Identifier
Mp00075:
Semistandard tableaux
—reading word permutation⟶
Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Images
=>
Cc0019;cc-rep-0Cc0020;cc-rep-2
[[1,2]]=>[1,2]=>([],2)=>[2]
[[2,2]]=>[1,2]=>([],2)=>[2]
[[1],[2]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[1,3]]=>[1,2]=>([],2)=>[2]
[[2,3]]=>[1,2]=>([],2)=>[2]
[[3,3]]=>[1,2]=>([],2)=>[2]
[[1],[3]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[2],[3]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[1,1,2]]=>[1,2,3]=>([],3)=>[3]
[[1,2,2]]=>[1,2,3]=>([],3)=>[3]
[[2,2,2]]=>[1,2,3]=>([],3)=>[3]
[[1,1],[2]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,2],[2]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,4]]=>[1,2]=>([],2)=>[2]
[[2,4]]=>[1,2]=>([],2)=>[2]
[[3,4]]=>[1,2]=>([],2)=>[2]
[[4,4]]=>[1,2]=>([],2)=>[2]
[[1],[4]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[2],[4]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[3],[4]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[1,1,3]]=>[1,2,3]=>([],3)=>[3]
[[1,2,3]]=>[1,2,3]=>([],3)=>[3]
[[1,3,3]]=>[1,2,3]=>([],3)=>[3]
[[2,2,3]]=>[1,2,3]=>([],3)=>[3]
[[2,3,3]]=>[1,2,3]=>([],3)=>[3]
[[3,3,3]]=>[1,2,3]=>([],3)=>[3]
[[1,1],[3]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,2],[3]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,3],[2]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,3],[3]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,2],[3]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,3],[3]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1],[2],[3]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1,1,1,2]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,2,2]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,2,2]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,2,2]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,1],[2]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,2],[2]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,2,2],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,1],[2,2]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,5]]=>[1,2]=>([],2)=>[2]
[[2,5]]=>[1,2]=>([],2)=>[2]
[[3,5]]=>[1,2]=>([],2)=>[2]
[[4,5]]=>[1,2]=>([],2)=>[2]
[[5,5]]=>[1,2]=>([],2)=>[2]
[[1],[5]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[2],[5]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[3],[5]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[4],[5]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[1,1,4]]=>[1,2,3]=>([],3)=>[3]
[[1,2,4]]=>[1,2,3]=>([],3)=>[3]
[[1,3,4]]=>[1,2,3]=>([],3)=>[3]
[[1,4,4]]=>[1,2,3]=>([],3)=>[3]
[[2,2,4]]=>[1,2,3]=>([],3)=>[3]
[[2,3,4]]=>[1,2,3]=>([],3)=>[3]
[[2,4,4]]=>[1,2,3]=>([],3)=>[3]
[[3,3,4]]=>[1,2,3]=>([],3)=>[3]
[[3,4,4]]=>[1,2,3]=>([],3)=>[3]
[[4,4,4]]=>[1,2,3]=>([],3)=>[3]
[[1,1],[4]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,2],[4]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,4],[2]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,3],[4]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,4],[3]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,4],[4]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,2],[4]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,3],[4]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,4],[3]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,4],[4]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[3,3],[4]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[3,4],[4]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1],[2],[4]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1],[3],[4]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[2],[3],[4]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1,1,1,3]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,2,3]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,3,3]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,2,3]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,3,3]]=>[1,2,3,4]=>([],4)=>[4]
[[1,3,3,3]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,2,3]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,3,3]]=>[1,2,3,4]=>([],4)=>[4]
[[2,3,3,3]]=>[1,2,3,4]=>([],4)=>[4]
[[3,3,3,3]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,1],[3]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,2],[3]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,3],[2]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,1,3],[3]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,2,2],[3]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,2,3],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,2,3],[3]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,3,3],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,3,3],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,2,2],[3]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,2,3],[3]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,3,3],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,1],[2,3]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[3,3]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,2],[2,3]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,2],[3,3]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,2],[3,3]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[2],[3]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,2],[2],[3]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,3],[2],[3]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,1,1,1,2]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,2,2]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,2,2,2]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,2,2,2]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,2,2,2]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,1],[2]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,2],[2]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,2,2],[2]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,2,2,2],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,1,1],[2,2]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,2],[2,2]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,6]]=>[1,2]=>([],2)=>[2]
[[2,6]]=>[1,2]=>([],2)=>[2]
[[3,6]]=>[1,2]=>([],2)=>[2]
[[4,6]]=>[1,2]=>([],2)=>[2]
[[5,6]]=>[1,2]=>([],2)=>[2]
[[6,6]]=>[1,2]=>([],2)=>[2]
[[1],[6]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[2],[6]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[3],[6]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[4],[6]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[5],[6]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[1,1,5]]=>[1,2,3]=>([],3)=>[3]
[[1,2,5]]=>[1,2,3]=>([],3)=>[3]
[[1,3,5]]=>[1,2,3]=>([],3)=>[3]
[[1,4,5]]=>[1,2,3]=>([],3)=>[3]
[[1,5,5]]=>[1,2,3]=>([],3)=>[3]
[[2,2,5]]=>[1,2,3]=>([],3)=>[3]
[[2,3,5]]=>[1,2,3]=>([],3)=>[3]
[[2,4,5]]=>[1,2,3]=>([],3)=>[3]
[[2,5,5]]=>[1,2,3]=>([],3)=>[3]
[[3,3,5]]=>[1,2,3]=>([],3)=>[3]
[[3,4,5]]=>[1,2,3]=>([],3)=>[3]
[[3,5,5]]=>[1,2,3]=>([],3)=>[3]
[[4,4,5]]=>[1,2,3]=>([],3)=>[3]
[[4,5,5]]=>[1,2,3]=>([],3)=>[3]
[[5,5,5]]=>[1,2,3]=>([],3)=>[3]
[[1,1],[5]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,2],[5]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,5],[2]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,3],[5]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,5],[3]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,4],[5]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,5],[4]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,5],[5]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,2],[5]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,3],[5]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,5],[3]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,4],[5]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,5],[4]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,5],[5]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[3,3],[5]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[3,4],[5]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[3,5],[4]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[3,5],[5]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[4,4],[5]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[4,5],[5]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1],[2],[5]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1],[3],[5]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1],[4],[5]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[2],[3],[5]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[2],[4],[5]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[3],[4],[5]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1,1,1,4]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,2,4]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,3,4]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,4,4]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,2,4]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,3,4]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,4,4]]=>[1,2,3,4]=>([],4)=>[4]
[[1,3,3,4]]=>[1,2,3,4]=>([],4)=>[4]
[[1,3,4,4]]=>[1,2,3,4]=>([],4)=>[4]
[[1,4,4,4]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,2,4]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,3,4]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,4,4]]=>[1,2,3,4]=>([],4)=>[4]
[[2,3,3,4]]=>[1,2,3,4]=>([],4)=>[4]
[[2,3,4,4]]=>[1,2,3,4]=>([],4)=>[4]
[[2,4,4,4]]=>[1,2,3,4]=>([],4)=>[4]
[[3,3,3,4]]=>[1,2,3,4]=>([],4)=>[4]
[[3,3,4,4]]=>[1,2,3,4]=>([],4)=>[4]
[[3,4,4,4]]=>[1,2,3,4]=>([],4)=>[4]
[[4,4,4,4]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,1],[4]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,2],[4]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,4],[2]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,1,3],[4]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,4],[3]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,1,4],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,2,2],[4]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,2,4],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,2,3],[4]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,2,4],[3]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,3,4],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,2,4],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,4,4],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,3,3],[4]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,3,4],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,3,4],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,4,4],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,4,4],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,2,2],[4]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,2,3],[4]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,2,4],[3]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,2,4],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,3,3],[4]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,3,4],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,3,4],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,4,4],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,4,4],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[3,3,3],[4]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[3,3,4],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[3,4,4],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,1],[2,4]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[3,4]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[4,4]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,2],[2,4]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,2],[3,4]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,3],[2,4]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,2],[4,4]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,3],[3,4]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,3],[4,4]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,2],[3,4]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,2],[4,4]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,3],[3,4]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[2,3],[4,4]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[3,3],[4,4]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[2],[4]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,1],[3],[4]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,2],[2],[4]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,2],[3],[4]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,3],[2],[4]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,4],[2],[3]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,4],[2],[4]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,3],[3],[4]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,4],[3],[4]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,2],[3],[4]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,3],[3],[4]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,4],[3],[4]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1],[2],[3],[4]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[1,1,1,1,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,2,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,3,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,2,2,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,2,3,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,3,3,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,2,2,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,2,3,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,3,3,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,3,3,3,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,2,2,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,2,3,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,3,3,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,3,3,3,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,3,3,3,3]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,1],[3]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,2],[3]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,3],[2]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,3],[3]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,2,2],[3]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,2,3],[2]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,2,3],[3]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,3,3],[2]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,3,3],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,2,2,2],[3]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,2,3],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,2,3],[3]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,3,3],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,3,3],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,3,3,3],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,3,3,3],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,2,2,2],[3]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,2,3],[3]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,3,3],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,3,3,3],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,1,1],[2,3]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,1],[3,3]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,2],[2,3]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,1,3],[2,2]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,2],[3,3]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,3],[2,3]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,3],[3,3]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,2,2],[2,3]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,2],[3,3]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,2,3],[2,3]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,3],[3,3]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,2],[3,3]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,3],[3,3]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,1],[2],[3]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,2],[2],[3]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,3],[2],[3]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,2],[2],[3]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,3],[2],[3]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,3],[2],[3]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1],[2,2],[3]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,1],[2,3],[3]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,2],[2,3],[3]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,1,1,1,1,2]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,1,2,2]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,2,2,2]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,2,2,2,2]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,2,2,2,2]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,2,2,2,2]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,1,1],[2]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,1,2],[2]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,2,2],[2]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,2,2,2],[2]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,2,2,2,2],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,1,1,1],[2,2]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,2],[2,2]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,2],[2,2]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1],[2,2,2]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,7]]=>[1,2]=>([],2)=>[2]
[[2,7]]=>[1,2]=>([],2)=>[2]
[[3,7]]=>[1,2]=>([],2)=>[2]
[[4,7]]=>[1,2]=>([],2)=>[2]
[[5,7]]=>[1,2]=>([],2)=>[2]
[[6,7]]=>[1,2]=>([],2)=>[2]
[[7,7]]=>[1,2]=>([],2)=>[2]
[[1],[7]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[2],[7]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[3],[7]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[4],[7]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[5],[7]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[6],[7]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[1,1,6]]=>[1,2,3]=>([],3)=>[3]
[[1,2,6]]=>[1,2,3]=>([],3)=>[3]
[[1,3,6]]=>[1,2,3]=>([],3)=>[3]
[[1,4,6]]=>[1,2,3]=>([],3)=>[3]
[[1,5,6]]=>[1,2,3]=>([],3)=>[3]
[[1,6,6]]=>[1,2,3]=>([],3)=>[3]
[[2,2,6]]=>[1,2,3]=>([],3)=>[3]
[[2,3,6]]=>[1,2,3]=>([],3)=>[3]
[[2,4,6]]=>[1,2,3]=>([],3)=>[3]
[[2,5,6]]=>[1,2,3]=>([],3)=>[3]
[[2,6,6]]=>[1,2,3]=>([],3)=>[3]
[[3,3,6]]=>[1,2,3]=>([],3)=>[3]
[[3,4,6]]=>[1,2,3]=>([],3)=>[3]
[[3,5,6]]=>[1,2,3]=>([],3)=>[3]
[[3,6,6]]=>[1,2,3]=>([],3)=>[3]
[[4,4,6]]=>[1,2,3]=>([],3)=>[3]
[[4,5,6]]=>[1,2,3]=>([],3)=>[3]
[[4,6,6]]=>[1,2,3]=>([],3)=>[3]
[[5,5,6]]=>[1,2,3]=>([],3)=>[3]
[[5,6,6]]=>[1,2,3]=>([],3)=>[3]
[[6,6,6]]=>[1,2,3]=>([],3)=>[3]
[[1,1],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,2],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,6],[2]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,3],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,6],[3]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,4],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,6],[4]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,5],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,6],[5]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,6],[6]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,2],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,3],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,6],[3]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,4],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,6],[4]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,5],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,6],[5]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,6],[6]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[3,3],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[3,4],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[3,6],[4]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[3,5],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[3,6],[5]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[3,6],[6]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[4,4],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[4,5],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[4,6],[5]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[4,6],[6]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[5,5],[6]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[5,6],[6]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1],[2],[6]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1],[3],[6]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1],[4],[6]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1],[5],[6]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[2],[3],[6]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[2],[4],[6]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[2],[5],[6]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[3],[4],[6]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[3],[5],[6]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[4],[5],[6]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1,1,1,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,2,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,3,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,4,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,2,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,3,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,4,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,3,3,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,3,4,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,3,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,4,4,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,4,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,5,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,2,5]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,3,5]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,4,5]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[2,3,3,5]]=>[1,2,3,4]=>([],4)=>[4]
[[2,3,4,5]]=>[1,2,3,4]=>([],4)=>[4]
[[2,3,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[2,4,4,5]]=>[1,2,3,4]=>([],4)=>[4]
[[2,4,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[2,5,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[3,3,3,5]]=>[1,2,3,4]=>([],4)=>[4]
[[3,3,4,5]]=>[1,2,3,4]=>([],4)=>[4]
[[3,3,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[3,4,4,5]]=>[1,2,3,4]=>([],4)=>[4]
[[3,4,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[3,5,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[4,4,4,5]]=>[1,2,3,4]=>([],4)=>[4]
[[4,4,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[4,5,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[5,5,5,5]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,1],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,2],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,5],[2]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,1,3],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,5],[3]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,1,4],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,5],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,1,5],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,2,2],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,2,5],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,2,3],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,2,5],[3]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,3,5],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,2,4],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,2,5],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,4,5],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,2,5],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,5,5],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,3,3],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,3,5],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,3,4],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,3,5],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,4,5],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,3,5],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,5,5],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,4,4],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,4,5],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,4,5],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,5,5],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,5,5],[5]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,2,2],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,2,3],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,2,5],[3]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,2,4],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,2,5],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,2,5],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,3,3],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,3,5],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,3,4],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,3,5],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,4,5],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,3,5],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,5,5],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,4,4],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,4,5],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,4,5],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,5,5],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,5,5],[5]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[3,3,3],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[3,3,4],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[3,3,5],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[3,3,5],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[3,4,4],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[3,4,5],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[3,4,5],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[3,5,5],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[3,5,5],[5]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[4,4,4],[5]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[4,4,5],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[4,5,5],[5]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,1],[2,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[3,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[4,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[5,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,2],[2,5]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,2],[3,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,3],[2,5]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,2],[4,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,4],[2,5]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,2],[5,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,3],[3,5]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,3],[4,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,4],[3,5]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,3],[5,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,4],[4,5]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,4],[5,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,2],[3,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,2],[4,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,2],[5,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,3],[3,5]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[2,3],[4,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,4],[3,5]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[2,3],[5,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,4],[4,5]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[2,4],[5,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[3,3],[4,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[3,3],[5,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[3,4],[4,5]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[3,4],[5,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[4,4],[5,5]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[2],[5]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,1],[3],[5]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,1],[4],[5]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,2],[2],[5]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,2],[3],[5]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,3],[2],[5]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,5],[2],[3]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,2],[4],[5]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,4],[2],[5]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,5],[2],[4]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,5],[2],[5]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,3],[3],[5]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,3],[4],[5]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,4],[3],[5]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,5],[3],[4]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,5],[3],[5]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,4],[4],[5]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,5],[4],[5]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,2],[3],[5]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,2],[4],[5]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,3],[3],[5]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,3],[4],[5]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,4],[3],[5]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,5],[3],[4]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,5],[3],[5]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,4],[4],[5]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,5],[4],[5]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[3,3],[4],[5]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[3,4],[4],[5]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[3,5],[4],[5]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1],[2],[3],[5]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[1],[2],[4],[5]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[1],[3],[4],[5]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[2],[3],[4],[5]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[1,1,1,1,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,2,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,3,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,2,2,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,2,3,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,2,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,3,3,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,3,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,4,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,2,2,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,2,3,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,2,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,3,3,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,3,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,4,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,3,3,3,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,3,3,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,3,4,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,4,4,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,2,2,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,2,3,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,2,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,3,3,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,3,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,4,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,3,3,3,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,3,3,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,3,4,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,4,4,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,3,3,3,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,3,3,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,3,4,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,4,4,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[4,4,4,4,4]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,1],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,2],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,4],[2]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,3],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,4],[3]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,4],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,2,2],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,2,4],[2]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,2,3],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,2,4],[3]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,3,4],[2]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,2,4],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,4,4],[2]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,3,3],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,3,4],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,3,4],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,4,4],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,4,4],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,2,2,2],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,2,4],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,2,3],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,2,4],[3]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,3,4],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,2,4],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,4,4],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,3,3],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,3,4],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,3,3,4],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,3,4],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,4,4],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,3,4,4],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,4,4],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,4,4,4],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,3,3,3],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,3,3,4],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,3,3,4],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,3,4,4],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,3,4,4],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,4,4,4],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,4,4,4],[4]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,2,2,2],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,2,3],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,2,4],[3]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,2,4],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,3,3],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,3,4],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,2,3,4],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,4,4],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,2,4,4],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,3,3,3],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,3,3,4],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,3,3,4],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,3,4,4],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,3,4,4],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,4,4,4],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,4,4,4],[4]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[3,3,3,3],[4]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[3,3,3,4],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[3,3,4,4],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[3,4,4,4],[4]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,1,1],[2,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,1],[3,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,1],[4,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,2],[2,4]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,1,4],[2,2]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,2],[3,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,3],[2,4]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,1,4],[2,3]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,2],[4,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,4],[2,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,3],[3,4]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,1,4],[3,3]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,3],[4,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,4],[3,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,4],[4,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,2,2],[2,4]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,2],[3,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,2,3],[2,4]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,4],[2,3]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,2],[4,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,2,4],[2,4]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,3],[3,4]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,2,4],[3,3]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,3,3],[2,4]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,3],[4,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,2,4],[3,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,3,4],[2,4]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,4],[4,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,3,3],[3,4]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,3,3],[4,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,3,4],[3,4]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,3,4],[4,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,2],[3,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,2],[4,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,3],[3,4]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[2,2,4],[3,3]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,3],[4,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,4],[3,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,4],[4,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,3,3],[3,4]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[2,3,3],[4,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,3,4],[3,4]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[2,3,4],[4,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[3,3,3],[4,4]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[3,3,4],[4,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,1],[2],[4]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,1],[3],[4]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,2],[2],[4]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,2],[3],[4]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,3],[2],[4]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,4],[2],[3]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,4],[2],[4]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,3],[3],[4]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,4],[3],[4]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,2],[2],[4]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,2],[3],[4]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,3],[2],[4]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,4],[2],[3]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,4],[2],[4]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,3],[3],[4]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,3],[2],[4]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,4],[2],[3]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,4],[3],[4]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,4],[2],[4]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,4,4],[2],[3]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,4,4],[2],[4]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,3],[3],[4]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,4],[3],[4]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,4,4],[3],[4]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,2,2],[3],[4]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,2,3],[3],[4]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,2,4],[3],[4]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,3,3],[3],[4]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,3,4],[3],[4]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,4,4],[3],[4]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1],[2,2],[4]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,1],[2,3],[4]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,1],[2,4],[3]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,1],[2,4],[4]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,1],[3,3],[4]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,1],[3,4],[4]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,2],[2,3],[4]]=>[5,2,4,1,3]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[2,4],[3]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[2,4],[4]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[3,3],[4]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,3],[2,4],[3]]=>[3,2,5,1,4]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[3,4],[4]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,3],[2,4],[4]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,3],[3,4],[4]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[2,2],[3,3],[4]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[2,2],[3,4],[4]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[2,3],[3,4],[4]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,1],[2],[3],[4]]=>[5,4,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,2],[2],[3],[4]]=>[5,4,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,3],[2],[3],[4]]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,4],[2],[3],[4]]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,1,1,1,1,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,1,2,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,1,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,2,2,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,2,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,3,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,2,2,2,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,2,2,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,2,3,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,3,3,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,2,2,2,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,2,2,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,2,3,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,3,3,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,3,3,3,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,2,2,2,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,2,2,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,2,3,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,3,3,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,3,3,3,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[3,3,3,3,3,3]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,1,1],[3]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,1,2],[3]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,1,3],[2]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,1,3],[3]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,2,2],[3]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,2,3],[2]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,2,3],[3]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,3,3],[2]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,3,3],[3]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,2,2,2],[3]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,2,2,3],[2]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,1,2,2,3],[3]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,2,3,3],[2]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,1,2,3,3],[3]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,3,3,3],[2]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,1,3,3,3],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,2,2,2,2],[3]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,2,2,3],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,2,2,2,3],[3]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,2,3,3],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,2,2,3,3],[3]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,3,3,3],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,2,3,3,3],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,3,3,3,3],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,3,3,3,3],[3]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[2,2,2,2,2],[3]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,2,2,3],[3]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,2,3,3],[3]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,3,3,3],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[2,3,3,3,3],[3]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,1,1,1],[2,3]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,1],[3,3]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,2],[2,3]]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,3],[2,2]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,2],[3,3]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,3],[2,3]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,3],[3,3]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,2],[2,3]]=>[3,6,1,2,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,1,2,3],[2,2]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,2],[3,3]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,3],[2,3]]=>[3,5,1,2,4,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,1,3,3],[2,2]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,3],[3,3]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,3,3],[2,3]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,3,3],[3,3]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,2,2],[2,3]]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,2,2],[3,3]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,2,3],[2,3]]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,2,3],[3,3]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,3,3],[2,3]]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,3,3],[3,3]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,2,2],[3,3]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,2,3],[3,3]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,3,3],[3,3]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,1],[2],[3]]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,1,2],[2],[3]]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,1,3],[2],[3]]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,2,2],[2],[3]]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,2,3],[2],[3]]=>[5,3,1,2,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,3,3],[2],[3]]=>[4,3,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,2,2],[2],[3]]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,2,3],[2],[3]]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,3,3],[2],[3]]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,3,3,3],[2],[3]]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,1],[2,2,3]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,1],[2,3,3]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,1],[3,3,3]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,2],[2,2,3]]=>[3,4,6,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,1,2],[2,3,3]]=>[3,5,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,3]
[[1,1,2],[3,3,3]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,2,2],[2,3,3]]=>[2,5,6,1,3,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,2,2],[3,3,3]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[2,2,2],[3,3,3]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,1],[2,2],[3]]=>[6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,1],[2,3],[3]]=>[5,4,6,1,2,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,2],[2,2],[3]]=>[6,3,4,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,2],[2,3],[3]]=>[5,3,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,1,3],[2,2],[3]]=>[5,3,4,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,3],[2,3],[3]]=>[4,3,5,1,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,2,2],[2,3],[3]]=>[5,2,6,1,3,4]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>[3,2,1]
[[1,2,3],[2,3],[3]]=>[4,2,5,1,3,6]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,1],[2,2],[3,3]]=>[5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]
[[1,1,1,1,1,1,2]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,1,1,2,2]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,1,2,2,2]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,2,2,2,2]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,2,2,2,2,2]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[2,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,1,1,1],[2]]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,1,1,2],[2]]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,1,2,2],[2]]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,2,2,2],[2]]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,2,2,2,2],[2]]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)=>[6,1]
[[1,2,2,2,2,2],[2]]=>[2,1,3,4,5,6,7]=>([(5,6)],7)=>[6,1]
[[1,1,1,1,1],[2,2]]=>[6,7,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,1,2],[2,2]]=>[5,6,1,2,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,2,2],[2,2]]=>[4,5,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,2,2,2],[2,2]]=>[3,4,1,2,5,6,7]=>([(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,1],[2,2,2]]=>[5,6,7,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,1,1,2],[2,2,2]]=>[4,5,6,1,2,3,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,8]]=>[1,2]=>([],2)=>[2]
[[2,8]]=>[1,2]=>([],2)=>[2]
[[3,8]]=>[1,2]=>([],2)=>[2]
[[4,8]]=>[1,2]=>([],2)=>[2]
[[5,8]]=>[1,2]=>([],2)=>[2]
[[6,8]]=>[1,2]=>([],2)=>[2]
[[7,8]]=>[1,2]=>([],2)=>[2]
[[8,8]]=>[1,2]=>([],2)=>[2]
[[1],[8]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[2],[8]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[3],[8]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[4],[8]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[5],[8]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[6],[8]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[7],[8]]=>[2,1]=>([(0,1)],2)=>[1,1]
[[1,1,7]]=>[1,2,3]=>([],3)=>[3]
[[1,2,7]]=>[1,2,3]=>([],3)=>[3]
[[1,3,7]]=>[1,2,3]=>([],3)=>[3]
[[1,4,7]]=>[1,2,3]=>([],3)=>[3]
[[1,5,7]]=>[1,2,3]=>([],3)=>[3]
[[1,6,7]]=>[1,2,3]=>([],3)=>[3]
[[1,7,7]]=>[1,2,3]=>([],3)=>[3]
[[2,2,7]]=>[1,2,3]=>([],3)=>[3]
[[2,3,7]]=>[1,2,3]=>([],3)=>[3]
[[2,4,7]]=>[1,2,3]=>([],3)=>[3]
[[2,5,7]]=>[1,2,3]=>([],3)=>[3]
[[2,6,7]]=>[1,2,3]=>([],3)=>[3]
[[2,7,7]]=>[1,2,3]=>([],3)=>[3]
[[3,3,7]]=>[1,2,3]=>([],3)=>[3]
[[3,4,7]]=>[1,2,3]=>([],3)=>[3]
[[3,5,7]]=>[1,2,3]=>([],3)=>[3]
[[3,6,7]]=>[1,2,3]=>([],3)=>[3]
[[3,7,7]]=>[1,2,3]=>([],3)=>[3]
[[4,4,7]]=>[1,2,3]=>([],3)=>[3]
[[4,5,7]]=>[1,2,3]=>([],3)=>[3]
[[4,6,7]]=>[1,2,3]=>([],3)=>[3]
[[4,7,7]]=>[1,2,3]=>([],3)=>[3]
[[5,5,7]]=>[1,2,3]=>([],3)=>[3]
[[5,6,7]]=>[1,2,3]=>([],3)=>[3]
[[5,7,7]]=>[1,2,3]=>([],3)=>[3]
[[6,6,7]]=>[1,2,3]=>([],3)=>[3]
[[6,7,7]]=>[1,2,3]=>([],3)=>[3]
[[7,7,7]]=>[1,2,3]=>([],3)=>[3]
[[1,1],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,2],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,7],[2]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,3],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,7],[3]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,4],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,7],[4]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,5],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,7],[5]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,6],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[1,7],[6]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1,7],[7]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,2],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,3],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,7],[3]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,4],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,7],[4]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,5],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,7],[5]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,6],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[2,7],[6]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[2,7],[7]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[3,3],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[3,4],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[3,7],[4]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[3,5],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[3,7],[5]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[3,6],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[3,7],[6]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[3,7],[7]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[4,4],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[4,5],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[4,7],[5]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[4,6],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[4,7],[6]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[4,7],[7]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[5,5],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[5,6],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[5,7],[6]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[5,7],[7]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[6,6],[7]]=>[3,1,2]=>([(0,2),(1,2)],3)=>[2,1]
[[6,7],[7]]=>[2,1,3]=>([(1,2)],3)=>[2,1]
[[1],[2],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1],[3],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1],[4],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1],[5],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1],[6],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[2],[3],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[2],[4],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[2],[5],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[2],[6],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[3],[4],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[3],[5],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[3],[6],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[4],[5],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[4],[6],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[5],[6],[7]]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>[1,1,1]
[[1,1,1,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,2,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,3,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,4,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,2,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,3,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,4,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,2,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,3,3,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,3,4,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,3,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,3,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,4,4,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,4,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,4,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,5,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,5,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,6,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,2,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,3,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,4,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,2,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,3,3,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,3,4,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,3,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,3,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,4,4,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,4,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,4,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,5,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,5,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[2,6,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[3,3,3,6]]=>[1,2,3,4]=>([],4)=>[4]
[[3,3,4,6]]=>[1,2,3,4]=>([],4)=>[4]
[[3,3,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[3,3,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[3,4,4,6]]=>[1,2,3,4]=>([],4)=>[4]
[[3,4,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[3,4,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[3,5,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[3,5,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[3,6,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[4,4,4,6]]=>[1,2,3,4]=>([],4)=>[4]
[[4,4,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[4,4,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[4,5,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[4,5,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[4,6,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[5,5,5,6]]=>[1,2,3,4]=>([],4)=>[4]
[[5,5,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[5,6,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[6,6,6,6]]=>[1,2,3,4]=>([],4)=>[4]
[[1,1,1],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,2],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,6],[2]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,1,3],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,6],[3]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,1,4],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,6],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,1,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,1,6],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,1,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,2,2],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,2,6],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,2,3],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,2,6],[3]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,3,6],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,2,4],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,2,6],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,4,6],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,2,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,2,6],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,5,6],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,2,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,6,6],[2]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,3,3],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,3,6],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,3,4],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,3,6],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,4,6],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,3,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,3,6],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,5,6],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,3,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,6,6],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,4,4],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,4,6],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,4,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,4,6],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,5,6],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,4,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,6,6],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,5,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[1,5,6],[5]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,5,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[1,6,6],[5]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,6,6],[6]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,2,2],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,2,3],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,2,6],[3]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,2,4],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,2,6],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,2,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,2,6],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,2,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,3,3],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,3,6],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,3,4],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,3,6],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,4,6],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,3,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,3,6],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,5,6],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,3,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,6,6],[3]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,4,4],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,4,6],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,4,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,4,6],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,5,6],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,4,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,6,6],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,5,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[2,5,6],[5]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,5,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[2,6,6],[5]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[2,6,6],[6]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[3,3,3],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[3,3,4],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[3,3,6],[4]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[3,3,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[3,3,6],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[3,3,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[3,4,4],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[3,4,6],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[3,4,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[3,4,6],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[3,5,6],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[3,4,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[3,6,6],[4]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[3,5,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[3,5,6],[5]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[3,5,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[3,6,6],[5]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[3,6,6],[6]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[4,4,4],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[4,4,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[4,4,6],[5]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[4,4,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[4,5,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[4,5,6],[5]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[4,5,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[4,6,6],[5]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[4,6,6],[6]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[5,5,5],[6]]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>[3,1]
[[5,5,6],[6]]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>[3,1]
[[5,6,6],[6]]=>[2,1,3,4]=>([(2,3)],4)=>[3,1]
[[1,1],[2,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[3,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[4,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[5,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,2],[2,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,2],[3,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,3],[2,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,2],[4,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,4],[2,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,2],[5,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,5],[2,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,2],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,3],[3,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,3],[4,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,4],[3,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,3],[5,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,5],[3,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,3],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,4],[4,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,4],[5,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,5],[4,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,4],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,5],[5,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[1,5],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,2],[3,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,2],[4,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,2],[5,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,2],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,3],[3,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[2,3],[4,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,4],[3,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[2,3],[5,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,5],[3,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[2,3],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,4],[4,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[2,4],[5,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,5],[4,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[2,4],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[2,5],[5,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[2,5],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[3,3],[4,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[3,3],[5,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[3,3],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[3,4],[4,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[3,4],[5,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[3,5],[4,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[3,4],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[3,5],[5,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[3,5],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[4,4],[5,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[4,4],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[4,5],[5,6]]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>[2,2]
[[4,5],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[5,5],[6,6]]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>[2,2]
[[1,1],[2],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,1],[3],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,1],[4],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,1],[5],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,2],[2],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,2],[3],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,3],[2],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,6],[2],[3]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,2],[4],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,4],[2],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,6],[2],[4]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,2],[5],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,5],[2],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,6],[2],[5]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,6],[2],[6]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,3],[3],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,3],[4],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,4],[3],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,6],[3],[4]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,3],[5],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,5],[3],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,6],[3],[5]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,6],[3],[6]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,4],[4],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,4],[5],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,5],[4],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,6],[4],[5]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,6],[4],[6]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,5],[5],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1,6],[5],[6]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,2],[3],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,2],[4],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,2],[5],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,3],[3],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,3],[4],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,4],[3],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,6],[3],[4]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,3],[5],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,5],[3],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,6],[3],[5]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,6],[3],[6]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,4],[4],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,4],[5],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,5],[4],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,6],[4],[5]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,6],[4],[6]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,5],[5],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[2,6],[5],[6]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[3,3],[4],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[3,3],[5],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[3,4],[4],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[3,4],[5],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[3,5],[4],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[3,6],[4],[5]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[3,6],[4],[6]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[3,5],[5],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[3,6],[5],[6]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[4,4],[5],[6]]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[4,5],[5],[6]]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[4,6],[5],[6]]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>[2,1,1]
[[1],[2],[3],[6]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[1],[2],[4],[6]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[1],[2],[5],[6]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[1],[3],[4],[6]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[1],[3],[5],[6]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[1],[4],[5],[6]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[2],[3],[4],[6]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[2],[3],[5],[6]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[2],[4],[5],[6]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[3],[4],[5],[6]]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]
[[1,1,1,1,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,2,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,3,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,2,2,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,2,3,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,2,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,2,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,3,3,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,3,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,3,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,4,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,4,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,2,2,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,2,3,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,2,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,2,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,3,3,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,3,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,3,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,4,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,4,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,2,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,3,3,3,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,3,3,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,3,3,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,3,4,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,3,4,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,3,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,4,4,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,4,4,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,4,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,5,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,2,2,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,2,3,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,2,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,2,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,3,3,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,3,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,3,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,4,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,4,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,2,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,3,3,3,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,3,3,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,3,3,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,3,4,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,3,4,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,3,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,4,4,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,4,4,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,4,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[2,5,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,3,3,3,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,3,3,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,3,3,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,3,4,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,3,4,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,3,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,4,4,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,4,4,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,4,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[3,5,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[4,4,4,4,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[4,4,4,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[4,4,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[4,5,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[5,5,5,5,5]]=>[1,2,3,4,5]=>([],5)=>[5]
[[1,1,1,1],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,2],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,5],[2]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,3],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,5],[3]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,5],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,1,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,2,2],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,2,5],[2]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,2,3],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,2,5],[3]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,3,5],[2]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,2,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,2,5],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,4,5],[2]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,2,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,5,5],[2]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,3,3],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,3,5],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,3,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,3,5],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,4,5],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,3,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,5,5],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,4,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,4,5],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,4,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,1,5,5],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,1,5,5],[5]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,2,2,2],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,2,5],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,2,3],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,2,5],[3]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,3,5],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,2,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,2,5],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,4,5],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,2,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,5,5],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,3,3],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,3,5],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,3,3,5],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,3,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,3,5],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,4,5],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,3,4,5],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,3,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,5,5],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,3,5,5],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,4,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,4,5],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,4,4,5],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,4,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,2,5,5],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,4,5,5],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,2,5,5],[5]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,5,5,5],[2]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,3,3,3],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,3,3,5],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,3,3,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,3,3,5],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,3,4,5],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,3,3,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,3,5,5],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,3,4,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,3,4,5],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,4,4,5],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,3,4,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,3,5,5],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,4,5,5],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,3,5,5],[5]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,5,5,5],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,4,4,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,4,4,5],[4]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,4,4,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[1,4,5,5],[4]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,4,5,5],[5]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[1,5,5,5],[4]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,5,5,5],[5]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,2,2,2],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,2,3],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,2,5],[3]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,2,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,2,5],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,2,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,3,3],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,3,5],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,2,3,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,3,5],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,4,5],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,2,3,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,5,5],[3]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,2,4,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,4,5],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,2,4,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,2,5,5],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,2,5,5],[5]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,3,3,3],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,3,3,5],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,3,3,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,3,3,5],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,3,4,5],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,3,3,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,3,5,5],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,3,4,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,3,4,5],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,4,4,5],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,3,4,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,3,5,5],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,4,5,5],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,3,5,5],[5]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,5,5,5],[3]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,4,4,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,4,4,5],[4]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,4,4,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[2,4,5,5],[4]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,4,5,5],[5]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[2,5,5,5],[4]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[2,5,5,5],[5]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[3,3,3,3],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[3,3,3,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[3,3,3,5],[4]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[3,3,3,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[3,3,4,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[3,3,4,5],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[3,3,4,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[3,3,5,5],[4]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[3,3,5,5],[5]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[3,4,4,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[3,4,4,5],[4]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[3,4,4,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[3,4,5,5],[4]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[3,4,5,5],[5]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[3,5,5,5],[4]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[3,5,5,5],[5]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[4,4,4,4],[5]]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>[4,1]
[[4,4,4,5],[5]]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>[4,1]
[[4,4,5,5],[5]]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>[4,1]
[[4,5,5,5],[5]]=>[2,1,3,4,5]=>([(3,4)],5)=>[4,1]
[[1,1,1],[2,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,1],[3,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,1],[4,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,1],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,2],[2,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,1,5],[2,2]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,2],[3,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,3],[2,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,1,5],[2,3]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,2],[4,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,4],[2,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,1,5],[2,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,2],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,5],[2,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,3],[3,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,1,5],[3,3]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,3],[4,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,4],[3,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,1,5],[3,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,3],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,5],[3,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,4],[4,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,1,5],[4,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,4],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,5],[4,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,5],[5,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,2,2],[2,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,2],[3,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,2,3],[2,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,5],[2,3]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,2],[4,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,2,4],[2,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,5],[2,4]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,2],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,2,5],[2,5]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,3],[3,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,2,5],[3,3]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,3,3],[2,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,3],[4,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,2,4],[3,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,2,5],[3,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,3,4],[2,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,3,5],[2,4]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,3],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,2,5],[3,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,3,5],[2,5]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,4],[4,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,2,5],[4,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,4,4],[2,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,4],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,2,5],[4,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,4,5],[2,5]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,2,5],[5,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,3,3],[3,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,3,3],[4,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,3,4],[3,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,3,5],[3,4]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,3,3],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,3,5],[3,5]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,3,4],[4,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[1,3,5],[4,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,4,4],[3,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,3,4],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,3,5],[4,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,4,5],[3,5]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,3,5],[5,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,4,4],[4,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,4,4],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,4,5],[4,5]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[1,4,5],[5,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,2],[3,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,2],[4,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,2],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,3],[3,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[2,2,5],[3,3]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,3],[4,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,4],[3,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[2,2,5],[3,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,3],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,5],[3,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,4],[4,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[2,2,5],[4,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,4],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,5],[4,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,2,5],[5,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,3,3],[3,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[2,3,3],[4,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,3,4],[3,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[2,3,5],[3,4]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[2,3,3],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,3,5],[3,5]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[2,3,4],[4,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[2,3,5],[4,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,4,4],[3,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[2,3,4],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,3,5],[4,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,4,5],[3,5]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[2,3,5],[5,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,4,4],[4,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[2,4,4],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[2,4,5],[4,5]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[2,4,5],[5,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[3,3,3],[4,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[3,3,3],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[3,3,4],[4,5]]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[3,2]
[[3,3,5],[4,4]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[3,3,4],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[3,3,5],[4,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[3,3,5],[5,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[3,4,4],[4,5]]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>[3,2]
[[3,4,4],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[3,4,5],[4,5]]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>[3,2]
[[3,4,5],[5,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[4,4,4],[5,5]]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[4,4,5],[5,5]]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>[3,2]
[[1,1,1],[2],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,1],[3],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,1],[4],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,2],[2],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,2],[3],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,3],[2],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,5],[2],[3]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,2],[4],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,4],[2],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,5],[2],[4]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,5],[2],[5]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,3],[3],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,3],[4],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,4],[3],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,5],[3],[4]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,5],[3],[5]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,4],[4],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1,5],[4],[5]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,2],[2],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,2],[3],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,3],[2],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,5],[2],[3]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,2],[4],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,4],[2],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,5],[2],[4]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,5],[2],[5]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,3],[3],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,3],[2],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,5],[2],[3]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,5],[3],[5]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,5],[2],[5]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,5,5],[2],[3]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,4],[4],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,4,4],[2],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,4,5],[2],[4]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,2,5],[4],[5]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,4,5],[2],[5]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,5,5],[2],[4]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,5,5],[2],[5]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,3],[3],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,3],[4],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,4],[3],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,5],[3],[4]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,5],[3],[5]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,4],[4],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,4,4],[3],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,4,5],[3],[4]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,3,5],[4],[5]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,4,5],[3],[5]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,5,5],[3],[4]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,5,5],[3],[5]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,4,4],[4],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,4,5],[4],[5]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,5,5],[4],[5]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,2,2],[3],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,2,2],[4],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,2,3],[3],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,2,3],[4],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,2,4],[3],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,2,5],[3],[4]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,2,5],[3],[5]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,2,4],[4],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,2,5],[4],[5]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,3,3],[3],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,3,3],[4],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,3,4],[3],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,3,5],[3],[4]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,3,5],[3],[5]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,3,4],[4],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,4,4],[3],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,4,5],[3],[4]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,3,5],[4],[5]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,4,5],[3],[5]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,5,5],[3],[4]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,5,5],[3],[5]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,4,4],[4],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,4,5],[4],[5]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[2,5,5],[4],[5]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[3,3,3],[4],[5]]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[3,3,4],[4],[5]]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[3,3,5],[4],[5]]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[3,4,4],[4],[5]]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[3,4,5],[4],[5]]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[3,5,5],[4],[5]]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>[3,1,1]
[[1,1],[2,2],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,1],[2,3],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,1],[2,5],[3]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,1],[2,4],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,1],[2,5],[4]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,1],[2,5],[5]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,1],[3,3],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,1],[3,4],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,1],[3,5],[4]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,1],[3,5],[5]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,1],[4,4],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,1],[4,5],[5]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,2],[2,3],[5]]=>[5,2,4,1,3]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[2,5],[3]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[2,4],[5]]=>[5,2,4,1,3]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[2,5],[4]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[2,5],[5]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[3,3],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,3],[2,5],[3]]=>[3,2,5,1,4]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[3,5],[5]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,3],[2,5],[5]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[4,4],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,4],[2,5],[4]]=>[3,2,5,1,4]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,2],[4,5],[5]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,4],[2,5],[5]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,3],[3,4],[5]]=>[5,2,4,1,3]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,3],[3,5],[4]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,3],[3,5],[5]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,3],[4,4],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,4],[3,5],[4]]=>[3,2,5,1,4]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[1,3],[4,5],[5]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[1,4],[3,5],[5]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,4],[4,5],[5]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[2,2],[3,3],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[2,2],[3,4],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[2,2],[3,5],[4]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[2,2],[3,5],[5]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[2,2],[4,4],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[2,2],[4,5],[5]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[2,3],[3,4],[5]]=>[5,2,4,1,3]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[2,3],[3,5],[4]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[2,3],[3,5],[5]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[2,3],[4,4],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[2,4],[3,5],[4]]=>[3,2,5,1,4]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[2,3],[4,5],[5]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[2,4],[3,5],[5]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[2,4],[4,5],[5]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[3,3],[4,4],[5]]=>[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]
[[3,3],[4,5],[5]]=>[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[2,2,1]
[[3,4],[4,5],[5]]=>[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[2,2,1]
[[1,1],[2],[3],[5]]=>[5,4,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,1],[2],[4],[5]]=>[5,4,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,1],[3],[4],[5]]=>[5,4,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,2],[2],[3],[5]]=>[5,4,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,2],[2],[4],[5]]=>[5,4,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,3],[2],[3],[5]]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,5],[2],[3],[5]]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,4],[2],[4],[5]]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,5],[2],[4],[5]]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,3],[3],[4],[5]]=>[5,4,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,4],[3],[4],[5]]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1,5],[3],[4],[5]]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[2,2],[3],[4],[5]]=>[5,4,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[2,3],[3],[4],[5]]=>[5,4,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[2,4],[3],[4],[5]]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[2,5],[3],[4],[5]]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]
[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[1,1,1,1,1]
[[1,1,1,1,1,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,1,2,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,1,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,1,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,2,2,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,2,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,2,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,3,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,3,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,2,2,2,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,2,2,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,2,2,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,2,3,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,2,3,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,2,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,3,3,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,3,3,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,3,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,4,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,2,2,2,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,2,2,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,2,2,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,2,3,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,2,3,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,2,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,3,3,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,3,3,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,3,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,4,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,3,3,3,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,3,3,3,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,3,3,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,3,4,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,4,4,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,2,2,2,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,2,2,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,2,2,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,2,3,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,2,3,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,2,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,3,3,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,3,3,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,3,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,2,4,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,3,3,3,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,3,3,3,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,3,3,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,3,4,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[2,4,4,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[3,3,3,3,3,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[3,3,3,3,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[3,3,3,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[3,3,4,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[3,4,4,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[4,4,4,4,4,4]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,1,1,1,1],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,1,2],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,1,4],[2]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,1,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,1,4],[3]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,1,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,2,2],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,2,4],[2]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,2,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,2,4],[3]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,3,4],[2]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,2,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,4,4],[2]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,3,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,3,4],[3]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,3,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,4,4],[3]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,1,4,4],[4]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,2,2,2],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,2,2,4],[2]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,1,2,2,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,2,2,4],[3]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,2,3,4],[2]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,1,2,2,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,2,4,4],[2]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,1,2,3,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,2,3,4],[3]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,3,3,4],[2]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,1,2,3,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,2,4,4],[3]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,3,4,4],[2]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,1,2,4,4],[4]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,4,4,4],[2]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,1,3,3,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,3,3,4],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,1,3,3,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,3,4,4],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,1,3,4,4],[4]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,1,4,4,4],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,1,4,4,4],[4]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,2,2,2,2],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,2,2,4],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,2,2,2,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,2,2,4],[3]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,2,3,4],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,2,2,2,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,2,4,4],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,2,2,3,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,2,3,4],[3]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,3,3,4],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,2,2,3,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,2,4,4],[3]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,3,4,4],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,2,2,4,4],[4]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,4,4,4],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,2,3,3,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,3,3,4],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,3,3,3,4],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,2,3,3,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,3,4,4],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,3,3,4,4],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,2,3,4,4],[4]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,4,4,4],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,3,4,4,4],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,2,4,4,4],[4]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,4,4,4,4],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,3,3,3,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,3,3,3,4],[3]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,3,3,3,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,3,3,4,4],[3]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,3,3,4,4],[4]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,3,4,4,4],[3]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,3,4,4,4],[4]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,4,4,4,4],[3]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,4,4,4,4],[4]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[2,2,2,2,2],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,2,2,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,2,2,4],[3]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,2,2,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,2,3,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,2,3,4],[3]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,2,3,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,2,4,4],[3]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,2,4,4],[4]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,3,3,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,3,3,4],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[2,2,3,3,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,3,4,4],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[2,2,3,4,4],[4]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,2,4,4,4],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[2,2,4,4,4],[4]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[2,3,3,3,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,3,3,3,4],[3]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[2,3,3,3,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,3,3,4,4],[3]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[2,3,3,4,4],[4]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[2,3,4,4,4],[3]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[2,3,4,4,4],[4]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[2,4,4,4,4],[3]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[2,4,4,4,4],[4]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[3,3,3,3,3],[4]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[3,3,3,3,4],[4]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[3,3,3,4,4],[4]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[3,3,4,4,4],[4]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[3,4,4,4,4],[4]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,1,1,1],[2,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,1],[3,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,1],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,2],[2,4]]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,4],[2,2]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,2],[3,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,3],[2,4]]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,4],[2,3]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,2],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,4],[2,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,3],[3,4]]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,4],[3,3]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,3],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,4],[3,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,4],[4,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,2],[2,4]]=>[3,6,1,2,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,1,2,4],[2,2]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,2],[3,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,3],[2,4]]=>[3,6,1,2,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,1,2,4],[2,3]]=>[3,5,1,2,4,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,1,3,4],[2,2]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,2],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,4],[2,4]]=>[3,5,1,2,4,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,1,4,4],[2,2]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,3],[3,4]]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,4],[3,3]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,3,3],[2,4]]=>[3,6,1,2,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,1,3,4],[2,3]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,3],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,4],[3,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,3,4],[2,4]]=>[3,5,1,2,4,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,1,4,4],[2,3]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,2,4],[4,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,4,4],[2,4]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,3,3],[3,4]]=>[3,6,1,2,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,1,3,4],[3,3]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,3,3],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,3,4],[3,4]]=>[3,5,1,2,4,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,1,4,4],[3,3]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,3,4],[4,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,4,4],[3,4]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,4,4],[4,4]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,2,2],[2,4]]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,2,2],[3,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,2,3],[2,4]]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,2,4],[2,3]]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,2,2],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,2,4],[2,4]]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,2,3],[3,4]]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,2,4],[3,3]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,3,3],[2,4]]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,3,4],[2,3]]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,2,3],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,2,4],[3,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,3,4],[2,4]]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,4,4],[2,3]]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,2,4],[4,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,4,4],[2,4]]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,3,3],[3,4]]=>[3,6,1,2,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,2,3,4],[3,3]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,3,3,3],[2,4]]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,3,3],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,3,4],[3,4]]=>[3,5,1,2,4,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,2,4,4],[3,3]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,3,3,4],[2,4]]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,3,4],[4,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,4,4],[3,4]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,3,4,4],[2,4]]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,2,4,4],[4,4]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,3,3,3],[3,4]]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,3,3,4],[3,4]]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,3,4,4],[3,4]]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,2,2],[3,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,2,2],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,2,3],[3,4]]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,2,4],[3,3]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,2,3],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,2,4],[3,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,2,4],[4,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,3,3],[3,4]]=>[3,6,1,2,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[2,2,3,4],[3,3]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,3,3],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,3,4],[3,4]]=>[3,5,1,2,4,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[2,2,4,4],[3,3]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,3,4],[4,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,4,4],[3,4]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,2,4,4],[4,4]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,3,3,3],[3,4]]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[2,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,3,3,4],[3,4]]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[2,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[2,3,4,4],[3,4]]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)=>[4,2]
[[2,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[3,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[3,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[3,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,1,1,1],[2],[4]]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,1,1],[3],[4]]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,1,2],[2],[4]]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,1,2],[3],[4]]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,1,3],[2],[4]]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,1,4],[2],[3]]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,1,4],[2],[4]]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,1,3],[3],[4]]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,1,4],[3],[4]]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,2,2],[2],[4]]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,2,2],[3],[4]]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,2,3],[2],[4]]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,2,4],[2],[3]]=>[5,3,1,2,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,2,4],[2],[4]]=>[5,3,1,2,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,2,3],[3],[4]]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,3,3],[2],[4]]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,3,4],[2],[3]]=>[4,3,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,2,4],[3],[4]]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,3,4],[2],[4]]=>[5,3,1,2,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,4,4],[2],[3]]=>[4,3,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,4,4],[2],[4]]=>[4,3,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,3,3],[3],[4]]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,3,4],[3],[4]]=>[5,3,1,2,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,4,4],[3],[4]]=>[4,3,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,2,2],[2],[4]]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,2,2],[3],[4]]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,2,3],[2],[4]]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,2,4],[2],[3]]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,2,4],[2],[4]]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,2,3],[3],[4]]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,3,3],[2],[4]]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,3,4],[2],[3]]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,2,4],[3],[4]]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,3,4],[2],[4]]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,4,4],[2],[3]]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,4,4],[2],[4]]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,3,3],[3],[4]]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,3,3,3],[2],[4]]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,3,3,4],[2],[3]]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,3,4],[3],[4]]=>[5,3,1,2,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,3,3,4],[2],[4]]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,3,4,4],[2],[3]]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,4,4],[3],[4]]=>[4,3,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,3,4,4],[2],[4]]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,4,4,4],[2],[3]]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,4,4,4],[2],[4]]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,3,3,3],[3],[4]]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,3,3,4],[3],[4]]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,3,4,4],[3],[4]]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,4,4,4],[3],[4]]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[2,2,2,2],[3],[4]]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[2,2,2,3],[3],[4]]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[2,2,2,4],[3],[4]]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[2,2,3,3],[3],[4]]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[2,2,3,4],[3],[4]]=>[5,3,1,2,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[2,2,4,4],[3],[4]]=>[4,3,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[2,3,3,3],[3],[4]]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[2,3,3,4],[3],[4]]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[2,3,4,4],[3],[4]]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[2,4,4,4],[3],[4]]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,1,1],[2,2,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,1],[2,3,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,1],[2,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,1],[3,3,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,1],[3,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,1],[4,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,2],[2,2,4]]=>[3,4,6,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,1,2],[2,3,4]]=>[3,5,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,3]
[[1,1,3],[2,2,4]]=>[3,4,6,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,1,2],[2,4,4]]=>[3,5,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,3]
[[1,1,2],[3,3,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,3],[2,3,4]]=>[3,4,6,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,1,2],[3,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,3],[2,4,4]]=>[3,5,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,3]
[[1,1,2],[4,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,3],[3,3,4]]=>[3,4,6,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,1,3],[3,4,4]]=>[3,5,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,3]
[[1,1,3],[4,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,2,2],[2,3,4]]=>[2,5,6,1,3,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,2,2],[2,4,4]]=>[2,5,6,1,3,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,2,2],[3,3,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,2,3],[2,3,4]]=>[2,4,6,1,3,5]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,2,2],[3,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,2,3],[2,4,4]]=>[2,5,6,1,3,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,2,2],[4,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,2,3],[3,3,4]]=>[3,4,6,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,2,3],[3,4,4]]=>[3,5,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,3]
[[1,3,3],[2,4,4]]=>[2,5,6,1,3,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,2,3],[4,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,3,3],[3,4,4]]=>[2,5,6,1,3,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[2,2,2],[3,3,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[2,2,2],[3,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[2,2,2],[4,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[2,2,3],[3,3,4]]=>[3,4,6,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[2,2,3],[3,4,4]]=>[3,5,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,3]
[[2,2,3],[4,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[2,3,3],[3,4,4]]=>[2,5,6,1,3,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[2,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[3,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,1,1],[2,2],[4]]=>[6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,1],[2,3],[4]]=>[6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,1],[2,4],[3]]=>[5,4,6,1,2,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,1],[2,4],[4]]=>[5,4,6,1,2,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,1],[3,3],[4]]=>[6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,1],[3,4],[4]]=>[5,4,6,1,2,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,2],[2,2],[4]]=>[6,3,4,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,2],[2,3],[4]]=>[6,3,5,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,2],[2,4],[3]]=>[5,3,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,1,3],[2,2],[4]]=>[6,3,4,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,4],[2,2],[3]]=>[5,3,4,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,2],[2,4],[4]]=>[5,3,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,1,4],[2,2],[4]]=>[5,3,4,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,2],[3,3],[4]]=>[6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,3],[2,3],[4]]=>[6,3,4,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,3],[2,4],[3]]=>[4,3,6,1,2,5]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,4],[2,3],[3]]=>[4,3,5,1,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,1,2],[3,4],[4]]=>[5,4,6,1,2,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,3],[2,4],[4]]=>[5,3,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,1,4],[2,3],[4]]=>[5,3,4,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,4],[2,4],[3]]=>[4,3,5,1,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,1,4],[2,4],[4]]=>[4,3,5,1,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,1,3],[3,3],[4]]=>[6,3,4,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,3],[3,4],[4]]=>[5,3,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,1,4],[3,3],[4]]=>[5,3,4,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,4],[3,4],[4]]=>[4,3,5,1,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,2,2],[2,3],[4]]=>[6,2,5,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,2],[2,4],[3]]=>[5,2,6,1,3,4]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>[3,2,1]
[[1,2,2],[2,4],[4]]=>[5,2,6,1,3,4]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>[3,2,1]
[[1,2,2],[3,3],[4]]=>[6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,3],[2,3],[4]]=>[6,2,4,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,3],[2,4],[3]]=>[4,2,6,1,3,5]=>([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,2,4],[2,3],[3]]=>[4,2,5,1,3,6]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,2],[3,4],[4]]=>[5,4,6,1,2,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,3],[2,4],[4]]=>[5,2,6,1,3,4]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>[3,2,1]
[[1,2,4],[2,3],[4]]=>[5,2,4,1,3,6]=>([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,4],[2,4],[3]]=>[4,2,5,1,3,6]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,4],[2,4],[4]]=>[4,2,5,1,3,6]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,3],[3,3],[4]]=>[6,3,4,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,3,3],[2,4],[3]]=>[3,2,6,1,4,5]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,3],[3,4],[4]]=>[5,3,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,2,4],[3,3],[4]]=>[5,3,4,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,3,3],[2,4],[4]]=>[5,2,6,1,3,4]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>[3,2,1]
[[1,3,4],[2,4],[3]]=>[3,2,5,1,4,6]=>([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,4],[3,4],[4]]=>[4,3,5,1,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,3,4],[2,4],[4]]=>[4,2,5,1,3,6]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,3,3],[3,4],[4]]=>[5,2,6,1,3,4]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>[3,2,1]
[[1,3,4],[3,4],[4]]=>[4,2,5,1,3,6]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[2,2,2],[3,3],[4]]=>[6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[2,2,2],[3,4],[4]]=>[5,4,6,1,2,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[2,2,3],[3,3],[4]]=>[6,3,4,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[2,2,3],[3,4],[4]]=>[5,3,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[2,2,4],[3,3],[4]]=>[5,3,4,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[2,2,4],[3,4],[4]]=>[4,3,5,1,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[2,3,3],[3,4],[4]]=>[5,2,6,1,3,4]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>[3,2,1]
[[2,3,4],[3,4],[4]]=>[4,2,5,1,3,6]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,1,1],[2],[3],[4]]=>[6,5,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,1,2],[2],[3],[4]]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,1,3],[2],[3],[4]]=>[6,4,3,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,1,4],[2],[3],[4]]=>[5,4,3,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,2,2],[2],[3],[4]]=>[6,5,2,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,2,3],[2],[3],[4]]=>[6,4,2,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,2,4],[2],[3],[4]]=>[5,4,2,1,3,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,3,3],[2],[3],[4]]=>[6,3,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,3,4],[2],[3],[4]]=>[5,3,2,1,4,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,4,4],[2],[3],[4]]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,1],[2,2],[3,4]]=>[5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]
[[1,1],[2,2],[4,4]]=>[5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]
[[1,1],[2,3],[3,4]]=>[4,6,3,5,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]
[[1,1],[2,3],[4,4]]=>[5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]
[[1,1],[3,3],[4,4]]=>[5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]
[[1,2],[2,3],[3,4]]=>[4,6,2,5,1,3]=>([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,2]
[[1,2],[2,3],[4,4]]=>[5,6,2,4,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]
[[1,2],[3,3],[4,4]]=>[5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]
[[2,2],[3,3],[4,4]]=>[5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]
[[1,1],[2,2],[3],[4]]=>[6,5,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]
[[1,1],[2,3],[3],[4]]=>[6,4,3,5,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[2,2,1,1]
[[1,1],[2,4],[3],[4]]=>[5,4,3,6,1,2]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,1,1]
[[1,2],[2,3],[3],[4]]=>[6,4,2,5,1,3]=>([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]
[[1,2],[2,4],[3],[4]]=>[5,4,2,6,1,3]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]
[[1,3],[2,4],[3],[4]]=>[5,3,2,6,1,4]=>([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]
[[1,1,1,1,1,1,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,1,1,2,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,1,1,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,1,2,2,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,1,2,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,1,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,2,2,2,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,2,2,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,2,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,3,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,2,2,2,2,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,2,2,2,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,2,2,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,2,3,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,2,2,2,2,2,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,2,2,2,2,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,2,2,2,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,2,2,3,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,2,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,3,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[2,2,2,2,2,2,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[2,2,2,2,2,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[2,2,2,2,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[2,2,2,3,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[2,2,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[2,3,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[3,3,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>([],7)=>[7]
[[1,1,1,1,1,1],[3]]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,1,1,2],[3]]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,1,1,3],[2]]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,1,1,3],[3]]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,1,2,2],[3]]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,1,2,3],[2]]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,1,2,3],[3]]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,1,3,3],[2]]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,1,3,3],[3]]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,2,2,3],[2]]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,2,3,3],[2]]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,3,3,3],[2]]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,1,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,2,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,2,2,2,3],[2]]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)=>[6,1]
[[1,1,2,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,2,2,3,3],[2]]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)=>[6,1]
[[1,1,2,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,2,3,3,3],[2]]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)=>[6,1]
[[1,1,2,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,1,3,3,3,3],[2]]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)=>[6,1]
[[1,1,3,3,3,3],[3]]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)=>[6,1]
[[1,2,2,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,2,2,2,2,3],[2]]=>[2,1,3,4,5,6,7]=>([(5,6)],7)=>[6,1]
[[1,2,2,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,2,2,2,3,3],[2]]=>[2,1,3,4,5,6,7]=>([(5,6)],7)=>[6,1]
[[1,2,2,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,2,2,3,3,3],[2]]=>[2,1,3,4,5,6,7]=>([(5,6)],7)=>[6,1]
[[1,2,2,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)=>[6,1]
[[1,2,3,3,3,3],[2]]=>[2,1,3,4,5,6,7]=>([(5,6)],7)=>[6,1]
[[1,2,3,3,3,3],[3]]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)=>[6,1]
[[1,3,3,3,3,3],[2]]=>[2,1,3,4,5,6,7]=>([(5,6)],7)=>[6,1]
[[1,3,3,3,3,3],[3]]=>[2,1,3,4,5,6,7]=>([(5,6)],7)=>[6,1]
[[2,2,2,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[2,2,2,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[2,2,2,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)=>[6,1]
[[2,2,2,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)=>[6,1]
[[2,2,3,3,3,3],[3]]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)=>[6,1]
[[2,3,3,3,3,3],[3]]=>[2,1,3,4,5,6,7]=>([(5,6)],7)=>[6,1]
[[1,1,1,1,1],[2,3]]=>[6,7,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,1,1],[3,3]]=>[6,7,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,1,2],[2,3]]=>[5,7,1,2,3,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,1,3],[2,2]]=>[5,6,1,2,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,1,2],[3,3]]=>[6,7,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,1,3],[2,3]]=>[5,6,1,2,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,1,3],[3,3]]=>[5,6,1,2,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,2,2],[2,3]]=>[4,7,1,2,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,2,3],[2,2]]=>[4,5,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,2,3],[2,3]]=>[4,6,1,2,3,5,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,3,3],[2,2]]=>[4,5,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,3,3],[2,3]]=>[4,5,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,2,2,2],[2,3]]=>[3,7,1,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,2,2,3],[2,2]]=>[3,4,1,2,5,6,7]=>([(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,2,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,2,2,3],[2,3]]=>[3,6,1,2,4,5,7]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[5,2]
[[1,1,2,3,3],[2,2]]=>[3,4,1,2,5,6,7]=>([(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,2,3,3],[2,3]]=>[3,5,1,2,4,6,7]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[5,2]
[[1,1,3,3,3],[2,2]]=>[3,4,1,2,5,6,7]=>([(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,3,3,3],[2,3]]=>[3,4,1,2,5,6,7]=>([(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>([(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,2,2,2,2],[2,3]]=>[2,7,1,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]
[[1,2,2,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,2,2,2,3],[2,3]]=>[2,6,1,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]
[[1,2,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,2,2,3,3],[2,3]]=>[2,5,1,3,4,6,7]=>([(2,6),(3,6),(4,5),(5,6)],7)=>[5,2]
[[1,2,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,2,3,3,3],[2,3]]=>[2,4,1,3,5,6,7]=>([(3,6),(4,5),(5,6)],7)=>[5,2]
[[1,2,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>([(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[2,2,2,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[2,2,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[2,2,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[2,2,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>([(3,5),(3,6),(4,5),(4,6)],7)=>[5,2]
[[1,1,1,1,1],[2],[3]]=>[7,6,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,1,1,1,2],[2],[3]]=>[7,5,1,2,3,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,1,1,1,3],[2],[3]]=>[6,5,1,2,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,1,1,2,2],[2],[3]]=>[7,4,1,2,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,1,1,2,3],[2],[3]]=>[6,4,1,2,3,5,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,1,1,3,3],[2],[3]]=>[5,4,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,1,2,2,2],[2],[3]]=>[7,3,1,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,1,2,2,3],[2],[3]]=>[6,3,1,2,4,5,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,1,2,3,3],[2],[3]]=>[5,3,1,2,4,6,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,1,3,3,3],[2],[3]]=>[4,3,1,2,5,6,7]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,2,2,2,2],[2],[3]]=>[7,2,1,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,2,2,2,3],[2],[3]]=>[6,2,1,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,2,2,3,3],[2],[3]]=>[5,2,1,3,4,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,2,3,3,3],[2],[3]]=>[4,2,1,3,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,3,3,3,3],[2],[3]]=>[3,2,1,4,5,6,7]=>([(4,5),(4,6),(5,6)],7)=>[5,1,1]
[[1,1,1,1],[2,2,3]]=>[5,6,7,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,1,1,1],[2,3,3]]=>[5,6,7,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,1,1,1],[3,3,3]]=>[5,6,7,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,1,1,2],[2,2,3]]=>[4,5,7,1,2,3,6]=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>[4,3]
[[1,1,1,3],[2,2,2]]=>[4,5,6,1,2,3,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,1,1,2],[2,3,3]]=>[4,6,7,1,2,3,5]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]
[[1,1,1,3],[2,2,3]]=>[4,5,6,1,2,3,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,1,1,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,1,1,3],[2,3,3]]=>[4,5,6,1,2,3,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,1,1,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,1,2,2],[2,2,3]]=>[3,4,7,1,2,5,6]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[4,3]
[[1,1,2,2],[2,3,3]]=>[3,6,7,1,2,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]
[[1,1,2,3],[2,2,3]]=>[3,4,6,1,2,5,7]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[4,3]
[[1,1,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,1,2,3],[2,3,3]]=>[3,5,6,1,2,4,7]=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]
[[1,1,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,2,2,2],[2,3,3]]=>[2,6,7,1,3,4,5]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,3]
[[1,2,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,2,2,3],[2,3,3]]=>[2,5,6,1,3,4,7]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[4,3]
[[1,2,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[2,2,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[2,2,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[4,3]
[[1,1,1,1],[2,2],[3]]=>[7,5,6,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]
[[1,1,1,1],[2,3],[3]]=>[6,5,7,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[4,2,1]
[[1,1,1,2],[2,2],[3]]=>[7,4,5,1,2,3,6]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]
[[1,1,1,2],[2,3],[3]]=>[6,4,7,1,2,3,5]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)=>[4,2,1]
[[1,1,1,3],[2,2],[3]]=>[6,4,5,1,2,3,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]
[[1,1,1,3],[2,3],[3]]=>[5,4,6,1,2,3,7]=>([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]
[[1,1,2,2],[2,2],[3]]=>[7,3,4,1,2,5,6]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]
[[1,1,2,2],[2,3],[3]]=>[6,3,7,1,2,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]
[[1,1,2,3],[2,2],[3]]=>[6,3,4,1,2,5,7]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]
[[1,1,2,3],[2,3],[3]]=>[5,3,6,1,2,4,7]=>([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]
[[1,1,3,3],[2,2],[3]]=>[5,3,4,1,2,6,7]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[4,2,1]
[[1,1,3,3],[2,3],[3]]=>[4,3,5,1,2,6,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[4,2,1]
[[1,2,2,2],[2,3],[3]]=>[6,2,7,1,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6)],7)=>[4,2,1]
[[1,2,2,3],[2,3],[3]]=>[5,2,6,1,3,4,7]=>([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[4,2,1]
[[1,2,3,3],[2,3],[3]]=>[4,2,5,1,3,6,7]=>([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[4,2,1]
[[1,1,1],[2,2,2],[3]]=>[7,4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)=>[3,3,1]
[[1,1,1],[2,2,3],[3]]=>[6,4,5,7,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)=>[3,3,1]
[[1,1,1],[2,3,3],[3]]=>[5,4,6,7,1,2,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[3,3,1]
[[1,1,2],[2,2,3],[3]]=>[6,3,4,7,1,2,5]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[3,3,1]
[[1,1,2],[2,3,3],[3]]=>[5,3,6,7,1,2,4]=>([(0,1),(0,2),(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]
[[1,2,2],[2,3,3],[3]]=>[5,2,6,7,1,3,4]=>([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5),(5,6)],7)=>[3,3,1]
[[1,1,1],[2,2],[3,3]]=>[6,7,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]
[[1,1,2],[2,2],[3,3]]=>[6,7,3,4,1,2,5]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]
[[1,1,3],[2,2],[3,3]]=>[5,6,3,4,1,2,7]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[3,2,2]
[[1]]=>[1]=>([],1)=>[1]
[[2]]=>[1]=>([],1)=>[1]
[[1,1]]=>[1,2]=>([],2)=>[2]
[[3]]=>[1]=>([],1)=>[1]
[[1,1,1]]=>[1,2,3]=>([],3)=>[3]
[[4]]=>[1]=>([],1)=>[1]
[[1,1,1,1]]=>[1,2,3,4]=>([],4)=>[4]
[[5]]=>[1]=>([],1)=>[1]
[[1,1,1,1,1]]=>[1,2,3,4,5]=>([],5)=>[5]
[[6]]=>[1]=>([],1)=>[1]
[[1,1,1,1,1,1]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>([],6)=>[6]
[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>[5,1]
[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>[5,1]
[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[4,2]
[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,1,1,1]
[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>([(4,5)],6)=>[5,1]
[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)=>[4,2]
[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]
[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>[3,2,1]
[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,1,1,1]
[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>[4,2]
[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[3,3]
[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,3]
[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]
[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>[4,1,1]
[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>[3,2,1]
[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,2]
[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]
[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,1,1,1]
[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[3,3]
[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[3,2,1]
[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[2,2,1,1]
[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[3,2,1]
[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,2]
[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]
[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]
[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]
[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]
[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,1,1,1]
[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,1,1]
[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]
[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]
[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[2,2,2]
[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]
[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,1,1,1]
[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
chromatic difference sequence
Description
The chromatic difference sequence of a graph.
Let $G$ be a simple graph with chromatic number $\kappa$. Let $\alpha_m$ be the maximum number of vertices in a $m$-colorable subgraph of $G$. Set $\delta_m=\alpha_m-\alpha_{m-1}$. The sequence $\delta_1,\delta_2,\dots\delta_\kappa$ is the chromatic difference sequence of $G$.
All entries of the chromatic difference sequence are positive: $\alpha_m > \alpha_{m-1}$ for $m < \kappa$, because we can assign any uncolored vertex of a partial coloring with $m-1$ colors the color $m$. Therefore, the chromatic difference sequence is a composition of the number of vertices of $G$ into $\kappa$ parts.
Let $G$ be a simple graph with chromatic number $\kappa$. Let $\alpha_m$ be the maximum number of vertices in a $m$-colorable subgraph of $G$. Set $\delta_m=\alpha_m-\alpha_{m-1}$. The sequence $\delta_1,\delta_2,\dots\delta_\kappa$ is the chromatic difference sequence of $G$.
All entries of the chromatic difference sequence are positive: $\alpha_m > \alpha_{m-1}$ for $m < \kappa$, because we can assign any uncolored vertex of a partial coloring with $m-1$ colors the color $m$. Therefore, the chromatic difference sequence is a composition of the number of vertices of $G$ into $\kappa$ parts.
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