Identifier
Mp00075:
Semistandard tableaux
—reading word permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Images
=>
Cc0019;cc-rep-0Cc0020;cc-rep-3
[[1,2]]=>[1,2]=>[1,2]=>([],2)
[[2,2]]=>[1,2]=>[1,2]=>([],2)
[[1],[2]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[1,3]]=>[1,2]=>[1,2]=>([],2)
[[2,3]]=>[1,2]=>[1,2]=>([],2)
[[3,3]]=>[1,2]=>[1,2]=>([],2)
[[1],[3]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[2],[3]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[1,1,2]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,2,2]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,2,2]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,1],[2]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,2],[2]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,4]]=>[1,2]=>[1,2]=>([],2)
[[2,4]]=>[1,2]=>[1,2]=>([],2)
[[3,4]]=>[1,2]=>[1,2]=>([],2)
[[4,4]]=>[1,2]=>[1,2]=>([],2)
[[1],[4]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[2],[4]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[3],[4]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[1,1,3]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,2,3]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,3,3]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,2,3]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,3,3]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,3,3]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,1],[3]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,2],[3]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,3],[2]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,3],[3]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,2],[3]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,3],[3]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1],[2],[3]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1,1,1,2]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,2,2]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,2,2]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,2,2]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,1],[2]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,2],[2]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,2,2],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,1],[2,2]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,5]]=>[1,2]=>[1,2]=>([],2)
[[2,5]]=>[1,2]=>[1,2]=>([],2)
[[3,5]]=>[1,2]=>[1,2]=>([],2)
[[4,5]]=>[1,2]=>[1,2]=>([],2)
[[5,5]]=>[1,2]=>[1,2]=>([],2)
[[1],[5]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[2],[5]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[3],[5]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[4],[5]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[1,1,4]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,2,4]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,3,4]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,4,4]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,2,4]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,3,4]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,4,4]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,3,4]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,4,4]]=>[1,2,3]=>[1,2,3]=>([],3)
[[4,4,4]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,1],[4]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,2],[4]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,4],[2]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,3],[4]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,4],[3]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,4],[4]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,2],[4]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,3],[4]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,4],[3]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,4],[4]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[3,3],[4]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[3,4],[4]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1],[2],[4]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1],[3],[4]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[2],[3],[4]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1,1,1,3]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,2,3]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,3,3]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,2,3]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,3,3]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,3,3,3]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,2,3]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,3,3]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,3,3,3]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,3,3,3]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,1],[3]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,2],[3]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,3],[2]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,1,3],[3]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,2,2],[3]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,2,3],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,2,3],[3]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,3,3],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,3,3],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,2,2],[3]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,2,3],[3]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,3,3],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,1],[2,3]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[3,3]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[2,3]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[3,3]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,2],[3,3]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[2],[3]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,2],[2],[3]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,3],[2],[3]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,1,1,1,2]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,2,2]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,2,2,2]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,2,2,2]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,2,2,2]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,1],[2]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,1,2],[2]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,2,2],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,2,2,2],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,1,1],[2,2]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,2],[2,2]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,6]]=>[1,2]=>[1,2]=>([],2)
[[2,6]]=>[1,2]=>[1,2]=>([],2)
[[3,6]]=>[1,2]=>[1,2]=>([],2)
[[4,6]]=>[1,2]=>[1,2]=>([],2)
[[5,6]]=>[1,2]=>[1,2]=>([],2)
[[6,6]]=>[1,2]=>[1,2]=>([],2)
[[1],[6]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[2],[6]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[3],[6]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[4],[6]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[5],[6]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[1,1,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,2,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,3,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,4,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,5,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,2,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,3,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,4,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,5,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,3,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,4,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,5,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[4,4,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[4,5,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[5,5,5]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,1],[5]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,2],[5]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,5],[2]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,3],[5]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,5],[3]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,4],[5]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,5],[4]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,5],[5]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,2],[5]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,3],[5]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,5],[3]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,4],[5]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,5],[4]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,5],[5]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[3,3],[5]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[3,4],[5]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[3,5],[4]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[3,5],[5]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[4,4],[5]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[4,5],[5]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1],[2],[5]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1],[3],[5]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1],[4],[5]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[2],[3],[5]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[2],[4],[5]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[3],[4],[5]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1,1,1,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,2,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,2,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,3,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,3,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,4,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,2,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,3,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,3,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,4,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,3,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,3,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,4,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[4,4,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,1],[4]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,2],[4]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,4],[2]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,1,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,4],[3]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,1,4],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,2,2],[4]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,2,4],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,2,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,2,4],[3]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,3,4],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,2,4],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,4,4],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,3,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,3,4],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,3,4],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,4,4],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,4,4],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,2,2],[4]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,2,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,2,4],[3]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,2,4],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,3,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,3,4],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,3,4],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,4,4],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,4,4],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[3,3,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[3,3,4],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[3,4,4],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,1],[2,4]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[3,4]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[4,4]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[2,4]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[3,4]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,3],[2,4]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[4,4]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,3],[3,4]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,3],[4,4]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,2],[3,4]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,2],[4,4]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,3],[3,4]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,3],[4,4]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,3],[4,4]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[2],[4]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,1],[3],[4]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,2],[2],[4]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,2],[3],[4]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,3],[2],[4]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,4],[2],[3]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,4],[2],[4]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,3],[3],[4]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,4],[3],[4]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[2,2],[3],[4]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[2,3],[3],[4]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[2,4],[3],[4]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1],[2],[3],[4]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[1,1,1,1,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,2,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,3,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,2,2,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,2,3,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,3,3,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,2,2,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,2,3,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,3,3,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,3,3,3,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,2,2,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,2,3,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,3,3,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,3,3,3,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,3,3,3,3]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,1],[3]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,1,2],[3]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,1,3],[2]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,1,3],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,2,2],[3]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,2,3],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,2,3],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,3,3],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,3,3],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,2,2,2],[3]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,2,2,3],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,2,3],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,2,3,3],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,3,3],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,3,3,3],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,3,3,3],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,2,2,2],[3]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,2,2,3],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,2,3,3],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,3,3,3],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,1,1],[2,3]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,1],[3,3]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,2],[2,3]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,3],[2,2]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,2],[3,3]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,3],[2,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,3],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,2],[2,3]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,2],[3,3]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,3],[2,3]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,3],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,2],[3,3]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,3],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,1],[2],[3]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,2],[2],[3]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,1,3],[2],[3]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,2,2],[2],[3]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,3],[2],[3]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,3,3],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,1],[2,2],[3]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,1],[2,3],[3]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[2,3],[3]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,1,1,1,2]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,1,2,2]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,2,2,2]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,2,2,2,2]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,2,2,2,2]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,2,2,2,2]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,1,1],[2]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,1,2],[2]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,2,2],[2]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,2,2,2],[2]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,2,2,2,2],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,1,1,1],[2,2]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,2],[2,2]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,2],[2,2]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1],[2,2,2]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,7]]=>[1,2]=>[1,2]=>([],2)
[[2,7]]=>[1,2]=>[1,2]=>([],2)
[[3,7]]=>[1,2]=>[1,2]=>([],2)
[[4,7]]=>[1,2]=>[1,2]=>([],2)
[[5,7]]=>[1,2]=>[1,2]=>([],2)
[[6,7]]=>[1,2]=>[1,2]=>([],2)
[[7,7]]=>[1,2]=>[1,2]=>([],2)
[[1],[7]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[2],[7]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[3],[7]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[4],[7]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[5],[7]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[6],[7]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[1,1,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,2,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,3,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,4,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,5,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,6,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,2,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,3,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,4,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,5,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,6,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,3,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,4,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,5,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,6,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[4,4,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[4,5,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[4,6,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[5,5,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[5,6,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[6,6,6]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,1],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,2],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,6],[2]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,3],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,6],[3]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,4],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,6],[4]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,5],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,6],[5]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,6],[6]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,2],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,3],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,6],[3]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,4],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,6],[4]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,5],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,6],[5]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,6],[6]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[3,3],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[3,4],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[3,6],[4]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[3,5],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[3,6],[5]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[3,6],[6]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[4,4],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[4,5],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[4,6],[5]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[4,6],[6]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[5,5],[6]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[5,6],[6]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1],[2],[6]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1],[3],[6]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1],[4],[6]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1],[5],[6]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[2],[3],[6]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[2],[4],[6]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[2],[5],[6]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[3],[4],[6]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[3],[5],[6]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[4],[5],[6]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1,1,1,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,2,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,3,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,4,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,2,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,3,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,4,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,3,3,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,3,4,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,3,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,4,4,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,4,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,5,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,2,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,3,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,4,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,3,3,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,3,4,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,3,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,4,4,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,4,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,5,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,3,3,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,3,4,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,3,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,4,4,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,4,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,5,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[4,4,4,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[4,4,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[4,5,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[5,5,5,5]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,1],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,2],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,5],[2]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,1,3],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,5],[3]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,1,4],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,5],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,1,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,2,2],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,2,5],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,2,3],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,2,5],[3]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,3,5],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,2,4],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,2,5],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,4,5],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,2,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,5,5],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,3,3],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,3,5],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,3,4],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,3,5],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,4,5],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,3,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,5,5],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,4,4],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,4,5],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,4,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,5,5],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,5,5],[5]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,2,2],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,2,3],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,2,5],[3]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,2,4],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,2,5],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,2,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,3,3],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,3,5],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,3,4],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,3,5],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,4,5],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,3,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,5,5],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,4,4],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,4,5],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,4,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,5,5],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,5,5],[5]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[3,3,3],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[3,3,4],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[3,3,5],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[3,3,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[3,4,4],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[3,4,5],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[3,4,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[3,5,5],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[3,5,5],[5]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[4,4,4],[5]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[4,4,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[4,5,5],[5]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,1],[2,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[3,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[4,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[5,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[2,5]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[3,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,3],[2,5]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[4,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,4],[2,5]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[5,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,3],[3,5]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,3],[4,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,4],[3,5]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,3],[5,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,4],[4,5]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,4],[5,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,2],[3,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,2],[4,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,2],[5,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,3],[3,5]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,3],[4,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,4],[3,5]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,3],[5,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,4],[4,5]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,4],[5,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,3],[4,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,3],[5,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,4],[4,5]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,4],[5,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[4,4],[5,5]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[2],[5]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,1],[3],[5]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,1],[4],[5]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,2],[2],[5]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,2],[3],[5]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,3],[2],[5]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,5],[2],[3]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,2],[4],[5]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,4],[2],[5]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,5],[2],[4]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,5],[2],[5]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,3],[3],[5]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,3],[4],[5]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,4],[3],[5]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,5],[3],[4]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,5],[3],[5]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,4],[4],[5]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,5],[4],[5]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[2,2],[3],[5]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[2,2],[4],[5]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[2,3],[3],[5]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[2,3],[4],[5]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[2,4],[3],[5]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[2,5],[3],[4]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[2,5],[3],[5]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[2,4],[4],[5]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[2,5],[4],[5]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[3,3],[4],[5]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[3,4],[4],[5]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[3,5],[4],[5]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1],[2],[3],[5]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[1],[2],[4],[5]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[1],[3],[4],[5]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[2],[3],[4],[5]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[1,1,1,1,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,2,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,2,2,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,2,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,2,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,3,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,3,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,2,2,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,2,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,2,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,3,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,3,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,3,3,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,3,3,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,3,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,4,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,2,2,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,2,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,2,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,3,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,3,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,3,3,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,3,3,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,3,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,4,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,3,3,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,3,3,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,3,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,4,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[4,4,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,1],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,1,2],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,1,4],[2]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,1,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,1,4],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,1,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,2,2],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,2,4],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,2,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,2,4],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,3,4],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,2,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,4,4],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,3,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,3,4],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,3,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,4,4],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,4,4],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,2,2,2],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,2,2,4],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,2,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,2,2,4],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,2,3,4],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,2,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,2,4,4],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,3,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,2,3,4],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,3,3,4],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,3,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,2,4,4],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,3,4,4],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,4,4],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,4,4,4],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,3,3,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,3,3,4],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,3,3,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,3,4,4],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,3,4,4],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,4,4,4],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,4,4,4],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,2,2,2],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,2,2,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,2,2,4],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,2,2,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,2,3,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,2,3,4],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,2,3,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,2,4,4],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,2,4,4],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,3,3,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,3,3,4],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,3,3,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,3,4,4],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,3,4,4],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,4,4,4],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,4,4,4],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[3,3,3,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[3,3,3,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[3,3,4,4],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[3,4,4,4],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,1,1],[2,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,1],[3,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,1],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,2],[2,4]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,4],[2,2]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,2],[3,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,3],[2,4]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,4],[2,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,2],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,4],[2,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,3],[3,4]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,4],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,3],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,4],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,4],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,2],[2,4]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,2],[3,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,3],[2,4]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,4],[2,3]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,2],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,4],[2,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,3],[3,4]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,4],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,3],[2,4]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,3],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,4],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,4],[2,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,4],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,3],[3,4]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,3],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,4],[3,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,4],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,2],[3,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,2],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,3],[3,4]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,4],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,3],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,4],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,4],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,3],[3,4]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,3],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,4],[3,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,4],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[3,3,3],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[3,3,4],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,1],[2],[4]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,1],[3],[4]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,2],[2],[4]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,1,2],[3],[4]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,3],[2],[4]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,1,4],[2],[3]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,1,4],[2],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,1,3],[3],[4]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,1,4],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,2,2],[2],[4]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,2],[3],[4]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,3],[2],[4]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,4],[2],[3]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,2,4],[2],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,2,3],[3],[4]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3,3],[2],[4]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,3,4],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,2,4],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,3,4],[2],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,4,4],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,4,4],[2],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,3,3],[3],[4]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,3,4],[3],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,4,4],[3],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[2,2,2],[3],[4]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[2,2,3],[3],[4]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[2,2,4],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[2,3,3],[3],[4]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[2,3,4],[3],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[2,4,4],[3],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,1],[2,2],[4]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,1],[2,3],[4]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,1],[2,4],[3]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1],[2,4],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1],[3,3],[4]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,1],[3,4],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[2,3],[4]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[1,2],[2,4],[3]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[2,4],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[3,3],[4]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,3],[2,4],[3]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[3,4],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3],[2,4],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3],[3,4],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2],[3,3],[4]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[2,2],[3,4],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3],[3,4],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1],[2],[3],[4]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2],[2],[3],[4]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3],[2],[3],[4]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,4],[2],[3],[4]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,1,1,1,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,1,2,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,1,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,2,2,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,2,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,3,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,2,2,2,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,2,2,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,2,3,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,3,3,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,2,2,2,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,2,2,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,2,3,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,3,3,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,3,3,3,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,2,2,2,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,2,2,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,2,3,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,3,3,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,3,3,3,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[3,3,3,3,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,1,1],[3]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,1,2],[3]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,1,3],[2]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,1,3],[3]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,2,2],[3]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,2,3],[2]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,1,2,3],[3]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,3,3],[2]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,1,3,3],[3]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,2,2,2],[3]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,2,2,3],[2]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,2,2,3],[3]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,2,3,3],[2]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,2,3,3],[3]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,3,3,3],[2]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,3,3,3],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,2,2,2,2],[3]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,2,2,3],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,2,2,2,3],[3]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,2,3,3],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,2,2,3,3],[3]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,2,3,3,3],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,2,3,3,3],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,3,3,3,3],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,3,3,3,3],[3]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[2,2,2,2,2],[3]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[2,2,2,2,3],[3]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[2,2,2,3,3],[3]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[2,2,3,3,3],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[2,3,3,3,3],[3]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,1,1,1],[2,3]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,1],[3,3]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,2],[2,3]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,3],[2,2]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,2],[3,3]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,3],[2,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,3],[3,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,2],[2,3]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,3],[2,2]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,2],[3,3]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,3],[2,3]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3,3],[2,2]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,3],[3,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3,3],[2,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3,3],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,2],[2,3]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,2],[3,3]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,3],[2,3]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,3],[3,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,3],[2,3]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,3],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2,2],[3,3]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2,3],[3,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,3,3],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,1],[2],[3]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,1,1,2],[2],[3]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,1,3],[2],[3]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,1,2,2],[2],[3]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,2,3],[2],[3]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>([(1,5),(2,4),(3,4),(3,5)],6)
[[1,1,3,3],[2],[3]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,2,2,2],[2],[3]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,2,3],[2],[3]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,3,3],[2],[3]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,3,3,3],[2],[3]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,1],[2,2,3]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1],[2,3,3]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1],[3,3,3]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2],[2,2,3]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2],[2,3,3]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,1,2],[3,3,3]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2],[2,3,3]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,2,2],[3,3,3]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2],[3,3,3]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1],[2,2],[3]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,1,1],[2,3],[3]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2],[2,2],[3]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,1,2],[2,3],[3]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3],[2,2],[3]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,1,3],[2,3],[3]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2],[2,3],[3]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3],[2,3],[3]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1],[2,2],[3,3]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[[1,1,1,1,1,1,2]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,1,1,2,2]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,1,2,2,2]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,2,2,2,2]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,2,2,2,2,2]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[2,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,1,1,1],[2]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,1,1,2],[2]]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,1,2,2],[2]]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,2,2,2],[2]]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)
[[1,1,2,2,2,2],[2]]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)
[[1,2,2,2,2,2],[2]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(5,6)],7)
[[1,1,1,1,1],[2,2]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,1,2],[2,2]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,2,2],[2,2]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,2,2],[2,2]]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,1],[2,2,2]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,2],[2,2,2]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,8]]=>[1,2]=>[1,2]=>([],2)
[[2,8]]=>[1,2]=>[1,2]=>([],2)
[[3,8]]=>[1,2]=>[1,2]=>([],2)
[[4,8]]=>[1,2]=>[1,2]=>([],2)
[[5,8]]=>[1,2]=>[1,2]=>([],2)
[[6,8]]=>[1,2]=>[1,2]=>([],2)
[[7,8]]=>[1,2]=>[1,2]=>([],2)
[[8,8]]=>[1,2]=>[1,2]=>([],2)
[[1],[8]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[2],[8]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[3],[8]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[4],[8]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[5],[8]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[6],[8]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[7],[8]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[1,1,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,2,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,3,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,4,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,5,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,6,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,7,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,2,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,3,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,4,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,5,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,6,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[2,7,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,3,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,4,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,5,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,6,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[3,7,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[4,4,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[4,5,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[4,6,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[4,7,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[5,5,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[5,6,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[5,7,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[6,6,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[6,7,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[7,7,7]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,1],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,2],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,7],[2]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,3],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,7],[3]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,4],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,7],[4]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,5],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,7],[5]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,6],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[1,7],[6]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1,7],[7]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,2],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,3],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,7],[3]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,4],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,7],[4]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,5],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,7],[5]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,6],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[2,7],[6]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[2,7],[7]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[3,3],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[3,4],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[3,7],[4]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[3,5],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[3,7],[5]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[3,6],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[3,7],[6]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[3,7],[7]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[4,4],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[4,5],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[4,7],[5]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[4,6],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[4,7],[6]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[4,7],[7]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[5,5],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[5,6],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[5,7],[6]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[5,7],[7]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[6,6],[7]]=>[3,1,2]=>[3,1,2]=>([(0,2),(1,2)],3)
[[6,7],[7]]=>[2,1,3]=>[2,1,3]=>([(1,2)],3)
[[1],[2],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1],[3],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1],[4],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1],[5],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1],[6],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[2],[3],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[2],[4],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[2],[5],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[2],[6],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[3],[4],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[3],[5],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[3],[6],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[4],[5],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[4],[6],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[5],[6],[7]]=>[3,2,1]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1,1,1,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,2,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,3,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,4,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,2,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,3,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,4,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,2,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,3,3,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,3,4,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,3,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,3,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,4,4,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,4,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,4,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,5,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,5,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,6,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,2,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,3,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,4,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,2,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,3,3,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,3,4,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,3,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,3,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,4,4,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,4,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,4,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,5,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,5,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[2,6,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,3,3,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,3,4,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,3,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,3,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,4,4,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,4,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,4,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,5,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,5,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[3,6,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[4,4,4,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[4,4,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[4,4,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[4,5,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[4,5,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[4,6,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[5,5,5,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[5,5,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[5,6,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[6,6,6,6]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,1,1],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,2],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,6],[2]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,1,3],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,6],[3]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,1,4],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,6],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,1,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,1,6],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,1,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,2,2],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,2,6],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,2,3],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,2,6],[3]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,3,6],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,2,4],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,2,6],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,4,6],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,2,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,2,6],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,5,6],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,2,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,6,6],[2]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,3,3],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,3,6],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,3,4],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,3,6],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,4,6],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,3,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,3,6],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,5,6],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,3,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,6,6],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,4,4],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,4,6],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,4,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,4,6],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,5,6],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,4,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,6,6],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,5,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[1,5,6],[5]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,5,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[1,6,6],[5]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,6,6],[6]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,2,2],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,2,3],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,2,6],[3]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,2,4],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,2,6],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,2,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,2,6],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,2,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,3,3],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,3,6],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,3,4],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,3,6],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,4,6],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,3,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,3,6],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,5,6],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,3,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,6,6],[3]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,4,4],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,4,6],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,4,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,4,6],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,5,6],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,4,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,6,6],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,5,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[2,5,6],[5]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,5,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[2,6,6],[5]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[2,6,6],[6]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[3,3,3],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[3,3,4],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[3,3,6],[4]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[3,3,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[3,3,6],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[3,3,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[3,4,4],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[3,4,6],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[3,4,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[3,4,6],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[3,5,6],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[3,4,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[3,6,6],[4]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[3,5,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[3,5,6],[5]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[3,5,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[3,6,6],[5]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[3,6,6],[6]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[4,4,4],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[4,4,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[4,4,6],[5]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[4,4,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[4,5,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[4,5,6],[5]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[4,5,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[4,6,6],[5]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[4,6,6],[6]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[5,5,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)
[[5,5,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>([(1,3),(2,3)],4)
[[5,6,6],[6]]=>[2,1,3,4]=>[2,1,3,4]=>([(2,3)],4)
[[1,1],[2,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[3,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[4,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[2,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[3,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,3],[2,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[4,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,4],[2,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,5],[2,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,3],[3,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,3],[4,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,4],[3,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,3],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,5],[3,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,3],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,4],[4,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,4],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,5],[4,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,4],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,5],[5,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,5],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,2],[3,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,2],[4,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,2],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,2],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,3],[3,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,3],[4,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,4],[3,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,3],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,5],[3,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,3],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,4],[4,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,4],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,5],[4,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,4],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,5],[5,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[2,5],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,3],[4,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,3],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,3],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,4],[4,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,4],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,5],[4,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,4],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,5],[5,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[3,5],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[4,4],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[4,4],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[4,5],[5,6]]=>[2,4,1,3]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[4,5],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[5,5],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,1],[2],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,1],[3],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,1],[4],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,1],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,2],[2],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,2],[3],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,3],[2],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,6],[2],[3]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,2],[4],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,4],[2],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,6],[2],[4]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,2],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,5],[2],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,6],[2],[5]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,6],[2],[6]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,3],[3],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,3],[4],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,4],[3],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,6],[3],[4]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,3],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,5],[3],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,6],[3],[5]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,6],[3],[6]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,4],[4],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,4],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[1,5],[4],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,6],[4],[5]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,6],[4],[6]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1,5],[5],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,6],[5],[6]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[2,2],[3],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[2,2],[4],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[2,2],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[2,3],[3],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[2,3],[4],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[2,4],[3],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[2,6],[3],[4]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[2,3],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[2,5],[3],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[2,6],[3],[5]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[2,6],[3],[6]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[2,4],[4],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[2,4],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[2,5],[4],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[2,6],[4],[5]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[2,6],[4],[6]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[2,5],[5],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[2,6],[5],[6]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[3,3],[4],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[3,3],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[3,4],[4],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[3,4],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[3,5],[4],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[3,6],[4],[5]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[3,6],[4],[6]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[3,5],[5],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[3,6],[5],[6]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[4,4],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)
[[4,5],[5],[6]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[4,6],[5],[6]]=>[3,2,1,4]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[1],[2],[3],[6]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[1],[2],[4],[6]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[1],[2],[5],[6]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[1],[3],[4],[6]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[1],[3],[5],[6]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[1],[4],[5],[6]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[2],[3],[4],[6]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[2],[3],[5],[6]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[2],[4],[5],[6]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[3],[4],[5],[6]]=>[4,3,2,1]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[1,1,1,1,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,2,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,2,2,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,2,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,2,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,2,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,3,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,3,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,2,2,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,2,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,2,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,2,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,3,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,3,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,2,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,3,3,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,3,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,3,3,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,3,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,3,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,3,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,4,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,4,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,4,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,5,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,2,2,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,2,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,2,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,2,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,3,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,3,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,2,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,3,3,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,3,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,3,3,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,3,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,3,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,3,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,4,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,4,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,4,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[2,5,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,3,3,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,3,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,3,3,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,3,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,3,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,3,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,4,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,4,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,4,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[3,5,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[4,4,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[4,4,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[4,4,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[4,5,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[5,5,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,1,1,1],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,1,2],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,1,5],[2]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,1,3],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,1,5],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,1,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,1,5],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,1,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,2,2],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,2,5],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,2,3],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,2,5],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,3,5],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,2,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,2,5],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,4,5],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,2,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,5,5],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,3,3],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,3,5],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,3,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,3,5],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,4,5],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,3,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,5,5],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,4,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,4,5],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,4,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,1,5,5],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,1,5,5],[5]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,2,2,2],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,2,2,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,2,3],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,2,2,5],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,2,3,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,2,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,2,2,5],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,2,4,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,2,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,2,5,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,3,3],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,2,3,5],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,3,3,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,3,4,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,3,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,2,5,5],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,3,5,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,4,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,2,4,5],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,4,4,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,4,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,2,5,5],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,4,5,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,2,5,5],[5]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,5,5,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,3,3,3],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,3,3,5],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,3,3,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,3,3,5],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,3,4,5],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,3,3,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,3,5,5],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,3,4,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,3,4,5],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,4,4,5],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,3,4,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,3,5,5],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,4,5,5],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,3,5,5],[5]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,5,5,5],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,4,4,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,4,4,5],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,4,4,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[1,4,5,5],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,4,5,5],[5]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[1,5,5,5],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,5,5,5],[5]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,2,2,2],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,2,2,3],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,2,2,5],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,2,2,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,2,2,5],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,2,2,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,2,3,3],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,2,3,5],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,2,3,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,2,3,5],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,2,4,5],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,2,3,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,2,5,5],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,2,4,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,2,4,5],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,2,4,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,2,5,5],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,2,5,5],[5]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,3,3,3],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,3,3,5],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,3,3,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,3,3,5],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,3,4,5],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,3,3,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,3,5,5],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,3,4,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,3,4,5],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,4,4,5],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,3,4,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,3,5,5],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,4,5,5],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,3,5,5],[5]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,5,5,5],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,4,4,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[2,4,4,5],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,4,4,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[2,4,5,5],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,4,5,5],[5]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[2,5,5,5],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[2,5,5,5],[5]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[3,3,3,3],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[3,3,3,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[3,3,3,5],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[3,3,3,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[3,3,4,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[3,3,4,5],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[3,3,4,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[3,3,5,5],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[3,3,5,5],[5]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[3,4,4,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[3,4,4,5],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[3,4,4,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[3,4,5,5],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[3,4,5,5],[5]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[3,5,5,5],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[3,5,5,5],[5]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[4,4,4,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[4,4,4,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)
[[4,4,5,5],[5]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)
[[4,5,5,5],[5]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(3,4)],5)
[[1,1,1],[2,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,1],[3,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,1],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,1],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,2],[2,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,5],[2,2]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,2],[3,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,3],[2,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,5],[2,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,2],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,4],[2,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,5],[2,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,2],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,5],[2,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,3],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,5],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,4],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,5],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,3],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,5],[3,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,4],[4,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,5],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,5],[4,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,2],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,2],[3,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,3],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,5],[2,3]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,2],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,4],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,5],[2,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,2],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,5],[2,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,3],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,5],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,3],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,4],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,5],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,4],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,5],[2,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,3],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,5],[3,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,5],[2,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,4],[4,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,5],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,4,4],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,5],[4,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,4,5],[2,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,3],[3,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,4],[3,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,5],[3,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,3],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,5],[3,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,4],[4,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,5],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,4,4],[3,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,5],[4,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,4,5],[3,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,4,4],[4,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,4,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,4,5],[4,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,4,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,2],[3,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,2],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,2],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,3],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,5],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,4],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,5],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,3],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,5],[3,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,4],[4,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,5],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,5],[4,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,2,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,3],[3,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,4],[3,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,5],[3,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,3],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,5],[3,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,4],[4,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,5],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,4,4],[3,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,5],[4,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,4,5],[3,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,3,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,4,4],[4,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,4,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[2,4,5],[4,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[2,4,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[3,3,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[3,3,3],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[3,3,4],[4,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[3,3,5],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[3,3,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[3,3,5],[4,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[3,3,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[3,4,4],[4,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[3,4,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[3,4,5],[4,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[3,4,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[4,4,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[4,4,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,1,1],[2],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,1],[3],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,1],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,2],[2],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,1,2],[3],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,3],[2],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,1,5],[2],[3]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,1,2],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,4],[2],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,1,5],[2],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,1,5],[2],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,1,3],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,1,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,4],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,1,5],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,1,5],[3],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,1,4],[4],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,1,5],[4],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,2,2],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,2],[3],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,3],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,5],[2],[3]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,2,2],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,4],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,5],[2],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,2,5],[2],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,2,3],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3,3],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,3,5],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,2,5],[3],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,3,5],[2],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,5,5],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,2,4],[4],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,4,4],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,4,5],[2],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,2,5],[4],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,4,5],[2],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,5,5],[2],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,5,5],[2],[5]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,3,3],[3],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,3,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,3,4],[3],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,3,5],[3],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,3,5],[3],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,3,4],[4],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,4,4],[3],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,4,5],[3],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,3,5],[4],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[1,4,5],[3],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,5,5],[3],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,5,5],[3],[5]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,4,4],[4],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,4,5],[4],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[1,5,5],[4],[5]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[2,2,2],[3],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[2,2,2],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[2,2,3],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[2,2,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[2,2,4],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[2,2,5],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[2,2,5],[3],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[2,2,4],[4],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[2,2,5],[4],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[2,3,3],[3],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[2,3,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[2,3,4],[3],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[2,3,5],[3],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[2,3,5],[3],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[2,3,4],[4],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[2,4,4],[3],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[2,4,5],[3],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[2,3,5],[4],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[2,4,5],[3],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[2,5,5],[3],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[2,5,5],[3],[5]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[2,4,4],[4],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[2,4,5],[4],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[2,5,5],[4],[5]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[3,3,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[3,3,4],[4],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[3,3,5],[4],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)
[[3,4,4],[4],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[3,4,5],[4],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)
[[3,5,5],[4],[5]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[1,1],[2,2],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,1],[2,3],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,1],[2,5],[3]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1],[2,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,1],[2,5],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1],[2,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1],[3,3],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,1],[3,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,1],[3,5],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1],[3,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1],[4,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,1],[4,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[2,3],[5]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[1,2],[2,5],[3]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[2,4],[5]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[1,2],[2,5],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[2,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[3,3],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,3],[2,5],[3]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[3,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3],[2,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[4,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,4],[2,5],[4]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[4,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,4],[2,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3],[3,4],[5]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[1,3],[3,5],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3],[3,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3],[4,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[1,4],[3,5],[4]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3],[4,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,4],[3,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,4],[4,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2],[3,3],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[2,2],[3,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[2,2],[3,5],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2],[3,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[2,2],[4,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[2,2],[4,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3],[3,4],[5]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[2,3],[3,5],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3],[3,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3],[4,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[2,4],[3,5],[4]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[2,3],[4,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[2,4],[3,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[2,4],[4,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[3,3],[4,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
[[3,3],[4,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[3,4],[4,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,1],[2],[3],[5]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1],[2],[4],[5]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1],[3],[4],[5]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2],[2],[3],[5]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2],[2],[4],[5]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3],[2],[3],[5]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5)
[[1,5],[2],[3],[5]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5)
[[1,4],[2],[4],[5]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,5],[2],[4],[5]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5)
[[1,3],[3],[4],[5]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[1,4],[3],[4],[5]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,5],[3],[4],[5]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5)
[[2,2],[3],[4],[5]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[2,3],[3],[4],[5]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>([(0,4),(1,3),(2,3),(2,4)],5)
[[2,4],[3],[4],[5]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[2,5],[3],[4],[5]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5)
[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,1,1,1,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,1,2,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,1,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,1,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,2,2,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,2,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,2,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,2,2,2,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,2,2,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,2,2,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,2,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,2,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,2,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,3,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,3,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,3,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,4,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,2,2,2,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,2,2,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,2,2,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,2,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,2,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,2,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,3,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,3,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,3,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,4,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,3,3,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,3,3,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,3,3,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,3,4,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,4,4,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,2,2,2,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,2,2,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,2,2,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,2,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,2,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,2,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,3,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,3,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,3,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,2,4,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,3,3,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,3,3,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,3,3,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,3,4,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[2,4,4,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[3,3,3,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[3,3,3,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[3,3,3,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[3,3,4,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[3,4,4,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[4,4,4,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,1,1,1,1],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,1,2],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,1,4],[2]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,1,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,1,4],[3]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,1,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,2,2],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,2,4],[2]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,1,2,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,2,4],[3]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,3,4],[2]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,1,2,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,4,4],[2]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,1,3,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,3,4],[3]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,1,3,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,4,4],[3]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,1,4,4],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,2,2,2],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,2,2,4],[2]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,2,2,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,2,2,4],[3]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,2,3,4],[2]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,2,2,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,2,4,4],[2]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,2,3,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,2,3,4],[3]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,3,3,4],[2]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,2,3,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,2,4,4],[3]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,3,4,4],[2]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,2,4,4],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,4,4,4],[2]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,3,3,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,3,3,4],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,3,3,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,3,4,4],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,3,4,4],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1,4,4,4],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,4,4,4],[4]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,2,2,2,2],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,2,2,4],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,2,2,2,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,2,2,4],[3]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,2,3,4],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,2,2,2,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,2,4,4],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,2,2,3,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,2,3,4],[3]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,2,3,3,4],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,2,2,3,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,2,4,4],[3]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,2,3,4,4],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,2,2,4,4],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,2,4,4,4],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,2,3,3,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,3,3,4],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,3,3,3,4],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,2,3,3,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,3,4,4],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,3,3,4,4],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,2,3,4,4],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,2,4,4,4],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,3,4,4,4],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,2,4,4,4],[4]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,4,4,4,4],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,3,3,3,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,3,3,3,4],[3]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,3,3,3,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,3,3,4,4],[3]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,3,3,4,4],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,3,4,4,4],[3]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,3,4,4,4],[4]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,4,4,4,4],[3]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,4,4,4,4],[4]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[2,2,2,2,2],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[2,2,2,2,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[2,2,2,2,4],[3]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[2,2,2,2,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[2,2,2,3,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[2,2,2,3,4],[3]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[2,2,2,3,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[2,2,2,4,4],[3]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[2,2,2,4,4],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[2,2,3,3,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[2,2,3,3,4],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[2,2,3,3,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[2,2,3,4,4],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[2,2,3,4,4],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[2,2,4,4,4],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[2,2,4,4,4],[4]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[2,3,3,3,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[2,3,3,3,4],[3]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[2,3,3,3,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[2,3,3,4,4],[3]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[2,3,3,4,4],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[2,3,4,4,4],[3]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[2,3,4,4,4],[4]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[2,4,4,4,4],[3]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[2,4,4,4,4],[4]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[3,3,3,3,3],[4]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[3,3,3,3,4],[4]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[3,3,3,4,4],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[3,3,4,4,4],[4]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[3,4,4,4,4],[4]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,1,1,1],[2,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,1],[3,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,1],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,2],[2,4]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,4],[2,2]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,2],[3,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,3],[2,4]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,4],[2,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,2],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,4],[2,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,3],[3,4]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,4],[3,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,4],[3,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,2],[2,4]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,4],[2,2]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,2],[3,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,3],[2,4]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,4],[2,3]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3,4],[2,2]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,2],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,4],[2,4]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,4,4],[2,2]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,3],[3,4]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,4],[3,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3,3],[2,4]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3,4],[2,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,4],[3,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3,4],[2,4]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,4,4],[2,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,4,4],[2,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3,3],[3,4]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3,4],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3,4],[3,4]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,4,4],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,4,4],[3,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,4,4],[4,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,2],[2,4]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,2],[3,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,3],[2,4]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,4],[2,3]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,2],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,4],[2,4]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,3],[3,4]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,4],[3,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,3],[2,4]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,4],[2,3]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,4],[3,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,4],[2,4]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4,4],[2,3]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4,4],[2,4]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,3],[3,4]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,4],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,3,3],[2,4]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,4],[3,4]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4,4],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,3,4],[2,4]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4,4],[3,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,4,4],[2,4]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4,4],[4,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,3,3],[3,4]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,3,4],[3,4]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,4,4],[3,4]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2,2],[3,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2,2],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2,3],[3,4]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2,4],[3,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2,4],[3,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,3,3],[3,4]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,3,4],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,3,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,3,4],[3,4]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,4,4],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,3,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,4,4],[3,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,4,4],[4,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[2,3,3,3],[3,4]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,3,3,4],[3,4]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[2,3,4,4],[3,4]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[2,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[3,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[3,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[3,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1,1],[2],[4]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,1,1,1],[3],[4]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,1,1,2],[2],[4]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,1,2],[3],[4]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,1,1,3],[2],[4]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,1,4],[2],[3]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,1,1,4],[2],[4]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,1,1,3],[3],[4]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,1,4],[3],[4]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,1,2,2],[2],[4]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,2,2],[3],[4]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,1,2,3],[2],[4]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,2,4],[2],[3]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>([(1,5),(2,4),(3,4),(3,5)],6)
[[1,1,2,4],[2],[4]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>([(1,5),(2,4),(3,4),(3,5)],6)
[[1,1,2,3],[3],[4]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,3,3],[2],[4]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,3,4],[2],[3]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,1,2,4],[3],[4]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,1,3,4],[2],[4]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>([(1,5),(2,4),(3,4),(3,5)],6)
[[1,1,4,4],[2],[3]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,1,4,4],[2],[4]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,1,3,3],[3],[4]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,3,4],[3],[4]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>([(1,5),(2,4),(3,4),(3,5)],6)
[[1,1,4,4],[3],[4]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,2,2,2],[2],[4]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,2,2],[3],[4]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,2,3],[2],[4]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,2,4],[2],[3]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,2,4],[2],[4]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,2,3],[3],[4]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,2,3,3],[2],[4]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,3,4],[2],[3]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,2,2,4],[3],[4]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,3,4],[2],[4]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,4,4],[2],[3]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,2,4,4],[2],[4]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,2,3,3],[3],[4]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,3,3,3],[2],[4]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,3,3,4],[2],[3]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)
[[1,2,3,4],[3],[4]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>([(1,5),(2,4),(3,4),(3,5)],6)
[[1,3,3,4],[2],[4]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,3,4,4],[2],[3]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)
[[1,2,4,4],[3],[4]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,3,4,4],[2],[4]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,4,4,4],[2],[3]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)
[[1,4,4,4],[2],[4]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)
[[1,3,3,3],[3],[4]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,3,3,4],[3],[4]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,3,4,4],[3],[4]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,4,4,4],[3],[4]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)
[[2,2,2,2],[3],[4]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[2,2,2,3],[3],[4]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[2,2,2,4],[3],[4]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[2,2,3,3],[3],[4]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[2,2,3,4],[3],[4]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>([(1,5),(2,4),(3,4),(3,5)],6)
[[2,2,4,4],[3],[4]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>([(2,5),(3,4),(4,5)],6)
[[2,3,3,3],[3],[4]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[2,3,3,4],[3],[4]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[2,3,4,4],[3],[4]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)
[[2,4,4,4],[3],[4]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)
[[1,1,1],[2,2,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1],[2,3,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1],[2,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1],[3,3,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1],[3,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2],[2,2,4]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2],[2,3,4]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,1,3],[2,2,4]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2],[2,4,4]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,1,2],[3,3,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3],[2,3,4]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2],[3,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3],[2,4,4]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,1,2],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3],[3,3,4]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3],[3,4,4]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,1,3],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2],[2,3,4]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,2,2],[2,4,4]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,2,2],[3,3,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3],[2,3,4]]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,2,2],[3,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3],[2,4,4]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,2,2],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3],[3,3,4]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3],[3,4,4]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,3,3],[2,4,4]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,2,3],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,3],[3,4,4]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2],[3,3,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2],[3,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,3],[3,3,4]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,3],[3,4,4]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[2,2,3],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[2,3,3],[3,4,4]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[2,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[3,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1],[2,2],[4]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,1,1],[2,3],[4]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,1,1],[2,4],[3]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1],[2,4],[4]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1],[3,3],[4]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,1,1],[3,4],[4]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2],[2,2],[4]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,1,2],[2,3],[4]]=>[6,3,5,1,2,4]=>[5,1,6,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[1,1,2],[2,4],[3]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3],[2,2],[4]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,1,4],[2,2],[3]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,1,2],[2,4],[4]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,4],[2,2],[4]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,1,2],[3,3],[4]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,1,3],[2,3],[4]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,1,3],[2,4],[3]]=>[4,3,6,1,2,5]=>[6,1,4,3,2,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,4],[2,3],[3]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,2],[3,4],[4]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3],[2,4],[4]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,4],[2,3],[4]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,1,4],[2,4],[3]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,4],[2,4],[4]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,3],[3,3],[4]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,1,3],[3,4],[4]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,4],[3,3],[4]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,1,4],[3,4],[4]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2],[2,3],[4]]=>[6,2,5,1,3,4]=>[5,6,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,2,2],[2,4],[3]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2],[2,4],[4]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2],[3,3],[4]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,2,3],[2,3],[4]]=>[6,2,4,1,3,5]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[1,2,3],[2,4],[3]]=>[4,2,6,1,3,5]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4],[2,3],[3]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,2],[3,4],[4]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3],[2,4],[4]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4],[2,3],[4]]=>[5,2,4,1,3,6]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[1,2,4],[2,4],[3]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4],[2,4],[4]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3],[3,3],[4]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,3,3],[2,4],[3]]=>[3,2,6,1,4,5]=>[6,3,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3],[3,4],[4]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4],[3,3],[4]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,3,3],[2,4],[4]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,4],[2,4],[3]]=>[3,2,5,1,4,6]=>[5,3,2,1,4,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4],[3,4],[4]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,4],[2,4],[4]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,3],[3,4],[4]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,4],[3,4],[4]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,2],[3,3],[4]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[2,2,2],[3,4],[4]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,3],[3,3],[4]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[2,2,3],[3,4],[4]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[2,2,4],[3,3],[4]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[2,2,4],[3,4],[4]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[2,3,3],[3,4],[4]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[2,3,4],[3,4],[4]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1,1],[2],[3],[4]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[1,1,2],[2],[3],[4]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,1,3],[2],[3],[4]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,4],[2],[3],[4]]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,2],[2],[3],[4]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[[1,2,3],[2],[3],[4]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,4],[2],[3],[4]]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>([(1,5),(2,4),(3,4),(3,5)],6)
[[1,3,3],[2],[3],[4]]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[1,3,4],[2],[3],[4]]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,4,4],[2],[3],[4]]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,1],[2,2],[3,4]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[[1,1],[2,2],[4,4]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[[1,1],[2,3],[3,4]]=>[4,6,3,5,1,2]=>[5,1,6,4,3,2]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1],[2,3],[4,4]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[[1,1],[3,3],[4,4]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[[1,2],[2,3],[3,4]]=>[4,6,2,5,1,3]=>[5,6,1,4,2,3]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,2],[2,3],[4,4]]=>[5,6,2,4,1,3]=>[4,6,1,2,5,3]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
[[1,2],[3,3],[4,4]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[[2,2],[3,3],[4,4]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[[1,1],[2,2],[3],[4]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1],[2,3],[3],[4]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,1],[2,4],[3],[4]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2],[2,3],[3],[4]]=>[6,4,2,5,1,3]=>[5,4,1,6,2,3]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2],[2,4],[3],[4]]=>[5,4,2,6,1,3]=>[6,4,1,5,2,3]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3],[2,4],[3],[4]]=>[5,3,2,6,1,4]=>[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)
[[1,1,1,1,1,1,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,1,1,2,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,1,1,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,1,2,2,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,1,2,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,1,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,2,2,2,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,2,2,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,2,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,3,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,2,2,2,2,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,2,2,2,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,2,2,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,2,3,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,2,2,2,2,2,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,2,2,2,2,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,2,2,2,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,2,2,3,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,2,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,3,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[2,2,2,2,2,2,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[2,2,2,2,2,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[2,2,2,2,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[2,2,2,3,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[2,2,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[2,3,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[3,3,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,1,1,1,1,1],[3]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,1,1,2],[3]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,1,1,3],[2]]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,1,1,3],[3]]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,1,2,2],[3]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,1,2,3],[2]]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,1,2,3],[3]]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,1,3,3],[2]]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,1,3,3],[3]]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,2,2,3],[2]]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)
[[1,1,1,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,2,3,3],[2]]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)
[[1,1,1,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,1,3,3,3],[2]]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)
[[1,1,1,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)
[[1,1,2,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,2,2,2,3],[2]]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)
[[1,1,2,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,2,2,3,3],[2]]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)
[[1,1,2,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[1,1,2,3,3,3],[2]]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)
[[1,1,2,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)
[[1,1,3,3,3,3],[2]]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)
[[1,1,3,3,3,3],[3]]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)
[[1,2,2,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,2,2,2,2,3],[2]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(5,6)],7)
[[1,2,2,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,2,2,2,3,3],[2]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(5,6)],7)
[[1,2,2,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[1,2,2,3,3,3],[2]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(5,6)],7)
[[1,2,2,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)
[[1,2,3,3,3,3],[2]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(5,6)],7)
[[1,2,3,3,3,3],[3]]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)
[[1,3,3,3,3,3],[2]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(5,6)],7)
[[1,3,3,3,3,3],[3]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(5,6)],7)
[[2,2,2,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[2,2,2,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[2,2,2,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[2,2,2,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)
[[2,2,3,3,3,3],[3]]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)
[[2,3,3,3,3,3],[3]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(5,6)],7)
[[1,1,1,1,1],[2,3]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,1,1],[3,3]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,1,2],[2,3]]=>[5,7,1,2,3,4,6]=>[7,1,2,3,5,4,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,1,3],[2,2]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,1,2],[3,3]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,1,3],[2,3]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,1,3],[3,3]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,2,2],[2,3]]=>[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,2,3],[2,2]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,2,3],[2,3]]=>[4,6,1,2,3,5,7]=>[6,1,2,4,3,5,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,3,3],[2,2]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,3,3],[2,3]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,2,2],[2,3]]=>[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,2,3],[2,2]]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,2,3],[2,3]]=>[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,3,3],[2,2]]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,3,3],[2,3]]=>[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,3,3,3],[2,2]]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,3,3,3],[2,3]]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,2,2,2],[2,3]]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,2,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,2,2,3],[2,3]]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,2,3,3],[2,3]]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3,3,3],[2,3]]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[2,2,2,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[2,2,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[2,2,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[2,2,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,1,1],[2],[3]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[1,1,1,1,2],[2],[3]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[1,1,1,1,3],[2],[3]]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[1,1,1,2,2],[2],[3]]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[[1,1,1,2,3],[2],[3]]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[1,1,1,3,3],[2],[3]]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>([(2,6),(3,6),(4,5),(5,6)],7)
[[1,1,2,2,2],[2],[3]]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[1,1,2,2,3],[2],[3]]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[1,1,2,3,3],[2],[3]]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>([(2,6),(3,5),(4,5),(4,6)],7)
[[1,1,3,3,3],[2],[3]]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>([(3,6),(4,5),(5,6)],7)
[[1,2,2,2,2],[2],[3]]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[1,2,2,2,3],[2],[3]]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[1,2,2,3,3],[2],[3]]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>([(2,6),(3,6),(4,5),(5,6)],7)
[[1,2,3,3,3],[2],[3]]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>([(3,6),(4,5),(5,6)],7)
[[1,3,3,3,3],[2],[3]]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>([(4,6),(5,6)],7)
[[1,1,1,1],[2,2,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,1],[2,3,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,1],[3,3,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,2],[2,2,3]]=>[4,5,7,1,2,3,6]=>[7,1,2,4,5,3,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,3],[2,2,2]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,2],[2,3,3]]=>[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[1,1,1,3],[2,2,3]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,3],[2,3,3]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,2],[2,2,3]]=>[3,4,7,1,2,5,6]=>[7,1,3,4,2,5,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,2],[2,3,3]]=>[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[1,1,2,3],[2,2,3]]=>[3,4,6,1,2,5,7]=>[6,1,3,4,2,5,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,3],[2,3,3]]=>[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[1,1,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,2,2],[2,3,3]]=>[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[1,2,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,2,3],[2,3,3]]=>[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[1,2,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[2,2,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[2,2,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,1],[2,2],[3]]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
[[1,1,1,1],[2,3],[3]]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,2],[2,2],[3]]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
[[1,1,1,2],[2,3],[3]]=>[6,4,7,1,2,3,5]=>[7,1,2,6,3,4,5]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1,3],[2,2],[3]]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
[[1,1,1,3],[2,3],[3]]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,2],[2,2],[3]]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
[[1,1,2,2],[2,3],[3]]=>[6,3,7,1,2,4,5]=>[7,1,6,2,4,3,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2,3],[2,2],[3]]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[[1,1,2,3],[2,3],[3]]=>[5,3,6,1,2,4,7]=>[6,1,5,2,3,4,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,3,3],[2,2],[3]]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
[[1,1,3,3],[2,3],[3]]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,2,2],[2,3],[3]]=>[6,2,7,1,3,4,5]=>[7,6,1,3,4,2,5]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,2,3],[2,3],[3]]=>[5,2,6,1,3,4,7]=>[6,5,1,3,2,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3,3],[2,3],[3]]=>[4,2,5,1,3,6,7]=>[5,4,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1],[2,2,2],[3]]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1],[2,2,3],[3]]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1],[2,3,3],[3]]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2],[2,2,3],[3]]=>[6,3,4,7,1,2,5]=>[7,1,6,3,2,4,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,2],[2,3,3],[3]]=>[5,3,6,7,1,2,4]=>[7,1,5,2,3,6,4]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,2],[2,3,3],[3]]=>[5,2,6,7,1,3,4]=>[7,5,1,3,2,6,4]=>([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,1,1],[2,2],[3,3]]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>([(0,5),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[[1,1,2],[2,2],[3,3]]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[[1,1,3],[2,2],[3,3]]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[[1,1,1,1,1,1,1,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>([],8)
[[1,1,1,1,1,1,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>([],8)
[[1,1,1,1,1,2,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>([],8)
[[1,1,1,1,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>([],8)
[[1,1,1,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>([],8)
[[1,1,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>([],8)
[[1,2,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>([],8)
[[2,2,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>([],8)
[[1,1,1,1,1,1,1],[2]]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[1,1,1,1,1,1,2],[2]]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[1,1,1,1,1,2,2],[2]]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[1,1,1,1,2,2,2],[2]]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>([(3,7),(4,7),(5,7),(6,7)],8)
[[1,1,1,2,2,2,2],[2]]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>([(4,7),(5,7),(6,7)],8)
[[1,1,2,2,2,2,2],[2]]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>([(5,7),(6,7)],8)
[[1,2,2,2,2,2,2],[2]]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>([(6,7)],8)
[[1,1,1,1,1,1],[2,2]]=>[7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,7,6]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
[[1,1,1,1,1,2],[2,2]]=>[6,7,1,2,3,4,5,8]=>[7,1,2,3,4,6,5,8]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
[[1,1,1,1,2,2],[2,2]]=>[5,6,1,2,3,4,7,8]=>[6,1,2,3,5,4,7,8]=>([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
[[1,1,1,2,2,2],[2,2]]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>([(3,7),(4,7),(5,6),(5,7),(6,7)],8)
[[1,1,2,2,2,2],[2,2]]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>([(4,7),(5,6),(5,7),(6,7)],8)
[[1,1,1,1,1],[2,2,2]]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,1,1,1,2],[2,2,2]]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,1,1,1],[2,2,2,2]]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1]]=>[1]=>[1]=>([],1)
[[2]]=>[1]=>[1]=>([],1)
[[1,1]]=>[1,2]=>[1,2]=>([],2)
[[3]]=>[1]=>[1]=>([],1)
[[1,1,1]]=>[1,2,3]=>[1,2,3]=>([],3)
[[4]]=>[1]=>[1]=>([],1)
[[1,1,1,1]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[5]]=>[1]=>[1]=>([],1)
[[1,1,1,1,1]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[6]]=>[1]=>[1]=>([],1)
[[1,1,1,1,1,1]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)
[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[5,1,6,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>([(1,5),(2,4),(3,4),(3,5)],6)
[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[6,1,4,3,2,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[5,6,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[4,5,1,2,6,3]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)
[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>([(1,5),(2,4),(3,4),(3,5)],6)
[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)
[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[6,3,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[5,3,2,1,4,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[5,6,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[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)
[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[5,6,1,4,2,3]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[5,4,1,6,2,3]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[5,1,6,4,3,2]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>([(2,5),(3,5),(4,5)],6)
[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[6,3,4,2,1,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[4,6,1,2,5,3]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[6,4,1,5,2,3]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[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)
[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,1,1,1,2,2,2],[3,4],[4]]=>[9,8,10,1,2,3,4,5,6,7]=>[10,1,2,3,4,5,6,9,8,7]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,1,1,2,2,2,2],[3,4],[4]]=>[9,8,10,1,2,3,4,5,6,7]=>[10,1,2,3,4,5,6,9,8,7]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,1,1,1,2,2,3],[3,4],[4]]=>[9,7,10,1,2,3,4,5,6,8]=>[10,1,2,3,4,5,9,6,7,8]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,1,1,2,2,2,3],[3,4],[4]]=>[9,7,10,1,2,3,4,5,6,8]=>[10,1,2,3,4,5,9,6,7,8]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,1,2,2,2,2,3],[3,4],[4]]=>[9,7,10,1,2,3,4,5,6,8]=>[10,1,2,3,4,5,9,6,7,8]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
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
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
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.
searching the database
Sorry, this map was not found in the database.