Identifier
Mp00075:
Semistandard tableaux
—reading word permutation⟶
Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Images
=>
Cc0019;cc-rep-0
[[1,2]]=>[1,2]=>1=>1
[[2,2]]=>[1,2]=>1=>1
[[1],[2]]=>[2,1]=>0=>0
[[1,3]]=>[1,2]=>1=>1
[[2,3]]=>[1,2]=>1=>1
[[3,3]]=>[1,2]=>1=>1
[[1],[3]]=>[2,1]=>0=>0
[[2],[3]]=>[2,1]=>0=>0
[[1,1,2]]=>[1,2,3]=>11=>11
[[1,2,2]]=>[1,2,3]=>11=>11
[[2,2,2]]=>[1,2,3]=>11=>11
[[1,1],[2]]=>[3,1,2]=>00=>00
[[1,2],[2]]=>[2,1,3]=>01=>01
[[1,4]]=>[1,2]=>1=>1
[[2,4]]=>[1,2]=>1=>1
[[3,4]]=>[1,2]=>1=>1
[[4,4]]=>[1,2]=>1=>1
[[1],[4]]=>[2,1]=>0=>0
[[2],[4]]=>[2,1]=>0=>0
[[3],[4]]=>[2,1]=>0=>0
[[1,1,3]]=>[1,2,3]=>11=>11
[[1,2,3]]=>[1,2,3]=>11=>11
[[1,3,3]]=>[1,2,3]=>11=>11
[[2,2,3]]=>[1,2,3]=>11=>11
[[2,3,3]]=>[1,2,3]=>11=>11
[[3,3,3]]=>[1,2,3]=>11=>11
[[1,1],[3]]=>[3,1,2]=>00=>00
[[1,2],[3]]=>[3,1,2]=>00=>00
[[1,3],[2]]=>[2,1,3]=>01=>01
[[1,3],[3]]=>[2,1,3]=>01=>01
[[2,2],[3]]=>[3,1,2]=>00=>00
[[2,3],[3]]=>[2,1,3]=>01=>01
[[1],[2],[3]]=>[3,2,1]=>00=>00
[[1,1,1,2]]=>[1,2,3,4]=>111=>111
[[1,1,2,2]]=>[1,2,3,4]=>111=>111
[[1,2,2,2]]=>[1,2,3,4]=>111=>111
[[2,2,2,2]]=>[1,2,3,4]=>111=>111
[[1,1,1],[2]]=>[4,1,2,3]=>000=>000
[[1,1,2],[2]]=>[3,1,2,4]=>001=>001
[[1,2,2],[2]]=>[2,1,3,4]=>011=>011
[[1,1],[2,2]]=>[3,4,1,2]=>000=>000
[[1,5]]=>[1,2]=>1=>1
[[2,5]]=>[1,2]=>1=>1
[[3,5]]=>[1,2]=>1=>1
[[4,5]]=>[1,2]=>1=>1
[[5,5]]=>[1,2]=>1=>1
[[1],[5]]=>[2,1]=>0=>0
[[2],[5]]=>[2,1]=>0=>0
[[3],[5]]=>[2,1]=>0=>0
[[4],[5]]=>[2,1]=>0=>0
[[1,1,4]]=>[1,2,3]=>11=>11
[[1,2,4]]=>[1,2,3]=>11=>11
[[1,3,4]]=>[1,2,3]=>11=>11
[[1,4,4]]=>[1,2,3]=>11=>11
[[2,2,4]]=>[1,2,3]=>11=>11
[[2,3,4]]=>[1,2,3]=>11=>11
[[2,4,4]]=>[1,2,3]=>11=>11
[[3,3,4]]=>[1,2,3]=>11=>11
[[3,4,4]]=>[1,2,3]=>11=>11
[[4,4,4]]=>[1,2,3]=>11=>11
[[1,1],[4]]=>[3,1,2]=>00=>00
[[1,2],[4]]=>[3,1,2]=>00=>00
[[1,4],[2]]=>[2,1,3]=>01=>01
[[1,3],[4]]=>[3,1,2]=>00=>00
[[1,4],[3]]=>[2,1,3]=>01=>01
[[1,4],[4]]=>[2,1,3]=>01=>01
[[2,2],[4]]=>[3,1,2]=>00=>00
[[2,3],[4]]=>[3,1,2]=>00=>00
[[2,4],[3]]=>[2,1,3]=>01=>01
[[2,4],[4]]=>[2,1,3]=>01=>01
[[3,3],[4]]=>[3,1,2]=>00=>00
[[3,4],[4]]=>[2,1,3]=>01=>01
[[1],[2],[4]]=>[3,2,1]=>00=>00
[[1],[3],[4]]=>[3,2,1]=>00=>00
[[2],[3],[4]]=>[3,2,1]=>00=>00
[[1,1,1,3]]=>[1,2,3,4]=>111=>111
[[1,1,2,3]]=>[1,2,3,4]=>111=>111
[[1,1,3,3]]=>[1,2,3,4]=>111=>111
[[1,2,2,3]]=>[1,2,3,4]=>111=>111
[[1,2,3,3]]=>[1,2,3,4]=>111=>111
[[1,3,3,3]]=>[1,2,3,4]=>111=>111
[[2,2,2,3]]=>[1,2,3,4]=>111=>111
[[2,2,3,3]]=>[1,2,3,4]=>111=>111
[[2,3,3,3]]=>[1,2,3,4]=>111=>111
[[3,3,3,3]]=>[1,2,3,4]=>111=>111
[[1,1,1],[3]]=>[4,1,2,3]=>000=>000
[[1,1,2],[3]]=>[4,1,2,3]=>000=>000
[[1,1,3],[2]]=>[3,1,2,4]=>001=>001
[[1,1,3],[3]]=>[3,1,2,4]=>001=>001
[[1,2,2],[3]]=>[4,1,2,3]=>000=>000
[[1,2,3],[2]]=>[2,1,3,4]=>011=>011
[[1,2,3],[3]]=>[3,1,2,4]=>001=>001
[[1,3,3],[2]]=>[2,1,3,4]=>011=>011
[[1,3,3],[3]]=>[2,1,3,4]=>011=>011
[[2,2,2],[3]]=>[4,1,2,3]=>000=>000
[[2,2,3],[3]]=>[3,1,2,4]=>001=>001
[[2,3,3],[3]]=>[2,1,3,4]=>011=>011
[[1,1],[2,3]]=>[3,4,1,2]=>000=>000
[[1,1],[3,3]]=>[3,4,1,2]=>000=>000
[[1,2],[2,3]]=>[2,4,1,3]=>000=>000
[[1,2],[3,3]]=>[3,4,1,2]=>000=>000
[[2,2],[3,3]]=>[3,4,1,2]=>000=>000
[[1,1],[2],[3]]=>[4,3,1,2]=>000=>000
[[1,2],[2],[3]]=>[4,2,1,3]=>000=>000
[[1,3],[2],[3]]=>[3,2,1,4]=>001=>001
[[1,1,1,1,2]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,2,2]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,2,2,2]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,2,2,2]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,2,2,2]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,1],[2]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,1,2],[2]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,2,2],[2]]=>[3,1,2,4,5]=>0011=>0011
[[1,2,2,2],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,1,1],[2,2]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,2],[2,2]]=>[3,4,1,2,5]=>0001=>0001
[[1,6]]=>[1,2]=>1=>1
[[2,6]]=>[1,2]=>1=>1
[[3,6]]=>[1,2]=>1=>1
[[4,6]]=>[1,2]=>1=>1
[[5,6]]=>[1,2]=>1=>1
[[6,6]]=>[1,2]=>1=>1
[[1],[6]]=>[2,1]=>0=>0
[[2],[6]]=>[2,1]=>0=>0
[[3],[6]]=>[2,1]=>0=>0
[[4],[6]]=>[2,1]=>0=>0
[[5],[6]]=>[2,1]=>0=>0
[[1,1,5]]=>[1,2,3]=>11=>11
[[1,2,5]]=>[1,2,3]=>11=>11
[[1,3,5]]=>[1,2,3]=>11=>11
[[1,4,5]]=>[1,2,3]=>11=>11
[[1,5,5]]=>[1,2,3]=>11=>11
[[2,2,5]]=>[1,2,3]=>11=>11
[[2,3,5]]=>[1,2,3]=>11=>11
[[2,4,5]]=>[1,2,3]=>11=>11
[[2,5,5]]=>[1,2,3]=>11=>11
[[3,3,5]]=>[1,2,3]=>11=>11
[[3,4,5]]=>[1,2,3]=>11=>11
[[3,5,5]]=>[1,2,3]=>11=>11
[[4,4,5]]=>[1,2,3]=>11=>11
[[4,5,5]]=>[1,2,3]=>11=>11
[[5,5,5]]=>[1,2,3]=>11=>11
[[1,1],[5]]=>[3,1,2]=>00=>00
[[1,2],[5]]=>[3,1,2]=>00=>00
[[1,5],[2]]=>[2,1,3]=>01=>01
[[1,3],[5]]=>[3,1,2]=>00=>00
[[1,5],[3]]=>[2,1,3]=>01=>01
[[1,4],[5]]=>[3,1,2]=>00=>00
[[1,5],[4]]=>[2,1,3]=>01=>01
[[1,5],[5]]=>[2,1,3]=>01=>01
[[2,2],[5]]=>[3,1,2]=>00=>00
[[2,3],[5]]=>[3,1,2]=>00=>00
[[2,5],[3]]=>[2,1,3]=>01=>01
[[2,4],[5]]=>[3,1,2]=>00=>00
[[2,5],[4]]=>[2,1,3]=>01=>01
[[2,5],[5]]=>[2,1,3]=>01=>01
[[3,3],[5]]=>[3,1,2]=>00=>00
[[3,4],[5]]=>[3,1,2]=>00=>00
[[3,5],[4]]=>[2,1,3]=>01=>01
[[3,5],[5]]=>[2,1,3]=>01=>01
[[4,4],[5]]=>[3,1,2]=>00=>00
[[4,5],[5]]=>[2,1,3]=>01=>01
[[1],[2],[5]]=>[3,2,1]=>00=>00
[[1],[3],[5]]=>[3,2,1]=>00=>00
[[1],[4],[5]]=>[3,2,1]=>00=>00
[[2],[3],[5]]=>[3,2,1]=>00=>00
[[2],[4],[5]]=>[3,2,1]=>00=>00
[[3],[4],[5]]=>[3,2,1]=>00=>00
[[1,1,1,4]]=>[1,2,3,4]=>111=>111
[[1,1,2,4]]=>[1,2,3,4]=>111=>111
[[1,1,3,4]]=>[1,2,3,4]=>111=>111
[[1,1,4,4]]=>[1,2,3,4]=>111=>111
[[1,2,2,4]]=>[1,2,3,4]=>111=>111
[[1,2,3,4]]=>[1,2,3,4]=>111=>111
[[1,2,4,4]]=>[1,2,3,4]=>111=>111
[[1,3,3,4]]=>[1,2,3,4]=>111=>111
[[1,3,4,4]]=>[1,2,3,4]=>111=>111
[[1,4,4,4]]=>[1,2,3,4]=>111=>111
[[2,2,2,4]]=>[1,2,3,4]=>111=>111
[[2,2,3,4]]=>[1,2,3,4]=>111=>111
[[2,2,4,4]]=>[1,2,3,4]=>111=>111
[[2,3,3,4]]=>[1,2,3,4]=>111=>111
[[2,3,4,4]]=>[1,2,3,4]=>111=>111
[[2,4,4,4]]=>[1,2,3,4]=>111=>111
[[3,3,3,4]]=>[1,2,3,4]=>111=>111
[[3,3,4,4]]=>[1,2,3,4]=>111=>111
[[3,4,4,4]]=>[1,2,3,4]=>111=>111
[[4,4,4,4]]=>[1,2,3,4]=>111=>111
[[1,1,1],[4]]=>[4,1,2,3]=>000=>000
[[1,1,2],[4]]=>[4,1,2,3]=>000=>000
[[1,1,4],[2]]=>[3,1,2,4]=>001=>001
[[1,1,3],[4]]=>[4,1,2,3]=>000=>000
[[1,1,4],[3]]=>[3,1,2,4]=>001=>001
[[1,1,4],[4]]=>[3,1,2,4]=>001=>001
[[1,2,2],[4]]=>[4,1,2,3]=>000=>000
[[1,2,4],[2]]=>[2,1,3,4]=>011=>011
[[1,2,3],[4]]=>[4,1,2,3]=>000=>000
[[1,2,4],[3]]=>[3,1,2,4]=>001=>001
[[1,3,4],[2]]=>[2,1,3,4]=>011=>011
[[1,2,4],[4]]=>[3,1,2,4]=>001=>001
[[1,4,4],[2]]=>[2,1,3,4]=>011=>011
[[1,3,3],[4]]=>[4,1,2,3]=>000=>000
[[1,3,4],[3]]=>[2,1,3,4]=>011=>011
[[1,3,4],[4]]=>[3,1,2,4]=>001=>001
[[1,4,4],[3]]=>[2,1,3,4]=>011=>011
[[1,4,4],[4]]=>[2,1,3,4]=>011=>011
[[2,2,2],[4]]=>[4,1,2,3]=>000=>000
[[2,2,3],[4]]=>[4,1,2,3]=>000=>000
[[2,2,4],[3]]=>[3,1,2,4]=>001=>001
[[2,2,4],[4]]=>[3,1,2,4]=>001=>001
[[2,3,3],[4]]=>[4,1,2,3]=>000=>000
[[2,3,4],[3]]=>[2,1,3,4]=>011=>011
[[2,3,4],[4]]=>[3,1,2,4]=>001=>001
[[2,4,4],[3]]=>[2,1,3,4]=>011=>011
[[2,4,4],[4]]=>[2,1,3,4]=>011=>011
[[3,3,3],[4]]=>[4,1,2,3]=>000=>000
[[3,3,4],[4]]=>[3,1,2,4]=>001=>001
[[3,4,4],[4]]=>[2,1,3,4]=>011=>011
[[1,1],[2,4]]=>[3,4,1,2]=>000=>000
[[1,1],[3,4]]=>[3,4,1,2]=>000=>000
[[1,1],[4,4]]=>[3,4,1,2]=>000=>000
[[1,2],[2,4]]=>[2,4,1,3]=>000=>000
[[1,2],[3,4]]=>[3,4,1,2]=>000=>000
[[1,3],[2,4]]=>[2,4,1,3]=>000=>000
[[1,2],[4,4]]=>[3,4,1,2]=>000=>000
[[1,3],[3,4]]=>[2,4,1,3]=>000=>000
[[1,3],[4,4]]=>[3,4,1,2]=>000=>000
[[2,2],[3,4]]=>[3,4,1,2]=>000=>000
[[2,2],[4,4]]=>[3,4,1,2]=>000=>000
[[2,3],[3,4]]=>[2,4,1,3]=>000=>000
[[2,3],[4,4]]=>[3,4,1,2]=>000=>000
[[3,3],[4,4]]=>[3,4,1,2]=>000=>000
[[1,1],[2],[4]]=>[4,3,1,2]=>000=>000
[[1,1],[3],[4]]=>[4,3,1,2]=>000=>000
[[1,2],[2],[4]]=>[4,2,1,3]=>000=>000
[[1,2],[3],[4]]=>[4,3,1,2]=>000=>000
[[1,3],[2],[4]]=>[4,2,1,3]=>000=>000
[[1,4],[2],[3]]=>[3,2,1,4]=>001=>001
[[1,4],[2],[4]]=>[3,2,1,4]=>001=>001
[[1,3],[3],[4]]=>[4,2,1,3]=>000=>000
[[1,4],[3],[4]]=>[3,2,1,4]=>001=>001
[[2,2],[3],[4]]=>[4,3,1,2]=>000=>000
[[2,3],[3],[4]]=>[4,2,1,3]=>000=>000
[[2,4],[3],[4]]=>[3,2,1,4]=>001=>001
[[1],[2],[3],[4]]=>[4,3,2,1]=>000=>000
[[1,1,1,1,3]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,2,3]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,3,3]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,2,2,3]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,2,3,3]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,3,3,3]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,2,2,3]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,2,3,3]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,3,3,3]]=>[1,2,3,4,5]=>1111=>1111
[[1,3,3,3,3]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,2,2,3]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,2,3,3]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,3,3,3]]=>[1,2,3,4,5]=>1111=>1111
[[2,3,3,3,3]]=>[1,2,3,4,5]=>1111=>1111
[[3,3,3,3,3]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,1],[3]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,1,2],[3]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,1,3],[2]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,1,3],[3]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,2,2],[3]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,2,3],[2]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,2,3],[3]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,3,3],[2]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,3,3],[3]]=>[3,1,2,4,5]=>0011=>0011
[[1,2,2,2],[3]]=>[5,1,2,3,4]=>0000=>0000
[[1,2,2,3],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,2,3],[3]]=>[4,1,2,3,5]=>0001=>0001
[[1,2,3,3],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,3,3],[3]]=>[3,1,2,4,5]=>0011=>0011
[[1,3,3,3],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,3,3,3],[3]]=>[2,1,3,4,5]=>0111=>0111
[[2,2,2,2],[3]]=>[5,1,2,3,4]=>0000=>0000
[[2,2,2,3],[3]]=>[4,1,2,3,5]=>0001=>0001
[[2,2,3,3],[3]]=>[3,1,2,4,5]=>0011=>0011
[[2,3,3,3],[3]]=>[2,1,3,4,5]=>0111=>0111
[[1,1,1],[2,3]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,1],[3,3]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,2],[2,3]]=>[3,5,1,2,4]=>0000=>0000
[[1,1,3],[2,2]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,2],[3,3]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,3],[2,3]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,3],[3,3]]=>[3,4,1,2,5]=>0001=>0001
[[1,2,2],[2,3]]=>[2,5,1,3,4]=>0000=>0000
[[1,2,2],[3,3]]=>[4,5,1,2,3]=>0000=>0000
[[1,2,3],[2,3]]=>[2,4,1,3,5]=>0001=>0001
[[1,2,3],[3,3]]=>[3,4,1,2,5]=>0001=>0001
[[2,2,2],[3,3]]=>[4,5,1,2,3]=>0000=>0000
[[2,2,3],[3,3]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,1],[2],[3]]=>[5,4,1,2,3]=>0000=>0000
[[1,1,2],[2],[3]]=>[5,3,1,2,4]=>0000=>0000
[[1,1,3],[2],[3]]=>[4,3,1,2,5]=>0001=>0001
[[1,2,2],[2],[3]]=>[5,2,1,3,4]=>0000=>0000
[[1,2,3],[2],[3]]=>[4,2,1,3,5]=>0001=>0001
[[1,3,3],[2],[3]]=>[3,2,1,4,5]=>0011=>0011
[[1,1],[2,2],[3]]=>[5,3,4,1,2]=>0000=>0000
[[1,1],[2,3],[3]]=>[4,3,5,1,2]=>0000=>0000
[[1,2],[2,3],[3]]=>[4,2,5,1,3]=>0000=>0000
[[1,1,1,1,1,2]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,1,2,2]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,2,2,2]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,2,2,2,2]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,2,2,2,2]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,2,2,2,2]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,1,1],[2]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,1,1,2],[2]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,1,2,2],[2]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,2,2,2],[2]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,2,2,2,2],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,1,1,1],[2,2]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,1,2],[2,2]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,2,2],[2,2]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,1],[2,2,2]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,7]]=>[1,2]=>1=>1
[[2,7]]=>[1,2]=>1=>1
[[3,7]]=>[1,2]=>1=>1
[[4,7]]=>[1,2]=>1=>1
[[5,7]]=>[1,2]=>1=>1
[[6,7]]=>[1,2]=>1=>1
[[7,7]]=>[1,2]=>1=>1
[[1],[7]]=>[2,1]=>0=>0
[[2],[7]]=>[2,1]=>0=>0
[[3],[7]]=>[2,1]=>0=>0
[[4],[7]]=>[2,1]=>0=>0
[[5],[7]]=>[2,1]=>0=>0
[[6],[7]]=>[2,1]=>0=>0
[[1,1,6]]=>[1,2,3]=>11=>11
[[1,2,6]]=>[1,2,3]=>11=>11
[[1,3,6]]=>[1,2,3]=>11=>11
[[1,4,6]]=>[1,2,3]=>11=>11
[[1,5,6]]=>[1,2,3]=>11=>11
[[1,6,6]]=>[1,2,3]=>11=>11
[[2,2,6]]=>[1,2,3]=>11=>11
[[2,3,6]]=>[1,2,3]=>11=>11
[[2,4,6]]=>[1,2,3]=>11=>11
[[2,5,6]]=>[1,2,3]=>11=>11
[[2,6,6]]=>[1,2,3]=>11=>11
[[3,3,6]]=>[1,2,3]=>11=>11
[[3,4,6]]=>[1,2,3]=>11=>11
[[3,5,6]]=>[1,2,3]=>11=>11
[[3,6,6]]=>[1,2,3]=>11=>11
[[4,4,6]]=>[1,2,3]=>11=>11
[[4,5,6]]=>[1,2,3]=>11=>11
[[4,6,6]]=>[1,2,3]=>11=>11
[[5,5,6]]=>[1,2,3]=>11=>11
[[5,6,6]]=>[1,2,3]=>11=>11
[[6,6,6]]=>[1,2,3]=>11=>11
[[1,1],[6]]=>[3,1,2]=>00=>00
[[1,2],[6]]=>[3,1,2]=>00=>00
[[1,6],[2]]=>[2,1,3]=>01=>01
[[1,3],[6]]=>[3,1,2]=>00=>00
[[1,6],[3]]=>[2,1,3]=>01=>01
[[1,4],[6]]=>[3,1,2]=>00=>00
[[1,6],[4]]=>[2,1,3]=>01=>01
[[1,5],[6]]=>[3,1,2]=>00=>00
[[1,6],[5]]=>[2,1,3]=>01=>01
[[1,6],[6]]=>[2,1,3]=>01=>01
[[2,2],[6]]=>[3,1,2]=>00=>00
[[2,3],[6]]=>[3,1,2]=>00=>00
[[2,6],[3]]=>[2,1,3]=>01=>01
[[2,4],[6]]=>[3,1,2]=>00=>00
[[2,6],[4]]=>[2,1,3]=>01=>01
[[2,5],[6]]=>[3,1,2]=>00=>00
[[2,6],[5]]=>[2,1,3]=>01=>01
[[2,6],[6]]=>[2,1,3]=>01=>01
[[3,3],[6]]=>[3,1,2]=>00=>00
[[3,4],[6]]=>[3,1,2]=>00=>00
[[3,6],[4]]=>[2,1,3]=>01=>01
[[3,5],[6]]=>[3,1,2]=>00=>00
[[3,6],[5]]=>[2,1,3]=>01=>01
[[3,6],[6]]=>[2,1,3]=>01=>01
[[4,4],[6]]=>[3,1,2]=>00=>00
[[4,5],[6]]=>[3,1,2]=>00=>00
[[4,6],[5]]=>[2,1,3]=>01=>01
[[4,6],[6]]=>[2,1,3]=>01=>01
[[5,5],[6]]=>[3,1,2]=>00=>00
[[5,6],[6]]=>[2,1,3]=>01=>01
[[1],[2],[6]]=>[3,2,1]=>00=>00
[[1],[3],[6]]=>[3,2,1]=>00=>00
[[1],[4],[6]]=>[3,2,1]=>00=>00
[[1],[5],[6]]=>[3,2,1]=>00=>00
[[2],[3],[6]]=>[3,2,1]=>00=>00
[[2],[4],[6]]=>[3,2,1]=>00=>00
[[2],[5],[6]]=>[3,2,1]=>00=>00
[[3],[4],[6]]=>[3,2,1]=>00=>00
[[3],[5],[6]]=>[3,2,1]=>00=>00
[[4],[5],[6]]=>[3,2,1]=>00=>00
[[1,1,1,5]]=>[1,2,3,4]=>111=>111
[[1,1,2,5]]=>[1,2,3,4]=>111=>111
[[1,1,3,5]]=>[1,2,3,4]=>111=>111
[[1,1,4,5]]=>[1,2,3,4]=>111=>111
[[1,1,5,5]]=>[1,2,3,4]=>111=>111
[[1,2,2,5]]=>[1,2,3,4]=>111=>111
[[1,2,3,5]]=>[1,2,3,4]=>111=>111
[[1,2,4,5]]=>[1,2,3,4]=>111=>111
[[1,2,5,5]]=>[1,2,3,4]=>111=>111
[[1,3,3,5]]=>[1,2,3,4]=>111=>111
[[1,3,4,5]]=>[1,2,3,4]=>111=>111
[[1,3,5,5]]=>[1,2,3,4]=>111=>111
[[1,4,4,5]]=>[1,2,3,4]=>111=>111
[[1,4,5,5]]=>[1,2,3,4]=>111=>111
[[1,5,5,5]]=>[1,2,3,4]=>111=>111
[[2,2,2,5]]=>[1,2,3,4]=>111=>111
[[2,2,3,5]]=>[1,2,3,4]=>111=>111
[[2,2,4,5]]=>[1,2,3,4]=>111=>111
[[2,2,5,5]]=>[1,2,3,4]=>111=>111
[[2,3,3,5]]=>[1,2,3,4]=>111=>111
[[2,3,4,5]]=>[1,2,3,4]=>111=>111
[[2,3,5,5]]=>[1,2,3,4]=>111=>111
[[2,4,4,5]]=>[1,2,3,4]=>111=>111
[[2,4,5,5]]=>[1,2,3,4]=>111=>111
[[2,5,5,5]]=>[1,2,3,4]=>111=>111
[[3,3,3,5]]=>[1,2,3,4]=>111=>111
[[3,3,4,5]]=>[1,2,3,4]=>111=>111
[[3,3,5,5]]=>[1,2,3,4]=>111=>111
[[3,4,4,5]]=>[1,2,3,4]=>111=>111
[[3,4,5,5]]=>[1,2,3,4]=>111=>111
[[3,5,5,5]]=>[1,2,3,4]=>111=>111
[[4,4,4,5]]=>[1,2,3,4]=>111=>111
[[4,4,5,5]]=>[1,2,3,4]=>111=>111
[[4,5,5,5]]=>[1,2,3,4]=>111=>111
[[5,5,5,5]]=>[1,2,3,4]=>111=>111
[[1,1,1],[5]]=>[4,1,2,3]=>000=>000
[[1,1,2],[5]]=>[4,1,2,3]=>000=>000
[[1,1,5],[2]]=>[3,1,2,4]=>001=>001
[[1,1,3],[5]]=>[4,1,2,3]=>000=>000
[[1,1,5],[3]]=>[3,1,2,4]=>001=>001
[[1,1,4],[5]]=>[4,1,2,3]=>000=>000
[[1,1,5],[4]]=>[3,1,2,4]=>001=>001
[[1,1,5],[5]]=>[3,1,2,4]=>001=>001
[[1,2,2],[5]]=>[4,1,2,3]=>000=>000
[[1,2,5],[2]]=>[2,1,3,4]=>011=>011
[[1,2,3],[5]]=>[4,1,2,3]=>000=>000
[[1,2,5],[3]]=>[3,1,2,4]=>001=>001
[[1,3,5],[2]]=>[2,1,3,4]=>011=>011
[[1,2,4],[5]]=>[4,1,2,3]=>000=>000
[[1,2,5],[4]]=>[3,1,2,4]=>001=>001
[[1,4,5],[2]]=>[2,1,3,4]=>011=>011
[[1,2,5],[5]]=>[3,1,2,4]=>001=>001
[[1,5,5],[2]]=>[2,1,3,4]=>011=>011
[[1,3,3],[5]]=>[4,1,2,3]=>000=>000
[[1,3,5],[3]]=>[2,1,3,4]=>011=>011
[[1,3,4],[5]]=>[4,1,2,3]=>000=>000
[[1,3,5],[4]]=>[3,1,2,4]=>001=>001
[[1,4,5],[3]]=>[2,1,3,4]=>011=>011
[[1,3,5],[5]]=>[3,1,2,4]=>001=>001
[[1,5,5],[3]]=>[2,1,3,4]=>011=>011
[[1,4,4],[5]]=>[4,1,2,3]=>000=>000
[[1,4,5],[4]]=>[2,1,3,4]=>011=>011
[[1,4,5],[5]]=>[3,1,2,4]=>001=>001
[[1,5,5],[4]]=>[2,1,3,4]=>011=>011
[[1,5,5],[5]]=>[2,1,3,4]=>011=>011
[[2,2,2],[5]]=>[4,1,2,3]=>000=>000
[[2,2,3],[5]]=>[4,1,2,3]=>000=>000
[[2,2,5],[3]]=>[3,1,2,4]=>001=>001
[[2,2,4],[5]]=>[4,1,2,3]=>000=>000
[[2,2,5],[4]]=>[3,1,2,4]=>001=>001
[[2,2,5],[5]]=>[3,1,2,4]=>001=>001
[[2,3,3],[5]]=>[4,1,2,3]=>000=>000
[[2,3,5],[3]]=>[2,1,3,4]=>011=>011
[[2,3,4],[5]]=>[4,1,2,3]=>000=>000
[[2,3,5],[4]]=>[3,1,2,4]=>001=>001
[[2,4,5],[3]]=>[2,1,3,4]=>011=>011
[[2,3,5],[5]]=>[3,1,2,4]=>001=>001
[[2,5,5],[3]]=>[2,1,3,4]=>011=>011
[[2,4,4],[5]]=>[4,1,2,3]=>000=>000
[[2,4,5],[4]]=>[2,1,3,4]=>011=>011
[[2,4,5],[5]]=>[3,1,2,4]=>001=>001
[[2,5,5],[4]]=>[2,1,3,4]=>011=>011
[[2,5,5],[5]]=>[2,1,3,4]=>011=>011
[[3,3,3],[5]]=>[4,1,2,3]=>000=>000
[[3,3,4],[5]]=>[4,1,2,3]=>000=>000
[[3,3,5],[4]]=>[3,1,2,4]=>001=>001
[[3,3,5],[5]]=>[3,1,2,4]=>001=>001
[[3,4,4],[5]]=>[4,1,2,3]=>000=>000
[[3,4,5],[4]]=>[2,1,3,4]=>011=>011
[[3,4,5],[5]]=>[3,1,2,4]=>001=>001
[[3,5,5],[4]]=>[2,1,3,4]=>011=>011
[[3,5,5],[5]]=>[2,1,3,4]=>011=>011
[[4,4,4],[5]]=>[4,1,2,3]=>000=>000
[[4,4,5],[5]]=>[3,1,2,4]=>001=>001
[[4,5,5],[5]]=>[2,1,3,4]=>011=>011
[[1,1],[2,5]]=>[3,4,1,2]=>000=>000
[[1,1],[3,5]]=>[3,4,1,2]=>000=>000
[[1,1],[4,5]]=>[3,4,1,2]=>000=>000
[[1,1],[5,5]]=>[3,4,1,2]=>000=>000
[[1,2],[2,5]]=>[2,4,1,3]=>000=>000
[[1,2],[3,5]]=>[3,4,1,2]=>000=>000
[[1,3],[2,5]]=>[2,4,1,3]=>000=>000
[[1,2],[4,5]]=>[3,4,1,2]=>000=>000
[[1,4],[2,5]]=>[2,4,1,3]=>000=>000
[[1,2],[5,5]]=>[3,4,1,2]=>000=>000
[[1,3],[3,5]]=>[2,4,1,3]=>000=>000
[[1,3],[4,5]]=>[3,4,1,2]=>000=>000
[[1,4],[3,5]]=>[2,4,1,3]=>000=>000
[[1,3],[5,5]]=>[3,4,1,2]=>000=>000
[[1,4],[4,5]]=>[2,4,1,3]=>000=>000
[[1,4],[5,5]]=>[3,4,1,2]=>000=>000
[[2,2],[3,5]]=>[3,4,1,2]=>000=>000
[[2,2],[4,5]]=>[3,4,1,2]=>000=>000
[[2,2],[5,5]]=>[3,4,1,2]=>000=>000
[[2,3],[3,5]]=>[2,4,1,3]=>000=>000
[[2,3],[4,5]]=>[3,4,1,2]=>000=>000
[[2,4],[3,5]]=>[2,4,1,3]=>000=>000
[[2,3],[5,5]]=>[3,4,1,2]=>000=>000
[[2,4],[4,5]]=>[2,4,1,3]=>000=>000
[[2,4],[5,5]]=>[3,4,1,2]=>000=>000
[[3,3],[4,5]]=>[3,4,1,2]=>000=>000
[[3,3],[5,5]]=>[3,4,1,2]=>000=>000
[[3,4],[4,5]]=>[2,4,1,3]=>000=>000
[[3,4],[5,5]]=>[3,4,1,2]=>000=>000
[[4,4],[5,5]]=>[3,4,1,2]=>000=>000
[[1,1],[2],[5]]=>[4,3,1,2]=>000=>000
[[1,1],[3],[5]]=>[4,3,1,2]=>000=>000
[[1,1],[4],[5]]=>[4,3,1,2]=>000=>000
[[1,2],[2],[5]]=>[4,2,1,3]=>000=>000
[[1,2],[3],[5]]=>[4,3,1,2]=>000=>000
[[1,3],[2],[5]]=>[4,2,1,3]=>000=>000
[[1,5],[2],[3]]=>[3,2,1,4]=>001=>001
[[1,2],[4],[5]]=>[4,3,1,2]=>000=>000
[[1,4],[2],[5]]=>[4,2,1,3]=>000=>000
[[1,5],[2],[4]]=>[3,2,1,4]=>001=>001
[[1,5],[2],[5]]=>[3,2,1,4]=>001=>001
[[1,3],[3],[5]]=>[4,2,1,3]=>000=>000
[[1,3],[4],[5]]=>[4,3,1,2]=>000=>000
[[1,4],[3],[5]]=>[4,2,1,3]=>000=>000
[[1,5],[3],[4]]=>[3,2,1,4]=>001=>001
[[1,5],[3],[5]]=>[3,2,1,4]=>001=>001
[[1,4],[4],[5]]=>[4,2,1,3]=>000=>000
[[1,5],[4],[5]]=>[3,2,1,4]=>001=>001
[[2,2],[3],[5]]=>[4,3,1,2]=>000=>000
[[2,2],[4],[5]]=>[4,3,1,2]=>000=>000
[[2,3],[3],[5]]=>[4,2,1,3]=>000=>000
[[2,3],[4],[5]]=>[4,3,1,2]=>000=>000
[[2,4],[3],[5]]=>[4,2,1,3]=>000=>000
[[2,5],[3],[4]]=>[3,2,1,4]=>001=>001
[[2,5],[3],[5]]=>[3,2,1,4]=>001=>001
[[2,4],[4],[5]]=>[4,2,1,3]=>000=>000
[[2,5],[4],[5]]=>[3,2,1,4]=>001=>001
[[3,3],[4],[5]]=>[4,3,1,2]=>000=>000
[[3,4],[4],[5]]=>[4,2,1,3]=>000=>000
[[3,5],[4],[5]]=>[3,2,1,4]=>001=>001
[[1],[2],[3],[5]]=>[4,3,2,1]=>000=>000
[[1],[2],[4],[5]]=>[4,3,2,1]=>000=>000
[[1],[3],[4],[5]]=>[4,3,2,1]=>000=>000
[[2],[3],[4],[5]]=>[4,3,2,1]=>000=>000
[[1,1,1,1,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,2,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,3,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,2,2,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,2,3,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,2,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,3,3,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,3,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,4,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,2,2,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,2,3,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,2,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,3,3,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,3,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,4,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,3,3,3,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,3,3,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,3,4,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,4,4,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,2,2,4]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,2,3,4]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,2,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,3,3,4]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,3,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,4,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[2,3,3,3,4]]=>[1,2,3,4,5]=>1111=>1111
[[2,3,3,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[2,3,4,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[2,4,4,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[3,3,3,3,4]]=>[1,2,3,4,5]=>1111=>1111
[[3,3,3,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[3,3,4,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[3,4,4,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[4,4,4,4,4]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,1],[4]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,1,2],[4]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,1,4],[2]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,1,3],[4]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,1,4],[3]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,1,4],[4]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,2,2],[4]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,2,4],[2]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,2,3],[4]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,2,4],[3]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,3,4],[2]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,2,4],[4]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,4,4],[2]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,3,3],[4]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,3,4],[3]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,3,4],[4]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,4,4],[3]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,4,4],[4]]=>[3,1,2,4,5]=>0011=>0011
[[1,2,2,2],[4]]=>[5,1,2,3,4]=>0000=>0000
[[1,2,2,4],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,2,3],[4]]=>[5,1,2,3,4]=>0000=>0000
[[1,2,2,4],[3]]=>[4,1,2,3,5]=>0001=>0001
[[1,2,3,4],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,2,4],[4]]=>[4,1,2,3,5]=>0001=>0001
[[1,2,4,4],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,3,3],[4]]=>[5,1,2,3,4]=>0000=>0000
[[1,2,3,4],[3]]=>[3,1,2,4,5]=>0011=>0011
[[1,3,3,4],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,3,4],[4]]=>[4,1,2,3,5]=>0001=>0001
[[1,2,4,4],[3]]=>[3,1,2,4,5]=>0011=>0011
[[1,3,4,4],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,4,4],[4]]=>[3,1,2,4,5]=>0011=>0011
[[1,4,4,4],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,3,3,3],[4]]=>[5,1,2,3,4]=>0000=>0000
[[1,3,3,4],[3]]=>[2,1,3,4,5]=>0111=>0111
[[1,3,3,4],[4]]=>[4,1,2,3,5]=>0001=>0001
[[1,3,4,4],[3]]=>[2,1,3,4,5]=>0111=>0111
[[1,3,4,4],[4]]=>[3,1,2,4,5]=>0011=>0011
[[1,4,4,4],[3]]=>[2,1,3,4,5]=>0111=>0111
[[1,4,4,4],[4]]=>[2,1,3,4,5]=>0111=>0111
[[2,2,2,2],[4]]=>[5,1,2,3,4]=>0000=>0000
[[2,2,2,3],[4]]=>[5,1,2,3,4]=>0000=>0000
[[2,2,2,4],[3]]=>[4,1,2,3,5]=>0001=>0001
[[2,2,2,4],[4]]=>[4,1,2,3,5]=>0001=>0001
[[2,2,3,3],[4]]=>[5,1,2,3,4]=>0000=>0000
[[2,2,3,4],[3]]=>[3,1,2,4,5]=>0011=>0011
[[2,2,3,4],[4]]=>[4,1,2,3,5]=>0001=>0001
[[2,2,4,4],[3]]=>[3,1,2,4,5]=>0011=>0011
[[2,2,4,4],[4]]=>[3,1,2,4,5]=>0011=>0011
[[2,3,3,3],[4]]=>[5,1,2,3,4]=>0000=>0000
[[2,3,3,4],[3]]=>[2,1,3,4,5]=>0111=>0111
[[2,3,3,4],[4]]=>[4,1,2,3,5]=>0001=>0001
[[2,3,4,4],[3]]=>[2,1,3,4,5]=>0111=>0111
[[2,3,4,4],[4]]=>[3,1,2,4,5]=>0011=>0011
[[2,4,4,4],[3]]=>[2,1,3,4,5]=>0111=>0111
[[2,4,4,4],[4]]=>[2,1,3,4,5]=>0111=>0111
[[3,3,3,3],[4]]=>[5,1,2,3,4]=>0000=>0000
[[3,3,3,4],[4]]=>[4,1,2,3,5]=>0001=>0001
[[3,3,4,4],[4]]=>[3,1,2,4,5]=>0011=>0011
[[3,4,4,4],[4]]=>[2,1,3,4,5]=>0111=>0111
[[1,1,1],[2,4]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,1],[3,4]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,1],[4,4]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,2],[2,4]]=>[3,5,1,2,4]=>0000=>0000
[[1,1,4],[2,2]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,2],[3,4]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,3],[2,4]]=>[3,5,1,2,4]=>0000=>0000
[[1,1,4],[2,3]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,2],[4,4]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,4],[2,4]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,3],[3,4]]=>[3,5,1,2,4]=>0000=>0000
[[1,1,4],[3,3]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,3],[4,4]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,4],[3,4]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,4],[4,4]]=>[3,4,1,2,5]=>0001=>0001
[[1,2,2],[2,4]]=>[2,5,1,3,4]=>0000=>0000
[[1,2,2],[3,4]]=>[4,5,1,2,3]=>0000=>0000
[[1,2,3],[2,4]]=>[2,5,1,3,4]=>0000=>0000
[[1,2,4],[2,3]]=>[2,4,1,3,5]=>0001=>0001
[[1,2,2],[4,4]]=>[4,5,1,2,3]=>0000=>0000
[[1,2,4],[2,4]]=>[2,4,1,3,5]=>0001=>0001
[[1,2,3],[3,4]]=>[3,5,1,2,4]=>0000=>0000
[[1,2,4],[3,3]]=>[3,4,1,2,5]=>0001=>0001
[[1,3,3],[2,4]]=>[2,5,1,3,4]=>0000=>0000
[[1,2,3],[4,4]]=>[4,5,1,2,3]=>0000=>0000
[[1,2,4],[3,4]]=>[3,4,1,2,5]=>0001=>0001
[[1,3,4],[2,4]]=>[2,4,1,3,5]=>0001=>0001
[[1,2,4],[4,4]]=>[3,4,1,2,5]=>0001=>0001
[[1,3,3],[3,4]]=>[2,5,1,3,4]=>0000=>0000
[[1,3,3],[4,4]]=>[4,5,1,2,3]=>0000=>0000
[[1,3,4],[3,4]]=>[2,4,1,3,5]=>0001=>0001
[[1,3,4],[4,4]]=>[3,4,1,2,5]=>0001=>0001
[[2,2,2],[3,4]]=>[4,5,1,2,3]=>0000=>0000
[[2,2,2],[4,4]]=>[4,5,1,2,3]=>0000=>0000
[[2,2,3],[3,4]]=>[3,5,1,2,4]=>0000=>0000
[[2,2,4],[3,3]]=>[3,4,1,2,5]=>0001=>0001
[[2,2,3],[4,4]]=>[4,5,1,2,3]=>0000=>0000
[[2,2,4],[3,4]]=>[3,4,1,2,5]=>0001=>0001
[[2,2,4],[4,4]]=>[3,4,1,2,5]=>0001=>0001
[[2,3,3],[3,4]]=>[2,5,1,3,4]=>0000=>0000
[[2,3,3],[4,4]]=>[4,5,1,2,3]=>0000=>0000
[[2,3,4],[3,4]]=>[2,4,1,3,5]=>0001=>0001
[[2,3,4],[4,4]]=>[3,4,1,2,5]=>0001=>0001
[[3,3,3],[4,4]]=>[4,5,1,2,3]=>0000=>0000
[[3,3,4],[4,4]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,1],[2],[4]]=>[5,4,1,2,3]=>0000=>0000
[[1,1,1],[3],[4]]=>[5,4,1,2,3]=>0000=>0000
[[1,1,2],[2],[4]]=>[5,3,1,2,4]=>0000=>0000
[[1,1,2],[3],[4]]=>[5,4,1,2,3]=>0000=>0000
[[1,1,3],[2],[4]]=>[5,3,1,2,4]=>0000=>0000
[[1,1,4],[2],[3]]=>[4,3,1,2,5]=>0001=>0001
[[1,1,4],[2],[4]]=>[4,3,1,2,5]=>0001=>0001
[[1,1,3],[3],[4]]=>[5,3,1,2,4]=>0000=>0000
[[1,1,4],[3],[4]]=>[4,3,1,2,5]=>0001=>0001
[[1,2,2],[2],[4]]=>[5,2,1,3,4]=>0000=>0000
[[1,2,2],[3],[4]]=>[5,4,1,2,3]=>0000=>0000
[[1,2,3],[2],[4]]=>[5,2,1,3,4]=>0000=>0000
[[1,2,4],[2],[3]]=>[4,2,1,3,5]=>0001=>0001
[[1,2,4],[2],[4]]=>[4,2,1,3,5]=>0001=>0001
[[1,2,3],[3],[4]]=>[5,3,1,2,4]=>0000=>0000
[[1,3,3],[2],[4]]=>[5,2,1,3,4]=>0000=>0000
[[1,3,4],[2],[3]]=>[3,2,1,4,5]=>0011=>0011
[[1,2,4],[3],[4]]=>[4,3,1,2,5]=>0001=>0001
[[1,3,4],[2],[4]]=>[4,2,1,3,5]=>0001=>0001
[[1,4,4],[2],[3]]=>[3,2,1,4,5]=>0011=>0011
[[1,4,4],[2],[4]]=>[3,2,1,4,5]=>0011=>0011
[[1,3,3],[3],[4]]=>[5,2,1,3,4]=>0000=>0000
[[1,3,4],[3],[4]]=>[4,2,1,3,5]=>0001=>0001
[[1,4,4],[3],[4]]=>[3,2,1,4,5]=>0011=>0011
[[2,2,2],[3],[4]]=>[5,4,1,2,3]=>0000=>0000
[[2,2,3],[3],[4]]=>[5,3,1,2,4]=>0000=>0000
[[2,2,4],[3],[4]]=>[4,3,1,2,5]=>0001=>0001
[[2,3,3],[3],[4]]=>[5,2,1,3,4]=>0000=>0000
[[2,3,4],[3],[4]]=>[4,2,1,3,5]=>0001=>0001
[[2,4,4],[3],[4]]=>[3,2,1,4,5]=>0011=>0011
[[1,1],[2,2],[4]]=>[5,3,4,1,2]=>0000=>0000
[[1,1],[2,3],[4]]=>[5,3,4,1,2]=>0000=>0000
[[1,1],[2,4],[3]]=>[4,3,5,1,2]=>0000=>0000
[[1,1],[2,4],[4]]=>[4,3,5,1,2]=>0000=>0000
[[1,1],[3,3],[4]]=>[5,3,4,1,2]=>0000=>0000
[[1,1],[3,4],[4]]=>[4,3,5,1,2]=>0000=>0000
[[1,2],[2,3],[4]]=>[5,2,4,1,3]=>0000=>0000
[[1,2],[2,4],[3]]=>[4,2,5,1,3]=>0000=>0000
[[1,2],[2,4],[4]]=>[4,2,5,1,3]=>0000=>0000
[[1,2],[3,3],[4]]=>[5,3,4,1,2]=>0000=>0000
[[1,3],[2,4],[3]]=>[3,2,5,1,4]=>0000=>0000
[[1,2],[3,4],[4]]=>[4,3,5,1,2]=>0000=>0000
[[1,3],[2,4],[4]]=>[4,2,5,1,3]=>0000=>0000
[[1,3],[3,4],[4]]=>[4,2,5,1,3]=>0000=>0000
[[2,2],[3,3],[4]]=>[5,3,4,1,2]=>0000=>0000
[[2,2],[3,4],[4]]=>[4,3,5,1,2]=>0000=>0000
[[2,3],[3,4],[4]]=>[4,2,5,1,3]=>0000=>0000
[[1,1],[2],[3],[4]]=>[5,4,3,1,2]=>0000=>0000
[[1,2],[2],[3],[4]]=>[5,4,2,1,3]=>0000=>0000
[[1,3],[2],[3],[4]]=>[5,3,2,1,4]=>0000=>0000
[[1,4],[2],[3],[4]]=>[4,3,2,1,5]=>0001=>0001
[[1,1,1,1,1,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,1,2,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,1,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,2,2,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,2,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,3,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,2,2,2,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,2,2,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,2,3,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,3,3,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,2,2,2,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,2,2,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,2,3,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,3,3,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,3,3,3,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,2,2,2,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,2,2,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,2,3,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,3,3,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,3,3,3,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[3,3,3,3,3,3]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,1,1],[3]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,1,1,2],[3]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,1,1,3],[2]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,1,1,3],[3]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,1,2,2],[3]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,1,2,3],[2]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,1,2,3],[3]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,1,3,3],[2]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,1,3,3],[3]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,2,2,2],[3]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,2,2,3],[2]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,1,2,2,3],[3]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,2,3,3],[2]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,1,2,3,3],[3]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,3,3,3],[2]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,1,3,3,3],[3]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,2,2,2,2],[3]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,2,2,2,3],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,2,2,2,3],[3]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,2,2,3,3],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,2,2,3,3],[3]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,2,3,3,3],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,2,3,3,3],[3]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,3,3,3,3],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,3,3,3,3],[3]]=>[2,1,3,4,5,6]=>01111=>01111
[[2,2,2,2,2],[3]]=>[6,1,2,3,4,5]=>00000=>00000
[[2,2,2,2,3],[3]]=>[5,1,2,3,4,6]=>00001=>00001
[[2,2,2,3,3],[3]]=>[4,1,2,3,5,6]=>00011=>00011
[[2,2,3,3,3],[3]]=>[3,1,2,4,5,6]=>00111=>00111
[[2,3,3,3,3],[3]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,1,1,1],[2,3]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,1,1],[3,3]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,1,2],[2,3]]=>[4,6,1,2,3,5]=>00000=>00000
[[1,1,1,3],[2,2]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,1,2],[3,3]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,1,3],[2,3]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,1,3],[3,3]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,2,2],[2,3]]=>[3,6,1,2,4,5]=>00000=>00000
[[1,1,2,3],[2,2]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,2,2],[3,3]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,2,3],[2,3]]=>[3,5,1,2,4,6]=>00001=>00001
[[1,1,3,3],[2,2]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,2,3],[3,3]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,3,3],[2,3]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,3,3],[3,3]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,2,2,2],[2,3]]=>[2,6,1,3,4,5]=>00000=>00000
[[1,2,2,2],[3,3]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,2,2,3],[2,3]]=>[2,5,1,3,4,6]=>00001=>00001
[[1,2,2,3],[3,3]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,2,3,3],[2,3]]=>[2,4,1,3,5,6]=>00011=>00011
[[1,2,3,3],[3,3]]=>[3,4,1,2,5,6]=>00011=>00011
[[2,2,2,2],[3,3]]=>[5,6,1,2,3,4]=>00000=>00000
[[2,2,2,3],[3,3]]=>[4,5,1,2,3,6]=>00001=>00001
[[2,2,3,3],[3,3]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,1,1],[2],[3]]=>[6,5,1,2,3,4]=>00000=>00000
[[1,1,1,2],[2],[3]]=>[6,4,1,2,3,5]=>00000=>00000
[[1,1,1,3],[2],[3]]=>[5,4,1,2,3,6]=>00001=>00001
[[1,1,2,2],[2],[3]]=>[6,3,1,2,4,5]=>00000=>00000
[[1,1,2,3],[2],[3]]=>[5,3,1,2,4,6]=>00001=>00001
[[1,1,3,3],[2],[3]]=>[4,3,1,2,5,6]=>00011=>00011
[[1,2,2,2],[2],[3]]=>[6,2,1,3,4,5]=>00000=>00000
[[1,2,2,3],[2],[3]]=>[5,2,1,3,4,6]=>00001=>00001
[[1,2,3,3],[2],[3]]=>[4,2,1,3,5,6]=>00011=>00011
[[1,3,3,3],[2],[3]]=>[3,2,1,4,5,6]=>00111=>00111
[[1,1,1],[2,2,3]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,1],[2,3,3]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,1],[3,3,3]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,2],[2,2,3]]=>[3,4,6,1,2,5]=>00000=>00000
[[1,1,2],[2,3,3]]=>[3,5,6,1,2,4]=>00000=>00000
[[1,1,2],[3,3,3]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,2,2],[2,3,3]]=>[2,5,6,1,3,4]=>00000=>00000
[[1,2,2],[3,3,3]]=>[4,5,6,1,2,3]=>00000=>00000
[[2,2,2],[3,3,3]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,1],[2,2],[3]]=>[6,4,5,1,2,3]=>00000=>00000
[[1,1,1],[2,3],[3]]=>[5,4,6,1,2,3]=>00000=>00000
[[1,1,2],[2,2],[3]]=>[6,3,4,1,2,5]=>00000=>00000
[[1,1,2],[2,3],[3]]=>[5,3,6,1,2,4]=>00000=>00000
[[1,1,3],[2,2],[3]]=>[5,3,4,1,2,6]=>00001=>00001
[[1,1,3],[2,3],[3]]=>[4,3,5,1,2,6]=>00001=>00001
[[1,2,2],[2,3],[3]]=>[5,2,6,1,3,4]=>00000=>00000
[[1,2,3],[2,3],[3]]=>[4,2,5,1,3,6]=>00001=>00001
[[1,1],[2,2],[3,3]]=>[5,6,3,4,1,2]=>00000=>00000
[[1,1,1,1,1,1,2]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,1,1,2,2]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,1,2,2,2]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,2,2,2,2]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,2,2,2,2,2]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[2,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,1,1,1],[2]]=>[7,1,2,3,4,5,6]=>000000=>000000
[[1,1,1,1,1,2],[2]]=>[6,1,2,3,4,5,7]=>000001=>000001
[[1,1,1,1,2,2],[2]]=>[5,1,2,3,4,6,7]=>000011=>000011
[[1,1,1,2,2,2],[2]]=>[4,1,2,3,5,6,7]=>000111=>000111
[[1,1,2,2,2,2],[2]]=>[3,1,2,4,5,6,7]=>001111=>001111
[[1,2,2,2,2,2],[2]]=>[2,1,3,4,5,6,7]=>011111=>011111
[[1,1,1,1,1],[2,2]]=>[6,7,1,2,3,4,5]=>000000=>000000
[[1,1,1,1,2],[2,2]]=>[5,6,1,2,3,4,7]=>000001=>000001
[[1,1,1,2,2],[2,2]]=>[4,5,1,2,3,6,7]=>000011=>000011
[[1,1,2,2,2],[2,2]]=>[3,4,1,2,5,6,7]=>000111=>000111
[[1,1,1,1],[2,2,2]]=>[5,6,7,1,2,3,4]=>000000=>000000
[[1,1,1,2],[2,2,2]]=>[4,5,6,1,2,3,7]=>000001=>000001
[[1,8]]=>[1,2]=>1=>1
[[2,8]]=>[1,2]=>1=>1
[[3,8]]=>[1,2]=>1=>1
[[4,8]]=>[1,2]=>1=>1
[[5,8]]=>[1,2]=>1=>1
[[6,8]]=>[1,2]=>1=>1
[[7,8]]=>[1,2]=>1=>1
[[8,8]]=>[1,2]=>1=>1
[[1],[8]]=>[2,1]=>0=>0
[[2],[8]]=>[2,1]=>0=>0
[[3],[8]]=>[2,1]=>0=>0
[[4],[8]]=>[2,1]=>0=>0
[[5],[8]]=>[2,1]=>0=>0
[[6],[8]]=>[2,1]=>0=>0
[[7],[8]]=>[2,1]=>0=>0
[[1,1,7]]=>[1,2,3]=>11=>11
[[1,2,7]]=>[1,2,3]=>11=>11
[[1,3,7]]=>[1,2,3]=>11=>11
[[1,4,7]]=>[1,2,3]=>11=>11
[[1,5,7]]=>[1,2,3]=>11=>11
[[1,6,7]]=>[1,2,3]=>11=>11
[[1,7,7]]=>[1,2,3]=>11=>11
[[2,2,7]]=>[1,2,3]=>11=>11
[[2,3,7]]=>[1,2,3]=>11=>11
[[2,4,7]]=>[1,2,3]=>11=>11
[[2,5,7]]=>[1,2,3]=>11=>11
[[2,6,7]]=>[1,2,3]=>11=>11
[[2,7,7]]=>[1,2,3]=>11=>11
[[3,3,7]]=>[1,2,3]=>11=>11
[[3,4,7]]=>[1,2,3]=>11=>11
[[3,5,7]]=>[1,2,3]=>11=>11
[[3,6,7]]=>[1,2,3]=>11=>11
[[3,7,7]]=>[1,2,3]=>11=>11
[[4,4,7]]=>[1,2,3]=>11=>11
[[4,5,7]]=>[1,2,3]=>11=>11
[[4,6,7]]=>[1,2,3]=>11=>11
[[4,7,7]]=>[1,2,3]=>11=>11
[[5,5,7]]=>[1,2,3]=>11=>11
[[5,6,7]]=>[1,2,3]=>11=>11
[[5,7,7]]=>[1,2,3]=>11=>11
[[6,6,7]]=>[1,2,3]=>11=>11
[[6,7,7]]=>[1,2,3]=>11=>11
[[7,7,7]]=>[1,2,3]=>11=>11
[[1,1],[7]]=>[3,1,2]=>00=>00
[[1,2],[7]]=>[3,1,2]=>00=>00
[[1,7],[2]]=>[2,1,3]=>01=>01
[[1,3],[7]]=>[3,1,2]=>00=>00
[[1,7],[3]]=>[2,1,3]=>01=>01
[[1,4],[7]]=>[3,1,2]=>00=>00
[[1,7],[4]]=>[2,1,3]=>01=>01
[[1,5],[7]]=>[3,1,2]=>00=>00
[[1,7],[5]]=>[2,1,3]=>01=>01
[[1,6],[7]]=>[3,1,2]=>00=>00
[[1,7],[6]]=>[2,1,3]=>01=>01
[[1,7],[7]]=>[2,1,3]=>01=>01
[[2,2],[7]]=>[3,1,2]=>00=>00
[[2,3],[7]]=>[3,1,2]=>00=>00
[[2,7],[3]]=>[2,1,3]=>01=>01
[[2,4],[7]]=>[3,1,2]=>00=>00
[[2,7],[4]]=>[2,1,3]=>01=>01
[[2,5],[7]]=>[3,1,2]=>00=>00
[[2,7],[5]]=>[2,1,3]=>01=>01
[[2,6],[7]]=>[3,1,2]=>00=>00
[[2,7],[6]]=>[2,1,3]=>01=>01
[[2,7],[7]]=>[2,1,3]=>01=>01
[[3,3],[7]]=>[3,1,2]=>00=>00
[[3,4],[7]]=>[3,1,2]=>00=>00
[[3,7],[4]]=>[2,1,3]=>01=>01
[[3,5],[7]]=>[3,1,2]=>00=>00
[[3,7],[5]]=>[2,1,3]=>01=>01
[[3,6],[7]]=>[3,1,2]=>00=>00
[[3,7],[6]]=>[2,1,3]=>01=>01
[[3,7],[7]]=>[2,1,3]=>01=>01
[[4,4],[7]]=>[3,1,2]=>00=>00
[[4,5],[7]]=>[3,1,2]=>00=>00
[[4,7],[5]]=>[2,1,3]=>01=>01
[[4,6],[7]]=>[3,1,2]=>00=>00
[[4,7],[6]]=>[2,1,3]=>01=>01
[[4,7],[7]]=>[2,1,3]=>01=>01
[[5,5],[7]]=>[3,1,2]=>00=>00
[[5,6],[7]]=>[3,1,2]=>00=>00
[[5,7],[6]]=>[2,1,3]=>01=>01
[[5,7],[7]]=>[2,1,3]=>01=>01
[[6,6],[7]]=>[3,1,2]=>00=>00
[[6,7],[7]]=>[2,1,3]=>01=>01
[[1],[2],[7]]=>[3,2,1]=>00=>00
[[1],[3],[7]]=>[3,2,1]=>00=>00
[[1],[4],[7]]=>[3,2,1]=>00=>00
[[1],[5],[7]]=>[3,2,1]=>00=>00
[[1],[6],[7]]=>[3,2,1]=>00=>00
[[2],[3],[7]]=>[3,2,1]=>00=>00
[[2],[4],[7]]=>[3,2,1]=>00=>00
[[2],[5],[7]]=>[3,2,1]=>00=>00
[[2],[6],[7]]=>[3,2,1]=>00=>00
[[3],[4],[7]]=>[3,2,1]=>00=>00
[[3],[5],[7]]=>[3,2,1]=>00=>00
[[3],[6],[7]]=>[3,2,1]=>00=>00
[[4],[5],[7]]=>[3,2,1]=>00=>00
[[4],[6],[7]]=>[3,2,1]=>00=>00
[[5],[6],[7]]=>[3,2,1]=>00=>00
[[1,1,1,6]]=>[1,2,3,4]=>111=>111
[[1,1,2,6]]=>[1,2,3,4]=>111=>111
[[1,1,3,6]]=>[1,2,3,4]=>111=>111
[[1,1,4,6]]=>[1,2,3,4]=>111=>111
[[1,1,5,6]]=>[1,2,3,4]=>111=>111
[[1,1,6,6]]=>[1,2,3,4]=>111=>111
[[1,2,2,6]]=>[1,2,3,4]=>111=>111
[[1,2,3,6]]=>[1,2,3,4]=>111=>111
[[1,2,4,6]]=>[1,2,3,4]=>111=>111
[[1,2,5,6]]=>[1,2,3,4]=>111=>111
[[1,2,6,6]]=>[1,2,3,4]=>111=>111
[[1,3,3,6]]=>[1,2,3,4]=>111=>111
[[1,3,4,6]]=>[1,2,3,4]=>111=>111
[[1,3,5,6]]=>[1,2,3,4]=>111=>111
[[1,3,6,6]]=>[1,2,3,4]=>111=>111
[[1,4,4,6]]=>[1,2,3,4]=>111=>111
[[1,4,5,6]]=>[1,2,3,4]=>111=>111
[[1,4,6,6]]=>[1,2,3,4]=>111=>111
[[1,5,5,6]]=>[1,2,3,4]=>111=>111
[[1,5,6,6]]=>[1,2,3,4]=>111=>111
[[1,6,6,6]]=>[1,2,3,4]=>111=>111
[[2,2,2,6]]=>[1,2,3,4]=>111=>111
[[2,2,3,6]]=>[1,2,3,4]=>111=>111
[[2,2,4,6]]=>[1,2,3,4]=>111=>111
[[2,2,5,6]]=>[1,2,3,4]=>111=>111
[[2,2,6,6]]=>[1,2,3,4]=>111=>111
[[2,3,3,6]]=>[1,2,3,4]=>111=>111
[[2,3,4,6]]=>[1,2,3,4]=>111=>111
[[2,3,5,6]]=>[1,2,3,4]=>111=>111
[[2,3,6,6]]=>[1,2,3,4]=>111=>111
[[2,4,4,6]]=>[1,2,3,4]=>111=>111
[[2,4,5,6]]=>[1,2,3,4]=>111=>111
[[2,4,6,6]]=>[1,2,3,4]=>111=>111
[[2,5,5,6]]=>[1,2,3,4]=>111=>111
[[2,5,6,6]]=>[1,2,3,4]=>111=>111
[[2,6,6,6]]=>[1,2,3,4]=>111=>111
[[3,3,3,6]]=>[1,2,3,4]=>111=>111
[[3,3,4,6]]=>[1,2,3,4]=>111=>111
[[3,3,5,6]]=>[1,2,3,4]=>111=>111
[[3,3,6,6]]=>[1,2,3,4]=>111=>111
[[3,4,4,6]]=>[1,2,3,4]=>111=>111
[[3,4,5,6]]=>[1,2,3,4]=>111=>111
[[3,4,6,6]]=>[1,2,3,4]=>111=>111
[[3,5,5,6]]=>[1,2,3,4]=>111=>111
[[3,5,6,6]]=>[1,2,3,4]=>111=>111
[[3,6,6,6]]=>[1,2,3,4]=>111=>111
[[4,4,4,6]]=>[1,2,3,4]=>111=>111
[[4,4,5,6]]=>[1,2,3,4]=>111=>111
[[4,4,6,6]]=>[1,2,3,4]=>111=>111
[[4,5,5,6]]=>[1,2,3,4]=>111=>111
[[4,5,6,6]]=>[1,2,3,4]=>111=>111
[[4,6,6,6]]=>[1,2,3,4]=>111=>111
[[5,5,5,6]]=>[1,2,3,4]=>111=>111
[[5,5,6,6]]=>[1,2,3,4]=>111=>111
[[5,6,6,6]]=>[1,2,3,4]=>111=>111
[[6,6,6,6]]=>[1,2,3,4]=>111=>111
[[1,1,1],[6]]=>[4,1,2,3]=>000=>000
[[1,1,2],[6]]=>[4,1,2,3]=>000=>000
[[1,1,6],[2]]=>[3,1,2,4]=>001=>001
[[1,1,3],[6]]=>[4,1,2,3]=>000=>000
[[1,1,6],[3]]=>[3,1,2,4]=>001=>001
[[1,1,4],[6]]=>[4,1,2,3]=>000=>000
[[1,1,6],[4]]=>[3,1,2,4]=>001=>001
[[1,1,5],[6]]=>[4,1,2,3]=>000=>000
[[1,1,6],[5]]=>[3,1,2,4]=>001=>001
[[1,1,6],[6]]=>[3,1,2,4]=>001=>001
[[1,2,2],[6]]=>[4,1,2,3]=>000=>000
[[1,2,6],[2]]=>[2,1,3,4]=>011=>011
[[1,2,3],[6]]=>[4,1,2,3]=>000=>000
[[1,2,6],[3]]=>[3,1,2,4]=>001=>001
[[1,3,6],[2]]=>[2,1,3,4]=>011=>011
[[1,2,4],[6]]=>[4,1,2,3]=>000=>000
[[1,2,6],[4]]=>[3,1,2,4]=>001=>001
[[1,4,6],[2]]=>[2,1,3,4]=>011=>011
[[1,2,5],[6]]=>[4,1,2,3]=>000=>000
[[1,2,6],[5]]=>[3,1,2,4]=>001=>001
[[1,5,6],[2]]=>[2,1,3,4]=>011=>011
[[1,2,6],[6]]=>[3,1,2,4]=>001=>001
[[1,6,6],[2]]=>[2,1,3,4]=>011=>011
[[1,3,3],[6]]=>[4,1,2,3]=>000=>000
[[1,3,6],[3]]=>[2,1,3,4]=>011=>011
[[1,3,4],[6]]=>[4,1,2,3]=>000=>000
[[1,3,6],[4]]=>[3,1,2,4]=>001=>001
[[1,4,6],[3]]=>[2,1,3,4]=>011=>011
[[1,3,5],[6]]=>[4,1,2,3]=>000=>000
[[1,3,6],[5]]=>[3,1,2,4]=>001=>001
[[1,5,6],[3]]=>[2,1,3,4]=>011=>011
[[1,3,6],[6]]=>[3,1,2,4]=>001=>001
[[1,6,6],[3]]=>[2,1,3,4]=>011=>011
[[1,4,4],[6]]=>[4,1,2,3]=>000=>000
[[1,4,6],[4]]=>[2,1,3,4]=>011=>011
[[1,4,5],[6]]=>[4,1,2,3]=>000=>000
[[1,4,6],[5]]=>[3,1,2,4]=>001=>001
[[1,5,6],[4]]=>[2,1,3,4]=>011=>011
[[1,4,6],[6]]=>[3,1,2,4]=>001=>001
[[1,6,6],[4]]=>[2,1,3,4]=>011=>011
[[1,5,5],[6]]=>[4,1,2,3]=>000=>000
[[1,5,6],[5]]=>[2,1,3,4]=>011=>011
[[1,5,6],[6]]=>[3,1,2,4]=>001=>001
[[1,6,6],[5]]=>[2,1,3,4]=>011=>011
[[1,6,6],[6]]=>[2,1,3,4]=>011=>011
[[2,2,2],[6]]=>[4,1,2,3]=>000=>000
[[2,2,3],[6]]=>[4,1,2,3]=>000=>000
[[2,2,6],[3]]=>[3,1,2,4]=>001=>001
[[2,2,4],[6]]=>[4,1,2,3]=>000=>000
[[2,2,6],[4]]=>[3,1,2,4]=>001=>001
[[2,2,5],[6]]=>[4,1,2,3]=>000=>000
[[2,2,6],[5]]=>[3,1,2,4]=>001=>001
[[2,2,6],[6]]=>[3,1,2,4]=>001=>001
[[2,3,3],[6]]=>[4,1,2,3]=>000=>000
[[2,3,6],[3]]=>[2,1,3,4]=>011=>011
[[2,3,4],[6]]=>[4,1,2,3]=>000=>000
[[2,3,6],[4]]=>[3,1,2,4]=>001=>001
[[2,4,6],[3]]=>[2,1,3,4]=>011=>011
[[2,3,5],[6]]=>[4,1,2,3]=>000=>000
[[2,3,6],[5]]=>[3,1,2,4]=>001=>001
[[2,5,6],[3]]=>[2,1,3,4]=>011=>011
[[2,3,6],[6]]=>[3,1,2,4]=>001=>001
[[2,6,6],[3]]=>[2,1,3,4]=>011=>011
[[2,4,4],[6]]=>[4,1,2,3]=>000=>000
[[2,4,6],[4]]=>[2,1,3,4]=>011=>011
[[2,4,5],[6]]=>[4,1,2,3]=>000=>000
[[2,4,6],[5]]=>[3,1,2,4]=>001=>001
[[2,5,6],[4]]=>[2,1,3,4]=>011=>011
[[2,4,6],[6]]=>[3,1,2,4]=>001=>001
[[2,6,6],[4]]=>[2,1,3,4]=>011=>011
[[2,5,5],[6]]=>[4,1,2,3]=>000=>000
[[2,5,6],[5]]=>[2,1,3,4]=>011=>011
[[2,5,6],[6]]=>[3,1,2,4]=>001=>001
[[2,6,6],[5]]=>[2,1,3,4]=>011=>011
[[2,6,6],[6]]=>[2,1,3,4]=>011=>011
[[3,3,3],[6]]=>[4,1,2,3]=>000=>000
[[3,3,4],[6]]=>[4,1,2,3]=>000=>000
[[3,3,6],[4]]=>[3,1,2,4]=>001=>001
[[3,3,5],[6]]=>[4,1,2,3]=>000=>000
[[3,3,6],[5]]=>[3,1,2,4]=>001=>001
[[3,3,6],[6]]=>[3,1,2,4]=>001=>001
[[3,4,4],[6]]=>[4,1,2,3]=>000=>000
[[3,4,6],[4]]=>[2,1,3,4]=>011=>011
[[3,4,5],[6]]=>[4,1,2,3]=>000=>000
[[3,4,6],[5]]=>[3,1,2,4]=>001=>001
[[3,5,6],[4]]=>[2,1,3,4]=>011=>011
[[3,4,6],[6]]=>[3,1,2,4]=>001=>001
[[3,6,6],[4]]=>[2,1,3,4]=>011=>011
[[3,5,5],[6]]=>[4,1,2,3]=>000=>000
[[3,5,6],[5]]=>[2,1,3,4]=>011=>011
[[3,5,6],[6]]=>[3,1,2,4]=>001=>001
[[3,6,6],[5]]=>[2,1,3,4]=>011=>011
[[3,6,6],[6]]=>[2,1,3,4]=>011=>011
[[4,4,4],[6]]=>[4,1,2,3]=>000=>000
[[4,4,5],[6]]=>[4,1,2,3]=>000=>000
[[4,4,6],[5]]=>[3,1,2,4]=>001=>001
[[4,4,6],[6]]=>[3,1,2,4]=>001=>001
[[4,5,5],[6]]=>[4,1,2,3]=>000=>000
[[4,5,6],[5]]=>[2,1,3,4]=>011=>011
[[4,5,6],[6]]=>[3,1,2,4]=>001=>001
[[4,6,6],[5]]=>[2,1,3,4]=>011=>011
[[4,6,6],[6]]=>[2,1,3,4]=>011=>011
[[5,5,5],[6]]=>[4,1,2,3]=>000=>000
[[5,5,6],[6]]=>[3,1,2,4]=>001=>001
[[5,6,6],[6]]=>[2,1,3,4]=>011=>011
[[1,1],[2,6]]=>[3,4,1,2]=>000=>000
[[1,1],[3,6]]=>[3,4,1,2]=>000=>000
[[1,1],[4,6]]=>[3,4,1,2]=>000=>000
[[1,1],[5,6]]=>[3,4,1,2]=>000=>000
[[1,1],[6,6]]=>[3,4,1,2]=>000=>000
[[1,2],[2,6]]=>[2,4,1,3]=>000=>000
[[1,2],[3,6]]=>[3,4,1,2]=>000=>000
[[1,3],[2,6]]=>[2,4,1,3]=>000=>000
[[1,2],[4,6]]=>[3,4,1,2]=>000=>000
[[1,4],[2,6]]=>[2,4,1,3]=>000=>000
[[1,2],[5,6]]=>[3,4,1,2]=>000=>000
[[1,5],[2,6]]=>[2,4,1,3]=>000=>000
[[1,2],[6,6]]=>[3,4,1,2]=>000=>000
[[1,3],[3,6]]=>[2,4,1,3]=>000=>000
[[1,3],[4,6]]=>[3,4,1,2]=>000=>000
[[1,4],[3,6]]=>[2,4,1,3]=>000=>000
[[1,3],[5,6]]=>[3,4,1,2]=>000=>000
[[1,5],[3,6]]=>[2,4,1,3]=>000=>000
[[1,3],[6,6]]=>[3,4,1,2]=>000=>000
[[1,4],[4,6]]=>[2,4,1,3]=>000=>000
[[1,4],[5,6]]=>[3,4,1,2]=>000=>000
[[1,5],[4,6]]=>[2,4,1,3]=>000=>000
[[1,4],[6,6]]=>[3,4,1,2]=>000=>000
[[1,5],[5,6]]=>[2,4,1,3]=>000=>000
[[1,5],[6,6]]=>[3,4,1,2]=>000=>000
[[2,2],[3,6]]=>[3,4,1,2]=>000=>000
[[2,2],[4,6]]=>[3,4,1,2]=>000=>000
[[2,2],[5,6]]=>[3,4,1,2]=>000=>000
[[2,2],[6,6]]=>[3,4,1,2]=>000=>000
[[2,3],[3,6]]=>[2,4,1,3]=>000=>000
[[2,3],[4,6]]=>[3,4,1,2]=>000=>000
[[2,4],[3,6]]=>[2,4,1,3]=>000=>000
[[2,3],[5,6]]=>[3,4,1,2]=>000=>000
[[2,5],[3,6]]=>[2,4,1,3]=>000=>000
[[2,3],[6,6]]=>[3,4,1,2]=>000=>000
[[2,4],[4,6]]=>[2,4,1,3]=>000=>000
[[2,4],[5,6]]=>[3,4,1,2]=>000=>000
[[2,5],[4,6]]=>[2,4,1,3]=>000=>000
[[2,4],[6,6]]=>[3,4,1,2]=>000=>000
[[2,5],[5,6]]=>[2,4,1,3]=>000=>000
[[2,5],[6,6]]=>[3,4,1,2]=>000=>000
[[3,3],[4,6]]=>[3,4,1,2]=>000=>000
[[3,3],[5,6]]=>[3,4,1,2]=>000=>000
[[3,3],[6,6]]=>[3,4,1,2]=>000=>000
[[3,4],[4,6]]=>[2,4,1,3]=>000=>000
[[3,4],[5,6]]=>[3,4,1,2]=>000=>000
[[3,5],[4,6]]=>[2,4,1,3]=>000=>000
[[3,4],[6,6]]=>[3,4,1,2]=>000=>000
[[3,5],[5,6]]=>[2,4,1,3]=>000=>000
[[3,5],[6,6]]=>[3,4,1,2]=>000=>000
[[4,4],[5,6]]=>[3,4,1,2]=>000=>000
[[4,4],[6,6]]=>[3,4,1,2]=>000=>000
[[4,5],[5,6]]=>[2,4,1,3]=>000=>000
[[4,5],[6,6]]=>[3,4,1,2]=>000=>000
[[5,5],[6,6]]=>[3,4,1,2]=>000=>000
[[1,1],[2],[6]]=>[4,3,1,2]=>000=>000
[[1,1],[3],[6]]=>[4,3,1,2]=>000=>000
[[1,1],[4],[6]]=>[4,3,1,2]=>000=>000
[[1,1],[5],[6]]=>[4,3,1,2]=>000=>000
[[1,2],[2],[6]]=>[4,2,1,3]=>000=>000
[[1,2],[3],[6]]=>[4,3,1,2]=>000=>000
[[1,3],[2],[6]]=>[4,2,1,3]=>000=>000
[[1,6],[2],[3]]=>[3,2,1,4]=>001=>001
[[1,2],[4],[6]]=>[4,3,1,2]=>000=>000
[[1,4],[2],[6]]=>[4,2,1,3]=>000=>000
[[1,6],[2],[4]]=>[3,2,1,4]=>001=>001
[[1,2],[5],[6]]=>[4,3,1,2]=>000=>000
[[1,5],[2],[6]]=>[4,2,1,3]=>000=>000
[[1,6],[2],[5]]=>[3,2,1,4]=>001=>001
[[1,6],[2],[6]]=>[3,2,1,4]=>001=>001
[[1,3],[3],[6]]=>[4,2,1,3]=>000=>000
[[1,3],[4],[6]]=>[4,3,1,2]=>000=>000
[[1,4],[3],[6]]=>[4,2,1,3]=>000=>000
[[1,6],[3],[4]]=>[3,2,1,4]=>001=>001
[[1,3],[5],[6]]=>[4,3,1,2]=>000=>000
[[1,5],[3],[6]]=>[4,2,1,3]=>000=>000
[[1,6],[3],[5]]=>[3,2,1,4]=>001=>001
[[1,6],[3],[6]]=>[3,2,1,4]=>001=>001
[[1,4],[4],[6]]=>[4,2,1,3]=>000=>000
[[1,4],[5],[6]]=>[4,3,1,2]=>000=>000
[[1,5],[4],[6]]=>[4,2,1,3]=>000=>000
[[1,6],[4],[5]]=>[3,2,1,4]=>001=>001
[[1,6],[4],[6]]=>[3,2,1,4]=>001=>001
[[1,5],[5],[6]]=>[4,2,1,3]=>000=>000
[[1,6],[5],[6]]=>[3,2,1,4]=>001=>001
[[2,2],[3],[6]]=>[4,3,1,2]=>000=>000
[[2,2],[4],[6]]=>[4,3,1,2]=>000=>000
[[2,2],[5],[6]]=>[4,3,1,2]=>000=>000
[[2,3],[3],[6]]=>[4,2,1,3]=>000=>000
[[2,3],[4],[6]]=>[4,3,1,2]=>000=>000
[[2,4],[3],[6]]=>[4,2,1,3]=>000=>000
[[2,6],[3],[4]]=>[3,2,1,4]=>001=>001
[[2,3],[5],[6]]=>[4,3,1,2]=>000=>000
[[2,5],[3],[6]]=>[4,2,1,3]=>000=>000
[[2,6],[3],[5]]=>[3,2,1,4]=>001=>001
[[2,6],[3],[6]]=>[3,2,1,4]=>001=>001
[[2,4],[4],[6]]=>[4,2,1,3]=>000=>000
[[2,4],[5],[6]]=>[4,3,1,2]=>000=>000
[[2,5],[4],[6]]=>[4,2,1,3]=>000=>000
[[2,6],[4],[5]]=>[3,2,1,4]=>001=>001
[[2,6],[4],[6]]=>[3,2,1,4]=>001=>001
[[2,5],[5],[6]]=>[4,2,1,3]=>000=>000
[[2,6],[5],[6]]=>[3,2,1,4]=>001=>001
[[3,3],[4],[6]]=>[4,3,1,2]=>000=>000
[[3,3],[5],[6]]=>[4,3,1,2]=>000=>000
[[3,4],[4],[6]]=>[4,2,1,3]=>000=>000
[[3,4],[5],[6]]=>[4,3,1,2]=>000=>000
[[3,5],[4],[6]]=>[4,2,1,3]=>000=>000
[[3,6],[4],[5]]=>[3,2,1,4]=>001=>001
[[3,6],[4],[6]]=>[3,2,1,4]=>001=>001
[[3,5],[5],[6]]=>[4,2,1,3]=>000=>000
[[3,6],[5],[6]]=>[3,2,1,4]=>001=>001
[[4,4],[5],[6]]=>[4,3,1,2]=>000=>000
[[4,5],[5],[6]]=>[4,2,1,3]=>000=>000
[[4,6],[5],[6]]=>[3,2,1,4]=>001=>001
[[1],[2],[3],[6]]=>[4,3,2,1]=>000=>000
[[1],[2],[4],[6]]=>[4,3,2,1]=>000=>000
[[1],[2],[5],[6]]=>[4,3,2,1]=>000=>000
[[1],[3],[4],[6]]=>[4,3,2,1]=>000=>000
[[1],[3],[5],[6]]=>[4,3,2,1]=>000=>000
[[1],[4],[5],[6]]=>[4,3,2,1]=>000=>000
[[2],[3],[4],[6]]=>[4,3,2,1]=>000=>000
[[2],[3],[5],[6]]=>[4,3,2,1]=>000=>000
[[2],[4],[5],[6]]=>[4,3,2,1]=>000=>000
[[3],[4],[5],[6]]=>[4,3,2,1]=>000=>000
[[1,1,1,1,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,2,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,3,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,2,2,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,2,3,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,2,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,2,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,3,3,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,3,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,3,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,4,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,4,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,2,2,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,2,3,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,2,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,2,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,3,3,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,3,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,3,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,4,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,4,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,2,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,3,3,3,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,3,3,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,3,3,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,3,4,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,3,4,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,3,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,4,4,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,4,4,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,4,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,5,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,2,2,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,2,3,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,2,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,2,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,3,3,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,3,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,3,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,4,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,4,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,2,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,3,3,3,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,3,3,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,3,3,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,3,4,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,3,4,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,3,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,4,4,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,4,4,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,4,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[2,5,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[3,3,3,3,5]]=>[1,2,3,4,5]=>1111=>1111
[[3,3,3,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[3,3,3,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[3,3,4,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[3,3,4,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[3,3,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[3,4,4,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[3,4,4,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[3,4,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[3,5,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[4,4,4,4,5]]=>[1,2,3,4,5]=>1111=>1111
[[4,4,4,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[4,4,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[4,5,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[5,5,5,5,5]]=>[1,2,3,4,5]=>1111=>1111
[[1,1,1,1],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,1,2],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,1,5],[2]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,1,3],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,1,5],[3]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,1,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,1,5],[4]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,1,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,2,2],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,2,5],[2]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,2,3],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,2,5],[3]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,3,5],[2]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,2,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,2,5],[4]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,4,5],[2]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,2,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,5,5],[2]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,3,3],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,3,5],[3]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,3,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,3,5],[4]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,4,5],[3]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,3,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,5,5],[3]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,4,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,1,4,5],[4]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,4,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[1,1,5,5],[4]]=>[3,1,2,4,5]=>0011=>0011
[[1,1,5,5],[5]]=>[3,1,2,4,5]=>0011=>0011
[[1,2,2,2],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,2,2,5],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,2,3],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,2,2,5],[3]]=>[4,1,2,3,5]=>0001=>0001
[[1,2,3,5],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,2,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,2,2,5],[4]]=>[4,1,2,3,5]=>0001=>0001
[[1,2,4,5],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,2,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[1,2,5,5],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,3,3],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,2,3,5],[3]]=>[3,1,2,4,5]=>0011=>0011
[[1,3,3,5],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,3,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,2,3,5],[4]]=>[4,1,2,3,5]=>0001=>0001
[[1,2,4,5],[3]]=>[3,1,2,4,5]=>0011=>0011
[[1,3,4,5],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,3,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[1,2,5,5],[3]]=>[3,1,2,4,5]=>0011=>0011
[[1,3,5,5],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,4,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,2,4,5],[4]]=>[3,1,2,4,5]=>0011=>0011
[[1,4,4,5],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,4,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[1,2,5,5],[4]]=>[3,1,2,4,5]=>0011=>0011
[[1,4,5,5],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,2,5,5],[5]]=>[3,1,2,4,5]=>0011=>0011
[[1,5,5,5],[2]]=>[2,1,3,4,5]=>0111=>0111
[[1,3,3,3],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,3,3,5],[3]]=>[2,1,3,4,5]=>0111=>0111
[[1,3,3,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,3,3,5],[4]]=>[4,1,2,3,5]=>0001=>0001
[[1,3,4,5],[3]]=>[2,1,3,4,5]=>0111=>0111
[[1,3,3,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[1,3,5,5],[3]]=>[2,1,3,4,5]=>0111=>0111
[[1,3,4,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,3,4,5],[4]]=>[3,1,2,4,5]=>0011=>0011
[[1,4,4,5],[3]]=>[2,1,3,4,5]=>0111=>0111
[[1,3,4,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[1,3,5,5],[4]]=>[3,1,2,4,5]=>0011=>0011
[[1,4,5,5],[3]]=>[2,1,3,4,5]=>0111=>0111
[[1,3,5,5],[5]]=>[3,1,2,4,5]=>0011=>0011
[[1,5,5,5],[3]]=>[2,1,3,4,5]=>0111=>0111
[[1,4,4,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[1,4,4,5],[4]]=>[2,1,3,4,5]=>0111=>0111
[[1,4,4,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[1,4,5,5],[4]]=>[2,1,3,4,5]=>0111=>0111
[[1,4,5,5],[5]]=>[3,1,2,4,5]=>0011=>0011
[[1,5,5,5],[4]]=>[2,1,3,4,5]=>0111=>0111
[[1,5,5,5],[5]]=>[2,1,3,4,5]=>0111=>0111
[[2,2,2,2],[5]]=>[5,1,2,3,4]=>0000=>0000
[[2,2,2,3],[5]]=>[5,1,2,3,4]=>0000=>0000
[[2,2,2,5],[3]]=>[4,1,2,3,5]=>0001=>0001
[[2,2,2,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[2,2,2,5],[4]]=>[4,1,2,3,5]=>0001=>0001
[[2,2,2,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[2,2,3,3],[5]]=>[5,1,2,3,4]=>0000=>0000
[[2,2,3,5],[3]]=>[3,1,2,4,5]=>0011=>0011
[[2,2,3,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[2,2,3,5],[4]]=>[4,1,2,3,5]=>0001=>0001
[[2,2,4,5],[3]]=>[3,1,2,4,5]=>0011=>0011
[[2,2,3,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[2,2,5,5],[3]]=>[3,1,2,4,5]=>0011=>0011
[[2,2,4,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[2,2,4,5],[4]]=>[3,1,2,4,5]=>0011=>0011
[[2,2,4,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[2,2,5,5],[4]]=>[3,1,2,4,5]=>0011=>0011
[[2,2,5,5],[5]]=>[3,1,2,4,5]=>0011=>0011
[[2,3,3,3],[5]]=>[5,1,2,3,4]=>0000=>0000
[[2,3,3,5],[3]]=>[2,1,3,4,5]=>0111=>0111
[[2,3,3,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[2,3,3,5],[4]]=>[4,1,2,3,5]=>0001=>0001
[[2,3,4,5],[3]]=>[2,1,3,4,5]=>0111=>0111
[[2,3,3,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[2,3,5,5],[3]]=>[2,1,3,4,5]=>0111=>0111
[[2,3,4,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[2,3,4,5],[4]]=>[3,1,2,4,5]=>0011=>0011
[[2,4,4,5],[3]]=>[2,1,3,4,5]=>0111=>0111
[[2,3,4,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[2,3,5,5],[4]]=>[3,1,2,4,5]=>0011=>0011
[[2,4,5,5],[3]]=>[2,1,3,4,5]=>0111=>0111
[[2,3,5,5],[5]]=>[3,1,2,4,5]=>0011=>0011
[[2,5,5,5],[3]]=>[2,1,3,4,5]=>0111=>0111
[[2,4,4,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[2,4,4,5],[4]]=>[2,1,3,4,5]=>0111=>0111
[[2,4,4,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[2,4,5,5],[4]]=>[2,1,3,4,5]=>0111=>0111
[[2,4,5,5],[5]]=>[3,1,2,4,5]=>0011=>0011
[[2,5,5,5],[4]]=>[2,1,3,4,5]=>0111=>0111
[[2,5,5,5],[5]]=>[2,1,3,4,5]=>0111=>0111
[[3,3,3,3],[5]]=>[5,1,2,3,4]=>0000=>0000
[[3,3,3,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[3,3,3,5],[4]]=>[4,1,2,3,5]=>0001=>0001
[[3,3,3,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[3,3,4,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[3,3,4,5],[4]]=>[3,1,2,4,5]=>0011=>0011
[[3,3,4,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[3,3,5,5],[4]]=>[3,1,2,4,5]=>0011=>0011
[[3,3,5,5],[5]]=>[3,1,2,4,5]=>0011=>0011
[[3,4,4,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[3,4,4,5],[4]]=>[2,1,3,4,5]=>0111=>0111
[[3,4,4,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[3,4,5,5],[4]]=>[2,1,3,4,5]=>0111=>0111
[[3,4,5,5],[5]]=>[3,1,2,4,5]=>0011=>0011
[[3,5,5,5],[4]]=>[2,1,3,4,5]=>0111=>0111
[[3,5,5,5],[5]]=>[2,1,3,4,5]=>0111=>0111
[[4,4,4,4],[5]]=>[5,1,2,3,4]=>0000=>0000
[[4,4,4,5],[5]]=>[4,1,2,3,5]=>0001=>0001
[[4,4,5,5],[5]]=>[3,1,2,4,5]=>0011=>0011
[[4,5,5,5],[5]]=>[2,1,3,4,5]=>0111=>0111
[[1,1,1],[2,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,1],[3,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,1],[4,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,1],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,2],[2,5]]=>[3,5,1,2,4]=>0000=>0000
[[1,1,5],[2,2]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,2],[3,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,3],[2,5]]=>[3,5,1,2,4]=>0000=>0000
[[1,1,5],[2,3]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,2],[4,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,4],[2,5]]=>[3,5,1,2,4]=>0000=>0000
[[1,1,5],[2,4]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,2],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,5],[2,5]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,3],[3,5]]=>[3,5,1,2,4]=>0000=>0000
[[1,1,5],[3,3]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,3],[4,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,4],[3,5]]=>[3,5,1,2,4]=>0000=>0000
[[1,1,5],[3,4]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,3],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,5],[3,5]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,4],[4,5]]=>[3,5,1,2,4]=>0000=>0000
[[1,1,5],[4,4]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,4],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,1,5],[4,5]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,5],[5,5]]=>[3,4,1,2,5]=>0001=>0001
[[1,2,2],[2,5]]=>[2,5,1,3,4]=>0000=>0000
[[1,2,2],[3,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,2,3],[2,5]]=>[2,5,1,3,4]=>0000=>0000
[[1,2,5],[2,3]]=>[2,4,1,3,5]=>0001=>0001
[[1,2,2],[4,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,2,4],[2,5]]=>[2,5,1,3,4]=>0000=>0000
[[1,2,5],[2,4]]=>[2,4,1,3,5]=>0001=>0001
[[1,2,2],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,2,5],[2,5]]=>[2,4,1,3,5]=>0001=>0001
[[1,2,3],[3,5]]=>[3,5,1,2,4]=>0000=>0000
[[1,2,5],[3,3]]=>[3,4,1,2,5]=>0001=>0001
[[1,3,3],[2,5]]=>[2,5,1,3,4]=>0000=>0000
[[1,2,3],[4,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,2,4],[3,5]]=>[3,5,1,2,4]=>0000=>0000
[[1,2,5],[3,4]]=>[3,4,1,2,5]=>0001=>0001
[[1,3,4],[2,5]]=>[2,5,1,3,4]=>0000=>0000
[[1,3,5],[2,4]]=>[2,4,1,3,5]=>0001=>0001
[[1,2,3],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,2,5],[3,5]]=>[3,4,1,2,5]=>0001=>0001
[[1,3,5],[2,5]]=>[2,4,1,3,5]=>0001=>0001
[[1,2,4],[4,5]]=>[3,5,1,2,4]=>0000=>0000
[[1,2,5],[4,4]]=>[3,4,1,2,5]=>0001=>0001
[[1,4,4],[2,5]]=>[2,5,1,3,4]=>0000=>0000
[[1,2,4],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,2,5],[4,5]]=>[3,4,1,2,5]=>0001=>0001
[[1,4,5],[2,5]]=>[2,4,1,3,5]=>0001=>0001
[[1,2,5],[5,5]]=>[3,4,1,2,5]=>0001=>0001
[[1,3,3],[3,5]]=>[2,5,1,3,4]=>0000=>0000
[[1,3,3],[4,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,3,4],[3,5]]=>[2,5,1,3,4]=>0000=>0000
[[1,3,5],[3,4]]=>[2,4,1,3,5]=>0001=>0001
[[1,3,3],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,3,5],[3,5]]=>[2,4,1,3,5]=>0001=>0001
[[1,3,4],[4,5]]=>[3,5,1,2,4]=>0000=>0000
[[1,3,5],[4,4]]=>[3,4,1,2,5]=>0001=>0001
[[1,4,4],[3,5]]=>[2,5,1,3,4]=>0000=>0000
[[1,3,4],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,3,5],[4,5]]=>[3,4,1,2,5]=>0001=>0001
[[1,4,5],[3,5]]=>[2,4,1,3,5]=>0001=>0001
[[1,3,5],[5,5]]=>[3,4,1,2,5]=>0001=>0001
[[1,4,4],[4,5]]=>[2,5,1,3,4]=>0000=>0000
[[1,4,4],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[1,4,5],[4,5]]=>[2,4,1,3,5]=>0001=>0001
[[1,4,5],[5,5]]=>[3,4,1,2,5]=>0001=>0001
[[2,2,2],[3,5]]=>[4,5,1,2,3]=>0000=>0000
[[2,2,2],[4,5]]=>[4,5,1,2,3]=>0000=>0000
[[2,2,2],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[2,2,3],[3,5]]=>[3,5,1,2,4]=>0000=>0000
[[2,2,5],[3,3]]=>[3,4,1,2,5]=>0001=>0001
[[2,2,3],[4,5]]=>[4,5,1,2,3]=>0000=>0000
[[2,2,4],[3,5]]=>[3,5,1,2,4]=>0000=>0000
[[2,2,5],[3,4]]=>[3,4,1,2,5]=>0001=>0001
[[2,2,3],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[2,2,5],[3,5]]=>[3,4,1,2,5]=>0001=>0001
[[2,2,4],[4,5]]=>[3,5,1,2,4]=>0000=>0000
[[2,2,5],[4,4]]=>[3,4,1,2,5]=>0001=>0001
[[2,2,4],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[2,2,5],[4,5]]=>[3,4,1,2,5]=>0001=>0001
[[2,2,5],[5,5]]=>[3,4,1,2,5]=>0001=>0001
[[2,3,3],[3,5]]=>[2,5,1,3,4]=>0000=>0000
[[2,3,3],[4,5]]=>[4,5,1,2,3]=>0000=>0000
[[2,3,4],[3,5]]=>[2,5,1,3,4]=>0000=>0000
[[2,3,5],[3,4]]=>[2,4,1,3,5]=>0001=>0001
[[2,3,3],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[2,3,5],[3,5]]=>[2,4,1,3,5]=>0001=>0001
[[2,3,4],[4,5]]=>[3,5,1,2,4]=>0000=>0000
[[2,3,5],[4,4]]=>[3,4,1,2,5]=>0001=>0001
[[2,4,4],[3,5]]=>[2,5,1,3,4]=>0000=>0000
[[2,3,4],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[2,3,5],[4,5]]=>[3,4,1,2,5]=>0001=>0001
[[2,4,5],[3,5]]=>[2,4,1,3,5]=>0001=>0001
[[2,3,5],[5,5]]=>[3,4,1,2,5]=>0001=>0001
[[2,4,4],[4,5]]=>[2,5,1,3,4]=>0000=>0000
[[2,4,4],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[2,4,5],[4,5]]=>[2,4,1,3,5]=>0001=>0001
[[2,4,5],[5,5]]=>[3,4,1,2,5]=>0001=>0001
[[3,3,3],[4,5]]=>[4,5,1,2,3]=>0000=>0000
[[3,3,3],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[3,3,4],[4,5]]=>[3,5,1,2,4]=>0000=>0000
[[3,3,5],[4,4]]=>[3,4,1,2,5]=>0001=>0001
[[3,3,4],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[3,3,5],[4,5]]=>[3,4,1,2,5]=>0001=>0001
[[3,3,5],[5,5]]=>[3,4,1,2,5]=>0001=>0001
[[3,4,4],[4,5]]=>[2,5,1,3,4]=>0000=>0000
[[3,4,4],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[3,4,5],[4,5]]=>[2,4,1,3,5]=>0001=>0001
[[3,4,5],[5,5]]=>[3,4,1,2,5]=>0001=>0001
[[4,4,4],[5,5]]=>[4,5,1,2,3]=>0000=>0000
[[4,4,5],[5,5]]=>[3,4,1,2,5]=>0001=>0001
[[1,1,1],[2],[5]]=>[5,4,1,2,3]=>0000=>0000
[[1,1,1],[3],[5]]=>[5,4,1,2,3]=>0000=>0000
[[1,1,1],[4],[5]]=>[5,4,1,2,3]=>0000=>0000
[[1,1,2],[2],[5]]=>[5,3,1,2,4]=>0000=>0000
[[1,1,2],[3],[5]]=>[5,4,1,2,3]=>0000=>0000
[[1,1,3],[2],[5]]=>[5,3,1,2,4]=>0000=>0000
[[1,1,5],[2],[3]]=>[4,3,1,2,5]=>0001=>0001
[[1,1,2],[4],[5]]=>[5,4,1,2,3]=>0000=>0000
[[1,1,4],[2],[5]]=>[5,3,1,2,4]=>0000=>0000
[[1,1,5],[2],[4]]=>[4,3,1,2,5]=>0001=>0001
[[1,1,5],[2],[5]]=>[4,3,1,2,5]=>0001=>0001
[[1,1,3],[3],[5]]=>[5,3,1,2,4]=>0000=>0000
[[1,1,3],[4],[5]]=>[5,4,1,2,3]=>0000=>0000
[[1,1,4],[3],[5]]=>[5,3,1,2,4]=>0000=>0000
[[1,1,5],[3],[4]]=>[4,3,1,2,5]=>0001=>0001
[[1,1,5],[3],[5]]=>[4,3,1,2,5]=>0001=>0001
[[1,1,4],[4],[5]]=>[5,3,1,2,4]=>0000=>0000
[[1,1,5],[4],[5]]=>[4,3,1,2,5]=>0001=>0001
[[1,2,2],[2],[5]]=>[5,2,1,3,4]=>0000=>0000
[[1,2,2],[3],[5]]=>[5,4,1,2,3]=>0000=>0000
[[1,2,3],[2],[5]]=>[5,2,1,3,4]=>0000=>0000
[[1,2,5],[2],[3]]=>[4,2,1,3,5]=>0001=>0001
[[1,2,2],[4],[5]]=>[5,4,1,2,3]=>0000=>0000
[[1,2,4],[2],[5]]=>[5,2,1,3,4]=>0000=>0000
[[1,2,5],[2],[4]]=>[4,2,1,3,5]=>0001=>0001
[[1,2,5],[2],[5]]=>[4,2,1,3,5]=>0001=>0001
[[1,2,3],[3],[5]]=>[5,3,1,2,4]=>0000=>0000
[[1,3,3],[2],[5]]=>[5,2,1,3,4]=>0000=>0000
[[1,3,5],[2],[3]]=>[3,2,1,4,5]=>0011=>0011
[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>0000=>0000
[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>0000=>0000
[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>0001=>0001
[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>0000=>0000
[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>0001=>0001
[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>0011=>0011
[[1,2,5],[3],[5]]=>[4,3,1,2,5]=>0001=>0001
[[1,3,5],[2],[5]]=>[4,2,1,3,5]=>0001=>0001
[[1,5,5],[2],[3]]=>[3,2,1,4,5]=>0011=>0011
[[1,2,4],[4],[5]]=>[5,3,1,2,4]=>0000=>0000
[[1,4,4],[2],[5]]=>[5,2,1,3,4]=>0000=>0000
[[1,4,5],[2],[4]]=>[3,2,1,4,5]=>0011=>0011
[[1,2,5],[4],[5]]=>[4,3,1,2,5]=>0001=>0001
[[1,4,5],[2],[5]]=>[4,2,1,3,5]=>0001=>0001
[[1,5,5],[2],[4]]=>[3,2,1,4,5]=>0011=>0011
[[1,5,5],[2],[5]]=>[3,2,1,4,5]=>0011=>0011
[[1,3,3],[3],[5]]=>[5,2,1,3,4]=>0000=>0000
[[1,3,3],[4],[5]]=>[5,4,1,2,3]=>0000=>0000
[[1,3,4],[3],[5]]=>[5,2,1,3,4]=>0000=>0000
[[1,3,5],[3],[4]]=>[4,2,1,3,5]=>0001=>0001
[[1,3,5],[3],[5]]=>[4,2,1,3,5]=>0001=>0001
[[1,3,4],[4],[5]]=>[5,3,1,2,4]=>0000=>0000
[[1,4,4],[3],[5]]=>[5,2,1,3,4]=>0000=>0000
[[1,4,5],[3],[4]]=>[3,2,1,4,5]=>0011=>0011
[[1,3,5],[4],[5]]=>[4,3,1,2,5]=>0001=>0001
[[1,4,5],[3],[5]]=>[4,2,1,3,5]=>0001=>0001
[[1,5,5],[3],[4]]=>[3,2,1,4,5]=>0011=>0011
[[1,5,5],[3],[5]]=>[3,2,1,4,5]=>0011=>0011
[[1,4,4],[4],[5]]=>[5,2,1,3,4]=>0000=>0000
[[1,4,5],[4],[5]]=>[4,2,1,3,5]=>0001=>0001
[[1,5,5],[4],[5]]=>[3,2,1,4,5]=>0011=>0011
[[2,2,2],[3],[5]]=>[5,4,1,2,3]=>0000=>0000
[[2,2,2],[4],[5]]=>[5,4,1,2,3]=>0000=>0000
[[2,2,3],[3],[5]]=>[5,3,1,2,4]=>0000=>0000
[[2,2,3],[4],[5]]=>[5,4,1,2,3]=>0000=>0000
[[2,2,4],[3],[5]]=>[5,3,1,2,4]=>0000=>0000
[[2,2,5],[3],[4]]=>[4,3,1,2,5]=>0001=>0001
[[2,2,5],[3],[5]]=>[4,3,1,2,5]=>0001=>0001
[[2,2,4],[4],[5]]=>[5,3,1,2,4]=>0000=>0000
[[2,2,5],[4],[5]]=>[4,3,1,2,5]=>0001=>0001
[[2,3,3],[3],[5]]=>[5,2,1,3,4]=>0000=>0000
[[2,3,3],[4],[5]]=>[5,4,1,2,3]=>0000=>0000
[[2,3,4],[3],[5]]=>[5,2,1,3,4]=>0000=>0000
[[2,3,5],[3],[4]]=>[4,2,1,3,5]=>0001=>0001
[[2,3,5],[3],[5]]=>[4,2,1,3,5]=>0001=>0001
[[2,3,4],[4],[5]]=>[5,3,1,2,4]=>0000=>0000
[[2,4,4],[3],[5]]=>[5,2,1,3,4]=>0000=>0000
[[2,4,5],[3],[4]]=>[3,2,1,4,5]=>0011=>0011
[[2,3,5],[4],[5]]=>[4,3,1,2,5]=>0001=>0001
[[2,4,5],[3],[5]]=>[4,2,1,3,5]=>0001=>0001
[[2,5,5],[3],[4]]=>[3,2,1,4,5]=>0011=>0011
[[2,5,5],[3],[5]]=>[3,2,1,4,5]=>0011=>0011
[[2,4,4],[4],[5]]=>[5,2,1,3,4]=>0000=>0000
[[2,4,5],[4],[5]]=>[4,2,1,3,5]=>0001=>0001
[[2,5,5],[4],[5]]=>[3,2,1,4,5]=>0011=>0011
[[3,3,3],[4],[5]]=>[5,4,1,2,3]=>0000=>0000
[[3,3,4],[4],[5]]=>[5,3,1,2,4]=>0000=>0000
[[3,3,5],[4],[5]]=>[4,3,1,2,5]=>0001=>0001
[[3,4,4],[4],[5]]=>[5,2,1,3,4]=>0000=>0000
[[3,4,5],[4],[5]]=>[4,2,1,3,5]=>0001=>0001
[[3,5,5],[4],[5]]=>[3,2,1,4,5]=>0011=>0011
[[1,1],[2,2],[5]]=>[5,3,4,1,2]=>0000=>0000
[[1,1],[2,3],[5]]=>[5,3,4,1,2]=>0000=>0000
[[1,1],[2,5],[3]]=>[4,3,5,1,2]=>0000=>0000
[[1,1],[2,4],[5]]=>[5,3,4,1,2]=>0000=>0000
[[1,1],[2,5],[4]]=>[4,3,5,1,2]=>0000=>0000
[[1,1],[2,5],[5]]=>[4,3,5,1,2]=>0000=>0000
[[1,1],[3,3],[5]]=>[5,3,4,1,2]=>0000=>0000
[[1,1],[3,4],[5]]=>[5,3,4,1,2]=>0000=>0000
[[1,1],[3,5],[4]]=>[4,3,5,1,2]=>0000=>0000
[[1,1],[3,5],[5]]=>[4,3,5,1,2]=>0000=>0000
[[1,1],[4,4],[5]]=>[5,3,4,1,2]=>0000=>0000
[[1,1],[4,5],[5]]=>[4,3,5,1,2]=>0000=>0000
[[1,2],[2,3],[5]]=>[5,2,4,1,3]=>0000=>0000
[[1,2],[2,5],[3]]=>[4,2,5,1,3]=>0000=>0000
[[1,2],[2,4],[5]]=>[5,2,4,1,3]=>0000=>0000
[[1,2],[2,5],[4]]=>[4,2,5,1,3]=>0000=>0000
[[1,2],[2,5],[5]]=>[4,2,5,1,3]=>0000=>0000
[[1,2],[3,3],[5]]=>[5,3,4,1,2]=>0000=>0000
[[1,3],[2,5],[3]]=>[3,2,5,1,4]=>0000=>0000
[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>0000=>0000
[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>0000=>0000
[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>0000=>0000
[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>0000=>0000
[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>0000=>0000
[[1,2],[3,5],[5]]=>[4,3,5,1,2]=>0000=>0000
[[1,3],[2,5],[5]]=>[4,2,5,1,3]=>0000=>0000
[[1,2],[4,4],[5]]=>[5,3,4,1,2]=>0000=>0000
[[1,4],[2,5],[4]]=>[3,2,5,1,4]=>0000=>0000
[[1,2],[4,5],[5]]=>[4,3,5,1,2]=>0000=>0000
[[1,4],[2,5],[5]]=>[4,2,5,1,3]=>0000=>0000
[[1,3],[3,4],[5]]=>[5,2,4,1,3]=>0000=>0000
[[1,3],[3,5],[4]]=>[4,2,5,1,3]=>0000=>0000
[[1,3],[3,5],[5]]=>[4,2,5,1,3]=>0000=>0000
[[1,3],[4,4],[5]]=>[5,3,4,1,2]=>0000=>0000
[[1,4],[3,5],[4]]=>[3,2,5,1,4]=>0000=>0000
[[1,3],[4,5],[5]]=>[4,3,5,1,2]=>0000=>0000
[[1,4],[3,5],[5]]=>[4,2,5,1,3]=>0000=>0000
[[1,4],[4,5],[5]]=>[4,2,5,1,3]=>0000=>0000
[[2,2],[3,3],[5]]=>[5,3,4,1,2]=>0000=>0000
[[2,2],[3,4],[5]]=>[5,3,4,1,2]=>0000=>0000
[[2,2],[3,5],[4]]=>[4,3,5,1,2]=>0000=>0000
[[2,2],[3,5],[5]]=>[4,3,5,1,2]=>0000=>0000
[[2,2],[4,4],[5]]=>[5,3,4,1,2]=>0000=>0000
[[2,2],[4,5],[5]]=>[4,3,5,1,2]=>0000=>0000
[[2,3],[3,4],[5]]=>[5,2,4,1,3]=>0000=>0000
[[2,3],[3,5],[4]]=>[4,2,5,1,3]=>0000=>0000
[[2,3],[3,5],[5]]=>[4,2,5,1,3]=>0000=>0000
[[2,3],[4,4],[5]]=>[5,3,4,1,2]=>0000=>0000
[[2,4],[3,5],[4]]=>[3,2,5,1,4]=>0000=>0000
[[2,3],[4,5],[5]]=>[4,3,5,1,2]=>0000=>0000
[[2,4],[3,5],[5]]=>[4,2,5,1,3]=>0000=>0000
[[2,4],[4,5],[5]]=>[4,2,5,1,3]=>0000=>0000
[[3,3],[4,4],[5]]=>[5,3,4,1,2]=>0000=>0000
[[3,3],[4,5],[5]]=>[4,3,5,1,2]=>0000=>0000
[[3,4],[4,5],[5]]=>[4,2,5,1,3]=>0000=>0000
[[1,1],[2],[3],[5]]=>[5,4,3,1,2]=>0000=>0000
[[1,1],[2],[4],[5]]=>[5,4,3,1,2]=>0000=>0000
[[1,1],[3],[4],[5]]=>[5,4,3,1,2]=>0000=>0000
[[1,2],[2],[3],[5]]=>[5,4,2,1,3]=>0000=>0000
[[1,2],[2],[4],[5]]=>[5,4,2,1,3]=>0000=>0000
[[1,3],[2],[3],[5]]=>[5,3,2,1,4]=>0000=>0000
[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>0000=>0000
[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>0000=>0000
[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>0000=>0000
[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>0001=>0001
[[1,5],[2],[3],[5]]=>[4,3,2,1,5]=>0001=>0001
[[1,4],[2],[4],[5]]=>[5,3,2,1,4]=>0000=>0000
[[1,5],[2],[4],[5]]=>[4,3,2,1,5]=>0001=>0001
[[1,3],[3],[4],[5]]=>[5,4,2,1,3]=>0000=>0000
[[1,4],[3],[4],[5]]=>[5,3,2,1,4]=>0000=>0000
[[1,5],[3],[4],[5]]=>[4,3,2,1,5]=>0001=>0001
[[2,2],[3],[4],[5]]=>[5,4,3,1,2]=>0000=>0000
[[2,3],[3],[4],[5]]=>[5,4,2,1,3]=>0000=>0000
[[2,4],[3],[4],[5]]=>[5,3,2,1,4]=>0000=>0000
[[2,5],[3],[4],[5]]=>[4,3,2,1,5]=>0001=>0001
[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>0000=>0000
[[1,1,1,1,1,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,1,2,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,1,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,1,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,2,2,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,2,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,2,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,3,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,3,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,2,2,2,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,2,2,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,2,2,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,2,3,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,2,3,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,2,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,3,3,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,3,3,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,3,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,4,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,2,2,2,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,2,2,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,2,2,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,2,3,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,2,3,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,2,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,3,3,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,3,3,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,3,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,2,4,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,3,3,3,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,3,3,3,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,3,3,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,3,4,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,4,4,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,2,2,2,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,2,2,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,2,2,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,2,3,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,2,3,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,2,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,3,3,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,3,3,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,3,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,2,4,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,3,3,3,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,3,3,3,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,3,3,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,3,4,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[2,4,4,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[3,3,3,3,3,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[3,3,3,3,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[3,3,3,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[3,3,4,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[3,4,4,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[4,4,4,4,4,4]]=>[1,2,3,4,5,6]=>11111=>11111
[[1,1,1,1,1],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,1,1,2],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,1,1,4],[2]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,1,1,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,1,1,4],[3]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,1,1,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,1,2,2],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,1,2,4],[2]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,1,2,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,1,2,4],[3]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,1,3,4],[2]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,1,2,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,1,4,4],[2]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,1,3,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,1,3,4],[3]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,1,3,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,1,4,4],[3]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,1,4,4],[4]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,2,2,2],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,2,2,4],[2]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,1,2,2,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,2,2,4],[3]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,2,3,4],[2]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,1,2,2,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,2,4,4],[2]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,1,2,3,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,2,3,4],[3]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,3,3,4],[2]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,1,2,3,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,2,4,4],[3]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,3,4,4],[2]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,1,2,4,4],[4]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,4,4,4],[2]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,1,3,3,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,1,3,3,4],[3]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,1,3,3,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,1,3,4,4],[3]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,1,3,4,4],[4]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,1,4,4,4],[3]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,1,4,4,4],[4]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,2,2,2,2],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,2,2,2,4],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,2,2,2,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,2,2,2,4],[3]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,2,2,3,4],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,2,2,2,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,2,2,4,4],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,2,2,3,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,2,2,3,4],[3]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,2,3,3,4],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,2,2,3,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,2,2,4,4],[3]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,2,3,4,4],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,2,2,4,4],[4]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,2,4,4,4],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,2,3,3,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,2,3,3,4],[3]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,3,3,3,4],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,2,3,3,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,2,3,4,4],[3]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,3,3,4,4],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,2,3,4,4],[4]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,2,4,4,4],[3]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,3,4,4,4],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,2,4,4,4],[4]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,4,4,4,4],[2]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,3,3,3,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[1,3,3,3,4],[3]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,3,3,3,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[1,3,3,4,4],[3]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,3,3,4,4],[4]]=>[4,1,2,3,5,6]=>00011=>00011
[[1,3,4,4,4],[3]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,3,4,4,4],[4]]=>[3,1,2,4,5,6]=>00111=>00111
[[1,4,4,4,4],[3]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,4,4,4,4],[4]]=>[2,1,3,4,5,6]=>01111=>01111
[[2,2,2,2,2],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[2,2,2,2,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[2,2,2,2,4],[3]]=>[5,1,2,3,4,6]=>00001=>00001
[[2,2,2,2,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[2,2,2,3,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[2,2,2,3,4],[3]]=>[4,1,2,3,5,6]=>00011=>00011
[[2,2,2,3,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[2,2,2,4,4],[3]]=>[4,1,2,3,5,6]=>00011=>00011
[[2,2,2,4,4],[4]]=>[4,1,2,3,5,6]=>00011=>00011
[[2,2,3,3,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[2,2,3,3,4],[3]]=>[3,1,2,4,5,6]=>00111=>00111
[[2,2,3,3,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[2,2,3,4,4],[3]]=>[3,1,2,4,5,6]=>00111=>00111
[[2,2,3,4,4],[4]]=>[4,1,2,3,5,6]=>00011=>00011
[[2,2,4,4,4],[3]]=>[3,1,2,4,5,6]=>00111=>00111
[[2,2,4,4,4],[4]]=>[3,1,2,4,5,6]=>00111=>00111
[[2,3,3,3,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[2,3,3,3,4],[3]]=>[2,1,3,4,5,6]=>01111=>01111
[[2,3,3,3,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[2,3,3,4,4],[3]]=>[2,1,3,4,5,6]=>01111=>01111
[[2,3,3,4,4],[4]]=>[4,1,2,3,5,6]=>00011=>00011
[[2,3,4,4,4],[3]]=>[2,1,3,4,5,6]=>01111=>01111
[[2,3,4,4,4],[4]]=>[3,1,2,4,5,6]=>00111=>00111
[[2,4,4,4,4],[3]]=>[2,1,3,4,5,6]=>01111=>01111
[[2,4,4,4,4],[4]]=>[2,1,3,4,5,6]=>01111=>01111
[[3,3,3,3,3],[4]]=>[6,1,2,3,4,5]=>00000=>00000
[[3,3,3,3,4],[4]]=>[5,1,2,3,4,6]=>00001=>00001
[[3,3,3,4,4],[4]]=>[4,1,2,3,5,6]=>00011=>00011
[[3,3,4,4,4],[4]]=>[3,1,2,4,5,6]=>00111=>00111
[[3,4,4,4,4],[4]]=>[2,1,3,4,5,6]=>01111=>01111
[[1,1,1,1],[2,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,1,1],[3,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,1,1],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,1,2],[2,4]]=>[4,6,1,2,3,5]=>00000=>00000
[[1,1,1,4],[2,2]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,1,2],[3,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,1,3],[2,4]]=>[4,6,1,2,3,5]=>00000=>00000
[[1,1,1,4],[2,3]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,1,2],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,1,4],[2,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,1,3],[3,4]]=>[4,6,1,2,3,5]=>00000=>00000
[[1,1,1,4],[3,3]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,1,3],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,1,4],[3,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,1,4],[4,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,2,2],[2,4]]=>[3,6,1,2,4,5]=>00000=>00000
[[1,1,2,4],[2,2]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,2,2],[3,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,2,3],[2,4]]=>[3,6,1,2,4,5]=>00000=>00000
[[1,1,2,4],[2,3]]=>[3,5,1,2,4,6]=>00001=>00001
[[1,1,3,4],[2,2]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,2,2],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,2,4],[2,4]]=>[3,5,1,2,4,6]=>00001=>00001
[[1,1,4,4],[2,2]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,2,3],[3,4]]=>[4,6,1,2,3,5]=>00000=>00000
[[1,1,2,4],[3,3]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,3,3],[2,4]]=>[3,6,1,2,4,5]=>00000=>00000
[[1,1,3,4],[2,3]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,2,3],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,2,4],[3,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,3,4],[2,4]]=>[3,5,1,2,4,6]=>00001=>00001
[[1,1,4,4],[2,3]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,2,4],[4,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,4,4],[2,4]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,3,3],[3,4]]=>[3,6,1,2,4,5]=>00000=>00000
[[1,1,3,4],[3,3]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,3,3],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,1,3,4],[3,4]]=>[3,5,1,2,4,6]=>00001=>00001
[[1,1,4,4],[3,3]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,3,4],[4,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,1,4,4],[3,4]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,4,4],[4,4]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,2,2,2],[2,4]]=>[2,6,1,3,4,5]=>00000=>00000
[[1,2,2,2],[3,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,2,2,3],[2,4]]=>[2,6,1,3,4,5]=>00000=>00000
[[1,2,2,4],[2,3]]=>[2,5,1,3,4,6]=>00001=>00001
[[1,2,2,2],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,2,2,4],[2,4]]=>[2,5,1,3,4,6]=>00001=>00001
[[1,2,2,3],[3,4]]=>[4,6,1,2,3,5]=>00000=>00000
[[1,2,2,4],[3,3]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,2,3,3],[2,4]]=>[2,6,1,3,4,5]=>00000=>00000
[[1,2,3,4],[2,3]]=>[2,4,1,3,5,6]=>00011=>00011
[[1,2,2,3],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,2,2,4],[3,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,2,3,4],[2,4]]=>[2,5,1,3,4,6]=>00001=>00001
[[1,2,4,4],[2,3]]=>[2,4,1,3,5,6]=>00011=>00011
[[1,2,2,4],[4,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,2,4,4],[2,4]]=>[2,4,1,3,5,6]=>00011=>00011
[[1,2,3,3],[3,4]]=>[3,6,1,2,4,5]=>00000=>00000
[[1,2,3,4],[3,3]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,3,3,3],[2,4]]=>[2,6,1,3,4,5]=>00000=>00000
[[1,2,3,3],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,2,3,4],[3,4]]=>[3,5,1,2,4,6]=>00001=>00001
[[1,2,4,4],[3,3]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,3,3,4],[2,4]]=>[2,5,1,3,4,6]=>00001=>00001
[[1,2,3,4],[4,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,2,4,4],[3,4]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,3,4,4],[2,4]]=>[2,4,1,3,5,6]=>00011=>00011
[[1,2,4,4],[4,4]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,3,3,3],[3,4]]=>[2,6,1,3,4,5]=>00000=>00000
[[1,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[1,3,3,4],[3,4]]=>[2,5,1,3,4,6]=>00001=>00001
[[1,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[1,3,4,4],[3,4]]=>[2,4,1,3,5,6]=>00011=>00011
[[1,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>00011=>00011
[[2,2,2,2],[3,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[2,2,2,2],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[2,2,2,3],[3,4]]=>[4,6,1,2,3,5]=>00000=>00000
[[2,2,2,4],[3,3]]=>[4,5,1,2,3,6]=>00001=>00001
[[2,2,2,3],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[2,2,2,4],[3,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[2,2,2,4],[4,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[2,2,3,3],[3,4]]=>[3,6,1,2,4,5]=>00000=>00000
[[2,2,3,4],[3,3]]=>[3,4,1,2,5,6]=>00011=>00011
[[2,2,3,3],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[2,2,3,4],[3,4]]=>[3,5,1,2,4,6]=>00001=>00001
[[2,2,4,4],[3,3]]=>[3,4,1,2,5,6]=>00011=>00011
[[2,2,3,4],[4,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[2,2,4,4],[3,4]]=>[3,4,1,2,5,6]=>00011=>00011
[[2,2,4,4],[4,4]]=>[3,4,1,2,5,6]=>00011=>00011
[[2,3,3,3],[3,4]]=>[2,6,1,3,4,5]=>00000=>00000
[[2,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[2,3,3,4],[3,4]]=>[2,5,1,3,4,6]=>00001=>00001
[[2,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[2,3,4,4],[3,4]]=>[2,4,1,3,5,6]=>00011=>00011
[[2,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>00011=>00011
[[3,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>00000=>00000
[[3,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>00001=>00001
[[3,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>00011=>00011
[[1,1,1,1],[2],[4]]=>[6,5,1,2,3,4]=>00000=>00000
[[1,1,1,1],[3],[4]]=>[6,5,1,2,3,4]=>00000=>00000
[[1,1,1,2],[2],[4]]=>[6,4,1,2,3,5]=>00000=>00000
[[1,1,1,2],[3],[4]]=>[6,5,1,2,3,4]=>00000=>00000
[[1,1,1,3],[2],[4]]=>[6,4,1,2,3,5]=>00000=>00000
[[1,1,1,4],[2],[3]]=>[5,4,1,2,3,6]=>00001=>00001
[[1,1,1,4],[2],[4]]=>[5,4,1,2,3,6]=>00001=>00001
[[1,1,1,3],[3],[4]]=>[6,4,1,2,3,5]=>00000=>00000
[[1,1,1,4],[3],[4]]=>[5,4,1,2,3,6]=>00001=>00001
[[1,1,2,2],[2],[4]]=>[6,3,1,2,4,5]=>00000=>00000
[[1,1,2,2],[3],[4]]=>[6,5,1,2,3,4]=>00000=>00000
[[1,1,2,3],[2],[4]]=>[6,3,1,2,4,5]=>00000=>00000
[[1,1,2,4],[2],[3]]=>[5,3,1,2,4,6]=>00001=>00001
[[1,1,2,4],[2],[4]]=>[5,3,1,2,4,6]=>00001=>00001
[[1,1,2,3],[3],[4]]=>[6,4,1,2,3,5]=>00000=>00000
[[1,1,3,3],[2],[4]]=>[6,3,1,2,4,5]=>00000=>00000
[[1,1,3,4],[2],[3]]=>[4,3,1,2,5,6]=>00011=>00011
[[1,1,2,4],[3],[4]]=>[5,4,1,2,3,6]=>00001=>00001
[[1,1,3,4],[2],[4]]=>[5,3,1,2,4,6]=>00001=>00001
[[1,1,4,4],[2],[3]]=>[4,3,1,2,5,6]=>00011=>00011
[[1,1,4,4],[2],[4]]=>[4,3,1,2,5,6]=>00011=>00011
[[1,1,3,3],[3],[4]]=>[6,3,1,2,4,5]=>00000=>00000
[[1,1,3,4],[3],[4]]=>[5,3,1,2,4,6]=>00001=>00001
[[1,1,4,4],[3],[4]]=>[4,3,1,2,5,6]=>00011=>00011
[[1,2,2,2],[2],[4]]=>[6,2,1,3,4,5]=>00000=>00000
[[1,2,2,2],[3],[4]]=>[6,5,1,2,3,4]=>00000=>00000
[[1,2,2,3],[2],[4]]=>[6,2,1,3,4,5]=>00000=>00000
[[1,2,2,4],[2],[3]]=>[5,2,1,3,4,6]=>00001=>00001
[[1,2,2,4],[2],[4]]=>[5,2,1,3,4,6]=>00001=>00001
[[1,2,2,3],[3],[4]]=>[6,4,1,2,3,5]=>00000=>00000
[[1,2,3,3],[2],[4]]=>[6,2,1,3,4,5]=>00000=>00000
[[1,2,3,4],[2],[3]]=>[4,2,1,3,5,6]=>00011=>00011
[[1,2,2,4],[3],[4]]=>[5,4,1,2,3,6]=>00001=>00001
[[1,2,3,4],[2],[4]]=>[5,2,1,3,4,6]=>00001=>00001
[[1,2,4,4],[2],[3]]=>[4,2,1,3,5,6]=>00011=>00011
[[1,2,4,4],[2],[4]]=>[4,2,1,3,5,6]=>00011=>00011
[[1,2,3,3],[3],[4]]=>[6,3,1,2,4,5]=>00000=>00000
[[1,3,3,3],[2],[4]]=>[6,2,1,3,4,5]=>00000=>00000
[[1,3,3,4],[2],[3]]=>[3,2,1,4,5,6]=>00111=>00111
[[1,2,3,4],[3],[4]]=>[5,3,1,2,4,6]=>00001=>00001
[[1,3,3,4],[2],[4]]=>[5,2,1,3,4,6]=>00001=>00001
[[1,3,4,4],[2],[3]]=>[3,2,1,4,5,6]=>00111=>00111
[[1,2,4,4],[3],[4]]=>[4,3,1,2,5,6]=>00011=>00011
[[1,3,4,4],[2],[4]]=>[4,2,1,3,5,6]=>00011=>00011
[[1,4,4,4],[2],[3]]=>[3,2,1,4,5,6]=>00111=>00111
[[1,4,4,4],[2],[4]]=>[3,2,1,4,5,6]=>00111=>00111
[[1,3,3,3],[3],[4]]=>[6,2,1,3,4,5]=>00000=>00000
[[1,3,3,4],[3],[4]]=>[5,2,1,3,4,6]=>00001=>00001
[[1,3,4,4],[3],[4]]=>[4,2,1,3,5,6]=>00011=>00011
[[1,4,4,4],[3],[4]]=>[3,2,1,4,5,6]=>00111=>00111
[[2,2,2,2],[3],[4]]=>[6,5,1,2,3,4]=>00000=>00000
[[2,2,2,3],[3],[4]]=>[6,4,1,2,3,5]=>00000=>00000
[[2,2,2,4],[3],[4]]=>[5,4,1,2,3,6]=>00001=>00001
[[2,2,3,3],[3],[4]]=>[6,3,1,2,4,5]=>00000=>00000
[[2,2,3,4],[3],[4]]=>[5,3,1,2,4,6]=>00001=>00001
[[2,2,4,4],[3],[4]]=>[4,3,1,2,5,6]=>00011=>00011
[[2,3,3,3],[3],[4]]=>[6,2,1,3,4,5]=>00000=>00000
[[2,3,3,4],[3],[4]]=>[5,2,1,3,4,6]=>00001=>00001
[[2,3,4,4],[3],[4]]=>[4,2,1,3,5,6]=>00011=>00011
[[2,4,4,4],[3],[4]]=>[3,2,1,4,5,6]=>00111=>00111
[[1,1,1],[2,2,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,1],[2,3,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,1],[2,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,1],[3,3,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,1],[3,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,1],[4,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,2],[2,2,4]]=>[3,4,6,1,2,5]=>00000=>00000
[[1,1,2],[2,3,4]]=>[3,5,6,1,2,4]=>00000=>00000
[[1,1,3],[2,2,4]]=>[3,4,6,1,2,5]=>00000=>00000
[[1,1,2],[2,4,4]]=>[3,5,6,1,2,4]=>00000=>00000
[[1,1,2],[3,3,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,3],[2,3,4]]=>[3,4,6,1,2,5]=>00000=>00000
[[1,1,2],[3,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,3],[2,4,4]]=>[3,5,6,1,2,4]=>00000=>00000
[[1,1,2],[4,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,3],[3,3,4]]=>[3,4,6,1,2,5]=>00000=>00000
[[1,1,3],[3,4,4]]=>[3,5,6,1,2,4]=>00000=>00000
[[1,1,3],[4,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,2,2],[2,3,4]]=>[2,5,6,1,3,4]=>00000=>00000
[[1,2,2],[2,4,4]]=>[2,5,6,1,3,4]=>00000=>00000
[[1,2,2],[3,3,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,2,3],[2,3,4]]=>[2,4,6,1,3,5]=>00000=>00000
[[1,2,2],[3,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,2,3],[2,4,4]]=>[2,5,6,1,3,4]=>00000=>00000
[[1,2,2],[4,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,2,3],[3,3,4]]=>[3,4,6,1,2,5]=>00000=>00000
[[1,2,3],[3,4,4]]=>[3,5,6,1,2,4]=>00000=>00000
[[1,3,3],[2,4,4]]=>[2,5,6,1,3,4]=>00000=>00000
[[1,2,3],[4,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,3,3],[3,4,4]]=>[2,5,6,1,3,4]=>00000=>00000
[[1,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[2,2,2],[3,3,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[2,2,2],[3,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[2,2,2],[4,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[2,2,3],[3,3,4]]=>[3,4,6,1,2,5]=>00000=>00000
[[2,2,3],[3,4,4]]=>[3,5,6,1,2,4]=>00000=>00000
[[2,2,3],[4,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[2,3,3],[3,4,4]]=>[2,5,6,1,3,4]=>00000=>00000
[[2,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[3,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>00000=>00000
[[1,1,1],[2,2],[4]]=>[6,4,5,1,2,3]=>00000=>00000
[[1,1,1],[2,3],[4]]=>[6,4,5,1,2,3]=>00000=>00000
[[1,1,1],[2,4],[3]]=>[5,4,6,1,2,3]=>00000=>00000
[[1,1,1],[2,4],[4]]=>[5,4,6,1,2,3]=>00000=>00000
[[1,1,1],[3,3],[4]]=>[6,4,5,1,2,3]=>00000=>00000
[[1,1,1],[3,4],[4]]=>[5,4,6,1,2,3]=>00000=>00000
[[1,1,2],[2,2],[4]]=>[6,3,4,1,2,5]=>00000=>00000
[[1,1,2],[2,3],[4]]=>[6,3,5,1,2,4]=>00000=>00000
[[1,1,2],[2,4],[3]]=>[5,3,6,1,2,4]=>00000=>00000
[[1,1,3],[2,2],[4]]=>[6,3,4,1,2,5]=>00000=>00000
[[1,1,4],[2,2],[3]]=>[5,3,4,1,2,6]=>00001=>00001
[[1,1,2],[2,4],[4]]=>[5,3,6,1,2,4]=>00000=>00000
[[1,1,4],[2,2],[4]]=>[5,3,4,1,2,6]=>00001=>00001
[[1,1,2],[3,3],[4]]=>[6,4,5,1,2,3]=>00000=>00000
[[1,1,3],[2,3],[4]]=>[6,3,4,1,2,5]=>00000=>00000
[[1,1,3],[2,4],[3]]=>[4,3,6,1,2,5]=>00000=>00000
[[1,1,4],[2,3],[3]]=>[4,3,5,1,2,6]=>00001=>00001
[[1,1,2],[3,4],[4]]=>[5,4,6,1,2,3]=>00000=>00000
[[1,1,3],[2,4],[4]]=>[5,3,6,1,2,4]=>00000=>00000
[[1,1,4],[2,3],[4]]=>[5,3,4,1,2,6]=>00001=>00001
[[1,1,4],[2,4],[3]]=>[4,3,5,1,2,6]=>00001=>00001
[[1,1,4],[2,4],[4]]=>[4,3,5,1,2,6]=>00001=>00001
[[1,1,3],[3,3],[4]]=>[6,3,4,1,2,5]=>00000=>00000
[[1,1,3],[3,4],[4]]=>[5,3,6,1,2,4]=>00000=>00000
[[1,1,4],[3,3],[4]]=>[5,3,4,1,2,6]=>00001=>00001
[[1,1,4],[3,4],[4]]=>[4,3,5,1,2,6]=>00001=>00001
[[1,2,2],[2,3],[4]]=>[6,2,5,1,3,4]=>00000=>00000
[[1,2,2],[2,4],[3]]=>[5,2,6,1,3,4]=>00000=>00000
[[1,2,2],[2,4],[4]]=>[5,2,6,1,3,4]=>00000=>00000
[[1,2,2],[3,3],[4]]=>[6,4,5,1,2,3]=>00000=>00000
[[1,2,3],[2,3],[4]]=>[6,2,4,1,3,5]=>00000=>00000
[[1,2,3],[2,4],[3]]=>[4,2,6,1,3,5]=>00000=>00000
[[1,2,4],[2,3],[3]]=>[4,2,5,1,3,6]=>00001=>00001
[[1,2,2],[3,4],[4]]=>[5,4,6,1,2,3]=>00000=>00000
[[1,2,3],[2,4],[4]]=>[5,2,6,1,3,4]=>00000=>00000
[[1,2,4],[2,3],[4]]=>[5,2,4,1,3,6]=>00001=>00001
[[1,2,4],[2,4],[3]]=>[4,2,5,1,3,6]=>00001=>00001
[[1,2,4],[2,4],[4]]=>[4,2,5,1,3,6]=>00001=>00001
[[1,2,3],[3,3],[4]]=>[6,3,4,1,2,5]=>00000=>00000
[[1,3,3],[2,4],[3]]=>[3,2,6,1,4,5]=>00000=>00000
[[1,2,3],[3,4],[4]]=>[5,3,6,1,2,4]=>00000=>00000
[[1,2,4],[3,3],[4]]=>[5,3,4,1,2,6]=>00001=>00001
[[1,3,3],[2,4],[4]]=>[5,2,6,1,3,4]=>00000=>00000
[[1,3,4],[2,4],[3]]=>[3,2,5,1,4,6]=>00001=>00001
[[1,2,4],[3,4],[4]]=>[4,3,5,1,2,6]=>00001=>00001
[[1,3,4],[2,4],[4]]=>[4,2,5,1,3,6]=>00001=>00001
[[1,3,3],[3,4],[4]]=>[5,2,6,1,3,4]=>00000=>00000
[[1,3,4],[3,4],[4]]=>[4,2,5,1,3,6]=>00001=>00001
[[2,2,2],[3,3],[4]]=>[6,4,5,1,2,3]=>00000=>00000
[[2,2,2],[3,4],[4]]=>[5,4,6,1,2,3]=>00000=>00000
[[2,2,3],[3,3],[4]]=>[6,3,4,1,2,5]=>00000=>00000
[[2,2,3],[3,4],[4]]=>[5,3,6,1,2,4]=>00000=>00000
[[2,2,4],[3,3],[4]]=>[5,3,4,1,2,6]=>00001=>00001
[[2,2,4],[3,4],[4]]=>[4,3,5,1,2,6]=>00001=>00001
[[2,3,3],[3,4],[4]]=>[5,2,6,1,3,4]=>00000=>00000
[[2,3,4],[3,4],[4]]=>[4,2,5,1,3,6]=>00001=>00001
[[1,1,1],[2],[3],[4]]=>[6,5,4,1,2,3]=>00000=>00000
[[1,1,2],[2],[3],[4]]=>[6,5,3,1,2,4]=>00000=>00000
[[1,1,3],[2],[3],[4]]=>[6,4,3,1,2,5]=>00000=>00000
[[1,1,4],[2],[3],[4]]=>[5,4,3,1,2,6]=>00001=>00001
[[1,2,2],[2],[3],[4]]=>[6,5,2,1,3,4]=>00000=>00000
[[1,2,3],[2],[3],[4]]=>[6,4,2,1,3,5]=>00000=>00000
[[1,2,4],[2],[3],[4]]=>[5,4,2,1,3,6]=>00001=>00001
[[1,3,3],[2],[3],[4]]=>[6,3,2,1,4,5]=>00000=>00000
[[1,3,4],[2],[3],[4]]=>[5,3,2,1,4,6]=>00001=>00001
[[1,4,4],[2],[3],[4]]=>[4,3,2,1,5,6]=>00011=>00011
[[1,1],[2,2],[3,4]]=>[5,6,3,4,1,2]=>00000=>00000
[[1,1],[2,2],[4,4]]=>[5,6,3,4,1,2]=>00000=>00000
[[1,1],[2,3],[3,4]]=>[4,6,3,5,1,2]=>00000=>00000
[[1,1],[2,3],[4,4]]=>[5,6,3,4,1,2]=>00000=>00000
[[1,1],[3,3],[4,4]]=>[5,6,3,4,1,2]=>00000=>00000
[[1,2],[2,3],[3,4]]=>[4,6,2,5,1,3]=>00000=>00000
[[1,2],[2,3],[4,4]]=>[5,6,2,4,1,3]=>00000=>00000
[[1,2],[3,3],[4,4]]=>[5,6,3,4,1,2]=>00000=>00000
[[2,2],[3,3],[4,4]]=>[5,6,3,4,1,2]=>00000=>00000
[[1,1],[2,2],[3],[4]]=>[6,5,3,4,1,2]=>00000=>00000
[[1,1],[2,3],[3],[4]]=>[6,4,3,5,1,2]=>00000=>00000
[[1,1],[2,4],[3],[4]]=>[5,4,3,6,1,2]=>00000=>00000
[[1,2],[2,3],[3],[4]]=>[6,4,2,5,1,3]=>00000=>00000
[[1,2],[2,4],[3],[4]]=>[5,4,2,6,1,3]=>00000=>00000
[[1,3],[2,4],[3],[4]]=>[5,3,2,6,1,4]=>00000=>00000
[[1,1,1,1,1,1,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,1,1,2,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,1,1,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,1,2,2,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,1,2,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,1,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,2,2,2,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,2,2,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,2,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,3,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,2,2,2,2,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,2,2,2,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,2,2,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,2,3,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,2,2,2,2,2,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,2,2,2,2,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,2,2,2,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,2,2,3,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,2,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,3,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[2,2,2,2,2,2,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[2,2,2,2,2,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[2,2,2,2,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[2,2,2,3,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[2,2,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[2,3,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[3,3,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>111111=>111111
[[1,1,1,1,1,1],[3]]=>[7,1,2,3,4,5,6]=>000000=>000000
[[1,1,1,1,1,2],[3]]=>[7,1,2,3,4,5,6]=>000000=>000000
[[1,1,1,1,1,3],[2]]=>[6,1,2,3,4,5,7]=>000001=>000001
[[1,1,1,1,1,3],[3]]=>[6,1,2,3,4,5,7]=>000001=>000001
[[1,1,1,1,2,2],[3]]=>[7,1,2,3,4,5,6]=>000000=>000000
[[1,1,1,1,2,3],[2]]=>[5,1,2,3,4,6,7]=>000011=>000011
[[1,1,1,1,2,3],[3]]=>[6,1,2,3,4,5,7]=>000001=>000001
[[1,1,1,1,3,3],[2]]=>[5,1,2,3,4,6,7]=>000011=>000011
[[1,1,1,1,3,3],[3]]=>[5,1,2,3,4,6,7]=>000011=>000011
[[1,1,1,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>000000=>000000
[[1,1,1,2,2,3],[2]]=>[4,1,2,3,5,6,7]=>000111=>000111
[[1,1,1,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>000001=>000001
[[1,1,1,2,3,3],[2]]=>[4,1,2,3,5,6,7]=>000111=>000111
[[1,1,1,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>000011=>000011
[[1,1,1,3,3,3],[2]]=>[4,1,2,3,5,6,7]=>000111=>000111
[[1,1,1,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>000111=>000111
[[1,1,2,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>000000=>000000
[[1,1,2,2,2,3],[2]]=>[3,1,2,4,5,6,7]=>001111=>001111
[[1,1,2,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>000001=>000001
[[1,1,2,2,3,3],[2]]=>[3,1,2,4,5,6,7]=>001111=>001111
[[1,1,2,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>000011=>000011
[[1,1,2,3,3,3],[2]]=>[3,1,2,4,5,6,7]=>001111=>001111
[[1,1,2,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>000111=>000111
[[1,1,3,3,3,3],[2]]=>[3,1,2,4,5,6,7]=>001111=>001111
[[1,1,3,3,3,3],[3]]=>[3,1,2,4,5,6,7]=>001111=>001111
[[1,2,2,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>000000=>000000
[[1,2,2,2,2,3],[2]]=>[2,1,3,4,5,6,7]=>011111=>011111
[[1,2,2,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>000001=>000001
[[1,2,2,2,3,3],[2]]=>[2,1,3,4,5,6,7]=>011111=>011111
[[1,2,2,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>000011=>000011
[[1,2,2,3,3,3],[2]]=>[2,1,3,4,5,6,7]=>011111=>011111
[[1,2,2,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>000111=>000111
[[1,2,3,3,3,3],[2]]=>[2,1,3,4,5,6,7]=>011111=>011111
[[1,2,3,3,3,3],[3]]=>[3,1,2,4,5,6,7]=>001111=>001111
[[1,3,3,3,3,3],[2]]=>[2,1,3,4,5,6,7]=>011111=>011111
[[1,3,3,3,3,3],[3]]=>[2,1,3,4,5,6,7]=>011111=>011111
[[2,2,2,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>000000=>000000
[[2,2,2,2,2,3],[3]]=>[6,1,2,3,4,5,7]=>000001=>000001
[[2,2,2,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>000011=>000011
[[2,2,2,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>000111=>000111
[[2,2,3,3,3,3],[3]]=>[3,1,2,4,5,6,7]=>001111=>001111
[[2,3,3,3,3,3],[3]]=>[2,1,3,4,5,6,7]=>011111=>011111
[[1,1,1,1,1],[2,3]]=>[6,7,1,2,3,4,5]=>000000=>000000
[[1,1,1,1,1],[3,3]]=>[6,7,1,2,3,4,5]=>000000=>000000
[[1,1,1,1,2],[2,3]]=>[5,7,1,2,3,4,6]=>000000=>000000
[[1,1,1,1,3],[2,2]]=>[5,6,1,2,3,4,7]=>000001=>000001
[[1,1,1,1,2],[3,3]]=>[6,7,1,2,3,4,5]=>000000=>000000
[[1,1,1,1,3],[2,3]]=>[5,6,1,2,3,4,7]=>000001=>000001
[[1,1,1,1,3],[3,3]]=>[5,6,1,2,3,4,7]=>000001=>000001
[[1,1,1,2,2],[2,3]]=>[4,7,1,2,3,5,6]=>000000=>000000
[[1,1,1,2,3],[2,2]]=>[4,5,1,2,3,6,7]=>000011=>000011
[[1,1,1,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>000000=>000000
[[1,1,1,2,3],[2,3]]=>[4,6,1,2,3,5,7]=>000001=>000001
[[1,1,1,3,3],[2,2]]=>[4,5,1,2,3,6,7]=>000011=>000011
[[1,1,1,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>000001=>000001
[[1,1,1,3,3],[2,3]]=>[4,5,1,2,3,6,7]=>000011=>000011
[[1,1,1,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>000011=>000011
[[1,1,2,2,2],[2,3]]=>[3,7,1,2,4,5,6]=>000000=>000000
[[1,1,2,2,3],[2,2]]=>[3,4,1,2,5,6,7]=>000111=>000111
[[1,1,2,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>000000=>000000
[[1,1,2,2,3],[2,3]]=>[3,6,1,2,4,5,7]=>000001=>000001
[[1,1,2,3,3],[2,2]]=>[3,4,1,2,5,6,7]=>000111=>000111
[[1,1,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>000001=>000001
[[1,1,2,3,3],[2,3]]=>[3,5,1,2,4,6,7]=>000011=>000011
[[1,1,3,3,3],[2,2]]=>[3,4,1,2,5,6,7]=>000111=>000111
[[1,1,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>000011=>000011
[[1,1,3,3,3],[2,3]]=>[3,4,1,2,5,6,7]=>000111=>000111
[[1,1,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>000111=>000111
[[1,2,2,2,2],[2,3]]=>[2,7,1,3,4,5,6]=>000000=>000000
[[1,2,2,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>000000=>000000
[[1,2,2,2,3],[2,3]]=>[2,6,1,3,4,5,7]=>000001=>000001
[[1,2,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>000001=>000001
[[1,2,2,3,3],[2,3]]=>[2,5,1,3,4,6,7]=>000011=>000011
[[1,2,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>000011=>000011
[[1,2,3,3,3],[2,3]]=>[2,4,1,3,5,6,7]=>000111=>000111
[[1,2,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>000111=>000111
[[2,2,2,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>000000=>000000
[[2,2,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>000001=>000001
[[2,2,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>000011=>000011
[[2,2,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>000111=>000111
[[1,1,1,1,1],[2],[3]]=>[7,6,1,2,3,4,5]=>000000=>000000
[[1,1,1,1,2],[2],[3]]=>[7,5,1,2,3,4,6]=>000000=>000000
[[1,1,1,1,3],[2],[3]]=>[6,5,1,2,3,4,7]=>000001=>000001
[[1,1,1,2,2],[2],[3]]=>[7,4,1,2,3,5,6]=>000000=>000000
[[1,1,1,2,3],[2],[3]]=>[6,4,1,2,3,5,7]=>000001=>000001
[[1,1,1,3,3],[2],[3]]=>[5,4,1,2,3,6,7]=>000011=>000011
[[1,1,2,2,2],[2],[3]]=>[7,3,1,2,4,5,6]=>000000=>000000
[[1,1,2,2,3],[2],[3]]=>[6,3,1,2,4,5,7]=>000001=>000001
[[1,1,2,3,3],[2],[3]]=>[5,3,1,2,4,6,7]=>000011=>000011
[[1,1,3,3,3],[2],[3]]=>[4,3,1,2,5,6,7]=>000111=>000111
[[1,2,2,2,2],[2],[3]]=>[7,2,1,3,4,5,6]=>000000=>000000
[[1,2,2,2,3],[2],[3]]=>[6,2,1,3,4,5,7]=>000001=>000001
[[1,2,2,3,3],[2],[3]]=>[5,2,1,3,4,6,7]=>000011=>000011
[[1,2,3,3,3],[2],[3]]=>[4,2,1,3,5,6,7]=>000111=>000111
[[1,3,3,3,3],[2],[3]]=>[3,2,1,4,5,6,7]=>001111=>001111
[[1,1,1,1],[2,2,3]]=>[5,6,7,1,2,3,4]=>000000=>000000
[[1,1,1,1],[2,3,3]]=>[5,6,7,1,2,3,4]=>000000=>000000
[[1,1,1,1],[3,3,3]]=>[5,6,7,1,2,3,4]=>000000=>000000
[[1,1,1,2],[2,2,3]]=>[4,5,7,1,2,3,6]=>000000=>000000
[[1,1,1,3],[2,2,2]]=>[4,5,6,1,2,3,7]=>000001=>000001
[[1,1,1,2],[2,3,3]]=>[4,6,7,1,2,3,5]=>000000=>000000
[[1,1,1,3],[2,2,3]]=>[4,5,6,1,2,3,7]=>000001=>000001
[[1,1,1,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>000000=>000000
[[1,1,1,3],[2,3,3]]=>[4,5,6,1,2,3,7]=>000001=>000001
[[1,1,1,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>000001=>000001
[[1,1,2,2],[2,2,3]]=>[3,4,7,1,2,5,6]=>000000=>000000
[[1,1,2,2],[2,3,3]]=>[3,6,7,1,2,4,5]=>000000=>000000
[[1,1,2,3],[2,2,3]]=>[3,4,6,1,2,5,7]=>000001=>000001
[[1,1,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>000000=>000000
[[1,1,2,3],[2,3,3]]=>[3,5,6,1,2,4,7]=>000001=>000001
[[1,1,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>000001=>000001
[[1,2,2,2],[2,3,3]]=>[2,6,7,1,3,4,5]=>000000=>000000
[[1,2,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>000000=>000000
[[1,2,2,3],[2,3,3]]=>[2,5,6,1,3,4,7]=>000001=>000001
[[1,2,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>000001=>000001
[[2,2,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>000000=>000000
[[2,2,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>000001=>000001
[[1,1,1,1],[2,2],[3]]=>[7,5,6,1,2,3,4]=>000000=>000000
[[1,1,1,1],[2,3],[3]]=>[6,5,7,1,2,3,4]=>000000=>000000
[[1,1,1,2],[2,2],[3]]=>[7,4,5,1,2,3,6]=>000000=>000000
[[1,1,1,2],[2,3],[3]]=>[6,4,7,1,2,3,5]=>000000=>000000
[[1,1,1,3],[2,2],[3]]=>[6,4,5,1,2,3,7]=>000001=>000001
[[1,1,1,3],[2,3],[3]]=>[5,4,6,1,2,3,7]=>000001=>000001
[[1,1,2,2],[2,2],[3]]=>[7,3,4,1,2,5,6]=>000000=>000000
[[1,1,2,2],[2,3],[3]]=>[6,3,7,1,2,4,5]=>000000=>000000
[[1,1,2,3],[2,2],[3]]=>[6,3,4,1,2,5,7]=>000001=>000001
[[1,1,2,3],[2,3],[3]]=>[5,3,6,1,2,4,7]=>000001=>000001
[[1,1,3,3],[2,2],[3]]=>[5,3,4,1,2,6,7]=>000011=>000011
[[1,1,3,3],[2,3],[3]]=>[4,3,5,1,2,6,7]=>000011=>000011
[[1,2,2,2],[2,3],[3]]=>[6,2,7,1,3,4,5]=>000000=>000000
[[1,2,2,3],[2,3],[3]]=>[5,2,6,1,3,4,7]=>000001=>000001
[[1,2,3,3],[2,3],[3]]=>[4,2,5,1,3,6,7]=>000011=>000011
[[1,1,1],[2,2,2],[3]]=>[7,4,5,6,1,2,3]=>000000=>000000
[[1,1,1],[2,2,3],[3]]=>[6,4,5,7,1,2,3]=>000000=>000000
[[1,1,1],[2,3,3],[3]]=>[5,4,6,7,1,2,3]=>000000=>000000
[[1,1,2],[2,2,3],[3]]=>[6,3,4,7,1,2,5]=>000000=>000000
[[1,1,2],[2,3,3],[3]]=>[5,3,6,7,1,2,4]=>000000=>000000
[[1,2,2],[2,3,3],[3]]=>[5,2,6,7,1,3,4]=>000000=>000000
[[1,1,1],[2,2],[3,3]]=>[6,7,4,5,1,2,3]=>000000=>000000
[[1,1,2],[2,2],[3,3]]=>[6,7,3,4,1,2,5]=>000000=>000000
[[1,1,3],[2,2],[3,3]]=>[5,6,3,4,1,2,7]=>000001=>000001
[[1,1,1,1,1,1,1,2]]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111
[[1,1,1,1,1,1,2,2]]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111
[[1,1,1,1,1,2,2,2]]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111
[[1,1,1,1,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111
[[1,1,1,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111
[[1,1,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111
[[1,2,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111
[[2,2,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111
[[1,1,1,1,1,1,2],[2]]=>[7,1,2,3,4,5,6,8]=>0000001=>0000001
[[1,1,1,1,2,2,2],[2]]=>[5,1,2,3,4,6,7,8]=>0000111=>0000111
[[1,1,1,2,2,2,2],[2]]=>[4,1,2,3,5,6,7,8]=>0001111=>0001111
[[1,1,2,2,2,2,2],[2]]=>[3,1,2,4,5,6,7,8]=>0011111=>0011111
[[1,2,2,2,2,2,2],[2]]=>[2,1,3,4,5,6,7,8]=>0111111=>0111111
[[1,1,1,1,1,1],[2,2]]=>[7,8,1,2,3,4,5,6]=>0000000=>0000000
[[1,1,1,1,1,2],[2,2]]=>[6,7,1,2,3,4,5,8]=>0000001=>0000001
[[1,1,1,2,2,2],[2,2]]=>[4,5,1,2,3,6,7,8]=>0000111=>0000111
[[1,1,2,2,2,2],[2,2]]=>[3,4,1,2,5,6,7,8]=>0001111=>0001111
[[1,1,1,1,1],[2,2,2]]=>[6,7,8,1,2,3,4,5]=>0000000=>0000000
[[1,1,1,1,2],[2,2,2]]=>[5,6,7,1,2,3,4,8]=>0000001=>0000001
[[1,1,1,1],[2,2,2,2]]=>[5,6,7,8,1,2,3,4]=>0000000=>0000000
[[1,1]]=>[1,2]=>1=>1
[[1,1,1]]=>[1,2,3]=>11=>11
[[1,1,1,1]]=>[1,2,3,4]=>111=>111
[[1,1,1,1,1]]=>[1,2,3,4,5]=>1111=>1111
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
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
Map
Foata bijection
Description
The Foata bijection $\phi$ is a bijection on the set of words of given content (by a slight generalization of Section 2 in [1]).
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$. At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
For instance, to compute $\phi(4154223)$, the sequence of words is
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$. At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
For instance, to compute $\phi(4154223)$, the sequence of words is
- 4,
- |4|1 -- > 41,
- |4|1|5 -- > 415,
- |415|4 -- > 5414,
- |5|4|14|2 -- > 54412,
- |5441|2|2 -- > 154422,
- |1|5442|2|3 -- > 1254423.
searching the database
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