1],[2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,2],[3,2]]=>[[3,3,2,1],[2,2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[1,1,1,1],[]]=>[[4],[]]=>([],1)=>([],0)
[[2,2,2,1],[1,1,1]]=>[[4,3],[3]]=>([(0,1)],2)=>([],1)
[[2,2,1,1],[1,1]]=>[[4,2],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,2,1],[2,2,1]]=>[[4,3,2],[3,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[2,1,1,1],[1]]=>[[4,1],[1]]=>([(0,1)],2)=>([],1)
[[3,2,2,1],[2,1,1]]=>[[4,3,1],[3,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,2,1,1],[2,1]]=>[[4,2,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3,2,1],[3,2,1]]=>[[4,3,2,1],[3,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5],[]]=>[[1,1,1,1,1],[]]=>([],1)=>([],0)
[[4,1],[]]=>[[2,1,1,1],[]]=>([],1)=>([],0)
[[5,1],[1]]=>[[2,1,1,1,1],[1]]=>([(0,1)],2)=>([],1)
[[3,2],[]]=>[[2,2,1],[]]=>([],1)=>([],0)
[[4,2],[1]]=>[[2,2,1,1],[1]]=>([(0,1)],2)=>([],1)
[[5,2],[2]]=>[[2,2,1,1,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,1,1],[]]=>[[3,1,1],[]]=>([],1)=>([],0)
[[4,2,1],[1,1]]=>[[3,2,1,1],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,1,1],[1]]=>[[3,1,1,1],[1]]=>([(0,1)],2)=>([],1)
[[5,2,1],[2,1]]=>[[3,2,1,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3],[1]]=>[[2,2,2],[1]]=>([],1)=>([],0)
[[4,3],[2]]=>[[2,2,2,1],[1,1]]=>([(0,1)],2)=>([],1)
[[5,3],[3]]=>[[2,2,2,1,1],[1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[2,2,1],[]]=>[[3,2],[]]=>([],1)=>([],0)
[[3,3,1],[1,1]]=>[[3,2,2],[2]]=>([(0,1)],2)=>([],1)
[[3,2,1],[1]]=>[[3,2,1],[1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,1],[2,1]]=>[[3,2,2,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,2,1],[2]]=>[[3,2,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,3,1],[3,1]]=>[[3,2,2,1,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[3,2,2],[1,1]]=>[[3,3,1],[2]]=>([(0,1)],2)=>([],1)
[[4,3,2],[2,2]]=>[[3,3,2,1],[2,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,2,2],[2,1]]=>[[3,3,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,3,2],[3,2]]=>[[3,3,2,1,1],[2,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[2,1,1,1],[]]=>[[4,1],[]]=>([],1)=>([],0)
[[3,2,2,1],[1,1,1]]=>[[4,3,1],[3]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,2,1,1],[1,1]]=>[[4,2,1],[2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3,2,1],[2,2,1]]=>[[4,3,2,1],[3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[3,1,1,1],[1]]=>[[4,1,1],[1]]=>([(0,1)],2)=>([],1)
[[4,2,2,1],[2,1,1]]=>[[4,3,1,1],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,2,1,1],[2,1]]=>[[4,2,1,1],[2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,3,2,1],[3,2,1]]=>[[4,3,2,1,1],[3,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4],[3]]=>[[2,2,2,2],[1,1,1]]=>([],1)=>([],0)
[[5,4],[4]]=>[[2,2,2,2,1],[1,1,1,1]]=>([(0,1)],2)=>([],1)
[[3,3,1],[2]]=>[[3,2,2],[1,1]]=>([(0,1)],2)=>([],1)
[[4,4,1],[3,1]]=>[[3,2,2,2],[2,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,1],[3]]=>[[3,2,2,1],[1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,4,1],[4,1]]=>[[3,2,2,2,1],[2,1,1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[2,2,2],[1]]=>[[3,3],[1]]=>([],1)=>([],0)
[[3,3,2],[2,1]]=>[[3,3,2],[2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,2],[3,2]]=>[[3,3,2,2],[2,2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,2,2],[2]]=>[[3,3,1],[1,1]]=>([(0,1)],2)=>([],1)
[[4,3,2],[3,1]]=>[[3,3,2,1],[2,1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,4,2],[4,2]]=>[[3,3,2,2,1],[2,2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[2,2,1,1],[1]]=>[[4,2],[1]]=>([(0,1)],2)=>([],1)
[[3,3,2,1],[2,1,1]]=>[[4,3,2],[3,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3,1,1],[2,1]]=>[[4,2,2],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,2,1],[3,2,1]]=>[[4,3,2,2],[3,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[3,2,1,1],[2]]=>[[4,2,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,2,1],[3,1,1]]=>[[4,3,2,1],[3,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,3,1,1],[3,1]]=>[[4,2,2,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,4,2,1],[4,2,1]]=>[[4,3,2,2,1],[3,2,1,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,3],[2,2]]=>[[3,3,3],[2,2]]=>([],1)=>([],0)
[[4,4,3],[3,3]]=>[[3,3,3,2],[2,2,2]]=>([(0,1)],2)=>([],1)
[[4,3,3],[3,2]]=>[[3,3,3,1],[2,2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,4,3],[4,3]]=>[[3,3,3,2,1],[2,2,2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[2,2,2,1],[1,1]]=>[[4,3],[2]]=>([(0,1)],2)=>([],1)
[[3,3,3,1],[2,2,1]]=>[[4,3,3],[3,2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,2,1],[2,2]]=>[[4,3,2],[2,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,3,1],[3,3,1]]=>[[4,3,3,2],[3,2,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[3,2,2,1],[2,1]]=>[[4,3,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3,3,1],[3,2,1]]=>[[4,3,3,1],[3,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,3,2,1],[3,2]]=>[[4,3,2,1],[2,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,4,3,1],[4,3,1]]=>[[4,3,3,2,1],[3,2,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,2,2],[1,1,1]]=>[[4,4],[3]]=>([],1)=>([],0)
[[3,3,3,2],[2,2,2]]=>[[4,4,3],[3,3]]=>([(0,1)],2)=>([],1)
[[3,3,2,2],[2,2,1]]=>[[4,4,2],[3,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,3,2],[3,3,2]]=>[[4,4,3,2],[3,3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[3,2,2,2],[2,1,1]]=>[[4,4,1],[3,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,3,2],[3,2,2]]=>[[4,4,3,1],[3,3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,3,2,2],[3,2,1]]=>[[4,4,2,1],[3,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,4,3,2],[4,3,2]]=>[[4,4,3,2,1],[3,3,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,1,1],[]]=>[[5],[]]=>([],1)=>([],0)
[[2,2,2,2,1],[1,1,1,1]]=>[[5,4],[4]]=>([(0,1)],2)=>([],1)
[[2,2,2,1,1],[1,1,1]]=>[[5,3],[3]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,3,2,1],[2,2,2,1]]=>[[5,4,3],[4,3]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[2,2,1,1,1],[1,1]]=>[[5,2],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,2,2,1],[2,2,1,1]]=>[[5,4,2],[4,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[3,3,2,1,1],[2,2,1]]=>[[5,3,2],[3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,4,3,2,1],[3,3,2,1]]=>[[5,4,3,2],[4,3,2]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[2,1,1,1,1],[1]]=>[[5,1],[1]]=>([(0,1)],2)=>([],1)
[[3,2,2,2,1],[2,1,1,1]]=>[[5,4,1],[4,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,2,2,1,1],[2,1,1]]=>[[5,3,1],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,3,3,2,1],[3,2,2,1]]=>[[5,4,3,1],[4,3,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[3,2,1,1,1],[2,1]]=>[[5,2,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3,2,2,1],[3,2,1,1]]=>[[5,4,2,1],[4,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,2,1,1],[3,2,1]]=>[[5,3,2,1],[3,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,2,1],[4,3,2,1]]=>[[5,4,3,2,1],[4,3,2,1]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[6],[]]=>[[1,1,1,1,1,1],[]]=>([],1)=>([],0)
[[5,1],[]]=>[[2,1,1,1,1],[]]=>([],1)=>([],0)
[[6,1],[1]]=>[[2,1,1,1,1,1],[1]]=>([(0,1)],2)=>([],1)
[[4,2],[]]=>[[2,2,1,1],[]]=>([],1)=>([],0)
[[5,2],[1]]=>[[2,2,1,1,1],[1]]=>([(0,1)],2)=>([],1)
[[6,2],[2]]=>[[2,2,1,1,1,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,1,1],[]]=>[[3,1,1,1],[]]=>([],1)=>([],0)
[[5,2,1],[1,1]]=>[[3,2,1,1,1],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,1,1],[1]]=>[[3,1,1,1,1],[1]]=>([(0,1)],2)=>([],1)
[[6,2,1],[2,1]]=>[[3,2,1,1,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3],[]]=>[[2,2,2],[]]=>([],1)=>([],0)
[[4,3],[1]]=>[[2,2,2,1],[1]]=>([(0,1)],2)=>([],1)
[[5,3],[2]]=>[[2,2,2,1,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[6,3],[3]]=>[[2,2,2,1,1,1],[1,1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,2,1],[]]=>[[3,2,1],[]]=>([],1)=>([],0)
[[4,3,1],[1,1]]=>[[3,2,2,1],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,2,1],[1]]=>[[3,2,1,1],[1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,3,1],[2,1]]=>[[3,2,2,1,1],[2,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[5,2,1],[2]]=>[[3,2,1,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[6,3,1],[3,1]]=>[[3,2,2,1,1,1],[2,1,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[4,2,2],[1,1]]=>[[3,3,1,1],[2]]=>([(0,1)],2)=>([],1)
[[5,3,2],[2,2]]=>[[3,3,2,1,1],[2,2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[5,2,2],[2,1]]=>[[3,3,1,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[6,3,2],[3,2]]=>[[3,3,2,1,1,1],[2,2,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[3,1,1,1],[]]=>[[4,1,1],[]]=>([],1)=>([],0)
[[4,2,2,1],[1,1,1]]=>[[4,3,1,1],[3]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,2,1,1],[1,1]]=>[[4,2,1,1],[2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,3,2,1],[2,2,1]]=>[[4,3,2,1,1],[3,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,1,1,1],[1]]=>[[4,1,1,1],[1]]=>([(0,1)],2)=>([],1)
[[5,2,2,1],[2,1,1]]=>[[4,3,1,1,1],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,2,1,1],[2,1]]=>[[4,2,1,1,1],[2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[6,3,2,1],[3,2,1]]=>[[4,3,2,1,1,1],[3,2,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4],[2]]=>[[2,2,2,2],[1,1]]=>([],1)=>([],0)
[[5,4],[3]]=>[[2,2,2,2,1],[1,1,1]]=>([(0,1)],2)=>([],1)
[[6,4],[4]]=>[[2,2,2,2,1,1],[1,1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,1],[1]]=>[[3,2,2],[1]]=>([(0,1)],2)=>([],1)
[[4,4,1],[2,1]]=>[[3,2,2,2],[2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,1],[2]]=>[[3,2,2,1],[1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],2)
[[5,4,1],[3,1]]=>[[3,2,2,2,1],[2,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[5,3,1],[3]]=>[[3,2,2,1,1],[1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[6,4,1],[4,1]]=>[[3,2,2,2,1,1],[2,1,1,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[2,2,2],[]]=>[[3,3],[]]=>([],1)=>([],0)
[[3,3,2],[1,1]]=>[[3,3,2],[2]]=>([(0,1)],2)=>([],1)
[[4,4,2],[2,2]]=>[[3,3,2,2],[2,2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,2,2],[1]]=>[[3,3,1],[1]]=>([(0,1)],2)=>([],1)
[[4,3,2],[2,1]]=>[[3,3,2,1],[2,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[5,4,2],[3,2]]=>[[3,3,2,2,1],[2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,2,2],[2]]=>[[3,3,1,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,3,2],[3,1]]=>[[3,3,2,1,1],[2,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[6,4,2],[4,2]]=>[[3,3,2,2,1,1],[2,2,1,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[2,2,1,1],[]]=>[[4,2],[]]=>([],1)=>([],0)
[[3,3,2,1],[1,1,1]]=>[[4,3,2],[3]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,1,1],[1,1]]=>[[4,2,2],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,2,1],[2,2,1]]=>[[4,3,2,2],[3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[3,2,1,1],[1]]=>[[4,2,1],[1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,2,1],[2,1,1]]=>[[4,3,2,1],[3,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[4,3,1,1],[2,1]]=>[[4,2,2,1],[2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[5,4,2,1],[3,2,1]]=>[[4,3,2,2,1],[3,2,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[4,2,1,1],[2]]=>[[4,2,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,3,2,1],[3,1,1]]=>[[4,3,2,1,1],[3,1,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[5,3,1,1],[3,1]]=>[[4,2,2,1,1],[2,1,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[6,4,2,1],[4,2,1]]=>[[4,3,2,2,1,1],[3,2,1,1]]=>([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)=>([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
[[4,3,3],[2,2]]=>[[3,3,3,1],[2,2]]=>([(0,1)],2)=>([],1)
[[5,4,3],[3,3]]=>[[3,3,3,2,1],[2,2,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,3,3],[3,2]]=>[[3,3,3,1,1],[2,2,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[6,4,3],[4,3]]=>[[3,3,3,2,1,1],[2,2,2,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[3,2,2,1],[1,1]]=>[[4,3,1],[2]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],2)
[[4,3,3,1],[2,2,1]]=>[[4,3,3,1],[3,2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[4,3,2,1],[2,2]]=>[[4,3,2,1],[2,2]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[5,4,3,1],[3,3,1]]=>[[4,3,3,2,1],[3,2,2]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[4,2,2,1],[2,1]]=>[[4,3,1,1],[2,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[5,3,3,1],[3,2,1]]=>[[4,3,3,1,1],[3,2,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[5,3,2,1],[3,2]]=>[[4,3,2,1,1],[2,2,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[6,4,3,1],[4,3,1]]=>[[4,3,3,2,1,1],[3,2,2,1]]=>([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)=>([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
[[3,2,2,2],[1,1,1]]=>[[4,4,1],[3]]=>([(0,1)],2)=>([],1)
[[4,3,3,2],[2,2,2]]=>[[4,4,3,1],[3,3]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3,2,2],[2,2,1]]=>[[4,4,2,1],[3,2]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[5,4,3,2],[3,3,2]]=>[[4,4,3,2,1],[3,3,2]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[4,2,2,2],[2,1,1]]=>[[4,4,1,1],[3,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,3,3,2],[3,2,2]]=>[[4,4,3,1,1],[3,3,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,3,2,2],[3,2,1]]=>[[4,4,2,1,1],[3,2,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[6,4,3,2],[4,3,2]]=>[[4,4,3,2,1,1],[3,3,2,1]]=>([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)=>([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
[[2,1,1,1,1],[]]=>[[5,1],[]]=>([],1)=>([],0)
[[3,2,2,2,1],[1,1,1,1]]=>[[5,4,1],[4]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,2,2,1,1],[1,1,1]]=>[[5,3,1],[3]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[4,3,3,2,1],[2,2,2,1]]=>[[5,4,3,1],[4,3]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[3,2,1,1,1],[1,1]]=>[[5,2,1],[2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3,2,2,1],[2,2,1,1]]=>[[5,4,2,1],[4,2]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[4,3,2,1,1],[2,2,1]]=>[[5,3,2,1],[3,2]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[5,4,3,2,1],[3,3,2,1]]=>[[5,4,3,2,1],[4,3,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[3,1,1,1,1],[1]]=>[[5,1,1],[1]]=>([(0,1)],2)=>([],1)
[[4,2,2,2,1],[2,1,1,1]]=>[[5,4,1,1],[4,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,2,2,1,1],[2,1,1]]=>[[5,3,1,1],[3,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,3,3,2,1],[3,2,2,1]]=>[[5,4,3,1,1],[4,3,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[4,2,1,1,1],[2,1]]=>[[5,2,1,1],[2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,3,2,2,1],[3,2,1,1]]=>[[5,4,2,1,1],[4,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,3,2,1,1],[3,2,1]]=>[[5,3,2,1,1],[3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,5],[4]]=>[[2,2,2,2,2],[1,1,1,1]]=>([],1)=>([],0)
[[6,5],[5]]=>[[2,2,2,2,2,1],[1,1,1,1,1]]=>([(0,1)],2)=>([],1)
[[4,4,1],[3]]=>[[3,2,2,2],[1,1,1]]=>([(0,1)],2)=>([],1)
[[5,5,1],[4,1]]=>[[3,2,2,2,2],[2,1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,4,1],[4]]=>[[3,2,2,2,1],[1,1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[6,5,1],[5,1]]=>[[3,2,2,2,2,1],[2,1,1,1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3,2],[2]]=>[[3,3,2],[1,1]]=>([(0,1)],2)=>([],1)
[[4,4,2],[3,1]]=>[[3,3,2,2],[2,1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],2)
[[5,5,2],[4,2]]=>[[3,3,2,2,2],[2,2,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[4,3,2],[3]]=>[[3,3,2,1],[1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,4,2],[4,1]]=>[[3,3,2,2,1],[2,1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[6,5,2],[5,2]]=>[[3,3,2,2,2,1],[2,2,1,1,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[3,3,1,1],[2]]=>[[4,2,2],[1,1]]=>([(0,1)],2)=>([],1)
[[4,4,2,1],[3,1,1]]=>[[4,3,2,2],[3,1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[4,4,1,1],[3,1]]=>[[4,2,2,2],[2,1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,5,2,1],[4,2,1]]=>[[4,3,2,2,2],[3,2,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,3,1,1],[3]]=>[[4,2,2,1],[1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,4,2,1],[4,1,1]]=>[[4,3,2,2,1],[3,1,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[5,4,1,1],[4,1]]=>[[4,2,2,2,1],[2,1,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[6,5,2,1],[5,2,1]]=>[[4,3,2,2,2,1],[3,2,1,1,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,3],[2,1]]=>[[3,3,3],[2,1]]=>([],1)=>([],0)
[[4,4,3],[3,2]]=>[[3,3,3,2],[2,2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,5,3],[4,3]]=>[[3,3,3,2,2],[2,2,2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3,3],[3,1]]=>[[3,3,3,1],[2,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,4,3],[4,2]]=>[[3,3,3,2,1],[2,2,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[6,5,3],[5,3]]=>[[3,3,3,2,2,1],[2,2,2,1,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[2,2,2,1],[1]]=>[[4,3],[1]]=>([(0,1)],2)=>([],1)
[[3,3,3,1],[2,1,1]]=>[[4,3,3],[3,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,2,1],[2,1]]=>[[4,3,2],[2,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[4,4,3,1],[3,2,1]]=>[[4,3,3,2],[3,2,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[4,4,2,1],[3,2]]=>[[4,3,2,2],[2,2,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[5,5,3,1],[4,3,1]]=>[[4,3,3,2,2],[3,2,2,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[3,2,2,1],[2]]=>[[4,3,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,3,1],[3,1,1]]=>[[4,3,3,1],[3,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,3,2,1],[3,1]]=>[[4,3,2,1],[2,1,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[5,4,3,1],[4,2,1]]=>[[4,3,3,2,1],[3,2,1,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[5,4,2,1],[4,2]]=>[[4,3,2,2,1],[2,2,1,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[6,5,3,1],[5,3,1]]=>[[4,3,3,2,2,1],[3,2,2,1,1]]=>([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)=>([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
[[3,3,2,2],[2,1,1]]=>[[4,4,2],[3,1]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],2)
[[4,4,3,2],[3,2,2]]=>[[4,4,3,2],[3,3,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[4,4,2,2],[3,2,1]]=>[[4,4,2,2],[3,2,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[5,5,3,2],[4,3,2]]=>[[4,4,3,2,2],[3,3,2,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[4,3,2,2],[3,1,1]]=>[[4,4,2,1],[3,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[5,4,3,2],[4,2,2]]=>[[4,4,3,2,1],[3,3,1,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[5,4,2,2],[4,2,1]]=>[[4,4,2,2,1],[3,2,1,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[6,5,3,2],[5,3,2]]=>[[4,4,3,2,2,1],[3,3,2,1,1]]=>([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)=>([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
[[2,2,1,1,1],[1]]=>[[5,2],[1]]=>([(0,1)],2)=>([],1)
[[3,3,2,2,1],[2,1,1,1]]=>[[5,4,2],[4,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[3,3,2,1,1],[2,1,1]]=>[[5,3,2],[3,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,4,3,2,1],[3,2,2,1]]=>[[5,4,3,2],[4,3,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[3,3,1,1,1],[2,1]]=>[[5,2,2],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,2,2,1],[3,2,1,1]]=>[[5,4,2,2],[4,2,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[4,4,2,1,1],[3,2,1]]=>[[5,3,2,2],[3,2,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[5,5,3,2,1],[4,3,2,1]]=>[[5,4,3,2,2],[4,3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[3,2,1,1,1],[2]]=>[[5,2,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,2,2,1],[3,1,1,1]]=>[[5,4,2,1],[4,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,3,2,1,1],[3,1,1]]=>[[5,3,2,1],[3,1,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[5,4,3,2,1],[4,2,2,1]]=>[[5,4,3,2,1],[4,3,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[4,3,1,1,1],[3,1]]=>[[5,2,2,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,4,2,2,1],[4,2,1,1]]=>[[5,4,2,2,1],[4,2,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,4,2,1,1],[4,2,1]]=>[[5,3,2,2,1],[3,2,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[4,4,4],[3,3]]=>[[3,3,3,3],[2,2,2]]=>([],1)=>([],0)
[[5,5,4],[4,4]]=>[[3,3,3,3,2],[2,2,2,2]]=>([(0,1)],2)=>([],1)
[[5,4,4],[4,3]]=>[[3,3,3,3,1],[2,2,2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[6,5,4],[5,4]]=>[[3,3,3,3,2,1],[2,2,2,2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3,3,1],[2,2]]=>[[4,3,3],[2,2]]=>([(0,1)],2)=>([],1)
[[4,4,4,1],[3,3,1]]=>[[4,3,3,3],[3,2,2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,3,1],[3,3]]=>[[4,3,3,2],[2,2,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,5,4,1],[4,4,1]]=>[[4,3,3,3,2],[3,2,2,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,3,3,1],[3,2]]=>[[4,3,3,1],[2,2,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[5,4,4,1],[4,3,1]]=>[[4,3,3,3,1],[3,2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[5,4,3,1],[4,3]]=>[[4,3,3,2,1],[2,2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[6,5,4,1],[5,4,1]]=>[[4,3,3,3,2,1],[3,2,2,2,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[2,2,2,2],[1,1]]=>[[4,4],[2]]=>([],1)=>([],0)
[[3,3,3,2],[2,2,1]]=>[[4,4,3],[3,2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,4,2],[3,3,2]]=>[[4,4,3,3],[3,3,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3,2,2],[2,2]]=>[[4,4,2],[2,2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,3,2],[3,3,1]]=>[[4,4,3,2],[3,2,2]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[5,5,4,2],[4,4,2]]=>[[4,4,3,3,2],[3,3,2,2]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[3,2,2,2],[2,1]]=>[[4,4,1],[2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,3,2],[3,2,1]]=>[[4,4,3,1],[3,2,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[5,4,4,2],[4,3,2]]=>[[4,4,3,3,1],[3,3,2,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[4,3,2,2],[3,2]]=>[[4,4,2,1],[2,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,4,3,2],[4,3,1]]=>[[4,4,3,2,1],[3,2,2,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[6,5,4,2],[5,4,2]]=>[[4,4,3,3,2,1],[3,3,2,2,1]]=>([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)=>([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
[[2,2,2,1,1],[1,1]]=>[[5,3],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,3,2,1],[2,2,1,1]]=>[[5,4,3],[4,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[3,3,3,1,1],[2,2,1]]=>[[5,3,3],[3,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[4,4,4,2,1],[3,3,2,1]]=>[[5,4,3,3],[4,3,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[3,3,2,1,1],[2,2]]=>[[5,3,2],[2,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[4,4,3,2,1],[3,3,1,1]]=>[[5,4,3,2],[4,2,2]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[4,4,3,1,1],[3,3,1]]=>[[5,3,3,2],[3,2,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,5,4,2,1],[4,4,2,1]]=>[[5,4,3,3,2],[4,3,2,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[3,2,2,1,1],[2,1]]=>[[5,3,1],[2,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[4,3,3,2,1],[3,2,1,1]]=>[[5,4,3,1],[4,2,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[4,3,3,1,1],[3,2,1]]=>[[5,3,3,1],[3,2,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[5,4,4,2,1],[4,3,2,1]]=>[[5,4,3,3,1],[4,3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[4,3,2,1,1],[3,2]]=>[[5,3,2,1],[2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[5,4,3,2,1],[4,3,1,1]]=>[[5,4,3,2,1],[4,2,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,4,3,1,1],[4,3,1]]=>[[5,3,3,2,1],[3,2,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[3,3,3,3],[2,2,2]]=>[[4,4,4],[3,3]]=>([],1)=>([],0)
[[4,4,4,3],[3,3,3]]=>[[4,4,4,3],[3,3,3]]=>([(0,1)],2)=>([],1)
[[4,4,3,3],[3,3,2]]=>[[4,4,4,2],[3,3,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,5,4,3],[4,4,3]]=>[[4,4,4,3,2],[3,3,3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,3,3,3],[3,2,2]]=>[[4,4,4,1],[3,3,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,4,4,3],[4,3,3]]=>[[4,4,4,3,1],[3,3,3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,4,3,3],[4,3,2]]=>[[4,4,4,2,1],[3,3,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[6,5,4,3],[5,4,3]]=>[[4,4,4,3,2,1],[3,3,3,2,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[2,2,2,2,1],[1,1,1]]=>[[5,4],[3]]=>([(0,1)],2)=>([],1)
[[3,3,3,3,1],[2,2,2,1]]=>[[5,4,4],[4,3]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,3,2,1],[2,2,2]]=>[[5,4,3],[3,3]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,4,3,1],[3,3,3,1]]=>[[5,4,4,3],[4,3,3]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[3,3,2,2,1],[2,2,1]]=>[[5,4,2],[3,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,4,3,3,1],[3,3,2,1]]=>[[5,4,4,2],[4,3,2]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[4,4,3,2,1],[3,3,2]]=>[[5,4,3,2],[3,3,2]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[5,5,4,3,1],[4,4,3,1]]=>[[5,4,4,3,2],[4,3,3,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[3,2,2,2,1],[2,1,1]]=>[[5,4,1],[3,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[4,3,3,3,1],[3,2,2,1]]=>[[5,4,4,1],[4,3,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,3,3,2,1],[3,2,2]]=>[[5,4,3,1],[3,3,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[5,4,4,3,1],[4,3,3,1]]=>[[5,4,4,3,1],[4,3,3,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[4,3,2,2,1],[3,2,1]]=>[[5,4,2,1],[3,2,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[5,4,3,3,1],[4,3,2,1]]=>[[5,4,4,2,1],[4,3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,4,3,2,1],[4,3,2]]=>[[5,4,3,2,1],[3,3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[2,2,2,2,2],[1,1,1,1]]=>[[5,5],[4]]=>([],1)=>([],0)
[[3,3,3,3,2],[2,2,2,2]]=>[[5,5,4],[4,4]]=>([(0,1)],2)=>([],1)
[[3,3,3,2,2],[2,2,2,1]]=>[[5,5,3],[4,3]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,4,3,2],[3,3,3,2]]=>[[5,5,4,3],[4,4,3]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[3,3,2,2,2],[2,2,1,1]]=>[[5,5,2],[4,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[4,4,3,3,2],[3,3,2,2]]=>[[5,5,4,2],[4,4,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,3,2,2],[3,3,2,1]]=>[[5,5,3,2],[4,3,2]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[5,5,4,3,2],[4,4,3,2]]=>[[5,5,4,3,2],[4,4,3,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[3,2,2,2,2],[2,1,1,1]]=>[[5,5,1],[4,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,3,3,2],[3,2,2,2]]=>[[5,5,4,1],[4,4,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,3,3,2,2],[3,2,2,1]]=>[[5,5,3,1],[4,3,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[5,4,4,3,2],[4,3,3,2]]=>[[5,5,4,3,1],[4,4,3,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[4,3,2,2,2],[3,2,1,1]]=>[[5,5,2,1],[4,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[5,4,3,3,2],[4,3,2,2]]=>[[5,5,4,2,1],[4,4,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,4,3,2,2],[4,3,2,1]]=>[[5,5,3,2,1],[4,3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[1,1,1,1,1,1],[]]=>[[6],[]]=>([],1)=>([],0)
[[2,2,2,2,2,1],[1,1,1,1,1]]=>[[6,5],[5]]=>([(0,1)],2)=>([],1)
[[2,2,2,2,1,1],[1,1,1,1]]=>[[6,4],[4]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,3,3,2,1],[2,2,2,2,1]]=>[[6,5,4],[5,4]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[2,2,2,1,1,1],[1,1,1]]=>[[6,3],[3]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3,3,2,2,1],[2,2,2,1,1]]=>[[6,5,3],[5,3]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[3,3,3,2,1,1],[2,2,2,1]]=>[[6,4,3],[4,3]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[4,4,4,3,2,1],[3,3,3,2,1]]=>[[6,5,4,3],[5,4,3]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[2,2,1,1,1,1],[1,1]]=>[[6,2],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,2,2,2,1],[2,2,1,1,1]]=>[[6,5,2],[5,2]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[3,3,2,2,1,1],[2,2,1,1]]=>[[6,4,2],[4,2]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,4,3,3,2,1],[3,3,2,2,1]]=>[[6,5,4,2],[5,4,2]]=>([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
[[3,3,2,1,1,1],[2,2,1]]=>[[6,3,2],[3,2]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[4,4,3,2,2,1],[3,3,2,1,1]]=>[[6,5,3,2],[5,3,2]]=>([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
[[4,4,3,2,1,1],[3,3,2,1]]=>[[6,4,3,2],[4,3,2]]=>([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
[[2,1,1,1,1,1],[1]]=>[[6,1],[1]]=>([(0,1)],2)=>([],1)
[[3,2,2,2,2,1],[2,1,1,1,1]]=>[[6,5,1],[5,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,2,2,2,1,1],[2,1,1,1]]=>[[6,4,1],[4,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[4,3,3,3,2,1],[3,2,2,2,1]]=>[[6,5,4,1],[5,4,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[3,2,2,1,1,1],[2,1,1]]=>[[6,3,1],[3,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[4,3,3,2,2,1],[3,2,2,1,1]]=>[[6,5,3,1],[5,3,1]]=>([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
[[4,3,3,2,1,1],[3,2,2,1]]=>[[6,4,3,1],[4,3,1]]=>([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
[[3,2,1,1,1,1],[2,1]]=>[[6,2,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3,2,2,2,1],[3,2,1,1,1]]=>[[6,5,2,1],[5,2,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,3,2,2,1,1],[3,2,1,1]]=>[[6,4,2,1],[4,2,1]]=>([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
[[4,3,2,1,1,1],[3,2,1]]=>[[6,3,2,1],[3,2,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[7],[]]=>[[1,1,1,1,1,1,1],[]]=>([],1)=>([],0)
[[6,1],[]]=>[[2,1,1,1,1,1],[]]=>([],1)=>([],0)
[[7,1],[1]]=>[[2,1,1,1,1,1,1],[1]]=>([(0,1)],2)=>([],1)
[[5,2],[]]=>[[2,2,1,1,1],[]]=>([],1)=>([],0)
[[6,2],[1]]=>[[2,2,1,1,1,1],[1]]=>([(0,1)],2)=>([],1)
[[7,2],[2]]=>[[2,2,1,1,1,1,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,1,1],[]]=>[[3,1,1,1,1],[]]=>([],1)=>([],0)
[[6,2,1],[1,1]]=>[[3,2,1,1,1,1],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[6,1,1],[1]]=>[[3,1,1,1,1,1],[1]]=>([(0,1)],2)=>([],1)
[[7,2,1],[2,1]]=>[[3,2,1,1,1,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3],[]]=>[[2,2,2,1],[]]=>([],1)=>([],0)
[[5,3],[1]]=>[[2,2,2,1,1],[1]]=>([(0,1)],2)=>([],1)
[[6,3],[2]]=>[[2,2,2,1,1,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[7,3],[3]]=>[[2,2,2,1,1,1,1],[1,1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,2,1],[]]=>[[3,2,1,1],[]]=>([],1)=>([],0)
[[5,3,1],[1,1]]=>[[3,2,2,1,1],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,2,1],[1]]=>[[3,2,1,1,1],[1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[6,3,1],[2,1]]=>[[3,2,2,1,1,1],[2,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[6,2,1],[2]]=>[[3,2,1,1,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[7,3,1],[3,1]]=>[[3,2,2,1,1,1,1],[2,1,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[5,2,2],[1,1]]=>[[3,3,1,1,1],[2]]=>([(0,1)],2)=>([],1)
[[6,3,2],[2,2]]=>[[3,3,2,1,1,1],[2,2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[6,2,2],[2,1]]=>[[3,3,1,1,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[7,3,2],[3,2]]=>[[3,3,2,1,1,1,1],[2,2,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[4,1,1,1],[]]=>[[4,1,1,1],[]]=>([],1)=>([],0)
[[5,2,2,1],[1,1,1]]=>[[4,3,1,1,1],[3]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,2,1,1],[1,1]]=>[[4,2,1,1,1],[2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[6,3,2,1],[2,2,1]]=>[[4,3,2,1,1,1],[3,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[5,1,1,1],[1]]=>[[4,1,1,1,1],[1]]=>([(0,1)],2)=>([],1)
[[6,2,2,1],[2,1,1]]=>[[4,3,1,1,1,1],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[6,2,1,1],[2,1]]=>[[4,2,1,1,1,1],[2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[7,3,2,1],[3,2,1]]=>[[4,3,2,1,1,1,1],[3,2,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4],[1]]=>[[2,2,2,2],[1]]=>([],1)=>([],0)
[[5,4],[2]]=>[[2,2,2,2,1],[1,1]]=>([(0,1)],2)=>([],1)
[[6,4],[3]]=>[[2,2,2,2,1,1],[1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[7,4],[4]]=>[[2,2,2,2,1,1,1],[1,1,1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3,1],[]]=>[[3,2,2],[]]=>([],1)=>([],0)
[[4,4,1],[1,1]]=>[[3,2,2,2],[2]]=>([(0,1)],2)=>([],1)
[[4,3,1],[1]]=>[[3,2,2,1],[1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,4,1],[2,1]]=>[[3,2,2,2,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,3,1],[2]]=>[[3,2,2,1,1],[1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[6,4,1],[3,1]]=>[[3,2,2,2,1,1],[2,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[6,3,1],[3]]=>[[3,2,2,1,1,1],[1,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[7,4,1],[4,1]]=>[[3,2,2,2,1,1,1],[2,1,1,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,2,2],[]]=>[[3,3,1],[]]=>([],1)=>([],0)
[[4,3,2],[1,1]]=>[[3,3,2,1],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,4,2],[2,2]]=>[[3,3,2,2,1],[2,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,2,2],[1]]=>[[3,3,1,1],[1]]=>([(0,1)],2)=>([],1)
[[5,3,2],[2,1]]=>[[3,3,2,1,1],[2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[6,4,2],[3,2]]=>[[3,3,2,2,1,1],[2,2,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,2,2],[2]]=>[[3,3,1,1,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[6,3,2],[3,1]]=>[[3,3,2,1,1,1],[2,1,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[7,4,2],[4,2]]=>[[3,3,2,2,1,1,1],[2,2,1,1]]=>([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,2,1,1],[]]=>[[4,2,1],[]]=>([],1)=>([],0)
[[4,3,2,1],[1,1,1]]=>[[4,3,2,1],[3]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3,1,1],[1,1]]=>[[4,2,2,1],[2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,4,2,1],[2,2,1]]=>[[4,3,2,2,1],[3,2]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[4,2,1,1],[1]]=>[[4,2,1,1],[1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,3,2,1],[2,1,1]]=>[[4,3,2,1,1],[3,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[5,3,1,1],[2,1]]=>[[4,2,2,1,1],[2,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[6,4,2,1],[3,2,1]]=>[[4,3,2,2,1,1],[3,2,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,2,1,1],[2]]=>[[4,2,1,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[6,3,2,1],[3,1,1]]=>[[4,3,2,1,1,1],[3,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[6,3,1,1],[3,1]]=>[[4,2,2,1,1,1],[2,1,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[5,3,3],[2,2]]=>[[3,3,3,1,1],[2,2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[6,4,3],[3,3]]=>[[3,3,3,2,1,1],[2,2,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[6,3,3],[3,2]]=>[[3,3,3,1,1,1],[2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[7,4,3],[4,3]]=>[[3,3,3,2,1,1,1],[2,2,2,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,2,2,1],[1,1]]=>[[4,3,1,1],[2]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],2)
[[5,3,3,1],[2,2,1]]=>[[4,3,3,1,1],[3,2]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>([(0,3),(1,2),(2,3)],4)
[[5,3,2,1],[2,2]]=>[[4,3,2,1,1],[2,2]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[6,4,3,1],[3,3,1]]=>[[4,3,3,2,1,1],[3,2,2]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,2,2,1],[2,1]]=>[[4,3,1,1,1],[2,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[6,3,3,1],[3,2,1]]=>[[4,3,3,1,1,1],[3,2,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[6,3,2,1],[3,2]]=>[[4,3,2,1,1,1],[2,2,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[4,2,2,2],[1,1,1]]=>[[4,4,1,1],[3]]=>([(0,1)],2)=>([],1)
[[5,3,3,2],[2,2,2]]=>[[4,4,3,1,1],[3,3]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[5,3,2,2],[2,2,1]]=>[[4,4,2,1,1],[3,2]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[6,4,3,2],[3,3,2]]=>[[4,4,3,2,1,1],[3,3,2]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,2,2,2],[2,1,1]]=>[[4,4,1,1,1],[3,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[6,3,3,2],[3,2,2]]=>[[4,4,3,1,1,1],[3,3,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[6,3,2,2],[3,2,1]]=>[[4,4,2,1,1,1],[3,2,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[3,1,1,1,1],[]]=>[[5,1,1],[]]=>([],1)=>([],0)
[[4,2,2,2,1],[1,1,1,1]]=>[[5,4,1,1],[4]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,2,2,1,1],[1,1,1]]=>[[5,3,1,1],[3]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[5,3,3,2,1],[2,2,2,1]]=>[[5,4,3,1,1],[4,3]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[4,2,1,1,1],[1,1]]=>[[5,2,1,1],[2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,3,2,2,1],[2,2,1,1]]=>[[5,4,2,1,1],[4,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,3,2,1,1],[2,2,1]]=>[[5,3,2,1,1],[3,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[4,1,1,1,1],[1]]=>[[5,1,1,1],[1]]=>([(0,1)],2)=>([],1)
[[5,2,2,2,1],[2,1,1,1]]=>[[5,4,1,1,1],[4,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,2,2,1,1],[2,1,1]]=>[[5,3,1,1,1],[3,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,2,1,1,1],[2,1]]=>[[5,2,1,1,1],[2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,5],[3]]=>[[2,2,2,2,2],[1,1,1]]=>([],1)=>([],0)
[[6,5],[4]]=>[[2,2,2,2,2,1],[1,1,1,1]]=>([(0,1)],2)=>([],1)
[[7,5],[5]]=>[[2,2,2,2,2,1,1],[1,1,1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,1],[2]]=>[[3,2,2,2],[1,1]]=>([(0,1)],2)=>([],1)
[[5,5,1],[3,1]]=>[[3,2,2,2,2],[2,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,4,1],[3]]=>[[3,2,2,2,1],[1,1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],2)
[[6,5,1],[4,1]]=>[[3,2,2,2,2,1],[2,1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[6,4,1],[4]]=>[[3,2,2,2,1,1],[1,1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[7,5,1],[5,1]]=>[[3,2,2,2,2,1,1],[2,1,1,1,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[3,3,2],[1]]=>[[3,3,2],[1]]=>([(0,1)],2)=>([],1)
[[4,4,2],[2,1]]=>[[3,3,2,2],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,5,2],[3,2]]=>[[3,3,2,2,2],[2,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,3,2],[2]]=>[[3,3,2,1],[1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,4,2],[3,1]]=>[[3,3,2,2,1],[2,1,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[6,5,2],[4,2]]=>[[3,3,2,2,2,1],[2,2,1,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,3,2],[3]]=>[[3,3,2,1,1],[1,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[6,4,2],[4,1]]=>[[3,3,2,2,1,1],[2,1,1,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[7,5,2],[5,2]]=>[[3,3,2,2,2,1,1],[2,2,1,1,1]]=>([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,3,1,1],[1]]=>[[4,2,2],[1]]=>([(0,1)],2)=>([],1)
[[4,4,2,1],[2,1,1]]=>[[4,3,2,2],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,4,1,1],[2,1]]=>[[4,2,2,2],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,5,2,1],[3,2,1]]=>[[4,3,2,2,2],[3,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,1,1],[2]]=>[[4,2,2,1],[1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],2)
[[5,4,2,1],[3,1,1]]=>[[4,3,2,2,1],[3,1,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[5,4,1,1],[3,1]]=>[[4,2,2,2,1],[2,1,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[6,5,2,1],[4,2,1]]=>[[4,3,2,2,2,1],[3,2,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,3,1,1],[3]]=>[[4,2,2,1,1],[1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[6,4,2,1],[4,1,1]]=>[[4,3,2,2,1,1],[3,1,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[6,4,1,1],[4,1]]=>[[4,2,2,2,1,1],[2,1,1,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[3,3,3],[1,1]]=>[[3,3,3],[2]]=>([],1)=>([],0)
[[4,4,3],[2,2]]=>[[3,3,3,2],[2,2]]=>([(0,1)],2)=>([],1)
[[5,5,3],[3,3]]=>[[3,3,3,2,2],[2,2,2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,3],[2,1]]=>[[3,3,3,1],[2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,4,3],[3,2]]=>[[3,3,3,2,1],[2,2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[6,5,3],[4,3]]=>[[3,3,3,2,2,1],[2,2,2,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,3,3],[3,1]]=>[[3,3,3,1,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[6,4,3],[4,2]]=>[[3,3,3,2,1,1],[2,2,1,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[7,5,3],[5,3]]=>[[3,3,3,2,2,1,1],[2,2,2,1,1]]=>([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[2,2,2,1],[]]=>[[4,3],[]]=>([],1)=>([],0)
[[3,3,3,1],[1,1,1]]=>[[4,3,3],[3]]=>([(0,1)],2)=>([],1)
[[3,3,2,1],[1,1]]=>[[4,3,2],[2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,3,1],[2,2,1]]=>[[4,3,3,2],[3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,4,2,1],[2,2]]=>[[4,3,2,2],[2,2]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[5,5,3,1],[3,3,1]]=>[[4,3,3,2,2],[3,2,2]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,2,2,1],[1]]=>[[4,3,1],[1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,3,1],[2,1,1]]=>[[4,3,3,1],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,3,2,1],[2,1]]=>[[4,3,2,1],[2,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[5,4,3,1],[3,2,1]]=>[[4,3,3,2,1],[3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,4,2,1],[3,2]]=>[[4,3,2,2,1],[2,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[4,2,2,1],[2]]=>[[4,3,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,3,3,1],[3,1,1]]=>[[4,3,3,1,1],[3,1,1]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,3,2,1],[3,1]]=>[[4,3,2,1,1],[2,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[3,3,2,2],[1,1,1]]=>[[4,4,2],[3]]=>([(0,1)],2)=>([],1)
[[4,4,3,2],[2,2,2]]=>[[4,4,3,2],[3,3]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,2,2],[2,2,1]]=>[[4,4,2,2],[3,2]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[5,5,3,2],[3,3,2]]=>[[4,4,3,2,2],[3,3,2]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,3,2,2],[2,1,1]]=>[[4,4,2,1],[3,1]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>([(0,2),(0,3),(3,1)],4)
[[5,4,3,2],[3,2,2]]=>[[4,4,3,2,1],[3,3,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,4,2,2],[3,2,1]]=>[[4,4,2,2,1],[3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,3,2,2],[3,1,1]]=>[[4,4,2,1,1],[3,1,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[2,2,1,1,1],[]]=>[[5,2],[]]=>([],1)=>([],0)
[[3,3,2,2,1],[1,1,1,1]]=>[[5,4,2],[4]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,2,1,1],[1,1,1]]=>[[5,3,2],[3]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,4,3,2,1],[2,2,2,1]]=>[[5,4,3,2],[4,3]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,1,1,1],[1,1]]=>[[5,2,2],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,2,2,1],[2,2,1,1]]=>[[5,4,2,2],[4,2]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,4,2,1,1],[2,2,1]]=>[[5,3,2,2],[3,2]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,5,3,2,1],[3,3,2,1]]=>[[5,4,3,2,2],[4,3,2]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[3,2,1,1,1],[1]]=>[[5,2,1],[1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,2,2,1],[2,1,1,1]]=>[[5,4,2,1],[4,1]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[4,3,2,1,1],[2,1,1]]=>[[5,3,2,1],[3,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,3,1,1,1],[2,1]]=>[[5,2,2,1],[2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[4,2,1,1,1],[2]]=>[[5,2,1,1],[1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,3,2,2,1],[3,1,1,1]]=>[[5,4,2,1,1],[4,1,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[5,3,1,1,1],[3,1]]=>[[5,2,2,1,1],[2,1,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,4,4],[3,3]]=>[[3,3,3,3,1],[2,2,2]]=>([(0,1)],2)=>([],1)
[[6,5,4],[4,4]]=>[[3,3,3,3,2,1],[2,2,2,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[6,4,4],[4,3]]=>[[3,3,3,3,1,1],[2,2,2,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[7,5,4],[5,4]]=>[[3,3,3,3,2,1,1],[2,2,2,2,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[4,3,3,1],[2,2]]=>[[4,3,3,1],[2,2]]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>([(1,2)],3)
[[5,4,4,1],[3,3,1]]=>[[4,3,3,3,1],[3,2,2]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>([(0,3),(1,2),(2,3)],4)
[[5,4,3,1],[3,3]]=>[[4,3,3,2,1],[2,2,2]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[6,5,4,1],[4,4,1]]=>[[4,3,3,3,2,1],[3,2,2,2]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,3,3,1],[3,2]]=>[[4,3,3,1,1],[2,2,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[6,4,4,1],[4,3,1]]=>[[4,3,3,3,1,1],[3,2,2,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[6,4,3,1],[4,3]]=>[[4,3,3,2,1,1],[2,2,2,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[3,2,2,2],[1,1]]=>[[4,4,1],[2]]=>([(0,1)],2)=>([],1)
[[4,3,3,2],[2,2,1]]=>[[4,4,3,1],[3,2]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>([(0,2),(0,3),(3,1)],4)
[[5,4,4,2],[3,3,2]]=>[[4,4,3,3,1],[3,3,2]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[4,3,2,2],[2,2]]=>[[4,4,2,1],[2,2]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,2],[3,3,1]]=>[[4,4,3,2,1],[3,2,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[4,2,2,2],[2,1]]=>[[4,4,1,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,3,3,2],[3,2,1]]=>[[4,4,3,1,1],[3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,3,2,2],[3,2]]=>[[4,4,2,1,1],[2,2,1]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,2,2,1,1],[1,1]]=>[[5,3,1],[2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[4,3,3,2,1],[2,2,1,1]]=>[[5,4,3,1],[4,2]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[4,3,3,1,1],[2,2,1]]=>[[5,3,3,1],[3,2]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[5,4,4,2,1],[3,3,2,1]]=>[[5,4,3,3,1],[4,3,2]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,3,2,1,1],[2,2]]=>[[5,3,2,1],[2,2]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[4,2,2,1,1],[2,1]]=>[[5,3,1,1],[2,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[5,3,2,1,1],[3,2]]=>[[5,3,2,1,1],[2,2,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,3,3,3],[2,2,2]]=>[[4,4,4,1],[3,3]]=>([(0,1)],2)=>([],1)
[[5,4,4,3],[3,3,3]]=>[[4,4,4,3,1],[3,3,3]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,4,3,3],[3,3,2]]=>[[4,4,4,2,1],[3,3,2]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[6,5,4,3],[4,4,3]]=>[[4,4,4,3,2,1],[3,3,3,2]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,3,3,3],[3,2,2]]=>[[4,4,4,1,1],[3,3,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[6,4,4,3],[4,3,3]]=>[[4,4,4,3,1,1],[3,3,3,1]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[6,4,3,3],[4,3,2]]=>[[4,4,4,2,1,1],[3,3,2,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[3,2,2,2,1],[1,1,1]]=>[[5,4,1],[3]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],2)
[[4,3,3,3,1],[2,2,2,1]]=>[[5,4,4,1],[4,3]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[4,3,3,2,1],[2,2,2]]=>[[5,4,3,1],[3,3]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[5,4,4,3,1],[3,3,3,1]]=>[[5,4,4,3,1],[4,3,3]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,3,2,2,1],[2,2,1]]=>[[5,4,2,1],[3,2]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,2,2,2,1],[2,1,1]]=>[[5,4,1,1],[3,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[5,3,3,3,1],[3,2,2,1]]=>[[5,4,4,1,1],[4,3,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[3,2,2,2,2],[1,1,1,1]]=>[[5,5,1],[4]]=>([(0,1)],2)=>([],1)
[[4,3,3,3,2],[2,2,2,2]]=>[[5,5,4,1],[4,4]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3,3,2,2],[2,2,2,1]]=>[[5,5,3,1],[4,3]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[5,4,4,3,2],[3,3,3,2]]=>[[5,5,4,3,1],[4,4,3]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,3,2,2,2],[2,2,1,1]]=>[[5,5,2,1],[4,2]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[4,2,2,2,2],[2,1,1,1]]=>[[5,5,1,1],[4,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,3,3,3,2],[3,2,2,2]]=>[[5,5,4,1,1],[4,4,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[5,3,2,2,2],[3,2,1,1]]=>[[5,5,2,1,1],[4,2,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[2,1,1,1,1,1],[]]=>[[6,1],[]]=>([],1)=>([],0)
[[3,2,2,2,2,1],[1,1,1,1,1]]=>[[6,5,1],[5]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,2,2,2,1,1],[1,1,1,1]]=>[[6,4,1],[4]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[4,3,3,3,2,1],[2,2,2,2,1]]=>[[6,5,4,1],[5,4]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[3,2,2,1,1,1],[1,1,1]]=>[[6,3,1],[3]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,3,3,2,2,1],[2,2,2,1,1]]=>[[6,5,3,1],[5,3]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,3,3,2,1,1],[2,2,2,1]]=>[[6,4,3,1],[4,3]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[3,2,1,1,1,1],[1,1]]=>[[6,2,1],[2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3,2,2,2,1],[2,2,1,1,1]]=>[[6,5,2,1],[5,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,3,2,1,1,1],[2,2,1]]=>[[6,3,2,1],[3,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[3,1,1,1,1,1],[1]]=>[[6,1,1],[1]]=>([(0,1)],2)=>([],1)
[[4,2,2,2,2,1],[2,1,1,1,1]]=>[[6,5,1,1],[5,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,2,2,2,1,1],[2,1,1,1]]=>[[6,4,1,1],[4,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[4,2,2,1,1,1],[2,1,1]]=>[[6,3,1,1],[3,1]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[4,2,1,1,1,1],[2,1]]=>[[6,2,1,1],[2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[6,6],[5]]=>[[2,2,2,2,2,2],[1,1,1,1,1]]=>([],1)=>([],0)
[[7,6],[6]]=>[[2,2,2,2,2,2,1],[1,1,1,1,1,1]]=>([(0,1)],2)=>([],1)
[[5,5,1],[4]]=>[[3,2,2,2,2],[1,1,1,1]]=>([(0,1)],2)=>([],1)
[[6,6,1],[5,1]]=>[[3,2,2,2,2,2],[2,1,1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[6,5,1],[5]]=>[[3,2,2,2,2,1],[1,1,1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[7,6,1],[6,1]]=>[[3,2,2,2,2,2,1],[2,1,1,1,1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,2],[3]]=>[[3,3,2,2],[1,1,1]]=>([(0,1)],2)=>([],1)
[[5,5,2],[4,1]]=>[[3,3,2,2,2],[2,1,1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],2)
[[6,6,2],[5,2]]=>[[3,3,2,2,2,2],[2,2,1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[5,4,2],[4]]=>[[3,3,2,2,1],[1,1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[6,5,2],[5,1]]=>[[3,3,2,2,2,1],[2,1,1,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[7,6,2],[6,2]]=>[[3,3,2,2,2,2,1],[2,2,1,1,1,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[4,4,1,1],[3]]=>[[4,2,2,2],[1,1,1]]=>([(0,1)],2)=>([],1)
[[5,5,2,1],[4,1,1]]=>[[4,3,2,2,2],[3,1,1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[5,5,1,1],[4,1]]=>[[4,2,2,2,2],[2,1,1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[6,6,2,1],[5,2,1]]=>[[4,3,2,2,2,2],[3,2,1,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[5,4,1,1],[4]]=>[[4,2,2,2,1],[1,1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[6,5,2,1],[5,1,1]]=>[[4,3,2,2,2,1],[3,1,1,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[6,5,1,1],[5,1]]=>[[4,2,2,2,2,1],[2,1,1,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[7,6,2,1],[6,2,1]]=>[[4,3,2,2,2,2,1],[3,2,1,1,1,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,3],[2]]=>[[3,3,3],[1,1]]=>([],1)=>([],0)
[[4,4,3],[3,1]]=>[[3,3,3,2],[2,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,5,3],[4,2]]=>[[3,3,3,2,2],[2,2,1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[6,6,3],[5,3]]=>[[3,3,3,2,2,2],[2,2,2,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,3,3],[3]]=>[[3,3,3,1],[1,1,1]]=>([(0,1)],2)=>([],1)
[[5,4,3],[4,1]]=>[[3,3,3,2,1],[2,1,1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[6,5,3],[5,2]]=>[[3,3,3,2,2,1],[2,2,1,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[7,6,3],[6,3]]=>[[3,3,3,2,2,2,1],[2,2,2,1,1,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,2,1],[2]]=>[[4,3,2],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,3,1],[3,1,1]]=>[[4,3,3,2],[3,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,4,2,1],[3,1]]=>[[4,3,2,2],[2,1,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>([(0,3),(1,2),(2,3)],4)
[[5,5,3,1],[4,2,1]]=>[[4,3,3,2,2],[3,2,1,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[5,5,2,1],[4,2]]=>[[4,3,2,2,2],[2,2,1,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[6,6,3,1],[5,3,1]]=>[[4,3,3,2,2,2],[3,2,2,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[4,3,2,1],[3]]=>[[4,3,2,1],[1,1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,4,3,1],[4,1,1]]=>[[4,3,3,2,1],[3,1,1,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,2,1],[4,1]]=>[[4,3,2,2,1],[2,1,1,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[6,5,3,1],[5,2,1]]=>[[4,3,3,2,2,1],[3,2,1,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[6,5,2,1],[5,2]]=>[[4,3,2,2,2,1],[2,2,1,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[4,4,2,2],[3,1,1]]=>[[4,4,2,2],[3,1,1]]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>([(1,2)],3)
[[5,5,3,2],[4,2,2]]=>[[4,4,3,2,2],[3,3,1,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[5,5,2,2],[4,2,1]]=>[[4,4,2,2,2],[3,2,1,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[6,6,3,2],[5,3,2]]=>[[4,4,3,2,2,2],[3,3,2,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,4,2,2],[4,1,1]]=>[[4,4,2,2,1],[3,1,1,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>([(0,3),(1,2),(2,3)],4)
[[6,5,3,2],[5,2,2]]=>[[4,4,3,2,2,1],[3,3,1,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[6,5,2,2],[5,2,1]]=>[[4,4,2,2,2,1],[3,2,1,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[3,3,1,1,1],[2]]=>[[5,2,2],[1,1]]=>([(0,1)],2)=>([],1)
[[4,4,2,2,1],[3,1,1,1]]=>[[5,4,2,2],[4,1,1]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>([(0,2),(0,3),(3,1)],4)
[[4,4,2,1,1],[3,1,1]]=>[[5,3,2,2],[3,1,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[5,5,3,2,1],[4,2,2,1]]=>[[5,4,3,2,2],[4,3,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[4,4,1,1,1],[3,1]]=>[[5,2,2,2],[2,1,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,5,2,2,1],[4,2,1,1]]=>[[5,4,2,2,2],[4,2,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,5,2,1,1],[4,2,1]]=>[[5,3,2,2,2],[3,2,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[4,3,1,1,1],[3]]=>[[5,2,2,1],[1,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,4,2,2,1],[4,1,1,1]]=>[[5,4,2,2,1],[4,1,1,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[5,4,2,1,1],[4,1,1]]=>[[5,3,2,2,1],[3,1,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,4,1,1,1],[4,1]]=>[[5,2,2,2,1],[2,1,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,4,4],[3,2]]=>[[3,3,3,3],[2,2,1]]=>([],1)=>([],0)
[[5,5,4],[4,3]]=>[[3,3,3,3,2],[2,2,2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[6,6,4],[5,4]]=>[[3,3,3,3,2,2],[2,2,2,2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,4,4],[4,2]]=>[[3,3,3,3,1],[2,2,1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[6,5,4],[5,3]]=>[[3,3,3,3,2,1],[2,2,2,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[7,6,4],[6,4]]=>[[3,3,3,3,2,2,1],[2,2,2,2,1,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[3,3,3,1],[2,1]]=>[[4,3,3],[2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,4,1],[3,2,1]]=>[[4,3,3,3],[3,2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,3,1],[3,2]]=>[[4,3,3,2],[2,2,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>([(0,3),(1,2),(2,3)],4)
[[5,5,4,1],[4,3,1]]=>[[4,3,3,3,2],[3,2,2,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[5,5,3,1],[4,3]]=>[[4,3,3,2,2],[2,2,2,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[6,6,4,1],[5,4,1]]=>[[4,3,3,3,2,2],[3,2,2,2,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[4,3,3,1],[3,1]]=>[[4,3,3,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,4,4,1],[4,2,1]]=>[[4,3,3,3,1],[3,2,1,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,1],[4,2]]=>[[4,3,3,2,1],[2,2,1,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[6,5,4,1],[5,3,1]]=>[[4,3,3,3,2,1],[3,2,2,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[6,5,3,1],[5,3]]=>[[4,3,3,2,2,1],[2,2,2,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[2,2,2,2],[1]]=>[[4,4],[1]]=>([],1)=>([],0)
[[3,3,3,2],[2,1,1]]=>[[4,4,3],[3,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,4,2],[3,2,2]]=>[[4,4,3,3],[3,3,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3,2,2],[2,1]]=>[[4,4,2],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,3,2],[3,2,1]]=>[[4,4,3,2],[3,2,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[5,5,4,2],[4,3,2]]=>[[4,4,3,3,2],[3,3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[4,4,2,2],[3,2]]=>[[4,4,2,2],[2,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[5,5,3,2],[4,3,1]]=>[[4,4,3,2,2],[3,2,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[3,2,2,2],[2]]=>[[4,4,1],[1,1]]=>([(0,1)],2)=>([],1)
[[4,3,3,2],[3,1,1]]=>[[4,4,3,1],[3,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,4,4,2],[4,2,2]]=>[[4,4,3,3,1],[3,3,1,1]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,3,2,2],[3,1]]=>[[4,4,2,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,4,3,2],[4,2,1]]=>[[4,4,3,2,1],[3,2,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,4,2,2],[4,2]]=>[[4,4,2,2,1],[2,2,1,1]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,2,1,1],[1]]=>[[5,3],[1]]=>([(0,1)],2)=>([],1)
[[3,3,3,2,1],[2,1,1,1]]=>[[5,4,3],[4,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3,3,1,1],[2,1,1]]=>[[5,3,3],[3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,4,4,2,1],[3,2,2,1]]=>[[5,4,3,3],[4,3,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,2,1,1],[2,1]]=>[[5,3,2],[2,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[4,4,3,2,1],[3,2,1,1]]=>[[5,4,3,2],[4,2,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,4,3,1,1],[3,2,1]]=>[[5,3,3,2],[3,2,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,4,2,1,1],[3,2]]=>[[5,3,2,2],[2,2,1]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[3,2,2,1,1],[2]]=>[[5,3,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,3,2,1],[3,1,1,1]]=>[[5,4,3,1],[4,1,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,3,1,1],[3,1,1]]=>[[5,3,3,1],[3,1,1]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[5,4,4,2,1],[4,2,2,1]]=>[[5,4,3,3,1],[4,3,1,1]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[4,3,2,1,1],[3,1]]=>[[5,3,2,1],[2,1,1]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[5,4,2,1,1],[4,2]]=>[[5,3,2,2,1],[2,2,1,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,4,3,3],[3,2,2]]=>[[4,4,4,2],[3,3,1]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],2)
[[5,5,4,3],[4,3,3]]=>[[4,4,4,3,2],[3,3,3,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[5,5,3,3],[4,3,2]]=>[[4,4,4,2,2],[3,3,2,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[6,6,4,3],[5,4,3]]=>[[4,4,4,3,2,2],[3,3,3,2,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,4,3,3],[4,2,2]]=>[[4,4,4,2,1],[3,3,1,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>([(0,3),(1,2),(2,3)],4)
[[6,5,4,3],[5,3,3]]=>[[4,4,4,3,2,1],[3,3,3,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[6,5,3,3],[5,3,2]]=>[[4,4,4,2,2,1],[3,3,2,1,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[3,3,2,2,1],[2,1,1]]=>[[5,4,2],[3,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[4,4,3,3,1],[3,2,2,1]]=>[[5,4,4,2],[4,3,1]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[4,4,3,2,1],[3,2,2]]=>[[5,4,3,2],[3,3,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,4,2,2,1],[3,2,1]]=>[[5,4,2,2],[3,2,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,3,2,2,1],[3,1,1]]=>[[5,4,2,1],[3,1,1]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[5,4,3,3,1],[4,2,2,1]]=>[[5,4,4,2,1],[4,3,1,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[3,3,2,2,2],[2,1,1,1]]=>[[5,5,2],[4,1]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],2)
[[4,4,3,3,2],[3,2,2,2]]=>[[5,5,4,2],[4,4,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[4,4,3,2,2],[3,2,2,1]]=>[[5,5,3,2],[4,3,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,4,2,2,2],[3,2,1,1]]=>[[5,5,2,2],[4,2,1]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[4,3,2,2,2],[3,1,1,1]]=>[[5,5,2,1],[4,1,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[5,4,3,3,2],[4,2,2,2]]=>[[5,5,4,2,1],[4,4,1,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[5,4,2,2,2],[4,2,1,1]]=>[[5,5,2,2,1],[4,2,1,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[2,2,1,1,1,1],[1]]=>[[6,2],[1]]=>([(0,1)],2)=>([],1)
[[3,3,2,2,2,1],[2,1,1,1,1]]=>[[6,5,2],[5,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[3,3,2,2,1,1],[2,1,1,1]]=>[[6,4,2],[4,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,3,3,2,1],[3,2,2,2,1]]=>[[6,5,4,2],[5,4,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[3,3,2,1,1,1],[2,1,1]]=>[[6,3,2],[3,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,1,1,1,1],[2,1]]=>[[6,2,2],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,2,2,2,1],[3,2,1,1,1]]=>[[6,5,2,2],[5,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,4,2,1,1,1],[3,2,1]]=>[[6,3,2,2],[3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[3,2,1,1,1,1],[2]]=>[[6,2,1],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,2,2,2,1],[3,1,1,1,1]]=>[[6,5,2,1],[5,1,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,3,2,2,1,1],[3,1,1,1]]=>[[6,4,2,1],[4,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,3,2,1,1,1],[3,1,1]]=>[[6,3,2,1],[3,1,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,3,1,1,1,1],[3,1]]=>[[6,2,2,1],[2,1,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,5,5],[4,4]]=>[[3,3,3,3,3],[2,2,2,2]]=>([],1)=>([],0)
[[6,6,5],[5,5]]=>[[3,3,3,3,3,2],[2,2,2,2,2]]=>([(0,1)],2)=>([],1)
[[6,5,5],[5,4]]=>[[3,3,3,3,3,1],[2,2,2,2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[7,6,5],[6,5]]=>[[3,3,3,3,3,2,1],[2,2,2,2,2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,4,1],[3,3]]=>[[4,3,3,3],[2,2,2]]=>([(0,1)],2)=>([],1)
[[5,5,5,1],[4,4,1]]=>[[4,3,3,3,3],[3,2,2,2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,5,4,1],[4,4]]=>[[4,3,3,3,2],[2,2,2,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[6,6,5,1],[5,5,1]]=>[[4,3,3,3,3,2],[3,2,2,2,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,4,4,1],[4,3]]=>[[4,3,3,3,1],[2,2,2,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[6,5,5,1],[5,4,1]]=>[[4,3,3,3,3,1],[3,2,2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[6,5,4,1],[5,4]]=>[[4,3,3,3,2,1],[2,2,2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[7,6,5,1],[6,5,1]]=>[[4,3,3,3,3,2,1],[3,2,2,2,2,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,3,2],[2,2]]=>[[4,4,3],[2,2]]=>([(0,1)],2)=>([],1)
[[4,4,4,2],[3,3,1]]=>[[4,4,3,3],[3,2,2]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],2)
[[5,5,5,2],[4,4,2]]=>[[4,4,3,3,3],[3,3,2,2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[4,4,3,2],[3,3]]=>[[4,4,3,2],[2,2,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,5,4,2],[4,4,1]]=>[[4,4,3,3,2],[3,2,2,2]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[6,6,5,2],[5,5,2]]=>[[4,4,3,3,3,2],[3,3,2,2,2]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[4,3,3,2],[3,2]]=>[[4,4,3,1],[2,2,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,4,4,2],[4,3,1]]=>[[4,4,3,3,1],[3,2,2,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[6,5,5,2],[5,4,2]]=>[[4,4,3,3,3,1],[3,3,2,2,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,4,3,2],[4,3]]=>[[4,4,3,2,1],[2,2,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[6,5,4,2],[5,4,1]]=>[[4,4,3,3,2,1],[3,2,2,2,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[3,3,3,1,1],[2,2]]=>[[5,3,3],[2,2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,4,2,1],[3,3,1,1]]=>[[5,4,3,3],[4,2,2]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>([(0,2),(0,3),(3,1)],4)
[[4,4,4,1,1],[3,3,1]]=>[[5,3,3,3],[3,2,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[5,5,5,2,1],[4,4,2,1]]=>[[5,4,3,3,3],[4,3,2,2]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[4,4,3,1,1],[3,3]]=>[[5,3,3,2],[2,2,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[5,5,4,2,1],[4,4,1,1]]=>[[5,4,3,3,2],[4,2,2,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,5,4,1,1],[4,4,1]]=>[[5,3,3,3,2],[3,2,2,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,3,3,1,1],[3,2]]=>[[5,3,3,1],[2,2,1]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>([(0,2),(0,3),(3,1)],4)
[[5,4,4,2,1],[4,3,1,1]]=>[[5,4,3,3,1],[4,2,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,4,4,1,1],[4,3,1]]=>[[5,3,3,3,1],[3,2,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,4,3,1,1],[4,3]]=>[[5,3,3,2,1],[2,2,2,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[3,3,3,3],[2,2,1]]=>[[4,4,4],[3,2]]=>([],1)=>([],0)
[[4,4,4,3],[3,3,2]]=>[[4,4,4,3],[3,3,2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,5,5,3],[4,4,3]]=>[[4,4,4,3,3],[3,3,3,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,3,3],[3,3,1]]=>[[4,4,4,2],[3,2,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,5,4,3],[4,4,2]]=>[[4,4,4,3,2],[3,3,2,2]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[6,6,5,3],[5,5,3]]=>[[4,4,4,3,3,2],[3,3,3,2,2]]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[4,3,3,3],[3,2,1]]=>[[4,4,4,1],[3,2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,4,4,3],[4,3,2]]=>[[4,4,4,3,1],[3,3,2,1]]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[6,5,5,3],[5,4,3]]=>[[4,4,4,3,3,1],[3,3,3,2,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[5,4,3,3],[4,3,1]]=>[[4,4,4,2,1],[3,2,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[6,5,4,3],[5,4,2]]=>[[4,4,4,3,2,1],[3,3,2,2,1]]=>([(0,5),(0,6),(1,8),(2,7),(3,7),(5,8),(6,1),(7,4),(8,2),(8,3)],9)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[2,2,2,2,1],[1,1]]=>[[5,4],[2]]=>([(0,1)],2)=>([],1)
[[3,3,3,3,1],[2,2,1,1]]=>[[5,4,4],[4,2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,3,2,1],[2,2,1]]=>[[5,4,3],[3,2]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,3),(3,2)],4)
[[4,4,4,3,1],[3,3,2,1]]=>[[5,4,4,3],[4,3,2]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[4,4,4,2,1],[3,3,2]]=>[[5,4,3,3],[3,3,2]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[5,5,5,3,1],[4,4,3,1]]=>[[5,4,4,3,3],[4,3,3,2]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[3,3,2,2,1],[2,2]]=>[[5,4,2],[2,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,4,3,3,1],[3,3,1,1]]=>[[5,4,4,2],[4,2,2]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,4,3,2,1],[3,3,1]]=>[[5,4,3,2],[3,2,2]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[3,2,2,2,1],[2,1]]=>[[5,4,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3,3,3,1],[3,2,1,1]]=>[[5,4,4,1],[4,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[4,3,3,2,1],[3,2,1]]=>[[5,4,3,1],[3,2,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,3,2,2,1],[3,2]]=>[[5,4,2,1],[2,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,3,1],[4,3,1,1]]=>[[5,4,4,2,1],[4,2,2,1]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[3,3,3,2,2],[2,2,1,1]]=>[[5,5,3],[4,2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,2),(1,2)],3)
[[4,4,4,3,2],[3,3,2,2]]=>[[5,5,4,3],[4,4,2]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,2),(0,3),(1,2),(1,3)],4)
[[4,4,4,2,2],[3,3,2,1]]=>[[5,5,3,3],[4,3,2]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[5,5,5,3,2],[4,4,3,2]]=>[[5,5,4,3,3],[4,4,3,2]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,4,3,2,2],[3,3,1,1]]=>[[5,5,3,2],[4,2,2]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[4,3,3,2,2],[3,2,1,1]]=>[[5,5,3,1],[4,2,1]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[5,4,3,2,2],[4,3,1,1]]=>[[5,5,3,2,1],[4,2,2,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[2,2,2,1,1,1],[1,1]]=>[[6,3],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,3,2,2,1],[2,2,1,1,1]]=>[[6,5,3],[5,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[3,3,3,2,1,1],[2,2,1,1]]=>[[6,4,3],[4,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,4,3,2,1],[3,3,2,2,1]]=>[[6,5,4,3],[5,4,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[3,3,3,1,1,1],[2,2,1]]=>[[6,3,3],[3,2]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,4,4,2,2,1],[3,3,2,1,1]]=>[[6,5,3,3],[5,3,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,4,4,2,1,1],[3,3,2,1]]=>[[6,4,3,3],[4,3,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[3,3,2,1,1,1],[2,2]]=>[[6,3,2],[2,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[4,4,3,2,2,1],[3,3,1,1,1]]=>[[6,5,3,2],[5,2,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,4,3,1,1,1],[3,3,1]]=>[[6,3,3,2],[3,2,2]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[3,2,2,1,1,1],[2,1]]=>[[6,3,1],[2,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[4,3,3,2,2,1],[3,2,1,1,1]]=>[[6,5,3,1],[5,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,3,3,1,1,1],[3,2,1]]=>[[6,3,3,1],[3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,3,2,1,1,1],[3,2]]=>[[6,3,2,1],[2,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,4,4,4],[3,3,3]]=>[[4,4,4,4],[3,3,3]]=>([],1)=>([],0)
[[5,5,5,4],[4,4,4]]=>[[4,4,4,4,3],[3,3,3,3]]=>([(0,1)],2)=>([],1)
[[5,5,4,4],[4,4,3]]=>[[4,4,4,4,2],[3,3,3,2]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[6,6,5,4],[5,5,4]]=>[[4,4,4,4,3,2],[3,3,3,3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,4,4,4],[4,3,3]]=>[[4,4,4,4,1],[3,3,3,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[6,5,5,4],[5,4,4]]=>[[4,4,4,4,3,1],[3,3,3,3,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[6,5,4,4],[5,4,3]]=>[[4,4,4,4,2,1],[3,3,3,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[7,6,5,4],[6,5,4]]=>[[4,4,4,4,3,2,1],[3,3,3,3,2,1]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[3,3,3,3,1],[2,2,2]]=>[[5,4,4],[3,3]]=>([(0,1)],2)=>([],1)
[[4,4,4,4,1],[3,3,3,1]]=>[[5,4,4,4],[4,3,3]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,4,3,1],[3,3,3]]=>[[5,4,4,3],[3,3,3]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,5,5,4,1],[4,4,4,1]]=>[[5,4,4,4,3],[4,3,3,3]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,4,3,3,1],[3,3,2]]=>[[5,4,4,2],[3,3,2]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[5,5,4,4,1],[4,4,3,1]]=>[[5,4,4,4,2],[4,3,3,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,5,4,3,1],[4,4,3]]=>[[5,4,4,3,2],[3,3,3,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[4,3,3,3,1],[3,2,2]]=>[[5,4,4,1],[3,3,1]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>([(0,2),(0,3),(3,1)],4)
[[5,4,4,4,1],[4,3,3,1]]=>[[5,4,4,4,1],[4,3,3,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[5,4,4,3,1],[4,3,3]]=>[[5,4,4,3,1],[3,3,3,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,4,3,3,1],[4,3,2]]=>[[5,4,4,2,1],[3,3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[2,2,2,2,2],[1,1,1]]=>[[5,5],[3]]=>([],1)=>([],0)
[[3,3,3,3,2],[2,2,2,1]]=>[[5,5,4],[4,3]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,4,4,2],[3,3,3,2]]=>[[5,5,4,4],[4,4,3]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3,3,2,2],[2,2,2]]=>[[5,5,3],[3,3]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,4,3,2],[3,3,3,1]]=>[[5,5,4,3],[4,3,3]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[5,5,5,4,2],[4,4,4,2]]=>[[5,5,4,4,3],[4,4,3,3]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[3,3,2,2,2],[2,2,1]]=>[[5,5,2],[3,2]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,4,3,3,2],[3,3,2,1]]=>[[5,5,4,2],[4,3,2]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,4,3,2,2],[3,3,2]]=>[[5,5,3,2],[3,3,2]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,2,2,2,2],[2,1,1]]=>[[5,5,1],[3,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,3,3,2],[3,2,2,1]]=>[[5,5,4,1],[4,3,1]]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[5,4,4,4,2],[4,3,3,2]]=>[[5,5,4,4,1],[4,4,3,1]]=>([(0,4),(0,5),(1,7),(3,7),(4,8),(5,8),(6,1),(7,2),(8,3),(8,6)],9)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[4,3,3,2,2],[3,2,2]]=>[[5,5,3,1],[3,3,1]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,3,2,2,2],[3,2,1]]=>[[5,5,2,1],[3,2,1]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)
[[5,4,3,2,2],[4,3,2]]=>[[5,5,3,2,1],[3,3,2,1]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[2,2,2,2,1,1],[1,1,1]]=>[[6,4],[3]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,3,3,2,1],[2,2,2,1,1]]=>[[6,5,4],[5,3]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[3,3,3,3,1,1],[2,2,2,1]]=>[[6,4,4],[4,3]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[4,4,4,4,2,1],[3,3,3,2,1]]=>[[6,5,4,4],[5,4,3]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[3,3,3,2,1,1],[2,2,2]]=>[[6,4,3],[3,3]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,4,4,3,2,1],[3,3,3,1,1]]=>[[6,5,4,3],[5,3,3]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,4,4,3,1,1],[3,3,3,1]]=>[[6,4,4,3],[4,3,3]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[3,3,2,2,1,1],[2,2,1]]=>[[6,4,2],[3,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,3,2,1,1],[3,3,2]]=>[[6,4,3,2],[3,3,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[3,2,2,2,1,1],[2,1,1]]=>[[6,4,1],[3,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,3,3,3,2,1],[3,2,2,1,1]]=>[[6,5,4,1],[5,3,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,3,3,3,1,1],[3,2,2,1]]=>[[6,4,4,1],[4,3,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,3,3,2,1,1],[3,2,2]]=>[[6,4,3,1],[3,3,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,3,2,2,1,1],[3,2,1]]=>[[6,4,2,1],[3,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[3,3,3,3,3],[2,2,2,2]]=>[[5,5,5],[4,4]]=>([],1)=>([],0)
[[4,4,4,4,3],[3,3,3,3]]=>[[5,5,5,4],[4,4,4]]=>([(0,1)],2)=>([],1)
[[4,4,4,3,3],[3,3,3,2]]=>[[5,5,5,3],[4,4,3]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[5,5,5,4,3],[4,4,4,3]]=>[[5,5,5,4,3],[4,4,4,3]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,4,3,3,3],[3,3,2,2]]=>[[5,5,5,2],[4,4,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[5,5,4,4,3],[4,4,3,3]]=>[[5,5,5,4,2],[4,4,4,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[5,5,4,3,3],[4,4,3,2]]=>[[5,5,5,3,2],[4,4,3,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[4,3,3,3,3],[3,2,2,2]]=>[[5,5,5,1],[4,4,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[5,4,4,4,3],[4,3,3,3]]=>[[5,5,5,4,1],[4,4,4,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[5,4,4,3,3],[4,3,3,2]]=>[[5,5,5,3,1],[4,4,3,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,2),(6,1),(6,5),(8,3),(8,4)],9)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[5,4,3,3,3],[4,3,2,2]]=>[[5,5,5,2,1],[4,4,2,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[2,2,2,2,2,1],[1,1,1,1]]=>[[6,5],[4]]=>([(0,1)],2)=>([],1)
[[3,3,3,3,3,1],[2,2,2,2,1]]=>[[6,5,5],[5,4]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,3,3,2,1],[2,2,2,2]]=>[[6,5,4],[4,4]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,4,4,3,1],[3,3,3,3,1]]=>[[6,5,5,4],[5,4,4]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[3,3,3,2,2,1],[2,2,2,1]]=>[[6,5,3],[4,3]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,4,3,3,1],[3,3,3,2,1]]=>[[6,5,5,3],[5,4,3]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,4,4,3,2,1],[3,3,3,2]]=>[[6,5,4,3],[4,4,3]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[3,3,2,2,2,1],[2,2,1,1]]=>[[6,5,2],[4,2]]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[4,4,3,3,3,1],[3,3,2,2,1]]=>[[6,5,5,2],[5,4,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[3,2,2,2,2,1],[2,1,1,1]]=>[[6,5,1],[4,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[4,3,3,3,3,1],[3,2,2,2,1]]=>[[6,5,5,1],[5,4,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,3,3,3,2,1],[3,2,2,2]]=>[[6,5,4,1],[4,4,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,3,2,2,2,1],[3,2,1,1]]=>[[6,5,2,1],[4,2,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[2,2,2,2,2,2],[1,1,1,1,1]]=>[[6,6],[5]]=>([],1)=>([],0)
[[3,3,3,3,3,2],[2,2,2,2,2]]=>[[6,6,5],[5,5]]=>([(0,1)],2)=>([],1)
[[3,3,3,3,2,2],[2,2,2,2,1]]=>[[6,6,4],[5,4]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,4,4,4,3,2],[3,3,3,3,2]]=>[[6,6,5,4],[5,5,4]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[3,3,3,2,2,2],[2,2,2,1,1]]=>[[6,6,3],[5,3]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[4,4,4,3,3,2],[3,3,3,2,2]]=>[[6,6,5,3],[5,5,3]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[4,4,4,3,2,2],[3,3,3,2,1]]=>[[6,6,4,3],[5,4,3]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[3,3,2,2,2,2],[2,2,1,1,1]]=>[[6,6,2],[5,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,1),(0,2)],3)
[[4,4,3,3,3,2],[3,3,2,2,2]]=>[[6,6,5,2],[5,5,2]]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[4,4,3,2,2,2],[3,3,2,1,1]]=>[[6,6,3,2],[5,3,2]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[3,2,2,2,2,2],[2,1,1,1,1]]=>[[6,6,1],[5,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,3,3,3,2],[3,2,2,2,2]]=>[[6,6,5,1],[5,5,1]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)
[[4,3,3,3,2,2],[3,2,2,2,1]]=>[[6,6,4,1],[5,4,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,3,3,2,2,2],[3,2,2,1,1]]=>[[6,6,3,1],[5,3,1]]=>([(0,6),(1,8),(2,8),(3,7),(4,7),(5,4),(6,1),(6,2),(8,3),(8,5)],9)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[4,3,2,2,2,2],[3,2,1,1,1]]=>[[6,6,2,1],[5,2,1]]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)
[[1,1,1,1,1,1,1],[]]=>[[7],[]]=>([],1)=>([],0)
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]]=>[[7,6],[6]]=>([(0,1)],2)=>([],1)
[[2,2,2,2,2,1,1],[1,1,1,1,1]]=>[[7,5],[5]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]]=>[[7,6,5],[6,5]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[2,2,2,2,1,1,1],[1,1,1,1]]=>[[7,4],[4]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]]=>[[7,6,4],[6,4]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[3,3,3,3,2,1,1],[2,2,2,2,1]]=>[[7,5,4],[5,4]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]]=>[[7,6,5,4],[6,5,4]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[2,2,2,1,1,1,1],[1,1,1]]=>[[7,3],[3]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]]=>[[7,6,3],[6,3]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[3,3,3,2,2,1,1],[2,2,2,1,1]]=>[[7,5,3],[5,3]]=>([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,3,3,2,1,1,1],[2,2,2,1]]=>[[7,4,3],[4,3]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[2,2,1,1,1,1,1],[1,1]]=>[[7,2],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,2,2,2,2,1],[2,2,1,1,1,1]]=>[[7,6,2],[6,2]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[3,3,2,2,2,1,1],[2,2,1,1,1]]=>[[7,5,2],[5,2]]=>([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,3,2,2,1,1,1],[2,2,1,1]]=>[[7,4,2],[4,2]]=>([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[3,3,2,1,1,1,1],[2,2,1]]=>[[7,3,2],[3,2]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[2,1,1,1,1,1,1],[1]]=>[[7,1],[1]]=>([(0,1)],2)=>([],1)
[[3,2,2,2,2,2,1],[2,1,1,1,1,1]]=>[[7,6,1],[6,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[3,2,2,2,2,1,1],[2,1,1,1,1]]=>[[7,5,1],[5,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[4,3,3,3,3,2,1],[3,2,2,2,2,1]]=>[[7,6,5,1],[6,5,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[3,2,2,2,1,1,1],[2,1,1,1]]=>[[7,4,1],[4,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[3,2,2,1,1,1,1],[2,1,1]]=>[[7,3,1],[3,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,3),(3,1),(3,2)],4)
[[3,2,1,1,1,1,1],[2,1]]=>[[7,2,1],[2,1]]=>([(0,3),(2,1),(3,2)],4)=>([(0,2),(2,1)],3)
[[4,3,2,2,2,2,1],[3,2,1,1,1,1]]=>[[7,6,2,1],[6,2,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[4,3,2,1,1,1,1],[3,2,1]]=>[[7,3,2,1],[3,2,1]]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[8],[]]=>[[1,1,1,1,1,1,1,1],[]]=>([],1)=>([],0)
[[7,1],[]]=>[[2,1,1,1,1,1,1],[]]=>([],1)=>([],0)
[[6,2],[]]=>[[2,2,1,1,1,1],[]]=>([],1)=>([],0)
[[6,1,1],[]]=>[[3,1,1,1,1,1],[]]=>([],1)=>([],0)
[[5,3],[]]=>[[2,2,2,1,1],[]]=>([],1)=>([],0)
[[5,2,1],[]]=>[[3,2,1,1,1],[]]=>([],1)=>([],0)
[[5,1,1,1],[]]=>[[4,1,1,1,1],[]]=>([],1)=>([],0)
[[4,4],[]]=>[[2,2,2,2],[]]=>([],1)=>([],0)
[[4,3,1],[]]=>[[3,2,2,1],[]]=>([],1)=>([],0)
[[4,2,2],[]]=>[[3,3,1,1],[]]=>([],1)=>([],0)
[[4,2,1,1],[]]=>[[4,2,1,1],[]]=>([],1)=>([],0)
[[4,1,1,1,1],[]]=>[[5,1,1,1],[]]=>([],1)=>([],0)
[[3,3,2],[]]=>[[3,3,2],[]]=>([],1)=>([],0)
[[3,3,1,1],[]]=>[[4,2,2],[]]=>([],1)=>([],0)
[[3,2,2,1],[]]=>[[4,3,1],[]]=>([],1)=>([],0)
[[3,2,1,1,1],[]]=>[[5,2,1],[]]=>([],1)=>([],0)
[[3,1,1,1,1,1],[]]=>[[6,1,1],[]]=>([],1)=>([],0)
[[2,2,2,2],[]]=>[[4,4],[]]=>([],1)=>([],0)
[[2,2,2,1,1],[]]=>[[5,3],[]]=>([],1)=>([],0)
[[2,2,1,1,1,1],[]]=>[[6,2],[]]=>([],1)=>([],0)
[[2,1,1,1,1,1,1],[]]=>[[7,1],[]]=>([],1)=>([],0)
[[1,1,1,1,1,1,1,1],[]]=>[[8],[]]=>([],1)=>([],0)
[[9],[]]=>[[1,1,1,1,1,1,1,1,1],[]]=>([],1)=>([],0)
[[8,1],[]]=>[[2,1,1,1,1,1,1,1],[]]=>([],1)=>([],0)
[[7,2],[]]=>[[2,2,1,1,1,1,1],[]]=>([],1)=>([],0)
[[7,1,1],[]]=>[[3,1,1,1,1,1,1],[]]=>([],1)=>([],0)
[[6,3],[]]=>[[2,2,2,1,1,1],[]]=>([],1)=>([],0)
[[6,2,1],[]]=>[[3,2,1,1,1,1],[]]=>([],1)=>([],0)
[[6,1,1,1],[]]=>[[4,1,1,1,1,1],[]]=>([],1)=>([],0)
[[5,4],[]]=>[[2,2,2,2,1],[]]=>([],1)=>([],0)
[[5,3,1],[]]=>[[3,2,2,1,1],[]]=>([],1)=>([],0)
[[5,2,2],[]]=>[[3,3,1,1,1],[]]=>([],1)=>([],0)
[[5,2,1,1],[]]=>[[4,2,1,1,1],[]]=>([],1)=>([],0)
[[5,1,1,1,1],[]]=>[[5,1,1,1,1],[]]=>([],1)=>([],0)
[[4,4,1],[]]=>[[3,2,2,2],[]]=>([],1)=>([],0)
[[4,3,2],[]]=>[[3,3,2,1],[]]=>([],1)=>([],0)
[[4,3,1,1],[]]=>[[4,2,2,1],[]]=>([],1)=>([],0)
[[4,2,2,1],[]]=>[[4,3,1,1],[]]=>([],1)=>([],0)
[[4,2,1,1,1],[]]=>[[5,2,1,1],[]]=>([],1)=>([],0)
[[4,1,1,1,1,1],[]]=>[[6,1,1,1],[]]=>([],1)=>([],0)
[[3,3,3],[]]=>[[3,3,3],[]]=>([],1)=>([],0)
[[3,3,2,1],[]]=>[[4,3,2],[]]=>([],1)=>([],0)
[[3,3,1,1,1],[]]=>[[5,2,2],[]]=>([],1)=>([],0)
[[3,2,2,2],[]]=>[[4,4,1],[]]=>([],1)=>([],0)
[[3,2,2,1,1],[]]=>[[5,3,1],[]]=>([],1)=>([],0)
[[3,2,1,1,1,1],[]]=>[[6,2,1],[]]=>([],1)=>([],0)
[[3,1,1,1,1,1,1],[]]=>[[7,1,1],[]]=>([],1)=>([],0)
[[2,2,2,2,1],[]]=>[[5,4],[]]=>([],1)=>([],0)
[[2,2,2,1,1,1],[]]=>[[6,3],[]]=>([],1)=>([],0)
[[2,2,1,1,1,1,1],[]]=>[[7,2],[]]=>([],1)=>([],0)
[[2,1,1,1,1,1,1,1],[]]=>[[8,1],[]]=>([],1)=>([],0)
[[1,1,1,1,1,1,1,1,1],[]]=>[[9],[]]=>([],1)=>([],0)
[[10],[]]=>[[1,1,1,1,1,1,1,1,1,1],[]]=>([],1)=>([],0)
[[9,1],[]]=>[[2,1,1,1,1,1,1,1,1],[]]=>([],1)=>([],0)
[[8,2],[]]=>[[2,2,1,1,1,1,1,1],[]]=>([],1)=>([],0)
[[8,1,1],[]]=>[[3,1,1,1,1,1,1,1],[]]=>([],1)=>([],0)
[[7,3],[]]=>[[2,2,2,1,1,1,1],[]]=>([],1)=>([],0)
[[7,2,1],[]]=>[[3,2,1,1,1,1,1],[]]=>([],1)=>([],0)
[[7,1,1,1],[]]=>[[4,1,1,1,1,1,1],[]]=>([],1)=>([],0)
[[6,4],[]]=>[[2,2,2,2,1,1],[]]=>([],1)=>([],0)
[[6,3,1],[]]=>[[3,2,2,1,1,1],[]]=>([],1)=>([],0)
[[6,2,2],[]]=>[[3,3,1,1,1,1],[]]=>([],1)=>([],0)
[[6,2,1,1],[]]=>[[4,2,1,1,1,1],[]]=>([],1)=>([],0)
[[6,1,1,1,1],[]]=>[[5,1,1,1,1,1],[]]=>([],1)=>([],0)
[[5,5],[]]=>[[2,2,2,2,2],[]]=>([],1)=>([],0)
[[5,4,1],[]]=>[[3,2,2,2,1],[]]=>([],1)=>([],0)
[[5,3,2],[]]=>[[3,3,2,1,1],[]]=>([],1)=>([],0)
[[5,3,1,1],[]]=>[[4,2,2,1,1],[]]=>([],1)=>([],0)
[[5,2,2,1],[]]=>[[4,3,1,1,1],[]]=>([],1)=>([],0)
[[5,2,1,1,1],[]]=>[[5,2,1,1,1],[]]=>([],1)=>([],0)
[[5,1,1,1,1,1],[]]=>[[6,1,1,1,1],[]]=>([],1)=>([],0)
[[4,4,2],[]]=>[[3,3,2,2],[]]=>([],1)=>([],0)
[[4,4,1,1],[]]=>[[4,2,2,2],[]]=>([],1)=>([],0)
[[4,3,3],[]]=>[[3,3,3,1],[]]=>([],1)=>([],0)
[[4,3,2,1],[]]=>[[4,3,2,1],[]]=>([],1)=>([],0)
[[4,3,1,1,1],[]]=>[[5,2,2,1],[]]=>([],1)=>([],0)
[[4,2,2,2],[]]=>[[4,4,1,1],[]]=>([],1)=>([],0)
[[4,2,2,1,1],[]]=>[[5,3,1,1],[]]=>([],1)=>([],0)
[[4,2,1,1,1,1],[]]=>[[6,2,1,1],[]]=>([],1)=>([],0)
[[4,1,1,1,1,1,1],[]]=>[[7,1,1,1],[]]=>([],1)=>([],0)
[[3,3,3,1],[]]=>[[4,3,3],[]]=>([],1)=>([],0)
[[3,3,2,2],[]]=>[[4,4,2],[]]=>([],1)=>([],0)
[[3,3,2,1,1],[]]=>[[5,3,2],[]]=>([],1)=>([],0)
[[3,3,1,1,1,1],[]]=>[[6,2,2],[]]=>([],1)=>([],0)
[[3,2,2,2,1],[]]=>[[5,4,1],[]]=>([],1)=>([],0)
[[3,2,2,1,1,1],[]]=>[[6,3,1],[]]=>([],1)=>([],0)
[[3,2,1,1,1,1,1],[]]=>[[7,2,1],[]]=>([],1)=>([],0)
[[3,1,1,1,1,1,1,1],[]]=>[[8,1,1],[]]=>([],1)=>([],0)
[[2,2,2,2,2],[]]=>[[5,5],[]]=>([],1)=>([],0)
[[2,2,2,2,1,1],[]]=>[[6,4],[]]=>([],1)=>([],0)
[[2,2,2,1,1,1,1],[]]=>[[7,3],[]]=>([],1)=>([],0)
[[2,2,1,1,1,1,1,1],[]]=>[[8,2],[]]=>([],1)=>([],0)
[[2,1,1,1,1,1,1,1,1],[]]=>[[9,1],[]]=>([],1)=>([],0)
[[1,1,1,1,1,1,1,1,1,1],[]]=>[[10],[]]=>([],1)=>([],0)
[[4,4,3],[]]=>[[3,3,3,2],[]]=>([],1)=>([],0)
[[3,3,3,2],[]]=>[[4,4,3],[]]=>([],1)=>([],0)
[[4,4,4],[]]=>[[3,3,3,3],[]]=>([],1)=>([],0)
[[3,3,3,3],[]]=>[[4,4,4],[]]=>([],1)=>([],0)
[[3,3,3],[1]]=>[[3,3,3],[1]]=>([],1)=>([],0)
[[3,3,3,1],[1,1]]=>[[4,3,3],[2]]=>([(0,1)],2)=>([],1)
[[4,4,1],[1]]=>[[3,2,2,2],[1]]=>([(0,1)],2)=>([],1)
[[3,3,2,1],[1]]=>[[4,3,2],[1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[2,2,2,2,1],[1]]=>[[5,4],[1]]=>([(0,1)],2)=>([],1)
[[3,3,3,1],[2]]=>[[4,3,3],[1,1]]=>([(0,1)],2)=>([],1)
[[3,3,3,1],[1]]=>[[4,3,3],[1]]=>([(0,1)],2)=>([],1)
[[3,3,3,2],[1,1,1]]=>[[4,4,3],[3]]=>([(0,1)],2)=>([],1)
[[4,4,2],[1,1]]=>[[3,3,2,2],[2]]=>([(0,1)],2)=>([],1)
[[4,4,4],[2,2]]=>[[3,3,3,3],[2,2]]=>([],1)=>([],0)
[[5,5],[2]]=>[[2,2,2,2,2],[1,1]]=>([],1)=>([],0)
[[4,4,3],[2,1]]=>[[3,3,3,2],[2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,3,3],[2,1,1]]=>[[4,4,4],[3,1]]=>([],1)=>([],0)
[[4,3,3],[1,1]]=>[[3,3,3,1],[2]]=>([(0,1)],2)=>([],1)
[[3,3,3,3],[1,1,1]]=>[[4,4,4],[3]]=>([],1)=>([],0)
[[4,4,3],[1,1]]=>[[3,3,3,2],[2]]=>([(0,1)],2)=>([],1)
[[4,4,4],[3,1]]=>[[3,3,3,3],[2,1,1]]=>([],1)=>([],0)
[[5,4],[1]]=>[[2,2,2,2,1],[1]]=>([(0,1)],2)=>([],1)
[[4,4,4],[2,1]]=>[[3,3,3,3],[2,1]]=>([],1)=>([],0)
[[5,5],[1]]=>[[2,2,2,2,2],[1]]=>([],1)=>([],0)
[[4,4,4],[1,1]]=>[[3,3,3,3],[2]]=>([],1)=>([],0)
[[3,3,2,2],[1,1]]=>[[4,4,2],[2]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,4,2],[2]]=>[[3,3,2,2],[1,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,3,2],[2,1]]=>[[4,4,3],[2,1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[4,3,2],[1]]=>[[3,3,2,1],[1]]=>([(0,2),(2,1)],3)=>([(0,1)],2)
[[3,3,3,2],[1,1]]=>[[4,4,3],[2]]=>([(0,1)],2)=>([],1)
[[4,4,2],[1]]=>[[3,3,2,2],[1]]=>([(0,1)],2)=>([],1)
[[2,2,2,2,2],[1,1]]=>[[5,5],[2]]=>([],1)=>([],0)
[[3,2,2,2],[1]]=>[[4,4,1],[1]]=>([(0,1)],2)=>([],1)
[[3,3,2,2],[2]]=>[[4,4,2],[1,1]]=>([(0,1)],2)=>([],1)
[[3,3,2,2],[1]]=>[[4,4,2],[1]]=>([(0,1)],2)=>([],1)
[[2,2,2,2,2],[1]]=>[[5,5],[1]]=>([],1)=>([],0)
[[3,3,3,2],[2]]=>[[4,4,3],[1,1]]=>([(0,1)],2)=>([],1)
[[3,3,3,2],[1]]=>[[4,4,3],[1]]=>([(0,1)],2)=>([],1)
[[3,3,3,3],[2,2]]=>[[4,4,4],[2,2]]=>([],1)=>([],0)
[[4,3,3],[2]]=>[[3,3,3,1],[1,1]]=>([(0,1)],2)=>([],1)
[[4,4,3],[3]]=>[[3,3,3,2],[1,1,1]]=>([(0,1)],2)=>([],1)
[[4,4,3],[2]]=>[[3,3,3,2],[1,1]]=>([(0,1)],2)=>([],1)
[[3,3,3,3],[2,1]]=>[[4,4,4],[2,1]]=>([],1)=>([],0)
[[4,3,3],[1]]=>[[3,3,3,1],[1]]=>([(0,1)],2)=>([],1)
[[3,3,3,3],[1,1]]=>[[4,4,4],[2]]=>([],1)=>([],0)
[[4,4,3],[1]]=>[[3,3,3,2],[1]]=>([(0,1)],2)=>([],1)
[[4,4,4],[3]]=>[[3,3,3,3],[1,1,1]]=>([],1)=>([],0)
[[4,4,4],[2]]=>[[3,3,3,3],[1,1]]=>([],1)=>([],0)
[[4,4,4],[1]]=>[[3,3,3,3],[1]]=>([],1)=>([],0)
[[3,3,3,3],[2]]=>[[4,4,4],[1,1]]=>([],1)=>([],0)
[[3,3,3,3],[1]]=>[[4,4,4],[1]]=>([],1)=>([],0)
Map
conjugate
Description
The conjugate of the skew partition.
The conjugate of a skew partition $\lambda$ is the skew partition $\lambda^*$ whose Ferrers diagram is obtained from the Ferrers diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate of a skew partition $\lambda$ is the skew partition $\lambda^*$ whose Ferrers diagram is obtained from the Ferrers diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
Map
dominating sublattice
Description
Return the sublattice of the dominance order induced by the support of the expansion of the skew Schur function into Schur functions.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the subposet of the dominance order whose elements are the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a lattice.
The example $\lambda = (5^2,4^2,1)$ and $\mu=(3,2)$ shows that this lattice is not a sublattice of the dominance order.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the subposet of the dominance order whose elements are the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a lattice.
The example $\lambda = (5^2,4^2,1)$ and $\mu=(3,2)$ shows that this lattice is not a sublattice of the dominance order.
Map
join irreducibles
Description
The poset of join irreducibles of a lattice.
searching the database
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