Identifier
Mp00075:
Semistandard tableaux
—reading word permutation⟶
Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00109: Permutations —descent word⟶ Binary words
Images
=>
Cc0019;cc-rep-0
[[1,2]]=>[1,2]=>0
[[2,2]]=>[1,2]=>0
[[1],[2]]=>[2,1]=>1
[[1,3]]=>[1,2]=>0
[[2,3]]=>[1,2]=>0
[[3,3]]=>[1,2]=>0
[[1],[3]]=>[2,1]=>1
[[2],[3]]=>[2,1]=>1
[[1,1,2]]=>[1,2,3]=>00
[[1,2,2]]=>[1,2,3]=>00
[[2,2,2]]=>[1,2,3]=>00
[[1,1],[2]]=>[3,1,2]=>10
[[1,2],[2]]=>[2,1,3]=>10
[[1,4]]=>[1,2]=>0
[[2,4]]=>[1,2]=>0
[[3,4]]=>[1,2]=>0
[[4,4]]=>[1,2]=>0
[[1],[4]]=>[2,1]=>1
[[2],[4]]=>[2,1]=>1
[[3],[4]]=>[2,1]=>1
[[1,1,3]]=>[1,2,3]=>00
[[1,2,3]]=>[1,2,3]=>00
[[1,3,3]]=>[1,2,3]=>00
[[2,2,3]]=>[1,2,3]=>00
[[2,3,3]]=>[1,2,3]=>00
[[3,3,3]]=>[1,2,3]=>00
[[1,1],[3]]=>[3,1,2]=>10
[[1,2],[3]]=>[3,1,2]=>10
[[1,3],[2]]=>[2,1,3]=>10
[[1,3],[3]]=>[2,1,3]=>10
[[2,2],[3]]=>[3,1,2]=>10
[[2,3],[3]]=>[2,1,3]=>10
[[1],[2],[3]]=>[3,2,1]=>11
[[1,1,1,2]]=>[1,2,3,4]=>000
[[1,1,2,2]]=>[1,2,3,4]=>000
[[1,2,2,2]]=>[1,2,3,4]=>000
[[2,2,2,2]]=>[1,2,3,4]=>000
[[1,1,1],[2]]=>[4,1,2,3]=>100
[[1,1,2],[2]]=>[3,1,2,4]=>100
[[1,2,2],[2]]=>[2,1,3,4]=>100
[[1,1],[2,2]]=>[3,4,1,2]=>010
[[1,5]]=>[1,2]=>0
[[2,5]]=>[1,2]=>0
[[3,5]]=>[1,2]=>0
[[4,5]]=>[1,2]=>0
[[5,5]]=>[1,2]=>0
[[1],[5]]=>[2,1]=>1
[[2],[5]]=>[2,1]=>1
[[3],[5]]=>[2,1]=>1
[[4],[5]]=>[2,1]=>1
[[1,1,4]]=>[1,2,3]=>00
[[1,2,4]]=>[1,2,3]=>00
[[1,3,4]]=>[1,2,3]=>00
[[1,4,4]]=>[1,2,3]=>00
[[2,2,4]]=>[1,2,3]=>00
[[2,3,4]]=>[1,2,3]=>00
[[2,4,4]]=>[1,2,3]=>00
[[3,3,4]]=>[1,2,3]=>00
[[3,4,4]]=>[1,2,3]=>00
[[4,4,4]]=>[1,2,3]=>00
[[1,1],[4]]=>[3,1,2]=>10
[[1,2],[4]]=>[3,1,2]=>10
[[1,4],[2]]=>[2,1,3]=>10
[[1,3],[4]]=>[3,1,2]=>10
[[1,4],[3]]=>[2,1,3]=>10
[[1,4],[4]]=>[2,1,3]=>10
[[2,2],[4]]=>[3,1,2]=>10
[[2,3],[4]]=>[3,1,2]=>10
[[2,4],[3]]=>[2,1,3]=>10
[[2,4],[4]]=>[2,1,3]=>10
[[3,3],[4]]=>[3,1,2]=>10
[[3,4],[4]]=>[2,1,3]=>10
[[1],[2],[4]]=>[3,2,1]=>11
[[1],[3],[4]]=>[3,2,1]=>11
[[2],[3],[4]]=>[3,2,1]=>11
[[1,1,1,3]]=>[1,2,3,4]=>000
[[1,1,2,3]]=>[1,2,3,4]=>000
[[1,1,3,3]]=>[1,2,3,4]=>000
[[1,2,2,3]]=>[1,2,3,4]=>000
[[1,2,3,3]]=>[1,2,3,4]=>000
[[1,3,3,3]]=>[1,2,3,4]=>000
[[2,2,2,3]]=>[1,2,3,4]=>000
[[2,2,3,3]]=>[1,2,3,4]=>000
[[2,3,3,3]]=>[1,2,3,4]=>000
[[3,3,3,3]]=>[1,2,3,4]=>000
[[1,1,1],[3]]=>[4,1,2,3]=>100
[[1,1,2],[3]]=>[4,1,2,3]=>100
[[1,1,3],[2]]=>[3,1,2,4]=>100
[[1,1,3],[3]]=>[3,1,2,4]=>100
[[1,2,2],[3]]=>[4,1,2,3]=>100
[[1,2,3],[2]]=>[2,1,3,4]=>100
[[1,2,3],[3]]=>[3,1,2,4]=>100
[[1,3,3],[2]]=>[2,1,3,4]=>100
[[1,3,3],[3]]=>[2,1,3,4]=>100
[[2,2,2],[3]]=>[4,1,2,3]=>100
[[2,2,3],[3]]=>[3,1,2,4]=>100
[[2,3,3],[3]]=>[2,1,3,4]=>100
[[1,1],[2,3]]=>[3,4,1,2]=>010
[[1,1],[3,3]]=>[3,4,1,2]=>010
[[1,2],[2,3]]=>[2,4,1,3]=>010
[[1,2],[3,3]]=>[3,4,1,2]=>010
[[2,2],[3,3]]=>[3,4,1,2]=>010
[[1,1],[2],[3]]=>[4,3,1,2]=>110
[[1,2],[2],[3]]=>[4,2,1,3]=>110
[[1,3],[2],[3]]=>[3,2,1,4]=>110
[[1,1,1,1,2]]=>[1,2,3,4,5]=>0000
[[1,1,1,2,2]]=>[1,2,3,4,5]=>0000
[[1,1,2,2,2]]=>[1,2,3,4,5]=>0000
[[1,2,2,2,2]]=>[1,2,3,4,5]=>0000
[[2,2,2,2,2]]=>[1,2,3,4,5]=>0000
[[1,1,1,1],[2]]=>[5,1,2,3,4]=>1000
[[1,1,1,2],[2]]=>[4,1,2,3,5]=>1000
[[1,1,2,2],[2]]=>[3,1,2,4,5]=>1000
[[1,2,2,2],[2]]=>[2,1,3,4,5]=>1000
[[1,1,1],[2,2]]=>[4,5,1,2,3]=>0100
[[1,1,2],[2,2]]=>[3,4,1,2,5]=>0100
[[1,6]]=>[1,2]=>0
[[2,6]]=>[1,2]=>0
[[3,6]]=>[1,2]=>0
[[4,6]]=>[1,2]=>0
[[5,6]]=>[1,2]=>0
[[6,6]]=>[1,2]=>0
[[1],[6]]=>[2,1]=>1
[[2],[6]]=>[2,1]=>1
[[3],[6]]=>[2,1]=>1
[[4],[6]]=>[2,1]=>1
[[5],[6]]=>[2,1]=>1
[[1,1,5]]=>[1,2,3]=>00
[[1,2,5]]=>[1,2,3]=>00
[[1,3,5]]=>[1,2,3]=>00
[[1,4,5]]=>[1,2,3]=>00
[[1,5,5]]=>[1,2,3]=>00
[[2,2,5]]=>[1,2,3]=>00
[[2,3,5]]=>[1,2,3]=>00
[[2,4,5]]=>[1,2,3]=>00
[[2,5,5]]=>[1,2,3]=>00
[[3,3,5]]=>[1,2,3]=>00
[[3,4,5]]=>[1,2,3]=>00
[[3,5,5]]=>[1,2,3]=>00
[[4,4,5]]=>[1,2,3]=>00
[[4,5,5]]=>[1,2,3]=>00
[[5,5,5]]=>[1,2,3]=>00
[[1,1],[5]]=>[3,1,2]=>10
[[1,2],[5]]=>[3,1,2]=>10
[[1,5],[2]]=>[2,1,3]=>10
[[1,3],[5]]=>[3,1,2]=>10
[[1,5],[3]]=>[2,1,3]=>10
[[1,4],[5]]=>[3,1,2]=>10
[[1,5],[4]]=>[2,1,3]=>10
[[1,5],[5]]=>[2,1,3]=>10
[[2,2],[5]]=>[3,1,2]=>10
[[2,3],[5]]=>[3,1,2]=>10
[[2,5],[3]]=>[2,1,3]=>10
[[2,4],[5]]=>[3,1,2]=>10
[[2,5],[4]]=>[2,1,3]=>10
[[2,5],[5]]=>[2,1,3]=>10
[[3,3],[5]]=>[3,1,2]=>10
[[3,4],[5]]=>[3,1,2]=>10
[[3,5],[4]]=>[2,1,3]=>10
[[3,5],[5]]=>[2,1,3]=>10
[[4,4],[5]]=>[3,1,2]=>10
[[4,5],[5]]=>[2,1,3]=>10
[[1],[2],[5]]=>[3,2,1]=>11
[[1],[3],[5]]=>[3,2,1]=>11
[[1],[4],[5]]=>[3,2,1]=>11
[[2],[3],[5]]=>[3,2,1]=>11
[[2],[4],[5]]=>[3,2,1]=>11
[[3],[4],[5]]=>[3,2,1]=>11
[[1,1,1,4]]=>[1,2,3,4]=>000
[[1,1,2,4]]=>[1,2,3,4]=>000
[[1,1,3,4]]=>[1,2,3,4]=>000
[[1,1,4,4]]=>[1,2,3,4]=>000
[[1,2,2,4]]=>[1,2,3,4]=>000
[[1,2,3,4]]=>[1,2,3,4]=>000
[[1,2,4,4]]=>[1,2,3,4]=>000
[[1,3,3,4]]=>[1,2,3,4]=>000
[[1,3,4,4]]=>[1,2,3,4]=>000
[[1,4,4,4]]=>[1,2,3,4]=>000
[[2,2,2,4]]=>[1,2,3,4]=>000
[[2,2,3,4]]=>[1,2,3,4]=>000
[[2,2,4,4]]=>[1,2,3,4]=>000
[[2,3,3,4]]=>[1,2,3,4]=>000
[[2,3,4,4]]=>[1,2,3,4]=>000
[[2,4,4,4]]=>[1,2,3,4]=>000
[[3,3,3,4]]=>[1,2,3,4]=>000
[[3,3,4,4]]=>[1,2,3,4]=>000
[[3,4,4,4]]=>[1,2,3,4]=>000
[[4,4,4,4]]=>[1,2,3,4]=>000
[[1,1,1],[4]]=>[4,1,2,3]=>100
[[1,1,2],[4]]=>[4,1,2,3]=>100
[[1,1,4],[2]]=>[3,1,2,4]=>100
[[1,1,3],[4]]=>[4,1,2,3]=>100
[[1,1,4],[3]]=>[3,1,2,4]=>100
[[1,1,4],[4]]=>[3,1,2,4]=>100
[[1,2,2],[4]]=>[4,1,2,3]=>100
[[1,2,4],[2]]=>[2,1,3,4]=>100
[[1,2,3],[4]]=>[4,1,2,3]=>100
[[1,2,4],[3]]=>[3,1,2,4]=>100
[[1,3,4],[2]]=>[2,1,3,4]=>100
[[1,2,4],[4]]=>[3,1,2,4]=>100
[[1,4,4],[2]]=>[2,1,3,4]=>100
[[1,3,3],[4]]=>[4,1,2,3]=>100
[[1,3,4],[3]]=>[2,1,3,4]=>100
[[1,3,4],[4]]=>[3,1,2,4]=>100
[[1,4,4],[3]]=>[2,1,3,4]=>100
[[1,4,4],[4]]=>[2,1,3,4]=>100
[[2,2,2],[4]]=>[4,1,2,3]=>100
[[2,2,3],[4]]=>[4,1,2,3]=>100
[[2,2,4],[3]]=>[3,1,2,4]=>100
[[2,2,4],[4]]=>[3,1,2,4]=>100
[[2,3,3],[4]]=>[4,1,2,3]=>100
[[2,3,4],[3]]=>[2,1,3,4]=>100
[[2,3,4],[4]]=>[3,1,2,4]=>100
[[2,4,4],[3]]=>[2,1,3,4]=>100
[[2,4,4],[4]]=>[2,1,3,4]=>100
[[3,3,3],[4]]=>[4,1,2,3]=>100
[[3,3,4],[4]]=>[3,1,2,4]=>100
[[3,4,4],[4]]=>[2,1,3,4]=>100
[[1,1],[2,4]]=>[3,4,1,2]=>010
[[1,1],[3,4]]=>[3,4,1,2]=>010
[[1,1],[4,4]]=>[3,4,1,2]=>010
[[1,2],[2,4]]=>[2,4,1,3]=>010
[[1,2],[3,4]]=>[3,4,1,2]=>010
[[1,3],[2,4]]=>[2,4,1,3]=>010
[[1,2],[4,4]]=>[3,4,1,2]=>010
[[1,3],[3,4]]=>[2,4,1,3]=>010
[[1,3],[4,4]]=>[3,4,1,2]=>010
[[2,2],[3,4]]=>[3,4,1,2]=>010
[[2,2],[4,4]]=>[3,4,1,2]=>010
[[2,3],[3,4]]=>[2,4,1,3]=>010
[[2,3],[4,4]]=>[3,4,1,2]=>010
[[3,3],[4,4]]=>[3,4,1,2]=>010
[[1,1],[2],[4]]=>[4,3,1,2]=>110
[[1,1],[3],[4]]=>[4,3,1,2]=>110
[[1,2],[2],[4]]=>[4,2,1,3]=>110
[[1,2],[3],[4]]=>[4,3,1,2]=>110
[[1,3],[2],[4]]=>[4,2,1,3]=>110
[[1,4],[2],[3]]=>[3,2,1,4]=>110
[[1,4],[2],[4]]=>[3,2,1,4]=>110
[[1,3],[3],[4]]=>[4,2,1,3]=>110
[[1,4],[3],[4]]=>[3,2,1,4]=>110
[[2,2],[3],[4]]=>[4,3,1,2]=>110
[[2,3],[3],[4]]=>[4,2,1,3]=>110
[[2,4],[3],[4]]=>[3,2,1,4]=>110
[[1],[2],[3],[4]]=>[4,3,2,1]=>111
[[1,1,1,1,3]]=>[1,2,3,4,5]=>0000
[[1,1,1,2,3]]=>[1,2,3,4,5]=>0000
[[1,1,1,3,3]]=>[1,2,3,4,5]=>0000
[[1,1,2,2,3]]=>[1,2,3,4,5]=>0000
[[1,1,2,3,3]]=>[1,2,3,4,5]=>0000
[[1,1,3,3,3]]=>[1,2,3,4,5]=>0000
[[1,2,2,2,3]]=>[1,2,3,4,5]=>0000
[[1,2,2,3,3]]=>[1,2,3,4,5]=>0000
[[1,2,3,3,3]]=>[1,2,3,4,5]=>0000
[[1,3,3,3,3]]=>[1,2,3,4,5]=>0000
[[2,2,2,2,3]]=>[1,2,3,4,5]=>0000
[[2,2,2,3,3]]=>[1,2,3,4,5]=>0000
[[2,2,3,3,3]]=>[1,2,3,4,5]=>0000
[[2,3,3,3,3]]=>[1,2,3,4,5]=>0000
[[3,3,3,3,3]]=>[1,2,3,4,5]=>0000
[[1,1,1,1],[3]]=>[5,1,2,3,4]=>1000
[[1,1,1,2],[3]]=>[5,1,2,3,4]=>1000
[[1,1,1,3],[2]]=>[4,1,2,3,5]=>1000
[[1,1,1,3],[3]]=>[4,1,2,3,5]=>1000
[[1,1,2,2],[3]]=>[5,1,2,3,4]=>1000
[[1,1,2,3],[2]]=>[3,1,2,4,5]=>1000
[[1,1,2,3],[3]]=>[4,1,2,3,5]=>1000
[[1,1,3,3],[2]]=>[3,1,2,4,5]=>1000
[[1,1,3,3],[3]]=>[3,1,2,4,5]=>1000
[[1,2,2,2],[3]]=>[5,1,2,3,4]=>1000
[[1,2,2,3],[2]]=>[2,1,3,4,5]=>1000
[[1,2,2,3],[3]]=>[4,1,2,3,5]=>1000
[[1,2,3,3],[2]]=>[2,1,3,4,5]=>1000
[[1,2,3,3],[3]]=>[3,1,2,4,5]=>1000
[[1,3,3,3],[2]]=>[2,1,3,4,5]=>1000
[[1,3,3,3],[3]]=>[2,1,3,4,5]=>1000
[[2,2,2,2],[3]]=>[5,1,2,3,4]=>1000
[[2,2,2,3],[3]]=>[4,1,2,3,5]=>1000
[[2,2,3,3],[3]]=>[3,1,2,4,5]=>1000
[[2,3,3,3],[3]]=>[2,1,3,4,5]=>1000
[[1,1,1],[2,3]]=>[4,5,1,2,3]=>0100
[[1,1,1],[3,3]]=>[4,5,1,2,3]=>0100
[[1,1,2],[2,3]]=>[3,5,1,2,4]=>0100
[[1,1,3],[2,2]]=>[3,4,1,2,5]=>0100
[[1,1,2],[3,3]]=>[4,5,1,2,3]=>0100
[[1,1,3],[2,3]]=>[3,4,1,2,5]=>0100
[[1,1,3],[3,3]]=>[3,4,1,2,5]=>0100
[[1,2,2],[2,3]]=>[2,5,1,3,4]=>0100
[[1,2,2],[3,3]]=>[4,5,1,2,3]=>0100
[[1,2,3],[2,3]]=>[2,4,1,3,5]=>0100
[[1,2,3],[3,3]]=>[3,4,1,2,5]=>0100
[[2,2,2],[3,3]]=>[4,5,1,2,3]=>0100
[[2,2,3],[3,3]]=>[3,4,1,2,5]=>0100
[[1,1,1],[2],[3]]=>[5,4,1,2,3]=>1100
[[1,1,2],[2],[3]]=>[5,3,1,2,4]=>1100
[[1,1,3],[2],[3]]=>[4,3,1,2,5]=>1100
[[1,2,2],[2],[3]]=>[5,2,1,3,4]=>1100
[[1,2,3],[2],[3]]=>[4,2,1,3,5]=>1100
[[1,3,3],[2],[3]]=>[3,2,1,4,5]=>1100
[[1,1],[2,2],[3]]=>[5,3,4,1,2]=>1010
[[1,1],[2,3],[3]]=>[4,3,5,1,2]=>1010
[[1,2],[2,3],[3]]=>[4,2,5,1,3]=>1010
[[1,1,1,1,1,2]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,1,2,2]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,2,2,2]]=>[1,2,3,4,5,6]=>00000
[[1,1,2,2,2,2]]=>[1,2,3,4,5,6]=>00000
[[1,2,2,2,2,2]]=>[1,2,3,4,5,6]=>00000
[[2,2,2,2,2,2]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,1,1],[2]]=>[6,1,2,3,4,5]=>10000
[[1,1,1,1,2],[2]]=>[5,1,2,3,4,6]=>10000
[[1,1,1,2,2],[2]]=>[4,1,2,3,5,6]=>10000
[[1,1,2,2,2],[2]]=>[3,1,2,4,5,6]=>10000
[[1,2,2,2,2],[2]]=>[2,1,3,4,5,6]=>10000
[[1,1,1,1],[2,2]]=>[5,6,1,2,3,4]=>01000
[[1,1,1,2],[2,2]]=>[4,5,1,2,3,6]=>01000
[[1,1,2,2],[2,2]]=>[3,4,1,2,5,6]=>01000
[[1,1,1],[2,2,2]]=>[4,5,6,1,2,3]=>00100
[[1,7]]=>[1,2]=>0
[[2,7]]=>[1,2]=>0
[[3,7]]=>[1,2]=>0
[[4,7]]=>[1,2]=>0
[[5,7]]=>[1,2]=>0
[[6,7]]=>[1,2]=>0
[[7,7]]=>[1,2]=>0
[[1],[7]]=>[2,1]=>1
[[2],[7]]=>[2,1]=>1
[[3],[7]]=>[2,1]=>1
[[4],[7]]=>[2,1]=>1
[[5],[7]]=>[2,1]=>1
[[6],[7]]=>[2,1]=>1
[[1,1,6]]=>[1,2,3]=>00
[[1,2,6]]=>[1,2,3]=>00
[[1,3,6]]=>[1,2,3]=>00
[[1,4,6]]=>[1,2,3]=>00
[[1,5,6]]=>[1,2,3]=>00
[[1,6,6]]=>[1,2,3]=>00
[[2,2,6]]=>[1,2,3]=>00
[[2,3,6]]=>[1,2,3]=>00
[[2,4,6]]=>[1,2,3]=>00
[[2,5,6]]=>[1,2,3]=>00
[[2,6,6]]=>[1,2,3]=>00
[[3,3,6]]=>[1,2,3]=>00
[[3,4,6]]=>[1,2,3]=>00
[[3,5,6]]=>[1,2,3]=>00
[[3,6,6]]=>[1,2,3]=>00
[[4,4,6]]=>[1,2,3]=>00
[[4,5,6]]=>[1,2,3]=>00
[[4,6,6]]=>[1,2,3]=>00
[[5,5,6]]=>[1,2,3]=>00
[[5,6,6]]=>[1,2,3]=>00
[[6,6,6]]=>[1,2,3]=>00
[[1,1],[6]]=>[3,1,2]=>10
[[1,2],[6]]=>[3,1,2]=>10
[[1,6],[2]]=>[2,1,3]=>10
[[1,3],[6]]=>[3,1,2]=>10
[[1,6],[3]]=>[2,1,3]=>10
[[1,4],[6]]=>[3,1,2]=>10
[[1,6],[4]]=>[2,1,3]=>10
[[1,5],[6]]=>[3,1,2]=>10
[[1,6],[5]]=>[2,1,3]=>10
[[1,6],[6]]=>[2,1,3]=>10
[[2,2],[6]]=>[3,1,2]=>10
[[2,3],[6]]=>[3,1,2]=>10
[[2,6],[3]]=>[2,1,3]=>10
[[2,4],[6]]=>[3,1,2]=>10
[[2,6],[4]]=>[2,1,3]=>10
[[2,5],[6]]=>[3,1,2]=>10
[[2,6],[5]]=>[2,1,3]=>10
[[2,6],[6]]=>[2,1,3]=>10
[[3,3],[6]]=>[3,1,2]=>10
[[3,4],[6]]=>[3,1,2]=>10
[[3,6],[4]]=>[2,1,3]=>10
[[3,5],[6]]=>[3,1,2]=>10
[[3,6],[5]]=>[2,1,3]=>10
[[3,6],[6]]=>[2,1,3]=>10
[[4,4],[6]]=>[3,1,2]=>10
[[4,5],[6]]=>[3,1,2]=>10
[[4,6],[5]]=>[2,1,3]=>10
[[4,6],[6]]=>[2,1,3]=>10
[[5,5],[6]]=>[3,1,2]=>10
[[5,6],[6]]=>[2,1,3]=>10
[[1],[2],[6]]=>[3,2,1]=>11
[[1],[3],[6]]=>[3,2,1]=>11
[[1],[4],[6]]=>[3,2,1]=>11
[[1],[5],[6]]=>[3,2,1]=>11
[[2],[3],[6]]=>[3,2,1]=>11
[[2],[4],[6]]=>[3,2,1]=>11
[[2],[5],[6]]=>[3,2,1]=>11
[[3],[4],[6]]=>[3,2,1]=>11
[[3],[5],[6]]=>[3,2,1]=>11
[[4],[5],[6]]=>[3,2,1]=>11
[[1,1,1,5]]=>[1,2,3,4]=>000
[[1,1,2,5]]=>[1,2,3,4]=>000
[[1,1,3,5]]=>[1,2,3,4]=>000
[[1,1,4,5]]=>[1,2,3,4]=>000
[[1,1,5,5]]=>[1,2,3,4]=>000
[[1,2,2,5]]=>[1,2,3,4]=>000
[[1,2,3,5]]=>[1,2,3,4]=>000
[[1,2,4,5]]=>[1,2,3,4]=>000
[[1,2,5,5]]=>[1,2,3,4]=>000
[[1,3,3,5]]=>[1,2,3,4]=>000
[[1,3,4,5]]=>[1,2,3,4]=>000
[[1,3,5,5]]=>[1,2,3,4]=>000
[[1,4,4,5]]=>[1,2,3,4]=>000
[[1,4,5,5]]=>[1,2,3,4]=>000
[[1,5,5,5]]=>[1,2,3,4]=>000
[[2,2,2,5]]=>[1,2,3,4]=>000
[[2,2,3,5]]=>[1,2,3,4]=>000
[[2,2,4,5]]=>[1,2,3,4]=>000
[[2,2,5,5]]=>[1,2,3,4]=>000
[[2,3,3,5]]=>[1,2,3,4]=>000
[[2,3,4,5]]=>[1,2,3,4]=>000
[[2,3,5,5]]=>[1,2,3,4]=>000
[[2,4,4,5]]=>[1,2,3,4]=>000
[[2,4,5,5]]=>[1,2,3,4]=>000
[[2,5,5,5]]=>[1,2,3,4]=>000
[[3,3,3,5]]=>[1,2,3,4]=>000
[[3,3,4,5]]=>[1,2,3,4]=>000
[[3,3,5,5]]=>[1,2,3,4]=>000
[[3,4,4,5]]=>[1,2,3,4]=>000
[[3,4,5,5]]=>[1,2,3,4]=>000
[[3,5,5,5]]=>[1,2,3,4]=>000
[[4,4,4,5]]=>[1,2,3,4]=>000
[[4,4,5,5]]=>[1,2,3,4]=>000
[[4,5,5,5]]=>[1,2,3,4]=>000
[[5,5,5,5]]=>[1,2,3,4]=>000
[[1,1,1],[5]]=>[4,1,2,3]=>100
[[1,1,2],[5]]=>[4,1,2,3]=>100
[[1,1,5],[2]]=>[3,1,2,4]=>100
[[1,1,3],[5]]=>[4,1,2,3]=>100
[[1,1,5],[3]]=>[3,1,2,4]=>100
[[1,1,4],[5]]=>[4,1,2,3]=>100
[[1,1,5],[4]]=>[3,1,2,4]=>100
[[1,1,5],[5]]=>[3,1,2,4]=>100
[[1,2,2],[5]]=>[4,1,2,3]=>100
[[1,2,5],[2]]=>[2,1,3,4]=>100
[[1,2,3],[5]]=>[4,1,2,3]=>100
[[1,2,5],[3]]=>[3,1,2,4]=>100
[[1,3,5],[2]]=>[2,1,3,4]=>100
[[1,2,4],[5]]=>[4,1,2,3]=>100
[[1,2,5],[4]]=>[3,1,2,4]=>100
[[1,4,5],[2]]=>[2,1,3,4]=>100
[[1,2,5],[5]]=>[3,1,2,4]=>100
[[1,5,5],[2]]=>[2,1,3,4]=>100
[[1,3,3],[5]]=>[4,1,2,3]=>100
[[1,3,5],[3]]=>[2,1,3,4]=>100
[[1,3,4],[5]]=>[4,1,2,3]=>100
[[1,3,5],[4]]=>[3,1,2,4]=>100
[[1,4,5],[3]]=>[2,1,3,4]=>100
[[1,3,5],[5]]=>[3,1,2,4]=>100
[[1,5,5],[3]]=>[2,1,3,4]=>100
[[1,4,4],[5]]=>[4,1,2,3]=>100
[[1,4,5],[4]]=>[2,1,3,4]=>100
[[1,4,5],[5]]=>[3,1,2,4]=>100
[[1,5,5],[4]]=>[2,1,3,4]=>100
[[1,5,5],[5]]=>[2,1,3,4]=>100
[[2,2,2],[5]]=>[4,1,2,3]=>100
[[2,2,3],[5]]=>[4,1,2,3]=>100
[[2,2,5],[3]]=>[3,1,2,4]=>100
[[2,2,4],[5]]=>[4,1,2,3]=>100
[[2,2,5],[4]]=>[3,1,2,4]=>100
[[2,2,5],[5]]=>[3,1,2,4]=>100
[[2,3,3],[5]]=>[4,1,2,3]=>100
[[2,3,5],[3]]=>[2,1,3,4]=>100
[[2,3,4],[5]]=>[4,1,2,3]=>100
[[2,3,5],[4]]=>[3,1,2,4]=>100
[[2,4,5],[3]]=>[2,1,3,4]=>100
[[2,3,5],[5]]=>[3,1,2,4]=>100
[[2,5,5],[3]]=>[2,1,3,4]=>100
[[2,4,4],[5]]=>[4,1,2,3]=>100
[[2,4,5],[4]]=>[2,1,3,4]=>100
[[2,4,5],[5]]=>[3,1,2,4]=>100
[[2,5,5],[4]]=>[2,1,3,4]=>100
[[2,5,5],[5]]=>[2,1,3,4]=>100
[[3,3,3],[5]]=>[4,1,2,3]=>100
[[3,3,4],[5]]=>[4,1,2,3]=>100
[[3,3,5],[4]]=>[3,1,2,4]=>100
[[3,3,5],[5]]=>[3,1,2,4]=>100
[[3,4,4],[5]]=>[4,1,2,3]=>100
[[3,4,5],[4]]=>[2,1,3,4]=>100
[[3,4,5],[5]]=>[3,1,2,4]=>100
[[3,5,5],[4]]=>[2,1,3,4]=>100
[[3,5,5],[5]]=>[2,1,3,4]=>100
[[4,4,4],[5]]=>[4,1,2,3]=>100
[[4,4,5],[5]]=>[3,1,2,4]=>100
[[4,5,5],[5]]=>[2,1,3,4]=>100
[[1,1],[2,5]]=>[3,4,1,2]=>010
[[1,1],[3,5]]=>[3,4,1,2]=>010
[[1,1],[4,5]]=>[3,4,1,2]=>010
[[1,1],[5,5]]=>[3,4,1,2]=>010
[[1,2],[2,5]]=>[2,4,1,3]=>010
[[1,2],[3,5]]=>[3,4,1,2]=>010
[[1,3],[2,5]]=>[2,4,1,3]=>010
[[1,2],[4,5]]=>[3,4,1,2]=>010
[[1,4],[2,5]]=>[2,4,1,3]=>010
[[1,2],[5,5]]=>[3,4,1,2]=>010
[[1,3],[3,5]]=>[2,4,1,3]=>010
[[1,3],[4,5]]=>[3,4,1,2]=>010
[[1,4],[3,5]]=>[2,4,1,3]=>010
[[1,3],[5,5]]=>[3,4,1,2]=>010
[[1,4],[4,5]]=>[2,4,1,3]=>010
[[1,4],[5,5]]=>[3,4,1,2]=>010
[[2,2],[3,5]]=>[3,4,1,2]=>010
[[2,2],[4,5]]=>[3,4,1,2]=>010
[[2,2],[5,5]]=>[3,4,1,2]=>010
[[2,3],[3,5]]=>[2,4,1,3]=>010
[[2,3],[4,5]]=>[3,4,1,2]=>010
[[2,4],[3,5]]=>[2,4,1,3]=>010
[[2,3],[5,5]]=>[3,4,1,2]=>010
[[2,4],[4,5]]=>[2,4,1,3]=>010
[[2,4],[5,5]]=>[3,4,1,2]=>010
[[3,3],[4,5]]=>[3,4,1,2]=>010
[[3,3],[5,5]]=>[3,4,1,2]=>010
[[3,4],[4,5]]=>[2,4,1,3]=>010
[[3,4],[5,5]]=>[3,4,1,2]=>010
[[4,4],[5,5]]=>[3,4,1,2]=>010
[[1,1],[2],[5]]=>[4,3,1,2]=>110
[[1,1],[3],[5]]=>[4,3,1,2]=>110
[[1,1],[4],[5]]=>[4,3,1,2]=>110
[[1,2],[2],[5]]=>[4,2,1,3]=>110
[[1,2],[3],[5]]=>[4,3,1,2]=>110
[[1,3],[2],[5]]=>[4,2,1,3]=>110
[[1,5],[2],[3]]=>[3,2,1,4]=>110
[[1,2],[4],[5]]=>[4,3,1,2]=>110
[[1,4],[2],[5]]=>[4,2,1,3]=>110
[[1,5],[2],[4]]=>[3,2,1,4]=>110
[[1,5],[2],[5]]=>[3,2,1,4]=>110
[[1,3],[3],[5]]=>[4,2,1,3]=>110
[[1,3],[4],[5]]=>[4,3,1,2]=>110
[[1,4],[3],[5]]=>[4,2,1,3]=>110
[[1,5],[3],[4]]=>[3,2,1,4]=>110
[[1,5],[3],[5]]=>[3,2,1,4]=>110
[[1,4],[4],[5]]=>[4,2,1,3]=>110
[[1,5],[4],[5]]=>[3,2,1,4]=>110
[[2,2],[3],[5]]=>[4,3,1,2]=>110
[[2,2],[4],[5]]=>[4,3,1,2]=>110
[[2,3],[3],[5]]=>[4,2,1,3]=>110
[[2,3],[4],[5]]=>[4,3,1,2]=>110
[[2,4],[3],[5]]=>[4,2,1,3]=>110
[[2,5],[3],[4]]=>[3,2,1,4]=>110
[[2,5],[3],[5]]=>[3,2,1,4]=>110
[[2,4],[4],[5]]=>[4,2,1,3]=>110
[[2,5],[4],[5]]=>[3,2,1,4]=>110
[[3,3],[4],[5]]=>[4,3,1,2]=>110
[[3,4],[4],[5]]=>[4,2,1,3]=>110
[[3,5],[4],[5]]=>[3,2,1,4]=>110
[[1],[2],[3],[5]]=>[4,3,2,1]=>111
[[1],[2],[4],[5]]=>[4,3,2,1]=>111
[[1],[3],[4],[5]]=>[4,3,2,1]=>111
[[2],[3],[4],[5]]=>[4,3,2,1]=>111
[[1,1,1,1,4]]=>[1,2,3,4,5]=>0000
[[1,1,1,2,4]]=>[1,2,3,4,5]=>0000
[[1,1,1,3,4]]=>[1,2,3,4,5]=>0000
[[1,1,1,4,4]]=>[1,2,3,4,5]=>0000
[[1,1,2,2,4]]=>[1,2,3,4,5]=>0000
[[1,1,2,3,4]]=>[1,2,3,4,5]=>0000
[[1,1,2,4,4]]=>[1,2,3,4,5]=>0000
[[1,1,3,3,4]]=>[1,2,3,4,5]=>0000
[[1,1,3,4,4]]=>[1,2,3,4,5]=>0000
[[1,1,4,4,4]]=>[1,2,3,4,5]=>0000
[[1,2,2,2,4]]=>[1,2,3,4,5]=>0000
[[1,2,2,3,4]]=>[1,2,3,4,5]=>0000
[[1,2,2,4,4]]=>[1,2,3,4,5]=>0000
[[1,2,3,3,4]]=>[1,2,3,4,5]=>0000
[[1,2,3,4,4]]=>[1,2,3,4,5]=>0000
[[1,2,4,4,4]]=>[1,2,3,4,5]=>0000
[[1,3,3,3,4]]=>[1,2,3,4,5]=>0000
[[1,3,3,4,4]]=>[1,2,3,4,5]=>0000
[[1,3,4,4,4]]=>[1,2,3,4,5]=>0000
[[1,4,4,4,4]]=>[1,2,3,4,5]=>0000
[[2,2,2,2,4]]=>[1,2,3,4,5]=>0000
[[2,2,2,3,4]]=>[1,2,3,4,5]=>0000
[[2,2,2,4,4]]=>[1,2,3,4,5]=>0000
[[2,2,3,3,4]]=>[1,2,3,4,5]=>0000
[[2,2,3,4,4]]=>[1,2,3,4,5]=>0000
[[2,2,4,4,4]]=>[1,2,3,4,5]=>0000
[[2,3,3,3,4]]=>[1,2,3,4,5]=>0000
[[2,3,3,4,4]]=>[1,2,3,4,5]=>0000
[[2,3,4,4,4]]=>[1,2,3,4,5]=>0000
[[2,4,4,4,4]]=>[1,2,3,4,5]=>0000
[[3,3,3,3,4]]=>[1,2,3,4,5]=>0000
[[3,3,3,4,4]]=>[1,2,3,4,5]=>0000
[[3,3,4,4,4]]=>[1,2,3,4,5]=>0000
[[3,4,4,4,4]]=>[1,2,3,4,5]=>0000
[[4,4,4,4,4]]=>[1,2,3,4,5]=>0000
[[1,1,1,1],[4]]=>[5,1,2,3,4]=>1000
[[1,1,1,2],[4]]=>[5,1,2,3,4]=>1000
[[1,1,1,4],[2]]=>[4,1,2,3,5]=>1000
[[1,1,1,3],[4]]=>[5,1,2,3,4]=>1000
[[1,1,1,4],[3]]=>[4,1,2,3,5]=>1000
[[1,1,1,4],[4]]=>[4,1,2,3,5]=>1000
[[1,1,2,2],[4]]=>[5,1,2,3,4]=>1000
[[1,1,2,4],[2]]=>[3,1,2,4,5]=>1000
[[1,1,2,3],[4]]=>[5,1,2,3,4]=>1000
[[1,1,2,4],[3]]=>[4,1,2,3,5]=>1000
[[1,1,3,4],[2]]=>[3,1,2,4,5]=>1000
[[1,1,2,4],[4]]=>[4,1,2,3,5]=>1000
[[1,1,4,4],[2]]=>[3,1,2,4,5]=>1000
[[1,1,3,3],[4]]=>[5,1,2,3,4]=>1000
[[1,1,3,4],[3]]=>[3,1,2,4,5]=>1000
[[1,1,3,4],[4]]=>[4,1,2,3,5]=>1000
[[1,1,4,4],[3]]=>[3,1,2,4,5]=>1000
[[1,1,4,4],[4]]=>[3,1,2,4,5]=>1000
[[1,2,2,2],[4]]=>[5,1,2,3,4]=>1000
[[1,2,2,4],[2]]=>[2,1,3,4,5]=>1000
[[1,2,2,3],[4]]=>[5,1,2,3,4]=>1000
[[1,2,2,4],[3]]=>[4,1,2,3,5]=>1000
[[1,2,3,4],[2]]=>[2,1,3,4,5]=>1000
[[1,2,2,4],[4]]=>[4,1,2,3,5]=>1000
[[1,2,4,4],[2]]=>[2,1,3,4,5]=>1000
[[1,2,3,3],[4]]=>[5,1,2,3,4]=>1000
[[1,2,3,4],[3]]=>[3,1,2,4,5]=>1000
[[1,3,3,4],[2]]=>[2,1,3,4,5]=>1000
[[1,2,3,4],[4]]=>[4,1,2,3,5]=>1000
[[1,2,4,4],[3]]=>[3,1,2,4,5]=>1000
[[1,3,4,4],[2]]=>[2,1,3,4,5]=>1000
[[1,2,4,4],[4]]=>[3,1,2,4,5]=>1000
[[1,4,4,4],[2]]=>[2,1,3,4,5]=>1000
[[1,3,3,3],[4]]=>[5,1,2,3,4]=>1000
[[1,3,3,4],[3]]=>[2,1,3,4,5]=>1000
[[1,3,3,4],[4]]=>[4,1,2,3,5]=>1000
[[1,3,4,4],[3]]=>[2,1,3,4,5]=>1000
[[1,3,4,4],[4]]=>[3,1,2,4,5]=>1000
[[1,4,4,4],[3]]=>[2,1,3,4,5]=>1000
[[1,4,4,4],[4]]=>[2,1,3,4,5]=>1000
[[2,2,2,2],[4]]=>[5,1,2,3,4]=>1000
[[2,2,2,3],[4]]=>[5,1,2,3,4]=>1000
[[2,2,2,4],[3]]=>[4,1,2,3,5]=>1000
[[2,2,2,4],[4]]=>[4,1,2,3,5]=>1000
[[2,2,3,3],[4]]=>[5,1,2,3,4]=>1000
[[2,2,3,4],[3]]=>[3,1,2,4,5]=>1000
[[2,2,3,4],[4]]=>[4,1,2,3,5]=>1000
[[2,2,4,4],[3]]=>[3,1,2,4,5]=>1000
[[2,2,4,4],[4]]=>[3,1,2,4,5]=>1000
[[2,3,3,3],[4]]=>[5,1,2,3,4]=>1000
[[2,3,3,4],[3]]=>[2,1,3,4,5]=>1000
[[2,3,3,4],[4]]=>[4,1,2,3,5]=>1000
[[2,3,4,4],[3]]=>[2,1,3,4,5]=>1000
[[2,3,4,4],[4]]=>[3,1,2,4,5]=>1000
[[2,4,4,4],[3]]=>[2,1,3,4,5]=>1000
[[2,4,4,4],[4]]=>[2,1,3,4,5]=>1000
[[3,3,3,3],[4]]=>[5,1,2,3,4]=>1000
[[3,3,3,4],[4]]=>[4,1,2,3,5]=>1000
[[3,3,4,4],[4]]=>[3,1,2,4,5]=>1000
[[3,4,4,4],[4]]=>[2,1,3,4,5]=>1000
[[1,1,1],[2,4]]=>[4,5,1,2,3]=>0100
[[1,1,1],[3,4]]=>[4,5,1,2,3]=>0100
[[1,1,1],[4,4]]=>[4,5,1,2,3]=>0100
[[1,1,2],[2,4]]=>[3,5,1,2,4]=>0100
[[1,1,4],[2,2]]=>[3,4,1,2,5]=>0100
[[1,1,2],[3,4]]=>[4,5,1,2,3]=>0100
[[1,1,3],[2,4]]=>[3,5,1,2,4]=>0100
[[1,1,4],[2,3]]=>[3,4,1,2,5]=>0100
[[1,1,2],[4,4]]=>[4,5,1,2,3]=>0100
[[1,1,4],[2,4]]=>[3,4,1,2,5]=>0100
[[1,1,3],[3,4]]=>[3,5,1,2,4]=>0100
[[1,1,4],[3,3]]=>[3,4,1,2,5]=>0100
[[1,1,3],[4,4]]=>[4,5,1,2,3]=>0100
[[1,1,4],[3,4]]=>[3,4,1,2,5]=>0100
[[1,1,4],[4,4]]=>[3,4,1,2,5]=>0100
[[1,2,2],[2,4]]=>[2,5,1,3,4]=>0100
[[1,2,2],[3,4]]=>[4,5,1,2,3]=>0100
[[1,2,3],[2,4]]=>[2,5,1,3,4]=>0100
[[1,2,4],[2,3]]=>[2,4,1,3,5]=>0100
[[1,2,2],[4,4]]=>[4,5,1,2,3]=>0100
[[1,2,4],[2,4]]=>[2,4,1,3,5]=>0100
[[1,2,3],[3,4]]=>[3,5,1,2,4]=>0100
[[1,2,4],[3,3]]=>[3,4,1,2,5]=>0100
[[1,3,3],[2,4]]=>[2,5,1,3,4]=>0100
[[1,2,3],[4,4]]=>[4,5,1,2,3]=>0100
[[1,2,4],[3,4]]=>[3,4,1,2,5]=>0100
[[1,3,4],[2,4]]=>[2,4,1,3,5]=>0100
[[1,2,4],[4,4]]=>[3,4,1,2,5]=>0100
[[1,3,3],[3,4]]=>[2,5,1,3,4]=>0100
[[1,3,3],[4,4]]=>[4,5,1,2,3]=>0100
[[1,3,4],[3,4]]=>[2,4,1,3,5]=>0100
[[1,3,4],[4,4]]=>[3,4,1,2,5]=>0100
[[2,2,2],[3,4]]=>[4,5,1,2,3]=>0100
[[2,2,2],[4,4]]=>[4,5,1,2,3]=>0100
[[2,2,3],[3,4]]=>[3,5,1,2,4]=>0100
[[2,2,4],[3,3]]=>[3,4,1,2,5]=>0100
[[2,2,3],[4,4]]=>[4,5,1,2,3]=>0100
[[2,2,4],[3,4]]=>[3,4,1,2,5]=>0100
[[2,2,4],[4,4]]=>[3,4,1,2,5]=>0100
[[2,3,3],[3,4]]=>[2,5,1,3,4]=>0100
[[2,3,3],[4,4]]=>[4,5,1,2,3]=>0100
[[2,3,4],[3,4]]=>[2,4,1,3,5]=>0100
[[2,3,4],[4,4]]=>[3,4,1,2,5]=>0100
[[3,3,3],[4,4]]=>[4,5,1,2,3]=>0100
[[3,3,4],[4,4]]=>[3,4,1,2,5]=>0100
[[1,1,1],[2],[4]]=>[5,4,1,2,3]=>1100
[[1,1,1],[3],[4]]=>[5,4,1,2,3]=>1100
[[1,1,2],[2],[4]]=>[5,3,1,2,4]=>1100
[[1,1,2],[3],[4]]=>[5,4,1,2,3]=>1100
[[1,1,3],[2],[4]]=>[5,3,1,2,4]=>1100
[[1,1,4],[2],[3]]=>[4,3,1,2,5]=>1100
[[1,1,4],[2],[4]]=>[4,3,1,2,5]=>1100
[[1,1,3],[3],[4]]=>[5,3,1,2,4]=>1100
[[1,1,4],[3],[4]]=>[4,3,1,2,5]=>1100
[[1,2,2],[2],[4]]=>[5,2,1,3,4]=>1100
[[1,2,2],[3],[4]]=>[5,4,1,2,3]=>1100
[[1,2,3],[2],[4]]=>[5,2,1,3,4]=>1100
[[1,2,4],[2],[3]]=>[4,2,1,3,5]=>1100
[[1,2,4],[2],[4]]=>[4,2,1,3,5]=>1100
[[1,2,3],[3],[4]]=>[5,3,1,2,4]=>1100
[[1,3,3],[2],[4]]=>[5,2,1,3,4]=>1100
[[1,3,4],[2],[3]]=>[3,2,1,4,5]=>1100
[[1,2,4],[3],[4]]=>[4,3,1,2,5]=>1100
[[1,3,4],[2],[4]]=>[4,2,1,3,5]=>1100
[[1,4,4],[2],[3]]=>[3,2,1,4,5]=>1100
[[1,4,4],[2],[4]]=>[3,2,1,4,5]=>1100
[[1,3,3],[3],[4]]=>[5,2,1,3,4]=>1100
[[1,3,4],[3],[4]]=>[4,2,1,3,5]=>1100
[[1,4,4],[3],[4]]=>[3,2,1,4,5]=>1100
[[2,2,2],[3],[4]]=>[5,4,1,2,3]=>1100
[[2,2,3],[3],[4]]=>[5,3,1,2,4]=>1100
[[2,2,4],[3],[4]]=>[4,3,1,2,5]=>1100
[[2,3,3],[3],[4]]=>[5,2,1,3,4]=>1100
[[2,3,4],[3],[4]]=>[4,2,1,3,5]=>1100
[[2,4,4],[3],[4]]=>[3,2,1,4,5]=>1100
[[1,1],[2,2],[4]]=>[5,3,4,1,2]=>1010
[[1,1],[2,3],[4]]=>[5,3,4,1,2]=>1010
[[1,1],[2,4],[3]]=>[4,3,5,1,2]=>1010
[[1,1],[2,4],[4]]=>[4,3,5,1,2]=>1010
[[1,1],[3,3],[4]]=>[5,3,4,1,2]=>1010
[[1,1],[3,4],[4]]=>[4,3,5,1,2]=>1010
[[1,2],[2,3],[4]]=>[5,2,4,1,3]=>1010
[[1,2],[2,4],[3]]=>[4,2,5,1,3]=>1010
[[1,2],[2,4],[4]]=>[4,2,5,1,3]=>1010
[[1,2],[3,3],[4]]=>[5,3,4,1,2]=>1010
[[1,3],[2,4],[3]]=>[3,2,5,1,4]=>1010
[[1,2],[3,4],[4]]=>[4,3,5,1,2]=>1010
[[1,3],[2,4],[4]]=>[4,2,5,1,3]=>1010
[[1,3],[3,4],[4]]=>[4,2,5,1,3]=>1010
[[2,2],[3,3],[4]]=>[5,3,4,1,2]=>1010
[[2,2],[3,4],[4]]=>[4,3,5,1,2]=>1010
[[2,3],[3,4],[4]]=>[4,2,5,1,3]=>1010
[[1,1],[2],[3],[4]]=>[5,4,3,1,2]=>1110
[[1,2],[2],[3],[4]]=>[5,4,2,1,3]=>1110
[[1,3],[2],[3],[4]]=>[5,3,2,1,4]=>1110
[[1,4],[2],[3],[4]]=>[4,3,2,1,5]=>1110
[[1,1,1,1,1,3]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,1,2,3]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,1,3,3]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,2,2,3]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,2,3,3]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,3,3,3]]=>[1,2,3,4,5,6]=>00000
[[1,1,2,2,2,3]]=>[1,2,3,4,5,6]=>00000
[[1,1,2,2,3,3]]=>[1,2,3,4,5,6]=>00000
[[1,1,2,3,3,3]]=>[1,2,3,4,5,6]=>00000
[[1,1,3,3,3,3]]=>[1,2,3,4,5,6]=>00000
[[1,2,2,2,2,3]]=>[1,2,3,4,5,6]=>00000
[[1,2,2,2,3,3]]=>[1,2,3,4,5,6]=>00000
[[1,2,2,3,3,3]]=>[1,2,3,4,5,6]=>00000
[[1,2,3,3,3,3]]=>[1,2,3,4,5,6]=>00000
[[1,3,3,3,3,3]]=>[1,2,3,4,5,6]=>00000
[[2,2,2,2,2,3]]=>[1,2,3,4,5,6]=>00000
[[2,2,2,2,3,3]]=>[1,2,3,4,5,6]=>00000
[[2,2,2,3,3,3]]=>[1,2,3,4,5,6]=>00000
[[2,2,3,3,3,3]]=>[1,2,3,4,5,6]=>00000
[[2,3,3,3,3,3]]=>[1,2,3,4,5,6]=>00000
[[3,3,3,3,3,3]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,1,1],[3]]=>[6,1,2,3,4,5]=>10000
[[1,1,1,1,2],[3]]=>[6,1,2,3,4,5]=>10000
[[1,1,1,1,3],[2]]=>[5,1,2,3,4,6]=>10000
[[1,1,1,1,3],[3]]=>[5,1,2,3,4,6]=>10000
[[1,1,1,2,2],[3]]=>[6,1,2,3,4,5]=>10000
[[1,1,1,2,3],[2]]=>[4,1,2,3,5,6]=>10000
[[1,1,1,2,3],[3]]=>[5,1,2,3,4,6]=>10000
[[1,1,1,3,3],[2]]=>[4,1,2,3,5,6]=>10000
[[1,1,1,3,3],[3]]=>[4,1,2,3,5,6]=>10000
[[1,1,2,2,2],[3]]=>[6,1,2,3,4,5]=>10000
[[1,1,2,2,3],[2]]=>[3,1,2,4,5,6]=>10000
[[1,1,2,2,3],[3]]=>[5,1,2,3,4,6]=>10000
[[1,1,2,3,3],[2]]=>[3,1,2,4,5,6]=>10000
[[1,1,2,3,3],[3]]=>[4,1,2,3,5,6]=>10000
[[1,1,3,3,3],[2]]=>[3,1,2,4,5,6]=>10000
[[1,1,3,3,3],[3]]=>[3,1,2,4,5,6]=>10000
[[1,2,2,2,2],[3]]=>[6,1,2,3,4,5]=>10000
[[1,2,2,2,3],[2]]=>[2,1,3,4,5,6]=>10000
[[1,2,2,2,3],[3]]=>[5,1,2,3,4,6]=>10000
[[1,2,2,3,3],[2]]=>[2,1,3,4,5,6]=>10000
[[1,2,2,3,3],[3]]=>[4,1,2,3,5,6]=>10000
[[1,2,3,3,3],[2]]=>[2,1,3,4,5,6]=>10000
[[1,2,3,3,3],[3]]=>[3,1,2,4,5,6]=>10000
[[1,3,3,3,3],[2]]=>[2,1,3,4,5,6]=>10000
[[1,3,3,3,3],[3]]=>[2,1,3,4,5,6]=>10000
[[2,2,2,2,2],[3]]=>[6,1,2,3,4,5]=>10000
[[2,2,2,2,3],[3]]=>[5,1,2,3,4,6]=>10000
[[2,2,2,3,3],[3]]=>[4,1,2,3,5,6]=>10000
[[2,2,3,3,3],[3]]=>[3,1,2,4,5,6]=>10000
[[2,3,3,3,3],[3]]=>[2,1,3,4,5,6]=>10000
[[1,1,1,1],[2,3]]=>[5,6,1,2,3,4]=>01000
[[1,1,1,1],[3,3]]=>[5,6,1,2,3,4]=>01000
[[1,1,1,2],[2,3]]=>[4,6,1,2,3,5]=>01000
[[1,1,1,3],[2,2]]=>[4,5,1,2,3,6]=>01000
[[1,1,1,2],[3,3]]=>[5,6,1,2,3,4]=>01000
[[1,1,1,3],[2,3]]=>[4,5,1,2,3,6]=>01000
[[1,1,1,3],[3,3]]=>[4,5,1,2,3,6]=>01000
[[1,1,2,2],[2,3]]=>[3,6,1,2,4,5]=>01000
[[1,1,2,3],[2,2]]=>[3,4,1,2,5,6]=>01000
[[1,1,2,2],[3,3]]=>[5,6,1,2,3,4]=>01000
[[1,1,2,3],[2,3]]=>[3,5,1,2,4,6]=>01000
[[1,1,3,3],[2,2]]=>[3,4,1,2,5,6]=>01000
[[1,1,2,3],[3,3]]=>[4,5,1,2,3,6]=>01000
[[1,1,3,3],[2,3]]=>[3,4,1,2,5,6]=>01000
[[1,1,3,3],[3,3]]=>[3,4,1,2,5,6]=>01000
[[1,2,2,2],[2,3]]=>[2,6,1,3,4,5]=>01000
[[1,2,2,2],[3,3]]=>[5,6,1,2,3,4]=>01000
[[1,2,2,3],[2,3]]=>[2,5,1,3,4,6]=>01000
[[1,2,2,3],[3,3]]=>[4,5,1,2,3,6]=>01000
[[1,2,3,3],[2,3]]=>[2,4,1,3,5,6]=>01000
[[1,2,3,3],[3,3]]=>[3,4,1,2,5,6]=>01000
[[2,2,2,2],[3,3]]=>[5,6,1,2,3,4]=>01000
[[2,2,2,3],[3,3]]=>[4,5,1,2,3,6]=>01000
[[2,2,3,3],[3,3]]=>[3,4,1,2,5,6]=>01000
[[1,1,1,1],[2],[3]]=>[6,5,1,2,3,4]=>11000
[[1,1,1,2],[2],[3]]=>[6,4,1,2,3,5]=>11000
[[1,1,1,3],[2],[3]]=>[5,4,1,2,3,6]=>11000
[[1,1,2,2],[2],[3]]=>[6,3,1,2,4,5]=>11000
[[1,1,2,3],[2],[3]]=>[5,3,1,2,4,6]=>11000
[[1,1,3,3],[2],[3]]=>[4,3,1,2,5,6]=>11000
[[1,2,2,2],[2],[3]]=>[6,2,1,3,4,5]=>11000
[[1,2,2,3],[2],[3]]=>[5,2,1,3,4,6]=>11000
[[1,2,3,3],[2],[3]]=>[4,2,1,3,5,6]=>11000
[[1,3,3,3],[2],[3]]=>[3,2,1,4,5,6]=>11000
[[1,1,1],[2,2,3]]=>[4,5,6,1,2,3]=>00100
[[1,1,1],[2,3,3]]=>[4,5,6,1,2,3]=>00100
[[1,1,1],[3,3,3]]=>[4,5,6,1,2,3]=>00100
[[1,1,2],[2,2,3]]=>[3,4,6,1,2,5]=>00100
[[1,1,2],[2,3,3]]=>[3,5,6,1,2,4]=>00100
[[1,1,2],[3,3,3]]=>[4,5,6,1,2,3]=>00100
[[1,2,2],[2,3,3]]=>[2,5,6,1,3,4]=>00100
[[1,2,2],[3,3,3]]=>[4,5,6,1,2,3]=>00100
[[2,2,2],[3,3,3]]=>[4,5,6,1,2,3]=>00100
[[1,1,1],[2,2],[3]]=>[6,4,5,1,2,3]=>10100
[[1,1,1],[2,3],[3]]=>[5,4,6,1,2,3]=>10100
[[1,1,2],[2,2],[3]]=>[6,3,4,1,2,5]=>10100
[[1,1,2],[2,3],[3]]=>[5,3,6,1,2,4]=>10100
[[1,1,3],[2,2],[3]]=>[5,3,4,1,2,6]=>10100
[[1,1,3],[2,3],[3]]=>[4,3,5,1,2,6]=>10100
[[1,2,2],[2,3],[3]]=>[5,2,6,1,3,4]=>10100
[[1,2,3],[2,3],[3]]=>[4,2,5,1,3,6]=>10100
[[1,1],[2,2],[3,3]]=>[5,6,3,4,1,2]=>01010
[[1,1,1,1,1,1,2]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,1,1,2,2]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,1,2,2,2]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,2,2,2,2]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,2,2,2,2,2]]=>[1,2,3,4,5,6,7]=>000000
[[1,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7]=>000000
[[2,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,1,1,1],[2]]=>[7,1,2,3,4,5,6]=>100000
[[1,1,1,1,1,2],[2]]=>[6,1,2,3,4,5,7]=>100000
[[1,1,1,1,2,2],[2]]=>[5,1,2,3,4,6,7]=>100000
[[1,1,1,2,2,2],[2]]=>[4,1,2,3,5,6,7]=>100000
[[1,1,2,2,2,2],[2]]=>[3,1,2,4,5,6,7]=>100000
[[1,2,2,2,2,2],[2]]=>[2,1,3,4,5,6,7]=>100000
[[1,1,1,1,1],[2,2]]=>[6,7,1,2,3,4,5]=>010000
[[1,1,1,1,2],[2,2]]=>[5,6,1,2,3,4,7]=>010000
[[1,1,1,2,2],[2,2]]=>[4,5,1,2,3,6,7]=>010000
[[1,1,2,2,2],[2,2]]=>[3,4,1,2,5,6,7]=>010000
[[1,1,1,1],[2,2,2]]=>[5,6,7,1,2,3,4]=>001000
[[1,1,1,2],[2,2,2]]=>[4,5,6,1,2,3,7]=>001000
[[1,8]]=>[1,2]=>0
[[2,8]]=>[1,2]=>0
[[3,8]]=>[1,2]=>0
[[4,8]]=>[1,2]=>0
[[5,8]]=>[1,2]=>0
[[6,8]]=>[1,2]=>0
[[7,8]]=>[1,2]=>0
[[8,8]]=>[1,2]=>0
[[1],[8]]=>[2,1]=>1
[[2],[8]]=>[2,1]=>1
[[3],[8]]=>[2,1]=>1
[[4],[8]]=>[2,1]=>1
[[5],[8]]=>[2,1]=>1
[[6],[8]]=>[2,1]=>1
[[7],[8]]=>[2,1]=>1
[[1,1,7]]=>[1,2,3]=>00
[[1,2,7]]=>[1,2,3]=>00
[[1,3,7]]=>[1,2,3]=>00
[[1,4,7]]=>[1,2,3]=>00
[[1,5,7]]=>[1,2,3]=>00
[[1,6,7]]=>[1,2,3]=>00
[[1,7,7]]=>[1,2,3]=>00
[[2,2,7]]=>[1,2,3]=>00
[[2,3,7]]=>[1,2,3]=>00
[[2,4,7]]=>[1,2,3]=>00
[[2,5,7]]=>[1,2,3]=>00
[[2,6,7]]=>[1,2,3]=>00
[[2,7,7]]=>[1,2,3]=>00
[[3,3,7]]=>[1,2,3]=>00
[[3,4,7]]=>[1,2,3]=>00
[[3,5,7]]=>[1,2,3]=>00
[[3,6,7]]=>[1,2,3]=>00
[[3,7,7]]=>[1,2,3]=>00
[[4,4,7]]=>[1,2,3]=>00
[[4,5,7]]=>[1,2,3]=>00
[[4,6,7]]=>[1,2,3]=>00
[[4,7,7]]=>[1,2,3]=>00
[[5,5,7]]=>[1,2,3]=>00
[[5,6,7]]=>[1,2,3]=>00
[[5,7,7]]=>[1,2,3]=>00
[[6,6,7]]=>[1,2,3]=>00
[[6,7,7]]=>[1,2,3]=>00
[[7,7,7]]=>[1,2,3]=>00
[[1,1],[7]]=>[3,1,2]=>10
[[1,2],[7]]=>[3,1,2]=>10
[[1,7],[2]]=>[2,1,3]=>10
[[1,3],[7]]=>[3,1,2]=>10
[[1,7],[3]]=>[2,1,3]=>10
[[1,4],[7]]=>[3,1,2]=>10
[[1,7],[4]]=>[2,1,3]=>10
[[1,5],[7]]=>[3,1,2]=>10
[[1,7],[5]]=>[2,1,3]=>10
[[1,6],[7]]=>[3,1,2]=>10
[[1,7],[6]]=>[2,1,3]=>10
[[1,7],[7]]=>[2,1,3]=>10
[[2,2],[7]]=>[3,1,2]=>10
[[2,3],[7]]=>[3,1,2]=>10
[[2,7],[3]]=>[2,1,3]=>10
[[2,4],[7]]=>[3,1,2]=>10
[[2,7],[4]]=>[2,1,3]=>10
[[2,5],[7]]=>[3,1,2]=>10
[[2,7],[5]]=>[2,1,3]=>10
[[2,6],[7]]=>[3,1,2]=>10
[[2,7],[6]]=>[2,1,3]=>10
[[2,7],[7]]=>[2,1,3]=>10
[[3,3],[7]]=>[3,1,2]=>10
[[3,4],[7]]=>[3,1,2]=>10
[[3,7],[4]]=>[2,1,3]=>10
[[3,5],[7]]=>[3,1,2]=>10
[[3,7],[5]]=>[2,1,3]=>10
[[3,6],[7]]=>[3,1,2]=>10
[[3,7],[6]]=>[2,1,3]=>10
[[3,7],[7]]=>[2,1,3]=>10
[[4,4],[7]]=>[3,1,2]=>10
[[4,5],[7]]=>[3,1,2]=>10
[[4,7],[5]]=>[2,1,3]=>10
[[4,6],[7]]=>[3,1,2]=>10
[[4,7],[6]]=>[2,1,3]=>10
[[4,7],[7]]=>[2,1,3]=>10
[[5,5],[7]]=>[3,1,2]=>10
[[5,6],[7]]=>[3,1,2]=>10
[[5,7],[6]]=>[2,1,3]=>10
[[5,7],[7]]=>[2,1,3]=>10
[[6,6],[7]]=>[3,1,2]=>10
[[6,7],[7]]=>[2,1,3]=>10
[[1],[2],[7]]=>[3,2,1]=>11
[[1],[3],[7]]=>[3,2,1]=>11
[[1],[4],[7]]=>[3,2,1]=>11
[[1],[5],[7]]=>[3,2,1]=>11
[[1],[6],[7]]=>[3,2,1]=>11
[[2],[3],[7]]=>[3,2,1]=>11
[[2],[4],[7]]=>[3,2,1]=>11
[[2],[5],[7]]=>[3,2,1]=>11
[[2],[6],[7]]=>[3,2,1]=>11
[[3],[4],[7]]=>[3,2,1]=>11
[[3],[5],[7]]=>[3,2,1]=>11
[[3],[6],[7]]=>[3,2,1]=>11
[[4],[5],[7]]=>[3,2,1]=>11
[[4],[6],[7]]=>[3,2,1]=>11
[[5],[6],[7]]=>[3,2,1]=>11
[[1,1,1,6]]=>[1,2,3,4]=>000
[[1,1,2,6]]=>[1,2,3,4]=>000
[[1,1,3,6]]=>[1,2,3,4]=>000
[[1,1,4,6]]=>[1,2,3,4]=>000
[[1,1,5,6]]=>[1,2,3,4]=>000
[[1,1,6,6]]=>[1,2,3,4]=>000
[[1,2,2,6]]=>[1,2,3,4]=>000
[[1,2,3,6]]=>[1,2,3,4]=>000
[[1,2,4,6]]=>[1,2,3,4]=>000
[[1,2,5,6]]=>[1,2,3,4]=>000
[[1,2,6,6]]=>[1,2,3,4]=>000
[[1,3,3,6]]=>[1,2,3,4]=>000
[[1,3,4,6]]=>[1,2,3,4]=>000
[[1,3,5,6]]=>[1,2,3,4]=>000
[[1,3,6,6]]=>[1,2,3,4]=>000
[[1,4,4,6]]=>[1,2,3,4]=>000
[[1,4,5,6]]=>[1,2,3,4]=>000
[[1,4,6,6]]=>[1,2,3,4]=>000
[[1,5,5,6]]=>[1,2,3,4]=>000
[[1,5,6,6]]=>[1,2,3,4]=>000
[[1,6,6,6]]=>[1,2,3,4]=>000
[[2,2,2,6]]=>[1,2,3,4]=>000
[[2,2,3,6]]=>[1,2,3,4]=>000
[[2,2,4,6]]=>[1,2,3,4]=>000
[[2,2,5,6]]=>[1,2,3,4]=>000
[[2,2,6,6]]=>[1,2,3,4]=>000
[[2,3,3,6]]=>[1,2,3,4]=>000
[[2,3,4,6]]=>[1,2,3,4]=>000
[[2,3,5,6]]=>[1,2,3,4]=>000
[[2,3,6,6]]=>[1,2,3,4]=>000
[[2,4,4,6]]=>[1,2,3,4]=>000
[[2,4,5,6]]=>[1,2,3,4]=>000
[[2,4,6,6]]=>[1,2,3,4]=>000
[[2,5,5,6]]=>[1,2,3,4]=>000
[[2,5,6,6]]=>[1,2,3,4]=>000
[[2,6,6,6]]=>[1,2,3,4]=>000
[[3,3,3,6]]=>[1,2,3,4]=>000
[[3,3,4,6]]=>[1,2,3,4]=>000
[[3,3,5,6]]=>[1,2,3,4]=>000
[[3,3,6,6]]=>[1,2,3,4]=>000
[[3,4,4,6]]=>[1,2,3,4]=>000
[[3,4,5,6]]=>[1,2,3,4]=>000
[[3,4,6,6]]=>[1,2,3,4]=>000
[[3,5,5,6]]=>[1,2,3,4]=>000
[[3,5,6,6]]=>[1,2,3,4]=>000
[[3,6,6,6]]=>[1,2,3,4]=>000
[[4,4,4,6]]=>[1,2,3,4]=>000
[[4,4,5,6]]=>[1,2,3,4]=>000
[[4,4,6,6]]=>[1,2,3,4]=>000
[[4,5,5,6]]=>[1,2,3,4]=>000
[[4,5,6,6]]=>[1,2,3,4]=>000
[[4,6,6,6]]=>[1,2,3,4]=>000
[[5,5,5,6]]=>[1,2,3,4]=>000
[[5,5,6,6]]=>[1,2,3,4]=>000
[[5,6,6,6]]=>[1,2,3,4]=>000
[[6,6,6,6]]=>[1,2,3,4]=>000
[[1,1,1],[6]]=>[4,1,2,3]=>100
[[1,1,2],[6]]=>[4,1,2,3]=>100
[[1,1,6],[2]]=>[3,1,2,4]=>100
[[1,1,3],[6]]=>[4,1,2,3]=>100
[[1,1,6],[3]]=>[3,1,2,4]=>100
[[1,1,4],[6]]=>[4,1,2,3]=>100
[[1,1,6],[4]]=>[3,1,2,4]=>100
[[1,1,5],[6]]=>[4,1,2,3]=>100
[[1,1,6],[5]]=>[3,1,2,4]=>100
[[1,1,6],[6]]=>[3,1,2,4]=>100
[[1,2,2],[6]]=>[4,1,2,3]=>100
[[1,2,6],[2]]=>[2,1,3,4]=>100
[[1,2,3],[6]]=>[4,1,2,3]=>100
[[1,2,6],[3]]=>[3,1,2,4]=>100
[[1,3,6],[2]]=>[2,1,3,4]=>100
[[1,2,4],[6]]=>[4,1,2,3]=>100
[[1,2,6],[4]]=>[3,1,2,4]=>100
[[1,4,6],[2]]=>[2,1,3,4]=>100
[[1,2,5],[6]]=>[4,1,2,3]=>100
[[1,2,6],[5]]=>[3,1,2,4]=>100
[[1,5,6],[2]]=>[2,1,3,4]=>100
[[1,2,6],[6]]=>[3,1,2,4]=>100
[[1,6,6],[2]]=>[2,1,3,4]=>100
[[1,3,3],[6]]=>[4,1,2,3]=>100
[[1,3,6],[3]]=>[2,1,3,4]=>100
[[1,3,4],[6]]=>[4,1,2,3]=>100
[[1,3,6],[4]]=>[3,1,2,4]=>100
[[1,4,6],[3]]=>[2,1,3,4]=>100
[[1,3,5],[6]]=>[4,1,2,3]=>100
[[1,3,6],[5]]=>[3,1,2,4]=>100
[[1,5,6],[3]]=>[2,1,3,4]=>100
[[1,3,6],[6]]=>[3,1,2,4]=>100
[[1,6,6],[3]]=>[2,1,3,4]=>100
[[1,4,4],[6]]=>[4,1,2,3]=>100
[[1,4,6],[4]]=>[2,1,3,4]=>100
[[1,4,5],[6]]=>[4,1,2,3]=>100
[[1,4,6],[5]]=>[3,1,2,4]=>100
[[1,5,6],[4]]=>[2,1,3,4]=>100
[[1,4,6],[6]]=>[3,1,2,4]=>100
[[1,6,6],[4]]=>[2,1,3,4]=>100
[[1,5,5],[6]]=>[4,1,2,3]=>100
[[1,5,6],[5]]=>[2,1,3,4]=>100
[[1,5,6],[6]]=>[3,1,2,4]=>100
[[1,6,6],[5]]=>[2,1,3,4]=>100
[[1,6,6],[6]]=>[2,1,3,4]=>100
[[2,2,2],[6]]=>[4,1,2,3]=>100
[[2,2,3],[6]]=>[4,1,2,3]=>100
[[2,2,6],[3]]=>[3,1,2,4]=>100
[[2,2,4],[6]]=>[4,1,2,3]=>100
[[2,2,6],[4]]=>[3,1,2,4]=>100
[[2,2,5],[6]]=>[4,1,2,3]=>100
[[2,2,6],[5]]=>[3,1,2,4]=>100
[[2,2,6],[6]]=>[3,1,2,4]=>100
[[2,3,3],[6]]=>[4,1,2,3]=>100
[[2,3,6],[3]]=>[2,1,3,4]=>100
[[2,3,4],[6]]=>[4,1,2,3]=>100
[[2,3,6],[4]]=>[3,1,2,4]=>100
[[2,4,6],[3]]=>[2,1,3,4]=>100
[[2,3,5],[6]]=>[4,1,2,3]=>100
[[2,3,6],[5]]=>[3,1,2,4]=>100
[[2,5,6],[3]]=>[2,1,3,4]=>100
[[2,3,6],[6]]=>[3,1,2,4]=>100
[[2,6,6],[3]]=>[2,1,3,4]=>100
[[2,4,4],[6]]=>[4,1,2,3]=>100
[[2,4,6],[4]]=>[2,1,3,4]=>100
[[2,4,5],[6]]=>[4,1,2,3]=>100
[[2,4,6],[5]]=>[3,1,2,4]=>100
[[2,5,6],[4]]=>[2,1,3,4]=>100
[[2,4,6],[6]]=>[3,1,2,4]=>100
[[2,6,6],[4]]=>[2,1,3,4]=>100
[[2,5,5],[6]]=>[4,1,2,3]=>100
[[2,5,6],[5]]=>[2,1,3,4]=>100
[[2,5,6],[6]]=>[3,1,2,4]=>100
[[2,6,6],[5]]=>[2,1,3,4]=>100
[[2,6,6],[6]]=>[2,1,3,4]=>100
[[3,3,3],[6]]=>[4,1,2,3]=>100
[[3,3,4],[6]]=>[4,1,2,3]=>100
[[3,3,6],[4]]=>[3,1,2,4]=>100
[[3,3,5],[6]]=>[4,1,2,3]=>100
[[3,3,6],[5]]=>[3,1,2,4]=>100
[[3,3,6],[6]]=>[3,1,2,4]=>100
[[3,4,4],[6]]=>[4,1,2,3]=>100
[[3,4,6],[4]]=>[2,1,3,4]=>100
[[3,4,5],[6]]=>[4,1,2,3]=>100
[[3,4,6],[5]]=>[3,1,2,4]=>100
[[3,5,6],[4]]=>[2,1,3,4]=>100
[[3,4,6],[6]]=>[3,1,2,4]=>100
[[3,6,6],[4]]=>[2,1,3,4]=>100
[[3,5,5],[6]]=>[4,1,2,3]=>100
[[3,5,6],[5]]=>[2,1,3,4]=>100
[[3,5,6],[6]]=>[3,1,2,4]=>100
[[3,6,6],[5]]=>[2,1,3,4]=>100
[[3,6,6],[6]]=>[2,1,3,4]=>100
[[4,4,4],[6]]=>[4,1,2,3]=>100
[[4,4,5],[6]]=>[4,1,2,3]=>100
[[4,4,6],[5]]=>[3,1,2,4]=>100
[[4,4,6],[6]]=>[3,1,2,4]=>100
[[4,5,5],[6]]=>[4,1,2,3]=>100
[[4,5,6],[5]]=>[2,1,3,4]=>100
[[4,5,6],[6]]=>[3,1,2,4]=>100
[[4,6,6],[5]]=>[2,1,3,4]=>100
[[4,6,6],[6]]=>[2,1,3,4]=>100
[[5,5,5],[6]]=>[4,1,2,3]=>100
[[5,5,6],[6]]=>[3,1,2,4]=>100
[[5,6,6],[6]]=>[2,1,3,4]=>100
[[1,1],[2,6]]=>[3,4,1,2]=>010
[[1,1],[3,6]]=>[3,4,1,2]=>010
[[1,1],[4,6]]=>[3,4,1,2]=>010
[[1,1],[5,6]]=>[3,4,1,2]=>010
[[1,1],[6,6]]=>[3,4,1,2]=>010
[[1,2],[2,6]]=>[2,4,1,3]=>010
[[1,2],[3,6]]=>[3,4,1,2]=>010
[[1,3],[2,6]]=>[2,4,1,3]=>010
[[1,2],[4,6]]=>[3,4,1,2]=>010
[[1,4],[2,6]]=>[2,4,1,3]=>010
[[1,2],[5,6]]=>[3,4,1,2]=>010
[[1,5],[2,6]]=>[2,4,1,3]=>010
[[1,2],[6,6]]=>[3,4,1,2]=>010
[[1,3],[3,6]]=>[2,4,1,3]=>010
[[1,3],[4,6]]=>[3,4,1,2]=>010
[[1,4],[3,6]]=>[2,4,1,3]=>010
[[1,3],[5,6]]=>[3,4,1,2]=>010
[[1,5],[3,6]]=>[2,4,1,3]=>010
[[1,3],[6,6]]=>[3,4,1,2]=>010
[[1,4],[4,6]]=>[2,4,1,3]=>010
[[1,4],[5,6]]=>[3,4,1,2]=>010
[[1,5],[4,6]]=>[2,4,1,3]=>010
[[1,4],[6,6]]=>[3,4,1,2]=>010
[[1,5],[5,6]]=>[2,4,1,3]=>010
[[1,5],[6,6]]=>[3,4,1,2]=>010
[[2,2],[3,6]]=>[3,4,1,2]=>010
[[2,2],[4,6]]=>[3,4,1,2]=>010
[[2,2],[5,6]]=>[3,4,1,2]=>010
[[2,2],[6,6]]=>[3,4,1,2]=>010
[[2,3],[3,6]]=>[2,4,1,3]=>010
[[2,3],[4,6]]=>[3,4,1,2]=>010
[[2,4],[3,6]]=>[2,4,1,3]=>010
[[2,3],[5,6]]=>[3,4,1,2]=>010
[[2,5],[3,6]]=>[2,4,1,3]=>010
[[2,3],[6,6]]=>[3,4,1,2]=>010
[[2,4],[4,6]]=>[2,4,1,3]=>010
[[2,4],[5,6]]=>[3,4,1,2]=>010
[[2,5],[4,6]]=>[2,4,1,3]=>010
[[2,4],[6,6]]=>[3,4,1,2]=>010
[[2,5],[5,6]]=>[2,4,1,3]=>010
[[2,5],[6,6]]=>[3,4,1,2]=>010
[[3,3],[4,6]]=>[3,4,1,2]=>010
[[3,3],[5,6]]=>[3,4,1,2]=>010
[[3,3],[6,6]]=>[3,4,1,2]=>010
[[3,4],[4,6]]=>[2,4,1,3]=>010
[[3,4],[5,6]]=>[3,4,1,2]=>010
[[3,5],[4,6]]=>[2,4,1,3]=>010
[[3,4],[6,6]]=>[3,4,1,2]=>010
[[3,5],[5,6]]=>[2,4,1,3]=>010
[[3,5],[6,6]]=>[3,4,1,2]=>010
[[4,4],[5,6]]=>[3,4,1,2]=>010
[[4,4],[6,6]]=>[3,4,1,2]=>010
[[4,5],[5,6]]=>[2,4,1,3]=>010
[[4,5],[6,6]]=>[3,4,1,2]=>010
[[5,5],[6,6]]=>[3,4,1,2]=>010
[[1,1],[2],[6]]=>[4,3,1,2]=>110
[[1,1],[3],[6]]=>[4,3,1,2]=>110
[[1,1],[4],[6]]=>[4,3,1,2]=>110
[[1,1],[5],[6]]=>[4,3,1,2]=>110
[[1,2],[2],[6]]=>[4,2,1,3]=>110
[[1,2],[3],[6]]=>[4,3,1,2]=>110
[[1,3],[2],[6]]=>[4,2,1,3]=>110
[[1,6],[2],[3]]=>[3,2,1,4]=>110
[[1,2],[4],[6]]=>[4,3,1,2]=>110
[[1,4],[2],[6]]=>[4,2,1,3]=>110
[[1,6],[2],[4]]=>[3,2,1,4]=>110
[[1,2],[5],[6]]=>[4,3,1,2]=>110
[[1,5],[2],[6]]=>[4,2,1,3]=>110
[[1,6],[2],[5]]=>[3,2,1,4]=>110
[[1,6],[2],[6]]=>[3,2,1,4]=>110
[[1,3],[3],[6]]=>[4,2,1,3]=>110
[[1,3],[4],[6]]=>[4,3,1,2]=>110
[[1,4],[3],[6]]=>[4,2,1,3]=>110
[[1,6],[3],[4]]=>[3,2,1,4]=>110
[[1,3],[5],[6]]=>[4,3,1,2]=>110
[[1,5],[3],[6]]=>[4,2,1,3]=>110
[[1,6],[3],[5]]=>[3,2,1,4]=>110
[[1,6],[3],[6]]=>[3,2,1,4]=>110
[[1,4],[4],[6]]=>[4,2,1,3]=>110
[[1,4],[5],[6]]=>[4,3,1,2]=>110
[[1,5],[4],[6]]=>[4,2,1,3]=>110
[[1,6],[4],[5]]=>[3,2,1,4]=>110
[[1,6],[4],[6]]=>[3,2,1,4]=>110
[[1,5],[5],[6]]=>[4,2,1,3]=>110
[[1,6],[5],[6]]=>[3,2,1,4]=>110
[[2,2],[3],[6]]=>[4,3,1,2]=>110
[[2,2],[4],[6]]=>[4,3,1,2]=>110
[[2,2],[5],[6]]=>[4,3,1,2]=>110
[[2,3],[3],[6]]=>[4,2,1,3]=>110
[[2,3],[4],[6]]=>[4,3,1,2]=>110
[[2,4],[3],[6]]=>[4,2,1,3]=>110
[[2,6],[3],[4]]=>[3,2,1,4]=>110
[[2,3],[5],[6]]=>[4,3,1,2]=>110
[[2,5],[3],[6]]=>[4,2,1,3]=>110
[[2,6],[3],[5]]=>[3,2,1,4]=>110
[[2,6],[3],[6]]=>[3,2,1,4]=>110
[[2,4],[4],[6]]=>[4,2,1,3]=>110
[[2,4],[5],[6]]=>[4,3,1,2]=>110
[[2,5],[4],[6]]=>[4,2,1,3]=>110
[[2,6],[4],[5]]=>[3,2,1,4]=>110
[[2,6],[4],[6]]=>[3,2,1,4]=>110
[[2,5],[5],[6]]=>[4,2,1,3]=>110
[[2,6],[5],[6]]=>[3,2,1,4]=>110
[[3,3],[4],[6]]=>[4,3,1,2]=>110
[[3,3],[5],[6]]=>[4,3,1,2]=>110
[[3,4],[4],[6]]=>[4,2,1,3]=>110
[[3,4],[5],[6]]=>[4,3,1,2]=>110
[[3,5],[4],[6]]=>[4,2,1,3]=>110
[[3,6],[4],[5]]=>[3,2,1,4]=>110
[[3,6],[4],[6]]=>[3,2,1,4]=>110
[[3,5],[5],[6]]=>[4,2,1,3]=>110
[[3,6],[5],[6]]=>[3,2,1,4]=>110
[[4,4],[5],[6]]=>[4,3,1,2]=>110
[[4,5],[5],[6]]=>[4,2,1,3]=>110
[[4,6],[5],[6]]=>[3,2,1,4]=>110
[[1],[2],[3],[6]]=>[4,3,2,1]=>111
[[1],[2],[4],[6]]=>[4,3,2,1]=>111
[[1],[2],[5],[6]]=>[4,3,2,1]=>111
[[1],[3],[4],[6]]=>[4,3,2,1]=>111
[[1],[3],[5],[6]]=>[4,3,2,1]=>111
[[1],[4],[5],[6]]=>[4,3,2,1]=>111
[[2],[3],[4],[6]]=>[4,3,2,1]=>111
[[2],[3],[5],[6]]=>[4,3,2,1]=>111
[[2],[4],[5],[6]]=>[4,3,2,1]=>111
[[3],[4],[5],[6]]=>[4,3,2,1]=>111
[[1,1,1,1,5]]=>[1,2,3,4,5]=>0000
[[1,1,1,2,5]]=>[1,2,3,4,5]=>0000
[[1,1,1,3,5]]=>[1,2,3,4,5]=>0000
[[1,1,1,4,5]]=>[1,2,3,4,5]=>0000
[[1,1,1,5,5]]=>[1,2,3,4,5]=>0000
[[1,1,2,2,5]]=>[1,2,3,4,5]=>0000
[[1,1,2,3,5]]=>[1,2,3,4,5]=>0000
[[1,1,2,4,5]]=>[1,2,3,4,5]=>0000
[[1,1,2,5,5]]=>[1,2,3,4,5]=>0000
[[1,1,3,3,5]]=>[1,2,3,4,5]=>0000
[[1,1,3,4,5]]=>[1,2,3,4,5]=>0000
[[1,1,3,5,5]]=>[1,2,3,4,5]=>0000
[[1,1,4,4,5]]=>[1,2,3,4,5]=>0000
[[1,1,4,5,5]]=>[1,2,3,4,5]=>0000
[[1,1,5,5,5]]=>[1,2,3,4,5]=>0000
[[1,2,2,2,5]]=>[1,2,3,4,5]=>0000
[[1,2,2,3,5]]=>[1,2,3,4,5]=>0000
[[1,2,2,4,5]]=>[1,2,3,4,5]=>0000
[[1,2,2,5,5]]=>[1,2,3,4,5]=>0000
[[1,2,3,3,5]]=>[1,2,3,4,5]=>0000
[[1,2,3,4,5]]=>[1,2,3,4,5]=>0000
[[1,2,3,5,5]]=>[1,2,3,4,5]=>0000
[[1,2,4,4,5]]=>[1,2,3,4,5]=>0000
[[1,2,4,5,5]]=>[1,2,3,4,5]=>0000
[[1,2,5,5,5]]=>[1,2,3,4,5]=>0000
[[1,3,3,3,5]]=>[1,2,3,4,5]=>0000
[[1,3,3,4,5]]=>[1,2,3,4,5]=>0000
[[1,3,3,5,5]]=>[1,2,3,4,5]=>0000
[[1,3,4,4,5]]=>[1,2,3,4,5]=>0000
[[1,3,4,5,5]]=>[1,2,3,4,5]=>0000
[[1,3,5,5,5]]=>[1,2,3,4,5]=>0000
[[1,4,4,4,5]]=>[1,2,3,4,5]=>0000
[[1,4,4,5,5]]=>[1,2,3,4,5]=>0000
[[1,4,5,5,5]]=>[1,2,3,4,5]=>0000
[[1,5,5,5,5]]=>[1,2,3,4,5]=>0000
[[2,2,2,2,5]]=>[1,2,3,4,5]=>0000
[[2,2,2,3,5]]=>[1,2,3,4,5]=>0000
[[2,2,2,4,5]]=>[1,2,3,4,5]=>0000
[[2,2,2,5,5]]=>[1,2,3,4,5]=>0000
[[2,2,3,3,5]]=>[1,2,3,4,5]=>0000
[[2,2,3,4,5]]=>[1,2,3,4,5]=>0000
[[2,2,3,5,5]]=>[1,2,3,4,5]=>0000
[[2,2,4,4,5]]=>[1,2,3,4,5]=>0000
[[2,2,4,5,5]]=>[1,2,3,4,5]=>0000
[[2,2,5,5,5]]=>[1,2,3,4,5]=>0000
[[2,3,3,3,5]]=>[1,2,3,4,5]=>0000
[[2,3,3,4,5]]=>[1,2,3,4,5]=>0000
[[2,3,3,5,5]]=>[1,2,3,4,5]=>0000
[[2,3,4,4,5]]=>[1,2,3,4,5]=>0000
[[2,3,4,5,5]]=>[1,2,3,4,5]=>0000
[[2,3,5,5,5]]=>[1,2,3,4,5]=>0000
[[2,4,4,4,5]]=>[1,2,3,4,5]=>0000
[[2,4,4,5,5]]=>[1,2,3,4,5]=>0000
[[2,4,5,5,5]]=>[1,2,3,4,5]=>0000
[[2,5,5,5,5]]=>[1,2,3,4,5]=>0000
[[3,3,3,3,5]]=>[1,2,3,4,5]=>0000
[[3,3,3,4,5]]=>[1,2,3,4,5]=>0000
[[3,3,3,5,5]]=>[1,2,3,4,5]=>0000
[[3,3,4,4,5]]=>[1,2,3,4,5]=>0000
[[3,3,4,5,5]]=>[1,2,3,4,5]=>0000
[[3,3,5,5,5]]=>[1,2,3,4,5]=>0000
[[3,4,4,4,5]]=>[1,2,3,4,5]=>0000
[[3,4,4,5,5]]=>[1,2,3,4,5]=>0000
[[3,4,5,5,5]]=>[1,2,3,4,5]=>0000
[[3,5,5,5,5]]=>[1,2,3,4,5]=>0000
[[4,4,4,4,5]]=>[1,2,3,4,5]=>0000
[[4,4,4,5,5]]=>[1,2,3,4,5]=>0000
[[4,4,5,5,5]]=>[1,2,3,4,5]=>0000
[[4,5,5,5,5]]=>[1,2,3,4,5]=>0000
[[5,5,5,5,5]]=>[1,2,3,4,5]=>0000
[[1,1,1,1],[5]]=>[5,1,2,3,4]=>1000
[[1,1,1,2],[5]]=>[5,1,2,3,4]=>1000
[[1,1,1,5],[2]]=>[4,1,2,3,5]=>1000
[[1,1,1,3],[5]]=>[5,1,2,3,4]=>1000
[[1,1,1,5],[3]]=>[4,1,2,3,5]=>1000
[[1,1,1,4],[5]]=>[5,1,2,3,4]=>1000
[[1,1,1,5],[4]]=>[4,1,2,3,5]=>1000
[[1,1,1,5],[5]]=>[4,1,2,3,5]=>1000
[[1,1,2,2],[5]]=>[5,1,2,3,4]=>1000
[[1,1,2,5],[2]]=>[3,1,2,4,5]=>1000
[[1,1,2,3],[5]]=>[5,1,2,3,4]=>1000
[[1,1,2,5],[3]]=>[4,1,2,3,5]=>1000
[[1,1,3,5],[2]]=>[3,1,2,4,5]=>1000
[[1,1,2,4],[5]]=>[5,1,2,3,4]=>1000
[[1,1,2,5],[4]]=>[4,1,2,3,5]=>1000
[[1,1,4,5],[2]]=>[3,1,2,4,5]=>1000
[[1,1,2,5],[5]]=>[4,1,2,3,5]=>1000
[[1,1,5,5],[2]]=>[3,1,2,4,5]=>1000
[[1,1,3,3],[5]]=>[5,1,2,3,4]=>1000
[[1,1,3,5],[3]]=>[3,1,2,4,5]=>1000
[[1,1,3,4],[5]]=>[5,1,2,3,4]=>1000
[[1,1,3,5],[4]]=>[4,1,2,3,5]=>1000
[[1,1,4,5],[3]]=>[3,1,2,4,5]=>1000
[[1,1,3,5],[5]]=>[4,1,2,3,5]=>1000
[[1,1,5,5],[3]]=>[3,1,2,4,5]=>1000
[[1,1,4,4],[5]]=>[5,1,2,3,4]=>1000
[[1,1,4,5],[4]]=>[3,1,2,4,5]=>1000
[[1,1,4,5],[5]]=>[4,1,2,3,5]=>1000
[[1,1,5,5],[4]]=>[3,1,2,4,5]=>1000
[[1,1,5,5],[5]]=>[3,1,2,4,5]=>1000
[[1,2,2,2],[5]]=>[5,1,2,3,4]=>1000
[[1,2,2,5],[2]]=>[2,1,3,4,5]=>1000
[[1,2,2,3],[5]]=>[5,1,2,3,4]=>1000
[[1,2,2,5],[3]]=>[4,1,2,3,5]=>1000
[[1,2,3,5],[2]]=>[2,1,3,4,5]=>1000
[[1,2,2,4],[5]]=>[5,1,2,3,4]=>1000
[[1,2,2,5],[4]]=>[4,1,2,3,5]=>1000
[[1,2,4,5],[2]]=>[2,1,3,4,5]=>1000
[[1,2,2,5],[5]]=>[4,1,2,3,5]=>1000
[[1,2,5,5],[2]]=>[2,1,3,4,5]=>1000
[[1,2,3,3],[5]]=>[5,1,2,3,4]=>1000
[[1,2,3,5],[3]]=>[3,1,2,4,5]=>1000
[[1,3,3,5],[2]]=>[2,1,3,4,5]=>1000
[[1,2,3,4],[5]]=>[5,1,2,3,4]=>1000
[[1,2,3,5],[4]]=>[4,1,2,3,5]=>1000
[[1,2,4,5],[3]]=>[3,1,2,4,5]=>1000
[[1,3,4,5],[2]]=>[2,1,3,4,5]=>1000
[[1,2,3,5],[5]]=>[4,1,2,3,5]=>1000
[[1,2,5,5],[3]]=>[3,1,2,4,5]=>1000
[[1,3,5,5],[2]]=>[2,1,3,4,5]=>1000
[[1,2,4,4],[5]]=>[5,1,2,3,4]=>1000
[[1,2,4,5],[4]]=>[3,1,2,4,5]=>1000
[[1,4,4,5],[2]]=>[2,1,3,4,5]=>1000
[[1,2,4,5],[5]]=>[4,1,2,3,5]=>1000
[[1,2,5,5],[4]]=>[3,1,2,4,5]=>1000
[[1,4,5,5],[2]]=>[2,1,3,4,5]=>1000
[[1,2,5,5],[5]]=>[3,1,2,4,5]=>1000
[[1,5,5,5],[2]]=>[2,1,3,4,5]=>1000
[[1,3,3,3],[5]]=>[5,1,2,3,4]=>1000
[[1,3,3,5],[3]]=>[2,1,3,4,5]=>1000
[[1,3,3,4],[5]]=>[5,1,2,3,4]=>1000
[[1,3,3,5],[4]]=>[4,1,2,3,5]=>1000
[[1,3,4,5],[3]]=>[2,1,3,4,5]=>1000
[[1,3,3,5],[5]]=>[4,1,2,3,5]=>1000
[[1,3,5,5],[3]]=>[2,1,3,4,5]=>1000
[[1,3,4,4],[5]]=>[5,1,2,3,4]=>1000
[[1,3,4,5],[4]]=>[3,1,2,4,5]=>1000
[[1,4,4,5],[3]]=>[2,1,3,4,5]=>1000
[[1,3,4,5],[5]]=>[4,1,2,3,5]=>1000
[[1,3,5,5],[4]]=>[3,1,2,4,5]=>1000
[[1,4,5,5],[3]]=>[2,1,3,4,5]=>1000
[[1,3,5,5],[5]]=>[3,1,2,4,5]=>1000
[[1,5,5,5],[3]]=>[2,1,3,4,5]=>1000
[[1,4,4,4],[5]]=>[5,1,2,3,4]=>1000
[[1,4,4,5],[4]]=>[2,1,3,4,5]=>1000
[[1,4,4,5],[5]]=>[4,1,2,3,5]=>1000
[[1,4,5,5],[4]]=>[2,1,3,4,5]=>1000
[[1,4,5,5],[5]]=>[3,1,2,4,5]=>1000
[[1,5,5,5],[4]]=>[2,1,3,4,5]=>1000
[[1,5,5,5],[5]]=>[2,1,3,4,5]=>1000
[[2,2,2,2],[5]]=>[5,1,2,3,4]=>1000
[[2,2,2,3],[5]]=>[5,1,2,3,4]=>1000
[[2,2,2,5],[3]]=>[4,1,2,3,5]=>1000
[[2,2,2,4],[5]]=>[5,1,2,3,4]=>1000
[[2,2,2,5],[4]]=>[4,1,2,3,5]=>1000
[[2,2,2,5],[5]]=>[4,1,2,3,5]=>1000
[[2,2,3,3],[5]]=>[5,1,2,3,4]=>1000
[[2,2,3,5],[3]]=>[3,1,2,4,5]=>1000
[[2,2,3,4],[5]]=>[5,1,2,3,4]=>1000
[[2,2,3,5],[4]]=>[4,1,2,3,5]=>1000
[[2,2,4,5],[3]]=>[3,1,2,4,5]=>1000
[[2,2,3,5],[5]]=>[4,1,2,3,5]=>1000
[[2,2,5,5],[3]]=>[3,1,2,4,5]=>1000
[[2,2,4,4],[5]]=>[5,1,2,3,4]=>1000
[[2,2,4,5],[4]]=>[3,1,2,4,5]=>1000
[[2,2,4,5],[5]]=>[4,1,2,3,5]=>1000
[[2,2,5,5],[4]]=>[3,1,2,4,5]=>1000
[[2,2,5,5],[5]]=>[3,1,2,4,5]=>1000
[[2,3,3,3],[5]]=>[5,1,2,3,4]=>1000
[[2,3,3,5],[3]]=>[2,1,3,4,5]=>1000
[[2,3,3,4],[5]]=>[5,1,2,3,4]=>1000
[[2,3,3,5],[4]]=>[4,1,2,3,5]=>1000
[[2,3,4,5],[3]]=>[2,1,3,4,5]=>1000
[[2,3,3,5],[5]]=>[4,1,2,3,5]=>1000
[[2,3,5,5],[3]]=>[2,1,3,4,5]=>1000
[[2,3,4,4],[5]]=>[5,1,2,3,4]=>1000
[[2,3,4,5],[4]]=>[3,1,2,4,5]=>1000
[[2,4,4,5],[3]]=>[2,1,3,4,5]=>1000
[[2,3,4,5],[5]]=>[4,1,2,3,5]=>1000
[[2,3,5,5],[4]]=>[3,1,2,4,5]=>1000
[[2,4,5,5],[3]]=>[2,1,3,4,5]=>1000
[[2,3,5,5],[5]]=>[3,1,2,4,5]=>1000
[[2,5,5,5],[3]]=>[2,1,3,4,5]=>1000
[[2,4,4,4],[5]]=>[5,1,2,3,4]=>1000
[[2,4,4,5],[4]]=>[2,1,3,4,5]=>1000
[[2,4,4,5],[5]]=>[4,1,2,3,5]=>1000
[[2,4,5,5],[4]]=>[2,1,3,4,5]=>1000
[[2,4,5,5],[5]]=>[3,1,2,4,5]=>1000
[[2,5,5,5],[4]]=>[2,1,3,4,5]=>1000
[[2,5,5,5],[5]]=>[2,1,3,4,5]=>1000
[[3,3,3,3],[5]]=>[5,1,2,3,4]=>1000
[[3,3,3,4],[5]]=>[5,1,2,3,4]=>1000
[[3,3,3,5],[4]]=>[4,1,2,3,5]=>1000
[[3,3,3,5],[5]]=>[4,1,2,3,5]=>1000
[[3,3,4,4],[5]]=>[5,1,2,3,4]=>1000
[[3,3,4,5],[4]]=>[3,1,2,4,5]=>1000
[[3,3,4,5],[5]]=>[4,1,2,3,5]=>1000
[[3,3,5,5],[4]]=>[3,1,2,4,5]=>1000
[[3,3,5,5],[5]]=>[3,1,2,4,5]=>1000
[[3,4,4,4],[5]]=>[5,1,2,3,4]=>1000
[[3,4,4,5],[4]]=>[2,1,3,4,5]=>1000
[[3,4,4,5],[5]]=>[4,1,2,3,5]=>1000
[[3,4,5,5],[4]]=>[2,1,3,4,5]=>1000
[[3,4,5,5],[5]]=>[3,1,2,4,5]=>1000
[[3,5,5,5],[4]]=>[2,1,3,4,5]=>1000
[[3,5,5,5],[5]]=>[2,1,3,4,5]=>1000
[[4,4,4,4],[5]]=>[5,1,2,3,4]=>1000
[[4,4,4,5],[5]]=>[4,1,2,3,5]=>1000
[[4,4,5,5],[5]]=>[3,1,2,4,5]=>1000
[[4,5,5,5],[5]]=>[2,1,3,4,5]=>1000
[[1,1,1],[2,5]]=>[4,5,1,2,3]=>0100
[[1,1,1],[3,5]]=>[4,5,1,2,3]=>0100
[[1,1,1],[4,5]]=>[4,5,1,2,3]=>0100
[[1,1,1],[5,5]]=>[4,5,1,2,3]=>0100
[[1,1,2],[2,5]]=>[3,5,1,2,4]=>0100
[[1,1,5],[2,2]]=>[3,4,1,2,5]=>0100
[[1,1,2],[3,5]]=>[4,5,1,2,3]=>0100
[[1,1,3],[2,5]]=>[3,5,1,2,4]=>0100
[[1,1,5],[2,3]]=>[3,4,1,2,5]=>0100
[[1,1,2],[4,5]]=>[4,5,1,2,3]=>0100
[[1,1,4],[2,5]]=>[3,5,1,2,4]=>0100
[[1,1,5],[2,4]]=>[3,4,1,2,5]=>0100
[[1,1,2],[5,5]]=>[4,5,1,2,3]=>0100
[[1,1,5],[2,5]]=>[3,4,1,2,5]=>0100
[[1,1,3],[3,5]]=>[3,5,1,2,4]=>0100
[[1,1,5],[3,3]]=>[3,4,1,2,5]=>0100
[[1,1,3],[4,5]]=>[4,5,1,2,3]=>0100
[[1,1,4],[3,5]]=>[3,5,1,2,4]=>0100
[[1,1,5],[3,4]]=>[3,4,1,2,5]=>0100
[[1,1,3],[5,5]]=>[4,5,1,2,3]=>0100
[[1,1,5],[3,5]]=>[3,4,1,2,5]=>0100
[[1,1,4],[4,5]]=>[3,5,1,2,4]=>0100
[[1,1,5],[4,4]]=>[3,4,1,2,5]=>0100
[[1,1,4],[5,5]]=>[4,5,1,2,3]=>0100
[[1,1,5],[4,5]]=>[3,4,1,2,5]=>0100
[[1,1,5],[5,5]]=>[3,4,1,2,5]=>0100
[[1,2,2],[2,5]]=>[2,5,1,3,4]=>0100
[[1,2,2],[3,5]]=>[4,5,1,2,3]=>0100
[[1,2,3],[2,5]]=>[2,5,1,3,4]=>0100
[[1,2,5],[2,3]]=>[2,4,1,3,5]=>0100
[[1,2,2],[4,5]]=>[4,5,1,2,3]=>0100
[[1,2,4],[2,5]]=>[2,5,1,3,4]=>0100
[[1,2,5],[2,4]]=>[2,4,1,3,5]=>0100
[[1,2,2],[5,5]]=>[4,5,1,2,3]=>0100
[[1,2,5],[2,5]]=>[2,4,1,3,5]=>0100
[[1,2,3],[3,5]]=>[3,5,1,2,4]=>0100
[[1,2,5],[3,3]]=>[3,4,1,2,5]=>0100
[[1,3,3],[2,5]]=>[2,5,1,3,4]=>0100
[[1,2,3],[4,5]]=>[4,5,1,2,3]=>0100
[[1,2,4],[3,5]]=>[3,5,1,2,4]=>0100
[[1,2,5],[3,4]]=>[3,4,1,2,5]=>0100
[[1,3,4],[2,5]]=>[2,5,1,3,4]=>0100
[[1,3,5],[2,4]]=>[2,4,1,3,5]=>0100
[[1,2,3],[5,5]]=>[4,5,1,2,3]=>0100
[[1,2,5],[3,5]]=>[3,4,1,2,5]=>0100
[[1,3,5],[2,5]]=>[2,4,1,3,5]=>0100
[[1,2,4],[4,5]]=>[3,5,1,2,4]=>0100
[[1,2,5],[4,4]]=>[3,4,1,2,5]=>0100
[[1,4,4],[2,5]]=>[2,5,1,3,4]=>0100
[[1,2,4],[5,5]]=>[4,5,1,2,3]=>0100
[[1,2,5],[4,5]]=>[3,4,1,2,5]=>0100
[[1,4,5],[2,5]]=>[2,4,1,3,5]=>0100
[[1,2,5],[5,5]]=>[3,4,1,2,5]=>0100
[[1,3,3],[3,5]]=>[2,5,1,3,4]=>0100
[[1,3,3],[4,5]]=>[4,5,1,2,3]=>0100
[[1,3,4],[3,5]]=>[2,5,1,3,4]=>0100
[[1,3,5],[3,4]]=>[2,4,1,3,5]=>0100
[[1,3,3],[5,5]]=>[4,5,1,2,3]=>0100
[[1,3,5],[3,5]]=>[2,4,1,3,5]=>0100
[[1,3,4],[4,5]]=>[3,5,1,2,4]=>0100
[[1,3,5],[4,4]]=>[3,4,1,2,5]=>0100
[[1,4,4],[3,5]]=>[2,5,1,3,4]=>0100
[[1,3,4],[5,5]]=>[4,5,1,2,3]=>0100
[[1,3,5],[4,5]]=>[3,4,1,2,5]=>0100
[[1,4,5],[3,5]]=>[2,4,1,3,5]=>0100
[[1,3,5],[5,5]]=>[3,4,1,2,5]=>0100
[[1,4,4],[4,5]]=>[2,5,1,3,4]=>0100
[[1,4,4],[5,5]]=>[4,5,1,2,3]=>0100
[[1,4,5],[4,5]]=>[2,4,1,3,5]=>0100
[[1,4,5],[5,5]]=>[3,4,1,2,5]=>0100
[[2,2,2],[3,5]]=>[4,5,1,2,3]=>0100
[[2,2,2],[4,5]]=>[4,5,1,2,3]=>0100
[[2,2,2],[5,5]]=>[4,5,1,2,3]=>0100
[[2,2,3],[3,5]]=>[3,5,1,2,4]=>0100
[[2,2,5],[3,3]]=>[3,4,1,2,5]=>0100
[[2,2,3],[4,5]]=>[4,5,1,2,3]=>0100
[[2,2,4],[3,5]]=>[3,5,1,2,4]=>0100
[[2,2,5],[3,4]]=>[3,4,1,2,5]=>0100
[[2,2,3],[5,5]]=>[4,5,1,2,3]=>0100
[[2,2,5],[3,5]]=>[3,4,1,2,5]=>0100
[[2,2,4],[4,5]]=>[3,5,1,2,4]=>0100
[[2,2,5],[4,4]]=>[3,4,1,2,5]=>0100
[[2,2,4],[5,5]]=>[4,5,1,2,3]=>0100
[[2,2,5],[4,5]]=>[3,4,1,2,5]=>0100
[[2,2,5],[5,5]]=>[3,4,1,2,5]=>0100
[[2,3,3],[3,5]]=>[2,5,1,3,4]=>0100
[[2,3,3],[4,5]]=>[4,5,1,2,3]=>0100
[[2,3,4],[3,5]]=>[2,5,1,3,4]=>0100
[[2,3,5],[3,4]]=>[2,4,1,3,5]=>0100
[[2,3,3],[5,5]]=>[4,5,1,2,3]=>0100
[[2,3,5],[3,5]]=>[2,4,1,3,5]=>0100
[[2,3,4],[4,5]]=>[3,5,1,2,4]=>0100
[[2,3,5],[4,4]]=>[3,4,1,2,5]=>0100
[[2,4,4],[3,5]]=>[2,5,1,3,4]=>0100
[[2,3,4],[5,5]]=>[4,5,1,2,3]=>0100
[[2,3,5],[4,5]]=>[3,4,1,2,5]=>0100
[[2,4,5],[3,5]]=>[2,4,1,3,5]=>0100
[[2,3,5],[5,5]]=>[3,4,1,2,5]=>0100
[[2,4,4],[4,5]]=>[2,5,1,3,4]=>0100
[[2,4,4],[5,5]]=>[4,5,1,2,3]=>0100
[[2,4,5],[4,5]]=>[2,4,1,3,5]=>0100
[[2,4,5],[5,5]]=>[3,4,1,2,5]=>0100
[[3,3,3],[4,5]]=>[4,5,1,2,3]=>0100
[[3,3,3],[5,5]]=>[4,5,1,2,3]=>0100
[[3,3,4],[4,5]]=>[3,5,1,2,4]=>0100
[[3,3,5],[4,4]]=>[3,4,1,2,5]=>0100
[[3,3,4],[5,5]]=>[4,5,1,2,3]=>0100
[[3,3,5],[4,5]]=>[3,4,1,2,5]=>0100
[[3,3,5],[5,5]]=>[3,4,1,2,5]=>0100
[[3,4,4],[4,5]]=>[2,5,1,3,4]=>0100
[[3,4,4],[5,5]]=>[4,5,1,2,3]=>0100
[[3,4,5],[4,5]]=>[2,4,1,3,5]=>0100
[[3,4,5],[5,5]]=>[3,4,1,2,5]=>0100
[[4,4,4],[5,5]]=>[4,5,1,2,3]=>0100
[[4,4,5],[5,5]]=>[3,4,1,2,5]=>0100
[[1,1,1],[2],[5]]=>[5,4,1,2,3]=>1100
[[1,1,1],[3],[5]]=>[5,4,1,2,3]=>1100
[[1,1,1],[4],[5]]=>[5,4,1,2,3]=>1100
[[1,1,2],[2],[5]]=>[5,3,1,2,4]=>1100
[[1,1,2],[3],[5]]=>[5,4,1,2,3]=>1100
[[1,1,3],[2],[5]]=>[5,3,1,2,4]=>1100
[[1,1,5],[2],[3]]=>[4,3,1,2,5]=>1100
[[1,1,2],[4],[5]]=>[5,4,1,2,3]=>1100
[[1,1,4],[2],[5]]=>[5,3,1,2,4]=>1100
[[1,1,5],[2],[4]]=>[4,3,1,2,5]=>1100
[[1,1,5],[2],[5]]=>[4,3,1,2,5]=>1100
[[1,1,3],[3],[5]]=>[5,3,1,2,4]=>1100
[[1,1,3],[4],[5]]=>[5,4,1,2,3]=>1100
[[1,1,4],[3],[5]]=>[5,3,1,2,4]=>1100
[[1,1,5],[3],[4]]=>[4,3,1,2,5]=>1100
[[1,1,5],[3],[5]]=>[4,3,1,2,5]=>1100
[[1,1,4],[4],[5]]=>[5,3,1,2,4]=>1100
[[1,1,5],[4],[5]]=>[4,3,1,2,5]=>1100
[[1,2,2],[2],[5]]=>[5,2,1,3,4]=>1100
[[1,2,2],[3],[5]]=>[5,4,1,2,3]=>1100
[[1,2,3],[2],[5]]=>[5,2,1,3,4]=>1100
[[1,2,5],[2],[3]]=>[4,2,1,3,5]=>1100
[[1,2,2],[4],[5]]=>[5,4,1,2,3]=>1100
[[1,2,4],[2],[5]]=>[5,2,1,3,4]=>1100
[[1,2,5],[2],[4]]=>[4,2,1,3,5]=>1100
[[1,2,5],[2],[5]]=>[4,2,1,3,5]=>1100
[[1,2,3],[3],[5]]=>[5,3,1,2,4]=>1100
[[1,3,3],[2],[5]]=>[5,2,1,3,4]=>1100
[[1,3,5],[2],[3]]=>[3,2,1,4,5]=>1100
[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>1100
[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>1100
[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>1100
[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>1100
[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>1100
[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>1100
[[1,2,5],[3],[5]]=>[4,3,1,2,5]=>1100
[[1,3,5],[2],[5]]=>[4,2,1,3,5]=>1100
[[1,5,5],[2],[3]]=>[3,2,1,4,5]=>1100
[[1,2,4],[4],[5]]=>[5,3,1,2,4]=>1100
[[1,4,4],[2],[5]]=>[5,2,1,3,4]=>1100
[[1,4,5],[2],[4]]=>[3,2,1,4,5]=>1100
[[1,2,5],[4],[5]]=>[4,3,1,2,5]=>1100
[[1,4,5],[2],[5]]=>[4,2,1,3,5]=>1100
[[1,5,5],[2],[4]]=>[3,2,1,4,5]=>1100
[[1,5,5],[2],[5]]=>[3,2,1,4,5]=>1100
[[1,3,3],[3],[5]]=>[5,2,1,3,4]=>1100
[[1,3,3],[4],[5]]=>[5,4,1,2,3]=>1100
[[1,3,4],[3],[5]]=>[5,2,1,3,4]=>1100
[[1,3,5],[3],[4]]=>[4,2,1,3,5]=>1100
[[1,3,5],[3],[5]]=>[4,2,1,3,5]=>1100
[[1,3,4],[4],[5]]=>[5,3,1,2,4]=>1100
[[1,4,4],[3],[5]]=>[5,2,1,3,4]=>1100
[[1,4,5],[3],[4]]=>[3,2,1,4,5]=>1100
[[1,3,5],[4],[5]]=>[4,3,1,2,5]=>1100
[[1,4,5],[3],[5]]=>[4,2,1,3,5]=>1100
[[1,5,5],[3],[4]]=>[3,2,1,4,5]=>1100
[[1,5,5],[3],[5]]=>[3,2,1,4,5]=>1100
[[1,4,4],[4],[5]]=>[5,2,1,3,4]=>1100
[[1,4,5],[4],[5]]=>[4,2,1,3,5]=>1100
[[1,5,5],[4],[5]]=>[3,2,1,4,5]=>1100
[[2,2,2],[3],[5]]=>[5,4,1,2,3]=>1100
[[2,2,2],[4],[5]]=>[5,4,1,2,3]=>1100
[[2,2,3],[3],[5]]=>[5,3,1,2,4]=>1100
[[2,2,3],[4],[5]]=>[5,4,1,2,3]=>1100
[[2,2,4],[3],[5]]=>[5,3,1,2,4]=>1100
[[2,2,5],[3],[4]]=>[4,3,1,2,5]=>1100
[[2,2,5],[3],[5]]=>[4,3,1,2,5]=>1100
[[2,2,4],[4],[5]]=>[5,3,1,2,4]=>1100
[[2,2,5],[4],[5]]=>[4,3,1,2,5]=>1100
[[2,3,3],[3],[5]]=>[5,2,1,3,4]=>1100
[[2,3,3],[4],[5]]=>[5,4,1,2,3]=>1100
[[2,3,4],[3],[5]]=>[5,2,1,3,4]=>1100
[[2,3,5],[3],[4]]=>[4,2,1,3,5]=>1100
[[2,3,5],[3],[5]]=>[4,2,1,3,5]=>1100
[[2,3,4],[4],[5]]=>[5,3,1,2,4]=>1100
[[2,4,4],[3],[5]]=>[5,2,1,3,4]=>1100
[[2,4,5],[3],[4]]=>[3,2,1,4,5]=>1100
[[2,3,5],[4],[5]]=>[4,3,1,2,5]=>1100
[[2,4,5],[3],[5]]=>[4,2,1,3,5]=>1100
[[2,5,5],[3],[4]]=>[3,2,1,4,5]=>1100
[[2,5,5],[3],[5]]=>[3,2,1,4,5]=>1100
[[2,4,4],[4],[5]]=>[5,2,1,3,4]=>1100
[[2,4,5],[4],[5]]=>[4,2,1,3,5]=>1100
[[2,5,5],[4],[5]]=>[3,2,1,4,5]=>1100
[[3,3,3],[4],[5]]=>[5,4,1,2,3]=>1100
[[3,3,4],[4],[5]]=>[5,3,1,2,4]=>1100
[[3,3,5],[4],[5]]=>[4,3,1,2,5]=>1100
[[3,4,4],[4],[5]]=>[5,2,1,3,4]=>1100
[[3,4,5],[4],[5]]=>[4,2,1,3,5]=>1100
[[3,5,5],[4],[5]]=>[3,2,1,4,5]=>1100
[[1,1],[2,2],[5]]=>[5,3,4,1,2]=>1010
[[1,1],[2,3],[5]]=>[5,3,4,1,2]=>1010
[[1,1],[2,5],[3]]=>[4,3,5,1,2]=>1010
[[1,1],[2,4],[5]]=>[5,3,4,1,2]=>1010
[[1,1],[2,5],[4]]=>[4,3,5,1,2]=>1010
[[1,1],[2,5],[5]]=>[4,3,5,1,2]=>1010
[[1,1],[3,3],[5]]=>[5,3,4,1,2]=>1010
[[1,1],[3,4],[5]]=>[5,3,4,1,2]=>1010
[[1,1],[3,5],[4]]=>[4,3,5,1,2]=>1010
[[1,1],[3,5],[5]]=>[4,3,5,1,2]=>1010
[[1,1],[4,4],[5]]=>[5,3,4,1,2]=>1010
[[1,1],[4,5],[5]]=>[4,3,5,1,2]=>1010
[[1,2],[2,3],[5]]=>[5,2,4,1,3]=>1010
[[1,2],[2,5],[3]]=>[4,2,5,1,3]=>1010
[[1,2],[2,4],[5]]=>[5,2,4,1,3]=>1010
[[1,2],[2,5],[4]]=>[4,2,5,1,3]=>1010
[[1,2],[2,5],[5]]=>[4,2,5,1,3]=>1010
[[1,2],[3,3],[5]]=>[5,3,4,1,2]=>1010
[[1,3],[2,5],[3]]=>[3,2,5,1,4]=>1010
[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>1010
[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>1010
[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>1010
[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>1010
[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>1010
[[1,2],[3,5],[5]]=>[4,3,5,1,2]=>1010
[[1,3],[2,5],[5]]=>[4,2,5,1,3]=>1010
[[1,2],[4,4],[5]]=>[5,3,4,1,2]=>1010
[[1,4],[2,5],[4]]=>[3,2,5,1,4]=>1010
[[1,2],[4,5],[5]]=>[4,3,5,1,2]=>1010
[[1,4],[2,5],[5]]=>[4,2,5,1,3]=>1010
[[1,3],[3,4],[5]]=>[5,2,4,1,3]=>1010
[[1,3],[3,5],[4]]=>[4,2,5,1,3]=>1010
[[1,3],[3,5],[5]]=>[4,2,5,1,3]=>1010
[[1,3],[4,4],[5]]=>[5,3,4,1,2]=>1010
[[1,4],[3,5],[4]]=>[3,2,5,1,4]=>1010
[[1,3],[4,5],[5]]=>[4,3,5,1,2]=>1010
[[1,4],[3,5],[5]]=>[4,2,5,1,3]=>1010
[[1,4],[4,5],[5]]=>[4,2,5,1,3]=>1010
[[2,2],[3,3],[5]]=>[5,3,4,1,2]=>1010
[[2,2],[3,4],[5]]=>[5,3,4,1,2]=>1010
[[2,2],[3,5],[4]]=>[4,3,5,1,2]=>1010
[[2,2],[3,5],[5]]=>[4,3,5,1,2]=>1010
[[2,2],[4,4],[5]]=>[5,3,4,1,2]=>1010
[[2,2],[4,5],[5]]=>[4,3,5,1,2]=>1010
[[2,3],[3,4],[5]]=>[5,2,4,1,3]=>1010
[[2,3],[3,5],[4]]=>[4,2,5,1,3]=>1010
[[2,3],[3,5],[5]]=>[4,2,5,1,3]=>1010
[[2,3],[4,4],[5]]=>[5,3,4,1,2]=>1010
[[2,4],[3,5],[4]]=>[3,2,5,1,4]=>1010
[[2,3],[4,5],[5]]=>[4,3,5,1,2]=>1010
[[2,4],[3,5],[5]]=>[4,2,5,1,3]=>1010
[[2,4],[4,5],[5]]=>[4,2,5,1,3]=>1010
[[3,3],[4,4],[5]]=>[5,3,4,1,2]=>1010
[[3,3],[4,5],[5]]=>[4,3,5,1,2]=>1010
[[3,4],[4,5],[5]]=>[4,2,5,1,3]=>1010
[[1,1],[2],[3],[5]]=>[5,4,3,1,2]=>1110
[[1,1],[2],[4],[5]]=>[5,4,3,1,2]=>1110
[[1,1],[3],[4],[5]]=>[5,4,3,1,2]=>1110
[[1,2],[2],[3],[5]]=>[5,4,2,1,3]=>1110
[[1,2],[2],[4],[5]]=>[5,4,2,1,3]=>1110
[[1,3],[2],[3],[5]]=>[5,3,2,1,4]=>1110
[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>1110
[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>1110
[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>1110
[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>1110
[[1,5],[2],[3],[5]]=>[4,3,2,1,5]=>1110
[[1,4],[2],[4],[5]]=>[5,3,2,1,4]=>1110
[[1,5],[2],[4],[5]]=>[4,3,2,1,5]=>1110
[[1,3],[3],[4],[5]]=>[5,4,2,1,3]=>1110
[[1,4],[3],[4],[5]]=>[5,3,2,1,4]=>1110
[[1,5],[3],[4],[5]]=>[4,3,2,1,5]=>1110
[[2,2],[3],[4],[5]]=>[5,4,3,1,2]=>1110
[[2,3],[3],[4],[5]]=>[5,4,2,1,3]=>1110
[[2,4],[3],[4],[5]]=>[5,3,2,1,4]=>1110
[[2,5],[3],[4],[5]]=>[4,3,2,1,5]=>1110
[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>1111
[[1,1,1,1,1,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,1,2,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,1,3,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,1,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,2,2,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,2,3,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,2,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,3,3,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,3,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,2,2,2,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,2,2,3,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,2,2,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,2,3,3,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,2,3,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,2,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,3,3,3,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,3,3,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,3,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,4,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,2,2,2,2,4]]=>[1,2,3,4,5,6]=>00000
[[1,2,2,2,3,4]]=>[1,2,3,4,5,6]=>00000
[[1,2,2,2,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,2,2,3,3,4]]=>[1,2,3,4,5,6]=>00000
[[1,2,2,3,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,2,2,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,2,3,3,3,4]]=>[1,2,3,4,5,6]=>00000
[[1,2,3,3,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,2,3,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,2,4,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,3,3,3,3,4]]=>[1,2,3,4,5,6]=>00000
[[1,3,3,3,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,3,3,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,3,4,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,4,4,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[2,2,2,2,2,4]]=>[1,2,3,4,5,6]=>00000
[[2,2,2,2,3,4]]=>[1,2,3,4,5,6]=>00000
[[2,2,2,2,4,4]]=>[1,2,3,4,5,6]=>00000
[[2,2,2,3,3,4]]=>[1,2,3,4,5,6]=>00000
[[2,2,2,3,4,4]]=>[1,2,3,4,5,6]=>00000
[[2,2,2,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[2,2,3,3,3,4]]=>[1,2,3,4,5,6]=>00000
[[2,2,3,3,4,4]]=>[1,2,3,4,5,6]=>00000
[[2,2,3,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[2,2,4,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[2,3,3,3,3,4]]=>[1,2,3,4,5,6]=>00000
[[2,3,3,3,4,4]]=>[1,2,3,4,5,6]=>00000
[[2,3,3,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[2,3,4,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[2,4,4,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[3,3,3,3,3,4]]=>[1,2,3,4,5,6]=>00000
[[3,3,3,3,4,4]]=>[1,2,3,4,5,6]=>00000
[[3,3,3,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[3,3,4,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[3,4,4,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[4,4,4,4,4,4]]=>[1,2,3,4,5,6]=>00000
[[1,1,1,1,1],[4]]=>[6,1,2,3,4,5]=>10000
[[1,1,1,1,2],[4]]=>[6,1,2,3,4,5]=>10000
[[1,1,1,1,4],[2]]=>[5,1,2,3,4,6]=>10000
[[1,1,1,1,3],[4]]=>[6,1,2,3,4,5]=>10000
[[1,1,1,1,4],[3]]=>[5,1,2,3,4,6]=>10000
[[1,1,1,1,4],[4]]=>[5,1,2,3,4,6]=>10000
[[1,1,1,2,2],[4]]=>[6,1,2,3,4,5]=>10000
[[1,1,1,2,4],[2]]=>[4,1,2,3,5,6]=>10000
[[1,1,1,2,3],[4]]=>[6,1,2,3,4,5]=>10000
[[1,1,1,2,4],[3]]=>[5,1,2,3,4,6]=>10000
[[1,1,1,3,4],[2]]=>[4,1,2,3,5,6]=>10000
[[1,1,1,2,4],[4]]=>[5,1,2,3,4,6]=>10000
[[1,1,1,4,4],[2]]=>[4,1,2,3,5,6]=>10000
[[1,1,1,3,3],[4]]=>[6,1,2,3,4,5]=>10000
[[1,1,1,3,4],[3]]=>[4,1,2,3,5,6]=>10000
[[1,1,1,3,4],[4]]=>[5,1,2,3,4,6]=>10000
[[1,1,1,4,4],[3]]=>[4,1,2,3,5,6]=>10000
[[1,1,1,4,4],[4]]=>[4,1,2,3,5,6]=>10000
[[1,1,2,2,2],[4]]=>[6,1,2,3,4,5]=>10000
[[1,1,2,2,4],[2]]=>[3,1,2,4,5,6]=>10000
[[1,1,2,2,3],[4]]=>[6,1,2,3,4,5]=>10000
[[1,1,2,2,4],[3]]=>[5,1,2,3,4,6]=>10000
[[1,1,2,3,4],[2]]=>[3,1,2,4,5,6]=>10000
[[1,1,2,2,4],[4]]=>[5,1,2,3,4,6]=>10000
[[1,1,2,4,4],[2]]=>[3,1,2,4,5,6]=>10000
[[1,1,2,3,3],[4]]=>[6,1,2,3,4,5]=>10000
[[1,1,2,3,4],[3]]=>[4,1,2,3,5,6]=>10000
[[1,1,3,3,4],[2]]=>[3,1,2,4,5,6]=>10000
[[1,1,2,3,4],[4]]=>[5,1,2,3,4,6]=>10000
[[1,1,2,4,4],[3]]=>[4,1,2,3,5,6]=>10000
[[1,1,3,4,4],[2]]=>[3,1,2,4,5,6]=>10000
[[1,1,2,4,4],[4]]=>[4,1,2,3,5,6]=>10000
[[1,1,4,4,4],[2]]=>[3,1,2,4,5,6]=>10000
[[1,1,3,3,3],[4]]=>[6,1,2,3,4,5]=>10000
[[1,1,3,3,4],[3]]=>[3,1,2,4,5,6]=>10000
[[1,1,3,3,4],[4]]=>[5,1,2,3,4,6]=>10000
[[1,1,3,4,4],[3]]=>[3,1,2,4,5,6]=>10000
[[1,1,3,4,4],[4]]=>[4,1,2,3,5,6]=>10000
[[1,1,4,4,4],[3]]=>[3,1,2,4,5,6]=>10000
[[1,1,4,4,4],[4]]=>[3,1,2,4,5,6]=>10000
[[1,2,2,2,2],[4]]=>[6,1,2,3,4,5]=>10000
[[1,2,2,2,4],[2]]=>[2,1,3,4,5,6]=>10000
[[1,2,2,2,3],[4]]=>[6,1,2,3,4,5]=>10000
[[1,2,2,2,4],[3]]=>[5,1,2,3,4,6]=>10000
[[1,2,2,3,4],[2]]=>[2,1,3,4,5,6]=>10000
[[1,2,2,2,4],[4]]=>[5,1,2,3,4,6]=>10000
[[1,2,2,4,4],[2]]=>[2,1,3,4,5,6]=>10000
[[1,2,2,3,3],[4]]=>[6,1,2,3,4,5]=>10000
[[1,2,2,3,4],[3]]=>[4,1,2,3,5,6]=>10000
[[1,2,3,3,4],[2]]=>[2,1,3,4,5,6]=>10000
[[1,2,2,3,4],[4]]=>[5,1,2,3,4,6]=>10000
[[1,2,2,4,4],[3]]=>[4,1,2,3,5,6]=>10000
[[1,2,3,4,4],[2]]=>[2,1,3,4,5,6]=>10000
[[1,2,2,4,4],[4]]=>[4,1,2,3,5,6]=>10000
[[1,2,4,4,4],[2]]=>[2,1,3,4,5,6]=>10000
[[1,2,3,3,3],[4]]=>[6,1,2,3,4,5]=>10000
[[1,2,3,3,4],[3]]=>[3,1,2,4,5,6]=>10000
[[1,3,3,3,4],[2]]=>[2,1,3,4,5,6]=>10000
[[1,2,3,3,4],[4]]=>[5,1,2,3,4,6]=>10000
[[1,2,3,4,4],[3]]=>[3,1,2,4,5,6]=>10000
[[1,3,3,4,4],[2]]=>[2,1,3,4,5,6]=>10000
[[1,2,3,4,4],[4]]=>[4,1,2,3,5,6]=>10000
[[1,2,4,4,4],[3]]=>[3,1,2,4,5,6]=>10000
[[1,3,4,4,4],[2]]=>[2,1,3,4,5,6]=>10000
[[1,2,4,4,4],[4]]=>[3,1,2,4,5,6]=>10000
[[1,4,4,4,4],[2]]=>[2,1,3,4,5,6]=>10000
[[1,3,3,3,3],[4]]=>[6,1,2,3,4,5]=>10000
[[1,3,3,3,4],[3]]=>[2,1,3,4,5,6]=>10000
[[1,3,3,3,4],[4]]=>[5,1,2,3,4,6]=>10000
[[1,3,3,4,4],[3]]=>[2,1,3,4,5,6]=>10000
[[1,3,3,4,4],[4]]=>[4,1,2,3,5,6]=>10000
[[1,3,4,4,4],[3]]=>[2,1,3,4,5,6]=>10000
[[1,3,4,4,4],[4]]=>[3,1,2,4,5,6]=>10000
[[1,4,4,4,4],[3]]=>[2,1,3,4,5,6]=>10000
[[1,4,4,4,4],[4]]=>[2,1,3,4,5,6]=>10000
[[2,2,2,2,2],[4]]=>[6,1,2,3,4,5]=>10000
[[2,2,2,2,3],[4]]=>[6,1,2,3,4,5]=>10000
[[2,2,2,2,4],[3]]=>[5,1,2,3,4,6]=>10000
[[2,2,2,2,4],[4]]=>[5,1,2,3,4,6]=>10000
[[2,2,2,3,3],[4]]=>[6,1,2,3,4,5]=>10000
[[2,2,2,3,4],[3]]=>[4,1,2,3,5,6]=>10000
[[2,2,2,3,4],[4]]=>[5,1,2,3,4,6]=>10000
[[2,2,2,4,4],[3]]=>[4,1,2,3,5,6]=>10000
[[2,2,2,4,4],[4]]=>[4,1,2,3,5,6]=>10000
[[2,2,3,3,3],[4]]=>[6,1,2,3,4,5]=>10000
[[2,2,3,3,4],[3]]=>[3,1,2,4,5,6]=>10000
[[2,2,3,3,4],[4]]=>[5,1,2,3,4,6]=>10000
[[2,2,3,4,4],[3]]=>[3,1,2,4,5,6]=>10000
[[2,2,3,4,4],[4]]=>[4,1,2,3,5,6]=>10000
[[2,2,4,4,4],[3]]=>[3,1,2,4,5,6]=>10000
[[2,2,4,4,4],[4]]=>[3,1,2,4,5,6]=>10000
[[2,3,3,3,3],[4]]=>[6,1,2,3,4,5]=>10000
[[2,3,3,3,4],[3]]=>[2,1,3,4,5,6]=>10000
[[2,3,3,3,4],[4]]=>[5,1,2,3,4,6]=>10000
[[2,3,3,4,4],[3]]=>[2,1,3,4,5,6]=>10000
[[2,3,3,4,4],[4]]=>[4,1,2,3,5,6]=>10000
[[2,3,4,4,4],[3]]=>[2,1,3,4,5,6]=>10000
[[2,3,4,4,4],[4]]=>[3,1,2,4,5,6]=>10000
[[2,4,4,4,4],[3]]=>[2,1,3,4,5,6]=>10000
[[2,4,4,4,4],[4]]=>[2,1,3,4,5,6]=>10000
[[3,3,3,3,3],[4]]=>[6,1,2,3,4,5]=>10000
[[3,3,3,3,4],[4]]=>[5,1,2,3,4,6]=>10000
[[3,3,3,4,4],[4]]=>[4,1,2,3,5,6]=>10000
[[3,3,4,4,4],[4]]=>[3,1,2,4,5,6]=>10000
[[3,4,4,4,4],[4]]=>[2,1,3,4,5,6]=>10000
[[1,1,1,1],[2,4]]=>[5,6,1,2,3,4]=>01000
[[1,1,1,1],[3,4]]=>[5,6,1,2,3,4]=>01000
[[1,1,1,1],[4,4]]=>[5,6,1,2,3,4]=>01000
[[1,1,1,2],[2,4]]=>[4,6,1,2,3,5]=>01000
[[1,1,1,4],[2,2]]=>[4,5,1,2,3,6]=>01000
[[1,1,1,2],[3,4]]=>[5,6,1,2,3,4]=>01000
[[1,1,1,3],[2,4]]=>[4,6,1,2,3,5]=>01000
[[1,1,1,4],[2,3]]=>[4,5,1,2,3,6]=>01000
[[1,1,1,2],[4,4]]=>[5,6,1,2,3,4]=>01000
[[1,1,1,4],[2,4]]=>[4,5,1,2,3,6]=>01000
[[1,1,1,3],[3,4]]=>[4,6,1,2,3,5]=>01000
[[1,1,1,4],[3,3]]=>[4,5,1,2,3,6]=>01000
[[1,1,1,3],[4,4]]=>[5,6,1,2,3,4]=>01000
[[1,1,1,4],[3,4]]=>[4,5,1,2,3,6]=>01000
[[1,1,1,4],[4,4]]=>[4,5,1,2,3,6]=>01000
[[1,1,2,2],[2,4]]=>[3,6,1,2,4,5]=>01000
[[1,1,2,4],[2,2]]=>[3,4,1,2,5,6]=>01000
[[1,1,2,2],[3,4]]=>[5,6,1,2,3,4]=>01000
[[1,1,2,3],[2,4]]=>[3,6,1,2,4,5]=>01000
[[1,1,2,4],[2,3]]=>[3,5,1,2,4,6]=>01000
[[1,1,3,4],[2,2]]=>[3,4,1,2,5,6]=>01000
[[1,1,2,2],[4,4]]=>[5,6,1,2,3,4]=>01000
[[1,1,2,4],[2,4]]=>[3,5,1,2,4,6]=>01000
[[1,1,4,4],[2,2]]=>[3,4,1,2,5,6]=>01000
[[1,1,2,3],[3,4]]=>[4,6,1,2,3,5]=>01000
[[1,1,2,4],[3,3]]=>[4,5,1,2,3,6]=>01000
[[1,1,3,3],[2,4]]=>[3,6,1,2,4,5]=>01000
[[1,1,3,4],[2,3]]=>[3,4,1,2,5,6]=>01000
[[1,1,2,3],[4,4]]=>[5,6,1,2,3,4]=>01000
[[1,1,2,4],[3,4]]=>[4,5,1,2,3,6]=>01000
[[1,1,3,4],[2,4]]=>[3,5,1,2,4,6]=>01000
[[1,1,4,4],[2,3]]=>[3,4,1,2,5,6]=>01000
[[1,1,2,4],[4,4]]=>[4,5,1,2,3,6]=>01000
[[1,1,4,4],[2,4]]=>[3,4,1,2,5,6]=>01000
[[1,1,3,3],[3,4]]=>[3,6,1,2,4,5]=>01000
[[1,1,3,4],[3,3]]=>[3,4,1,2,5,6]=>01000
[[1,1,3,3],[4,4]]=>[5,6,1,2,3,4]=>01000
[[1,1,3,4],[3,4]]=>[3,5,1,2,4,6]=>01000
[[1,1,4,4],[3,3]]=>[3,4,1,2,5,6]=>01000
[[1,1,3,4],[4,4]]=>[4,5,1,2,3,6]=>01000
[[1,1,4,4],[3,4]]=>[3,4,1,2,5,6]=>01000
[[1,1,4,4],[4,4]]=>[3,4,1,2,5,6]=>01000
[[1,2,2,2],[2,4]]=>[2,6,1,3,4,5]=>01000
[[1,2,2,2],[3,4]]=>[5,6,1,2,3,4]=>01000
[[1,2,2,3],[2,4]]=>[2,6,1,3,4,5]=>01000
[[1,2,2,4],[2,3]]=>[2,5,1,3,4,6]=>01000
[[1,2,2,2],[4,4]]=>[5,6,1,2,3,4]=>01000
[[1,2,2,4],[2,4]]=>[2,5,1,3,4,6]=>01000
[[1,2,2,3],[3,4]]=>[4,6,1,2,3,5]=>01000
[[1,2,2,4],[3,3]]=>[4,5,1,2,3,6]=>01000
[[1,2,3,3],[2,4]]=>[2,6,1,3,4,5]=>01000
[[1,2,3,4],[2,3]]=>[2,4,1,3,5,6]=>01000
[[1,2,2,3],[4,4]]=>[5,6,1,2,3,4]=>01000
[[1,2,2,4],[3,4]]=>[4,5,1,2,3,6]=>01000
[[1,2,3,4],[2,4]]=>[2,5,1,3,4,6]=>01000
[[1,2,4,4],[2,3]]=>[2,4,1,3,5,6]=>01000
[[1,2,2,4],[4,4]]=>[4,5,1,2,3,6]=>01000
[[1,2,4,4],[2,4]]=>[2,4,1,3,5,6]=>01000
[[1,2,3,3],[3,4]]=>[3,6,1,2,4,5]=>01000
[[1,2,3,4],[3,3]]=>[3,4,1,2,5,6]=>01000
[[1,3,3,3],[2,4]]=>[2,6,1,3,4,5]=>01000
[[1,2,3,3],[4,4]]=>[5,6,1,2,3,4]=>01000
[[1,2,3,4],[3,4]]=>[3,5,1,2,4,6]=>01000
[[1,2,4,4],[3,3]]=>[3,4,1,2,5,6]=>01000
[[1,3,3,4],[2,4]]=>[2,5,1,3,4,6]=>01000
[[1,2,3,4],[4,4]]=>[4,5,1,2,3,6]=>01000
[[1,2,4,4],[3,4]]=>[3,4,1,2,5,6]=>01000
[[1,3,4,4],[2,4]]=>[2,4,1,3,5,6]=>01000
[[1,2,4,4],[4,4]]=>[3,4,1,2,5,6]=>01000
[[1,3,3,3],[3,4]]=>[2,6,1,3,4,5]=>01000
[[1,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>01000
[[1,3,3,4],[3,4]]=>[2,5,1,3,4,6]=>01000
[[1,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>01000
[[1,3,4,4],[3,4]]=>[2,4,1,3,5,6]=>01000
[[1,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>01000
[[2,2,2,2],[3,4]]=>[5,6,1,2,3,4]=>01000
[[2,2,2,2],[4,4]]=>[5,6,1,2,3,4]=>01000
[[2,2,2,3],[3,4]]=>[4,6,1,2,3,5]=>01000
[[2,2,2,4],[3,3]]=>[4,5,1,2,3,6]=>01000
[[2,2,2,3],[4,4]]=>[5,6,1,2,3,4]=>01000
[[2,2,2,4],[3,4]]=>[4,5,1,2,3,6]=>01000
[[2,2,2,4],[4,4]]=>[4,5,1,2,3,6]=>01000
[[2,2,3,3],[3,4]]=>[3,6,1,2,4,5]=>01000
[[2,2,3,4],[3,3]]=>[3,4,1,2,5,6]=>01000
[[2,2,3,3],[4,4]]=>[5,6,1,2,3,4]=>01000
[[2,2,3,4],[3,4]]=>[3,5,1,2,4,6]=>01000
[[2,2,4,4],[3,3]]=>[3,4,1,2,5,6]=>01000
[[2,2,3,4],[4,4]]=>[4,5,1,2,3,6]=>01000
[[2,2,4,4],[3,4]]=>[3,4,1,2,5,6]=>01000
[[2,2,4,4],[4,4]]=>[3,4,1,2,5,6]=>01000
[[2,3,3,3],[3,4]]=>[2,6,1,3,4,5]=>01000
[[2,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>01000
[[2,3,3,4],[3,4]]=>[2,5,1,3,4,6]=>01000
[[2,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>01000
[[2,3,4,4],[3,4]]=>[2,4,1,3,5,6]=>01000
[[2,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>01000
[[3,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>01000
[[3,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>01000
[[3,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>01000
[[1,1,1,1],[2],[4]]=>[6,5,1,2,3,4]=>11000
[[1,1,1,1],[3],[4]]=>[6,5,1,2,3,4]=>11000
[[1,1,1,2],[2],[4]]=>[6,4,1,2,3,5]=>11000
[[1,1,1,2],[3],[4]]=>[6,5,1,2,3,4]=>11000
[[1,1,1,3],[2],[4]]=>[6,4,1,2,3,5]=>11000
[[1,1,1,4],[2],[3]]=>[5,4,1,2,3,6]=>11000
[[1,1,1,4],[2],[4]]=>[5,4,1,2,3,6]=>11000
[[1,1,1,3],[3],[4]]=>[6,4,1,2,3,5]=>11000
[[1,1,1,4],[3],[4]]=>[5,4,1,2,3,6]=>11000
[[1,1,2,2],[2],[4]]=>[6,3,1,2,4,5]=>11000
[[1,1,2,2],[3],[4]]=>[6,5,1,2,3,4]=>11000
[[1,1,2,3],[2],[4]]=>[6,3,1,2,4,5]=>11000
[[1,1,2,4],[2],[3]]=>[5,3,1,2,4,6]=>11000
[[1,1,2,4],[2],[4]]=>[5,3,1,2,4,6]=>11000
[[1,1,2,3],[3],[4]]=>[6,4,1,2,3,5]=>11000
[[1,1,3,3],[2],[4]]=>[6,3,1,2,4,5]=>11000
[[1,1,3,4],[2],[3]]=>[4,3,1,2,5,6]=>11000
[[1,1,2,4],[3],[4]]=>[5,4,1,2,3,6]=>11000
[[1,1,3,4],[2],[4]]=>[5,3,1,2,4,6]=>11000
[[1,1,4,4],[2],[3]]=>[4,3,1,2,5,6]=>11000
[[1,1,4,4],[2],[4]]=>[4,3,1,2,5,6]=>11000
[[1,1,3,3],[3],[4]]=>[6,3,1,2,4,5]=>11000
[[1,1,3,4],[3],[4]]=>[5,3,1,2,4,6]=>11000
[[1,1,4,4],[3],[4]]=>[4,3,1,2,5,6]=>11000
[[1,2,2,2],[2],[4]]=>[6,2,1,3,4,5]=>11000
[[1,2,2,2],[3],[4]]=>[6,5,1,2,3,4]=>11000
[[1,2,2,3],[2],[4]]=>[6,2,1,3,4,5]=>11000
[[1,2,2,4],[2],[3]]=>[5,2,1,3,4,6]=>11000
[[1,2,2,4],[2],[4]]=>[5,2,1,3,4,6]=>11000
[[1,2,2,3],[3],[4]]=>[6,4,1,2,3,5]=>11000
[[1,2,3,3],[2],[4]]=>[6,2,1,3,4,5]=>11000
[[1,2,3,4],[2],[3]]=>[4,2,1,3,5,6]=>11000
[[1,2,2,4],[3],[4]]=>[5,4,1,2,3,6]=>11000
[[1,2,3,4],[2],[4]]=>[5,2,1,3,4,6]=>11000
[[1,2,4,4],[2],[3]]=>[4,2,1,3,5,6]=>11000
[[1,2,4,4],[2],[4]]=>[4,2,1,3,5,6]=>11000
[[1,2,3,3],[3],[4]]=>[6,3,1,2,4,5]=>11000
[[1,3,3,3],[2],[4]]=>[6,2,1,3,4,5]=>11000
[[1,3,3,4],[2],[3]]=>[3,2,1,4,5,6]=>11000
[[1,2,3,4],[3],[4]]=>[5,3,1,2,4,6]=>11000
[[1,3,3,4],[2],[4]]=>[5,2,1,3,4,6]=>11000
[[1,3,4,4],[2],[3]]=>[3,2,1,4,5,6]=>11000
[[1,2,4,4],[3],[4]]=>[4,3,1,2,5,6]=>11000
[[1,3,4,4],[2],[4]]=>[4,2,1,3,5,6]=>11000
[[1,4,4,4],[2],[3]]=>[3,2,1,4,5,6]=>11000
[[1,4,4,4],[2],[4]]=>[3,2,1,4,5,6]=>11000
[[1,3,3,3],[3],[4]]=>[6,2,1,3,4,5]=>11000
[[1,3,3,4],[3],[4]]=>[5,2,1,3,4,6]=>11000
[[1,3,4,4],[3],[4]]=>[4,2,1,3,5,6]=>11000
[[1,4,4,4],[3],[4]]=>[3,2,1,4,5,6]=>11000
[[2,2,2,2],[3],[4]]=>[6,5,1,2,3,4]=>11000
[[2,2,2,3],[3],[4]]=>[6,4,1,2,3,5]=>11000
[[2,2,2,4],[3],[4]]=>[5,4,1,2,3,6]=>11000
[[2,2,3,3],[3],[4]]=>[6,3,1,2,4,5]=>11000
[[2,2,3,4],[3],[4]]=>[5,3,1,2,4,6]=>11000
[[2,2,4,4],[3],[4]]=>[4,3,1,2,5,6]=>11000
[[2,3,3,3],[3],[4]]=>[6,2,1,3,4,5]=>11000
[[2,3,3,4],[3],[4]]=>[5,2,1,3,4,6]=>11000
[[2,3,4,4],[3],[4]]=>[4,2,1,3,5,6]=>11000
[[2,4,4,4],[3],[4]]=>[3,2,1,4,5,6]=>11000
[[1,1,1],[2,2,4]]=>[4,5,6,1,2,3]=>00100
[[1,1,1],[2,3,4]]=>[4,5,6,1,2,3]=>00100
[[1,1,1],[2,4,4]]=>[4,5,6,1,2,3]=>00100
[[1,1,1],[3,3,4]]=>[4,5,6,1,2,3]=>00100
[[1,1,1],[3,4,4]]=>[4,5,6,1,2,3]=>00100
[[1,1,1],[4,4,4]]=>[4,5,6,1,2,3]=>00100
[[1,1,2],[2,2,4]]=>[3,4,6,1,2,5]=>00100
[[1,1,2],[2,3,4]]=>[3,5,6,1,2,4]=>00100
[[1,1,3],[2,2,4]]=>[3,4,6,1,2,5]=>00100
[[1,1,2],[2,4,4]]=>[3,5,6,1,2,4]=>00100
[[1,1,2],[3,3,4]]=>[4,5,6,1,2,3]=>00100
[[1,1,3],[2,3,4]]=>[3,4,6,1,2,5]=>00100
[[1,1,2],[3,4,4]]=>[4,5,6,1,2,3]=>00100
[[1,1,3],[2,4,4]]=>[3,5,6,1,2,4]=>00100
[[1,1,2],[4,4,4]]=>[4,5,6,1,2,3]=>00100
[[1,1,3],[3,3,4]]=>[3,4,6,1,2,5]=>00100
[[1,1,3],[3,4,4]]=>[3,5,6,1,2,4]=>00100
[[1,1,3],[4,4,4]]=>[4,5,6,1,2,3]=>00100
[[1,2,2],[2,3,4]]=>[2,5,6,1,3,4]=>00100
[[1,2,2],[2,4,4]]=>[2,5,6,1,3,4]=>00100
[[1,2,2],[3,3,4]]=>[4,5,6,1,2,3]=>00100
[[1,2,3],[2,3,4]]=>[2,4,6,1,3,5]=>00100
[[1,2,2],[3,4,4]]=>[4,5,6,1,2,3]=>00100
[[1,2,3],[2,4,4]]=>[2,5,6,1,3,4]=>00100
[[1,2,2],[4,4,4]]=>[4,5,6,1,2,3]=>00100
[[1,2,3],[3,3,4]]=>[3,4,6,1,2,5]=>00100
[[1,2,3],[3,4,4]]=>[3,5,6,1,2,4]=>00100
[[1,3,3],[2,4,4]]=>[2,5,6,1,3,4]=>00100
[[1,2,3],[4,4,4]]=>[4,5,6,1,2,3]=>00100
[[1,3,3],[3,4,4]]=>[2,5,6,1,3,4]=>00100
[[1,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>00100
[[2,2,2],[3,3,4]]=>[4,5,6,1,2,3]=>00100
[[2,2,2],[3,4,4]]=>[4,5,6,1,2,3]=>00100
[[2,2,2],[4,4,4]]=>[4,5,6,1,2,3]=>00100
[[2,2,3],[3,3,4]]=>[3,4,6,1,2,5]=>00100
[[2,2,3],[3,4,4]]=>[3,5,6,1,2,4]=>00100
[[2,2,3],[4,4,4]]=>[4,5,6,1,2,3]=>00100
[[2,3,3],[3,4,4]]=>[2,5,6,1,3,4]=>00100
[[2,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>00100
[[3,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>00100
[[1,1,1],[2,2],[4]]=>[6,4,5,1,2,3]=>10100
[[1,1,1],[2,3],[4]]=>[6,4,5,1,2,3]=>10100
[[1,1,1],[2,4],[3]]=>[5,4,6,1,2,3]=>10100
[[1,1,1],[2,4],[4]]=>[5,4,6,1,2,3]=>10100
[[1,1,1],[3,3],[4]]=>[6,4,5,1,2,3]=>10100
[[1,1,1],[3,4],[4]]=>[5,4,6,1,2,3]=>10100
[[1,1,2],[2,2],[4]]=>[6,3,4,1,2,5]=>10100
[[1,1,2],[2,3],[4]]=>[6,3,5,1,2,4]=>10100
[[1,1,2],[2,4],[3]]=>[5,3,6,1,2,4]=>10100
[[1,1,3],[2,2],[4]]=>[6,3,4,1,2,5]=>10100
[[1,1,4],[2,2],[3]]=>[5,3,4,1,2,6]=>10100
[[1,1,2],[2,4],[4]]=>[5,3,6,1,2,4]=>10100
[[1,1,4],[2,2],[4]]=>[5,3,4,1,2,6]=>10100
[[1,1,2],[3,3],[4]]=>[6,4,5,1,2,3]=>10100
[[1,1,3],[2,3],[4]]=>[6,3,4,1,2,5]=>10100
[[1,1,3],[2,4],[3]]=>[4,3,6,1,2,5]=>10100
[[1,1,4],[2,3],[3]]=>[4,3,5,1,2,6]=>10100
[[1,1,2],[3,4],[4]]=>[5,4,6,1,2,3]=>10100
[[1,1,3],[2,4],[4]]=>[5,3,6,1,2,4]=>10100
[[1,1,4],[2,3],[4]]=>[5,3,4,1,2,6]=>10100
[[1,1,4],[2,4],[3]]=>[4,3,5,1,2,6]=>10100
[[1,1,4],[2,4],[4]]=>[4,3,5,1,2,6]=>10100
[[1,1,3],[3,3],[4]]=>[6,3,4,1,2,5]=>10100
[[1,1,3],[3,4],[4]]=>[5,3,6,1,2,4]=>10100
[[1,1,4],[3,3],[4]]=>[5,3,4,1,2,6]=>10100
[[1,1,4],[3,4],[4]]=>[4,3,5,1,2,6]=>10100
[[1,2,2],[2,3],[4]]=>[6,2,5,1,3,4]=>10100
[[1,2,2],[2,4],[3]]=>[5,2,6,1,3,4]=>10100
[[1,2,2],[2,4],[4]]=>[5,2,6,1,3,4]=>10100
[[1,2,2],[3,3],[4]]=>[6,4,5,1,2,3]=>10100
[[1,2,3],[2,3],[4]]=>[6,2,4,1,3,5]=>10100
[[1,2,3],[2,4],[3]]=>[4,2,6,1,3,5]=>10100
[[1,2,4],[2,3],[3]]=>[4,2,5,1,3,6]=>10100
[[1,2,2],[3,4],[4]]=>[5,4,6,1,2,3]=>10100
[[1,2,3],[2,4],[4]]=>[5,2,6,1,3,4]=>10100
[[1,2,4],[2,3],[4]]=>[5,2,4,1,3,6]=>10100
[[1,2,4],[2,4],[3]]=>[4,2,5,1,3,6]=>10100
[[1,2,4],[2,4],[4]]=>[4,2,5,1,3,6]=>10100
[[1,2,3],[3,3],[4]]=>[6,3,4,1,2,5]=>10100
[[1,3,3],[2,4],[3]]=>[3,2,6,1,4,5]=>10100
[[1,2,3],[3,4],[4]]=>[5,3,6,1,2,4]=>10100
[[1,2,4],[3,3],[4]]=>[5,3,4,1,2,6]=>10100
[[1,3,3],[2,4],[4]]=>[5,2,6,1,3,4]=>10100
[[1,3,4],[2,4],[3]]=>[3,2,5,1,4,6]=>10100
[[1,2,4],[3,4],[4]]=>[4,3,5,1,2,6]=>10100
[[1,3,4],[2,4],[4]]=>[4,2,5,1,3,6]=>10100
[[1,3,3],[3,4],[4]]=>[5,2,6,1,3,4]=>10100
[[1,3,4],[3,4],[4]]=>[4,2,5,1,3,6]=>10100
[[2,2,2],[3,3],[4]]=>[6,4,5,1,2,3]=>10100
[[2,2,2],[3,4],[4]]=>[5,4,6,1,2,3]=>10100
[[2,2,3],[3,3],[4]]=>[6,3,4,1,2,5]=>10100
[[2,2,3],[3,4],[4]]=>[5,3,6,1,2,4]=>10100
[[2,2,4],[3,3],[4]]=>[5,3,4,1,2,6]=>10100
[[2,2,4],[3,4],[4]]=>[4,3,5,1,2,6]=>10100
[[2,3,3],[3,4],[4]]=>[5,2,6,1,3,4]=>10100
[[2,3,4],[3,4],[4]]=>[4,2,5,1,3,6]=>10100
[[1,1,1],[2],[3],[4]]=>[6,5,4,1,2,3]=>11100
[[1,1,2],[2],[3],[4]]=>[6,5,3,1,2,4]=>11100
[[1,1,3],[2],[3],[4]]=>[6,4,3,1,2,5]=>11100
[[1,1,4],[2],[3],[4]]=>[5,4,3,1,2,6]=>11100
[[1,2,2],[2],[3],[4]]=>[6,5,2,1,3,4]=>11100
[[1,2,3],[2],[3],[4]]=>[6,4,2,1,3,5]=>11100
[[1,2,4],[2],[3],[4]]=>[5,4,2,1,3,6]=>11100
[[1,3,3],[2],[3],[4]]=>[6,3,2,1,4,5]=>11100
[[1,3,4],[2],[3],[4]]=>[5,3,2,1,4,6]=>11100
[[1,4,4],[2],[3],[4]]=>[4,3,2,1,5,6]=>11100
[[1,1],[2,2],[3,4]]=>[5,6,3,4,1,2]=>01010
[[1,1],[2,2],[4,4]]=>[5,6,3,4,1,2]=>01010
[[1,1],[2,3],[3,4]]=>[4,6,3,5,1,2]=>01010
[[1,1],[2,3],[4,4]]=>[5,6,3,4,1,2]=>01010
[[1,1],[3,3],[4,4]]=>[5,6,3,4,1,2]=>01010
[[1,2],[2,3],[3,4]]=>[4,6,2,5,1,3]=>01010
[[1,2],[2,3],[4,4]]=>[5,6,2,4,1,3]=>01010
[[1,2],[3,3],[4,4]]=>[5,6,3,4,1,2]=>01010
[[2,2],[3,3],[4,4]]=>[5,6,3,4,1,2]=>01010
[[1,1],[2,2],[3],[4]]=>[6,5,3,4,1,2]=>11010
[[1,1],[2,3],[3],[4]]=>[6,4,3,5,1,2]=>11010
[[1,1],[2,4],[3],[4]]=>[5,4,3,6,1,2]=>11010
[[1,2],[2,3],[3],[4]]=>[6,4,2,5,1,3]=>11010
[[1,2],[2,4],[3],[4]]=>[5,4,2,6,1,3]=>11010
[[1,3],[2,4],[3],[4]]=>[5,3,2,6,1,4]=>11010
[[1,1,1,1,1,1,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,1,1,2,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,1,1,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,1,2,2,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,1,2,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,1,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,2,2,2,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,2,2,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,2,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,3,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,2,2,2,2,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,2,2,2,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,2,2,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,2,3,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,2,2,2,2,2,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,2,2,2,2,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,2,2,2,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,2,2,3,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,2,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,3,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[2,2,2,2,2,2,3]]=>[1,2,3,4,5,6,7]=>000000
[[2,2,2,2,2,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[2,2,2,2,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[2,2,2,3,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[2,2,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[2,3,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[3,3,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>000000
[[1,1,1,1,1,1],[3]]=>[7,1,2,3,4,5,6]=>100000
[[1,1,1,1,1,2],[3]]=>[7,1,2,3,4,5,6]=>100000
[[1,1,1,1,1,3],[2]]=>[6,1,2,3,4,5,7]=>100000
[[1,1,1,1,1,3],[3]]=>[6,1,2,3,4,5,7]=>100000
[[1,1,1,1,2,2],[3]]=>[7,1,2,3,4,5,6]=>100000
[[1,1,1,1,2,3],[2]]=>[5,1,2,3,4,6,7]=>100000
[[1,1,1,1,2,3],[3]]=>[6,1,2,3,4,5,7]=>100000
[[1,1,1,1,3,3],[2]]=>[5,1,2,3,4,6,7]=>100000
[[1,1,1,1,3,3],[3]]=>[5,1,2,3,4,6,7]=>100000
[[1,1,1,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>100000
[[1,1,1,2,2,3],[2]]=>[4,1,2,3,5,6,7]=>100000
[[1,1,1,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>100000
[[1,1,1,2,3,3],[2]]=>[4,1,2,3,5,6,7]=>100000
[[1,1,1,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>100000
[[1,1,1,3,3,3],[2]]=>[4,1,2,3,5,6,7]=>100000
[[1,1,1,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>100000
[[1,1,2,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>100000
[[1,1,2,2,2,3],[2]]=>[3,1,2,4,5,6,7]=>100000
[[1,1,2,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>100000
[[1,1,2,2,3,3],[2]]=>[3,1,2,4,5,6,7]=>100000
[[1,1,2,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>100000
[[1,1,2,3,3,3],[2]]=>[3,1,2,4,5,6,7]=>100000
[[1,1,2,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>100000
[[1,1,3,3,3,3],[2]]=>[3,1,2,4,5,6,7]=>100000
[[1,1,3,3,3,3],[3]]=>[3,1,2,4,5,6,7]=>100000
[[1,2,2,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>100000
[[1,2,2,2,2,3],[2]]=>[2,1,3,4,5,6,7]=>100000
[[1,2,2,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>100000
[[1,2,2,2,3,3],[2]]=>[2,1,3,4,5,6,7]=>100000
[[1,2,2,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>100000
[[1,2,2,3,3,3],[2]]=>[2,1,3,4,5,6,7]=>100000
[[1,2,2,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>100000
[[1,2,3,3,3,3],[2]]=>[2,1,3,4,5,6,7]=>100000
[[1,2,3,3,3,3],[3]]=>[3,1,2,4,5,6,7]=>100000
[[1,3,3,3,3,3],[2]]=>[2,1,3,4,5,6,7]=>100000
[[1,3,3,3,3,3],[3]]=>[2,1,3,4,5,6,7]=>100000
[[2,2,2,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>100000
[[2,2,2,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>100000
[[2,2,2,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>100000
[[2,2,2,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>100000
[[2,2,3,3,3,3],[3]]=>[3,1,2,4,5,6,7]=>100000
[[2,3,3,3,3,3],[3]]=>[2,1,3,4,5,6,7]=>100000
[[1,1,1,1,1],[2,3]]=>[6,7,1,2,3,4,5]=>010000
[[1,1,1,1,1],[3,3]]=>[6,7,1,2,3,4,5]=>010000
[[1,1,1,1,2],[2,3]]=>[5,7,1,2,3,4,6]=>010000
[[1,1,1,1,3],[2,2]]=>[5,6,1,2,3,4,7]=>010000
[[1,1,1,1,2],[3,3]]=>[6,7,1,2,3,4,5]=>010000
[[1,1,1,1,3],[2,3]]=>[5,6,1,2,3,4,7]=>010000
[[1,1,1,1,3],[3,3]]=>[5,6,1,2,3,4,7]=>010000
[[1,1,1,2,2],[2,3]]=>[4,7,1,2,3,5,6]=>010000
[[1,1,1,2,3],[2,2]]=>[4,5,1,2,3,6,7]=>010000
[[1,1,1,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>010000
[[1,1,1,2,3],[2,3]]=>[4,6,1,2,3,5,7]=>010000
[[1,1,1,3,3],[2,2]]=>[4,5,1,2,3,6,7]=>010000
[[1,1,1,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>010000
[[1,1,1,3,3],[2,3]]=>[4,5,1,2,3,6,7]=>010000
[[1,1,1,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>010000
[[1,1,2,2,2],[2,3]]=>[3,7,1,2,4,5,6]=>010000
[[1,1,2,2,3],[2,2]]=>[3,4,1,2,5,6,7]=>010000
[[1,1,2,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>010000
[[1,1,2,2,3],[2,3]]=>[3,6,1,2,4,5,7]=>010000
[[1,1,2,3,3],[2,2]]=>[3,4,1,2,5,6,7]=>010000
[[1,1,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>010000
[[1,1,2,3,3],[2,3]]=>[3,5,1,2,4,6,7]=>010000
[[1,1,3,3,3],[2,2]]=>[3,4,1,2,5,6,7]=>010000
[[1,1,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>010000
[[1,1,3,3,3],[2,3]]=>[3,4,1,2,5,6,7]=>010000
[[1,1,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>010000
[[1,2,2,2,2],[2,3]]=>[2,7,1,3,4,5,6]=>010000
[[1,2,2,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>010000
[[1,2,2,2,3],[2,3]]=>[2,6,1,3,4,5,7]=>010000
[[1,2,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>010000
[[1,2,2,3,3],[2,3]]=>[2,5,1,3,4,6,7]=>010000
[[1,2,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>010000
[[1,2,3,3,3],[2,3]]=>[2,4,1,3,5,6,7]=>010000
[[1,2,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>010000
[[2,2,2,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>010000
[[2,2,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>010000
[[2,2,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>010000
[[2,2,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>010000
[[1,1,1,1,1],[2],[3]]=>[7,6,1,2,3,4,5]=>110000
[[1,1,1,1,2],[2],[3]]=>[7,5,1,2,3,4,6]=>110000
[[1,1,1,1,3],[2],[3]]=>[6,5,1,2,3,4,7]=>110000
[[1,1,1,2,2],[2],[3]]=>[7,4,1,2,3,5,6]=>110000
[[1,1,1,2,3],[2],[3]]=>[6,4,1,2,3,5,7]=>110000
[[1,1,1,3,3],[2],[3]]=>[5,4,1,2,3,6,7]=>110000
[[1,1,2,2,2],[2],[3]]=>[7,3,1,2,4,5,6]=>110000
[[1,1,2,2,3],[2],[3]]=>[6,3,1,2,4,5,7]=>110000
[[1,1,2,3,3],[2],[3]]=>[5,3,1,2,4,6,7]=>110000
[[1,1,3,3,3],[2],[3]]=>[4,3,1,2,5,6,7]=>110000
[[1,2,2,2,2],[2],[3]]=>[7,2,1,3,4,5,6]=>110000
[[1,2,2,2,3],[2],[3]]=>[6,2,1,3,4,5,7]=>110000
[[1,2,2,3,3],[2],[3]]=>[5,2,1,3,4,6,7]=>110000
[[1,2,3,3,3],[2],[3]]=>[4,2,1,3,5,6,7]=>110000
[[1,3,3,3,3],[2],[3]]=>[3,2,1,4,5,6,7]=>110000
[[1,1,1,1],[2,2,3]]=>[5,6,7,1,2,3,4]=>001000
[[1,1,1,1],[2,3,3]]=>[5,6,7,1,2,3,4]=>001000
[[1,1,1,1],[3,3,3]]=>[5,6,7,1,2,3,4]=>001000
[[1,1,1,2],[2,2,3]]=>[4,5,7,1,2,3,6]=>001000
[[1,1,1,3],[2,2,2]]=>[4,5,6,1,2,3,7]=>001000
[[1,1,1,2],[2,3,3]]=>[4,6,7,1,2,3,5]=>001000
[[1,1,1,3],[2,2,3]]=>[4,5,6,1,2,3,7]=>001000
[[1,1,1,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>001000
[[1,1,1,3],[2,3,3]]=>[4,5,6,1,2,3,7]=>001000
[[1,1,1,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>001000
[[1,1,2,2],[2,2,3]]=>[3,4,7,1,2,5,6]=>001000
[[1,1,2,2],[2,3,3]]=>[3,6,7,1,2,4,5]=>001000
[[1,1,2,3],[2,2,3]]=>[3,4,6,1,2,5,7]=>001000
[[1,1,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>001000
[[1,1,2,3],[2,3,3]]=>[3,5,6,1,2,4,7]=>001000
[[1,1,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>001000
[[1,2,2,2],[2,3,3]]=>[2,6,7,1,3,4,5]=>001000
[[1,2,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>001000
[[1,2,2,3],[2,3,3]]=>[2,5,6,1,3,4,7]=>001000
[[1,2,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>001000
[[2,2,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>001000
[[2,2,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>001000
[[1,1,1,1],[2,2],[3]]=>[7,5,6,1,2,3,4]=>101000
[[1,1,1,1],[2,3],[3]]=>[6,5,7,1,2,3,4]=>101000
[[1,1,1,2],[2,2],[3]]=>[7,4,5,1,2,3,6]=>101000
[[1,1,1,2],[2,3],[3]]=>[6,4,7,1,2,3,5]=>101000
[[1,1,1,3],[2,2],[3]]=>[6,4,5,1,2,3,7]=>101000
[[1,1,1,3],[2,3],[3]]=>[5,4,6,1,2,3,7]=>101000
[[1,1,2,2],[2,2],[3]]=>[7,3,4,1,2,5,6]=>101000
[[1,1,2,2],[2,3],[3]]=>[6,3,7,1,2,4,5]=>101000
[[1,1,2,3],[2,2],[3]]=>[6,3,4,1,2,5,7]=>101000
[[1,1,2,3],[2,3],[3]]=>[5,3,6,1,2,4,7]=>101000
[[1,1,3,3],[2,2],[3]]=>[5,3,4,1,2,6,7]=>101000
[[1,1,3,3],[2,3],[3]]=>[4,3,5,1,2,6,7]=>101000
[[1,2,2,2],[2,3],[3]]=>[6,2,7,1,3,4,5]=>101000
[[1,2,2,3],[2,3],[3]]=>[5,2,6,1,3,4,7]=>101000
[[1,2,3,3],[2,3],[3]]=>[4,2,5,1,3,6,7]=>101000
[[1,1,1],[2,2,2],[3]]=>[7,4,5,6,1,2,3]=>100100
[[1,1,1],[2,2,3],[3]]=>[6,4,5,7,1,2,3]=>100100
[[1,1,1],[2,3,3],[3]]=>[5,4,6,7,1,2,3]=>100100
[[1,1,2],[2,2,3],[3]]=>[6,3,4,7,1,2,5]=>100100
[[1,1,2],[2,3,3],[3]]=>[5,3,6,7,1,2,4]=>100100
[[1,2,2],[2,3,3],[3]]=>[5,2,6,7,1,3,4]=>100100
[[1,1,1],[2,2],[3,3]]=>[6,7,4,5,1,2,3]=>010100
[[1,1,2],[2,2],[3,3]]=>[6,7,3,4,1,2,5]=>010100
[[1,1,3],[2,2],[3,3]]=>[5,6,3,4,1,2,7]=>010100
[[1,1,1,1,1,1,1,2]]=>[1,2,3,4,5,6,7,8]=>0000000
[[1,1,1,1,1,1,2,2]]=>[1,2,3,4,5,6,7,8]=>0000000
[[1,1,1,1,1,2,2,2]]=>[1,2,3,4,5,6,7,8]=>0000000
[[1,1,1,1,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>0000000
[[1,1,1,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>0000000
[[1,1,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>0000000
[[1,2,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>0000000
[[2,2,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>0000000
[[1,1,1,1,1,1,1],[2]]=>[8,1,2,3,4,5,6,7]=>1000000
[[1,1,1,1,1,1,2],[2]]=>[7,1,2,3,4,5,6,8]=>1000000
[[1,1,1,1,1,2,2],[2]]=>[6,1,2,3,4,5,7,8]=>1000000
[[1,1,1,1,2,2,2],[2]]=>[5,1,2,3,4,6,7,8]=>1000000
[[1,1,1,2,2,2,2],[2]]=>[4,1,2,3,5,6,7,8]=>1000000
[[1,1,2,2,2,2,2],[2]]=>[3,1,2,4,5,6,7,8]=>1000000
[[1,2,2,2,2,2,2],[2]]=>[2,1,3,4,5,6,7,8]=>1000000
[[1,1,1,1,1,1],[2,2]]=>[7,8,1,2,3,4,5,6]=>0100000
[[1,1,1,1,1,2],[2,2]]=>[6,7,1,2,3,4,5,8]=>0100000
[[1,1,1,2,2,2],[2,2]]=>[4,5,1,2,3,6,7,8]=>0100000
[[1,1,2,2,2,2],[2,2]]=>[3,4,1,2,5,6,7,8]=>0100000
[[1,1,1,1,1],[2,2,2]]=>[6,7,8,1,2,3,4,5]=>0010000
[[1,1,1,1,2],[2,2,2]]=>[5,6,7,1,2,3,4,8]=>0010000
[[1,1,1,2,2],[2,2,2]]=>[4,5,6,1,2,3,7,8]=>0010000
[[1,1,1,1],[2,2,2,2]]=>[5,6,7,8,1,2,3,4]=>0001000
[[1]]=>[1]=>
[[1,1,1,1],[2,2,2],[3,3],[4]]=>[10,8,9,5,6,7,1,2,3,4]=>101001000
[[1,1,1,2],[2,2,2],[3,3],[4]]=>[10,8,9,4,5,6,1,2,3,7]=>101001000
[[1,1,1,1],[2,2,3],[3,3],[4]]=>[10,7,8,5,6,9,1,2,3,4]=>101001000
[[1,1,1,2],[2,2,3],[3,3],[4]]=>[10,7,8,4,5,9,1,2,3,6]=>101001000
[[1,1,1,3],[2,2,3],[3,3],[4]]=>[10,6,7,4,5,8,1,2,3,9]=>101001000
[[1,1,2,2],[2,2,3],[3,3],[4]]=>[10,7,8,3,4,9,1,2,5,6]=>101001000
[[1,1,2,3],[2,2,3],[3,3],[4]]=>[10,6,7,3,4,8,1,2,5,9]=>101001000
[[1,1,1,1],[2,2,2],[3,4],[4]]=>[9,8,10,5,6,7,1,2,3,4]=>101001000
[[1,1,1,2],[2,2,2],[3,4],[4]]=>[9,8,10,4,5,6,1,2,3,7]=>101001000
[[1,1,1,1],[2,2,3],[3,4],[4]]=>[9,7,10,5,6,8,1,2,3,4]=>101001000
[[1,1,1,2],[2,2,3],[3,4],[4]]=>[9,7,10,4,5,8,1,2,3,6]=>101001000
[[1,1,1,3],[2,2,3],[3,4],[4]]=>[9,6,10,4,5,7,1,2,3,8]=>101001000
[[1,1,2,2],[2,2,3],[3,4],[4]]=>[9,7,10,3,4,8,1,2,5,6]=>101001000
[[1,1,2,3],[2,2,3],[3,4],[4]]=>[9,6,10,3,4,7,1,2,5,8]=>101001000
[[1,1,1,1],[2,2,4],[3,4],[4]]=>[8,7,9,5,6,10,1,2,3,4]=>101001000
[[1,1,1,2],[2,2,4],[3,4],[4]]=>[8,7,9,4,5,10,1,2,3,6]=>101001000
[[1,1,1,3],[2,2,4],[3,4],[4]]=>[8,6,9,4,5,10,1,2,3,7]=>101001000
[[1,1,1,4],[2,2,4],[3,4],[4]]=>[7,6,8,4,5,9,1,2,3,10]=>101001000
[[1,1,2,2],[2,2,4],[3,4],[4]]=>[8,7,9,3,4,10,1,2,5,6]=>101001000
[[1,1,2,3],[2,2,4],[3,4],[4]]=>[8,6,9,3,4,10,1,2,5,7]=>101001000
[[1,1,2,4],[2,2,4],[3,4],[4]]=>[7,6,8,3,4,9,1,2,5,10]=>101001000
[[1,1,1,1],[2,3,3],[3,4],[4]]=>[9,6,10,5,7,8,1,2,3,4]=>101001000
[[1,1,1,2],[2,3,3],[3,4],[4]]=>[9,6,10,4,7,8,1,2,3,5]=>101001000
[[1,1,1,3],[2,3,3],[3,4],[4]]=>[9,5,10,4,6,7,1,2,3,8]=>101001000
[[1,1,2,2],[2,3,3],[3,4],[4]]=>[9,6,10,3,7,8,1,2,4,5]=>101001000
[[1,1,2,3],[2,3,3],[3,4],[4]]=>[9,5,10,3,6,7,1,2,4,8]=>101001000
[[1,1,1,1],[2,3,4],[3,4],[4]]=>[8,6,9,5,7,10,1,2,3,4]=>101001000
[[1,1,1,2],[2,3,4],[3,4],[4]]=>[8,6,9,4,7,10,1,2,3,5]=>101001000
[[1,1,1,3],[2,3,4],[3,4],[4]]=>[8,5,9,4,6,10,1,2,3,7]=>101001000
[[1,1,1,4],[2,3,4],[3,4],[4]]=>[7,5,8,4,6,9,1,2,3,10]=>101001000
[[1,1,2,2],[2,3,4],[3,4],[4]]=>[8,6,9,3,7,10,1,2,4,5]=>101001000
[[1,1,2,3],[2,3,4],[3,4],[4]]=>[8,5,9,3,6,10,1,2,4,7]=>101001000
[[1,1,2,4],[2,3,4],[3,4],[4]]=>[7,5,8,3,6,9,1,2,4,10]=>101001000
[[1,1,3,3],[2,3,4],[3,4],[4]]=>[8,4,9,3,5,10,1,2,6,7]=>101001000
[[1,1,3,4],[2,3,4],[3,4],[4]]=>[7,4,8,3,5,9,1,2,6,10]=>101001000
[[1,2,2,2],[2,3,3],[3,4],[4]]=>[9,6,10,2,7,8,1,3,4,5]=>101001000
[[1,2,2,3],[2,3,3],[3,4],[4]]=>[9,5,10,2,6,7,1,3,4,8]=>101001000
[[1,2,2,2],[2,3,4],[3,4],[4]]=>[8,6,9,2,7,10,1,3,4,5]=>101001000
[[1,2,2,3],[2,3,4],[3,4],[4]]=>[8,5,9,2,6,10,1,3,4,7]=>101001000
[[1,2,2,4],[2,3,4],[3,4],[4]]=>[7,5,8,2,6,9,1,3,4,10]=>101001000
[[1,2,3,3],[2,3,4],[3,4],[4]]=>[8,4,9,2,5,10,1,3,6,7]=>101001000
[[1,2,3,4],[2,3,4],[3,4],[4]]=>[7,4,8,2,5,9,1,3,6,10]=>101001000
[[2]]=>[1]=>
[[1,1]]=>[1,2]=>0
[[3]]=>[1]=>
[[1,1,1]]=>[1,2,3]=>00
[[4]]=>[1]=>
[[1,1,1,1]]=>[1,2,3,4]=>000
[[5]]=>[1]=>
[[1,1,1,1,1]]=>[1,2,3,4,5]=>0000
[[6]]=>[1]=>
[[1,1,1,1,1,1]]=>[1,2,3,4,5,6]=>00000
[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>00000
[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>10000
[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>10000
[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>11000
[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>10000
[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>01000
[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>11000
[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>01000
[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>11000
[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>11100
[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>10000
[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>01000
[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>01000
[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>10100
[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>11000
[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>11000
[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>11100
[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>01000
[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>10100
[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>11000
[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>10100
[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>11100
[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>10100
[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>10100
[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>11100
[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>11110
[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>10000
[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>01000
[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>01000
[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>10100
[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>01000
[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>00100
[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>10100
[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>00100
[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>10100
[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>11010
[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>11000
[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>11000
[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>11100
[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>11000
[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>10100
[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>11100
[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>10100
[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>11100
[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>11110
[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>01000
[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>00100
[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>10100
[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>00100
[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>10100
[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>11010
[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>11000
[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>10100
[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>10100
[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>01010
[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>11010
[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>11100
[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>11100
[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>11110
[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>00100
[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>10100
[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>11010
[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>10100
[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>01010
[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>11010
[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>01010
[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>11100
[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>11010
[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>11110
[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>11010
[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>01010
[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>11010
[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>01010
[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>11010
[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>11110
[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>11111
[[1,1,1,1,2,2,2],[3,3],[4]]=>[10,8,9,1,2,3,4,5,6,7]=>101000000
[[1,1,1,2,2,2,2],[3,3],[4]]=>[10,8,9,1,2,3,4,5,6,7]=>101000000
[[1,1,1,1,2,2,3],[3,3],[4]]=>[10,7,8,1,2,3,4,5,6,9]=>101000000
[[1,1,1,2,2,2,3],[3,3],[4]]=>[10,7,8,1,2,3,4,5,6,9]=>101000000
[[1,1,2,2,2,2,3],[3,3],[4]]=>[10,7,8,1,2,3,4,5,6,9]=>101000000
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 word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
searching the database
Sorry, this map was not found in the database.