Identifier
Mp00060:
Permutations
—Robinson-Schensted tableau shape⟶
Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00134: Standard tableaux —descent word⟶ Binary words
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00134: Standard tableaux —descent word⟶ Binary words
Images
=>
Cc0002;cc-rep-1Cc0007;cc-rep-2
[1]=>[1]=>[[1]]=>
[1,2]=>[2]=>[[1,2]]=>0
[2,1]=>[1,1]=>[[1],[2]]=>1
[1,2,3]=>[3]=>[[1,2,3]]=>00
[1,3,2]=>[2,1]=>[[1,3],[2]]=>10
[2,1,3]=>[2,1]=>[[1,3],[2]]=>10
[2,3,1]=>[2,1]=>[[1,3],[2]]=>10
[3,1,2]=>[2,1]=>[[1,3],[2]]=>10
[3,2,1]=>[1,1,1]=>[[1],[2],[3]]=>11
[1,2,3,4]=>[4]=>[[1,2,3,4]]=>000
[1,2,4,3]=>[3,1]=>[[1,3,4],[2]]=>100
[1,3,2,4]=>[3,1]=>[[1,3,4],[2]]=>100
[1,3,4,2]=>[3,1]=>[[1,3,4],[2]]=>100
[1,4,2,3]=>[3,1]=>[[1,3,4],[2]]=>100
[1,4,3,2]=>[2,1,1]=>[[1,4],[2],[3]]=>110
[2,1,3,4]=>[3,1]=>[[1,3,4],[2]]=>100
[2,1,4,3]=>[2,2]=>[[1,2],[3,4]]=>010
[2,3,1,4]=>[3,1]=>[[1,3,4],[2]]=>100
[2,3,4,1]=>[3,1]=>[[1,3,4],[2]]=>100
[2,4,1,3]=>[2,2]=>[[1,2],[3,4]]=>010
[2,4,3,1]=>[2,1,1]=>[[1,4],[2],[3]]=>110
[3,1,2,4]=>[3,1]=>[[1,3,4],[2]]=>100
[3,1,4,2]=>[2,2]=>[[1,2],[3,4]]=>010
[3,2,1,4]=>[2,1,1]=>[[1,4],[2],[3]]=>110
[3,2,4,1]=>[2,1,1]=>[[1,4],[2],[3]]=>110
[3,4,1,2]=>[2,2]=>[[1,2],[3,4]]=>010
[3,4,2,1]=>[2,1,1]=>[[1,4],[2],[3]]=>110
[4,1,2,3]=>[3,1]=>[[1,3,4],[2]]=>100
[4,1,3,2]=>[2,1,1]=>[[1,4],[2],[3]]=>110
[4,2,1,3]=>[2,1,1]=>[[1,4],[2],[3]]=>110
[4,2,3,1]=>[2,1,1]=>[[1,4],[2],[3]]=>110
[4,3,1,2]=>[2,1,1]=>[[1,4],[2],[3]]=>110
[4,3,2,1]=>[1,1,1,1]=>[[1],[2],[3],[4]]=>111
[1,2,3,4,5]=>[5]=>[[1,2,3,4,5]]=>0000
[1,2,3,5,4]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[1,2,4,3,5]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[1,2,4,5,3]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[1,2,5,3,4]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[1,2,5,4,3]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[1,3,2,4,5]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[1,3,2,5,4]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[1,3,4,2,5]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[1,3,4,5,2]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[1,3,5,2,4]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[1,3,5,4,2]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[1,4,2,3,5]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[1,4,2,5,3]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[1,4,3,2,5]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[1,4,3,5,2]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[1,4,5,2,3]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[1,4,5,3,2]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[1,5,2,3,4]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[1,5,2,4,3]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[1,5,3,2,4]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[1,5,3,4,2]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[1,5,4,2,3]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[1,5,4,3,2]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[2,1,3,4,5]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[2,1,3,5,4]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[2,1,4,3,5]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[2,1,4,5,3]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[2,1,5,3,4]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[2,1,5,4,3]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[2,3,1,4,5]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[2,3,1,5,4]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[2,3,4,1,5]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[2,3,4,5,1]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[2,3,5,1,4]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[2,3,5,4,1]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[2,4,1,3,5]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[2,4,1,5,3]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[2,4,3,1,5]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[2,4,3,5,1]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[2,4,5,1,3]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[2,4,5,3,1]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[2,5,1,3,4]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[2,5,1,4,3]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[2,5,3,1,4]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[2,5,3,4,1]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[2,5,4,1,3]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[2,5,4,3,1]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[3,1,2,4,5]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[3,1,2,5,4]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[3,1,4,2,5]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[3,1,4,5,2]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[3,1,5,2,4]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[3,1,5,4,2]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[3,2,1,4,5]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[3,2,1,5,4]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[3,2,4,1,5]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[3,2,4,5,1]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[3,2,5,1,4]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[3,2,5,4,1]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[3,4,1,2,5]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[3,4,1,5,2]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[3,4,2,1,5]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[3,4,2,5,1]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[3,4,5,1,2]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[3,4,5,2,1]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[3,5,1,2,4]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[3,5,1,4,2]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[3,5,2,1,4]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[3,5,2,4,1]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[3,5,4,1,2]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[3,5,4,2,1]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[4,1,2,3,5]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[4,1,2,5,3]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[4,1,3,2,5]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[4,1,3,5,2]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[4,1,5,2,3]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[4,1,5,3,2]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[4,2,1,3,5]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[4,2,1,5,3]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[4,2,3,1,5]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[4,2,3,5,1]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[4,2,5,1,3]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[4,2,5,3,1]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[4,3,1,2,5]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[4,3,1,5,2]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[4,3,2,1,5]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[4,3,2,5,1]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[4,3,5,1,2]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[4,3,5,2,1]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[4,5,1,2,3]=>[3,2]=>[[1,2,5],[3,4]]=>0100
[4,5,1,3,2]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[4,5,2,1,3]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[4,5,2,3,1]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[4,5,3,1,2]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[4,5,3,2,1]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[5,1,2,3,4]=>[4,1]=>[[1,3,4,5],[2]]=>1000
[5,1,2,4,3]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[5,1,3,2,4]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[5,1,3,4,2]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[5,1,4,2,3]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[5,1,4,3,2]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[5,2,1,3,4]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[5,2,1,4,3]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[5,2,3,1,4]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[5,2,3,4,1]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[5,2,4,1,3]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[5,2,4,3,1]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[5,3,1,2,4]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[5,3,1,4,2]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[5,3,2,1,4]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[5,3,2,4,1]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[5,3,4,1,2]=>[2,2,1]=>[[1,3],[2,5],[4]]=>1010
[5,3,4,2,1]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[5,4,1,2,3]=>[3,1,1]=>[[1,4,5],[2],[3]]=>1100
[5,4,1,3,2]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[5,4,2,1,3]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[5,4,2,3,1]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[5,4,3,1,2]=>[2,1,1,1]=>[[1,5],[2],[3],[4]]=>1110
[5,4,3,2,1]=>[1,1,1,1,1]=>[[1],[2],[3],[4],[5]]=>1111
[1,2,3,4,5,6]=>[6]=>[[1,2,3,4,5,6]]=>00000
[1,2,3,4,6,5]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,2,3,5,4,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,2,3,5,6,4]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,2,3,6,4,5]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,2,3,6,5,4]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,2,4,3,5,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,2,4,3,6,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,2,4,5,3,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,2,4,5,6,3]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,2,4,6,3,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,2,4,6,5,3]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,2,5,3,4,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,2,5,3,6,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,2,5,4,3,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,2,5,4,6,3]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,2,5,6,3,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,2,5,6,4,3]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,2,6,3,4,5]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,2,6,3,5,4]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,2,6,4,3,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,2,6,4,5,3]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,2,6,5,3,4]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,2,6,5,4,3]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,3,2,4,5,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,3,2,4,6,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,3,2,5,4,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,3,2,5,6,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,3,2,6,4,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,3,2,6,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,3,4,2,5,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,3,4,2,6,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,3,4,5,2,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,3,4,5,6,2]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,3,4,6,2,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,3,4,6,5,2]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,3,5,2,4,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,3,5,2,6,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,3,5,4,2,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,3,5,4,6,2]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,3,5,6,2,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,3,5,6,4,2]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,3,6,2,4,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,3,6,2,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,3,6,4,2,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,3,6,4,5,2]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,3,6,5,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,3,6,5,4,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,4,2,3,5,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,4,2,3,6,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,4,2,5,3,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,4,2,5,6,3]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,4,2,6,3,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,4,2,6,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,4,3,2,5,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,4,3,2,6,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,4,3,5,2,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,4,3,5,6,2]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,4,3,6,2,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,4,3,6,5,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,4,5,2,3,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,4,5,2,6,3]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,4,5,3,2,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,4,5,3,6,2]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,4,5,6,2,3]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,4,5,6,3,2]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,4,6,2,3,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,4,6,2,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,4,6,3,2,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,4,6,3,5,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,4,6,5,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,4,6,5,3,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,5,2,3,4,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,5,2,3,6,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,5,2,4,3,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,5,2,4,6,3]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,5,2,6,3,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,5,2,6,4,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,5,3,2,4,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,5,3,2,6,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,5,3,4,2,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,5,3,4,6,2]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,5,3,6,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,5,3,6,4,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,5,4,2,3,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,5,4,2,6,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,5,4,3,2,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,5,4,3,6,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,5,4,6,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,5,4,6,3,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,5,6,2,3,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[1,5,6,2,4,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,5,6,3,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,5,6,3,4,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,5,6,4,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,5,6,4,3,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,6,2,3,4,5]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[1,6,2,3,5,4]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,6,2,4,3,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,6,2,4,5,3]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,6,2,5,3,4]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,6,2,5,4,3]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,6,3,2,4,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,6,3,2,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,6,3,4,2,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,6,3,4,5,2]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,6,3,5,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,6,3,5,4,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,6,4,2,3,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,6,4,2,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,6,4,3,2,5]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,6,4,3,5,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,6,4,5,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[1,6,4,5,3,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,6,5,2,3,4]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[1,6,5,2,4,3]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,6,5,3,2,4]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,6,5,3,4,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,6,5,4,2,3]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[1,6,5,4,3,2]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[2,1,3,4,5,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[2,1,3,4,6,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,1,3,5,4,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,1,3,5,6,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,1,3,6,4,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,1,3,6,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,1,4,3,5,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,1,4,3,6,5]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[2,1,4,5,3,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,1,4,5,6,3]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,1,4,6,3,5]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[2,1,4,6,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,1,5,3,4,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,1,5,3,6,4]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[2,1,5,4,3,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,1,5,4,6,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,1,5,6,3,4]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[2,1,5,6,4,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,1,6,3,4,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,1,6,3,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,1,6,4,3,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,1,6,4,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,1,6,5,3,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,1,6,5,4,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[2,3,1,4,5,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[2,3,1,4,6,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,3,1,5,4,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,3,1,5,6,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,3,1,6,4,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,3,1,6,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,3,4,1,5,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[2,3,4,1,6,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,3,4,5,1,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[2,3,4,5,6,1]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[2,3,4,6,1,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,3,4,6,5,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,3,5,1,4,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,3,5,1,6,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,3,5,4,1,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,3,5,4,6,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,3,5,6,1,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,3,5,6,4,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,3,6,1,4,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,3,6,1,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,3,6,4,1,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,3,6,4,5,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,3,6,5,1,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,3,6,5,4,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[2,4,1,3,5,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,4,1,3,6,5]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[2,4,1,5,3,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,4,1,5,6,3]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,4,1,6,3,5]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[2,4,1,6,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,4,3,1,5,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,4,3,1,6,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,4,3,5,1,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,4,3,5,6,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,4,3,6,1,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,4,3,6,5,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,4,5,1,3,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,4,5,1,6,3]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,4,5,3,1,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,4,5,3,6,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,4,5,6,1,3]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,4,5,6,3,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,4,6,1,3,5]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[2,4,6,1,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,4,6,3,1,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,4,6,3,5,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,4,6,5,1,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,4,6,5,3,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[2,5,1,3,4,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,5,1,3,6,4]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[2,5,1,4,3,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,5,1,4,6,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,5,1,6,3,4]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[2,5,1,6,4,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,5,3,1,4,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,5,3,1,6,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,5,3,4,1,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,5,3,4,6,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,5,3,6,1,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,5,3,6,4,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,5,4,1,3,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,5,4,1,6,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,5,4,3,1,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[2,5,4,3,6,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[2,5,4,6,1,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,5,4,6,3,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[2,5,6,1,3,4]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[2,5,6,1,4,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,5,6,3,1,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,5,6,3,4,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,5,6,4,1,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,5,6,4,3,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[2,6,1,3,4,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[2,6,1,3,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,6,1,4,3,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,6,1,4,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,6,1,5,3,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,6,1,5,4,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[2,6,3,1,4,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,6,3,1,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,6,3,4,1,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,6,3,4,5,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[2,6,3,5,1,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,6,3,5,4,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[2,6,4,1,3,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,6,4,1,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,6,4,3,1,5]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[2,6,4,3,5,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[2,6,4,5,1,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,6,4,5,3,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[2,6,5,1,3,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[2,6,5,1,4,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[2,6,5,3,1,4]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[2,6,5,3,4,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[2,6,5,4,1,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[2,6,5,4,3,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[3,1,2,4,5,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[3,1,2,4,6,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,1,2,5,4,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,1,2,5,6,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,1,2,6,4,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,1,2,6,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,1,4,2,5,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,1,4,2,6,5]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[3,1,4,5,2,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,1,4,5,6,2]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,1,4,6,2,5]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[3,1,4,6,5,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,1,5,2,4,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,1,5,2,6,4]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[3,1,5,4,2,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,1,5,4,6,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,1,5,6,2,4]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[3,1,5,6,4,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,1,6,2,4,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,1,6,2,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,1,6,4,2,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,1,6,4,5,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,1,6,5,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,1,6,5,4,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[3,2,1,4,5,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[3,2,1,4,6,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,1,5,4,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,1,5,6,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,1,6,4,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,1,6,5,4]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[3,2,4,1,5,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[3,2,4,1,6,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,4,5,1,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[3,2,4,5,6,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[3,2,4,6,1,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,4,6,5,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,5,1,4,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,5,1,6,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,5,4,1,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,5,4,6,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,5,6,1,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,5,6,4,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,6,1,4,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,6,1,5,4]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[3,2,6,4,1,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,6,4,5,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,2,6,5,1,4]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[3,2,6,5,4,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[3,4,1,2,5,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,4,1,2,6,5]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[3,4,1,5,2,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,4,1,5,6,2]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,4,1,6,2,5]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[3,4,1,6,5,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,4,2,1,5,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[3,4,2,1,6,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,4,2,5,1,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[3,4,2,5,6,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[3,4,2,6,1,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,4,2,6,5,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,4,5,1,2,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,4,5,1,6,2]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,4,5,2,1,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[3,4,5,2,6,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[3,4,5,6,1,2]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,4,5,6,2,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[3,4,6,1,2,5]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[3,4,6,1,5,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,4,6,2,1,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,4,6,2,5,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,4,6,5,1,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,4,6,5,2,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[3,5,1,2,4,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,5,1,2,6,4]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[3,5,1,4,2,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,1,4,6,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,1,6,2,4]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[3,5,1,6,4,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,2,1,4,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,2,1,6,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,2,4,1,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,2,4,6,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,2,6,1,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,2,6,4,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,4,1,2,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,4,1,6,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,4,2,1,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[3,5,4,2,6,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[3,5,4,6,1,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,4,6,2,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[3,5,6,1,2,4]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[3,5,6,1,4,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,6,2,1,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,6,2,4,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,6,4,1,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,5,6,4,2,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[3,6,1,2,4,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[3,6,1,2,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,6,1,4,2,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,6,1,4,5,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,6,1,5,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,6,1,5,4,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[3,6,2,1,4,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,6,2,1,5,4]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[3,6,2,4,1,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,6,2,4,5,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,6,2,5,1,4]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[3,6,2,5,4,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[3,6,4,1,2,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,6,4,1,5,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,6,4,2,1,5]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[3,6,4,2,5,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[3,6,4,5,1,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,6,4,5,2,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[3,6,5,1,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[3,6,5,1,4,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[3,6,5,2,1,4]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[3,6,5,2,4,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[3,6,5,4,1,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[3,6,5,4,2,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[4,1,2,3,5,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[4,1,2,3,6,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[4,1,2,5,3,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[4,1,2,5,6,3]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[4,1,2,6,3,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[4,1,2,6,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,1,3,2,5,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[4,1,3,2,6,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,1,3,5,2,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[4,1,3,5,6,2]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[4,1,3,6,2,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,1,3,6,5,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,1,5,2,3,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[4,1,5,2,6,3]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[4,1,5,3,2,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,1,5,3,6,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,1,5,6,2,3]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[4,1,5,6,3,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,1,6,2,3,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[4,1,6,2,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,1,6,3,2,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,1,6,3,5,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,1,6,5,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,1,6,5,3,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,2,1,3,5,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[4,2,1,3,6,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,1,5,3,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,1,5,6,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,1,6,3,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,1,6,5,3]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[4,2,3,1,5,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[4,2,3,1,6,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,3,5,1,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[4,2,3,5,6,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[4,2,3,6,1,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,3,6,5,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,5,1,3,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,5,1,6,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,5,3,1,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,5,3,6,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,5,6,1,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,5,6,3,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,6,1,3,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,6,1,5,3]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[4,2,6,3,1,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,6,3,5,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,2,6,5,1,3]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[4,2,6,5,3,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,3,1,2,5,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[4,3,1,2,6,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,3,1,5,2,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,3,1,5,6,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,3,1,6,2,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,3,1,6,5,2]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[4,3,2,1,5,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[4,3,2,1,6,5]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,3,2,5,1,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[4,3,2,5,6,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[4,3,2,6,1,5]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,3,2,6,5,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,3,5,1,2,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,3,5,1,6,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,3,5,2,1,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[4,3,5,2,6,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[4,3,5,6,1,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,3,5,6,2,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[4,3,6,1,2,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,3,6,1,5,2]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[4,3,6,2,1,5]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,3,6,2,5,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,3,6,5,1,2]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[4,3,6,5,2,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,5,1,2,3,6]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[4,5,1,2,6,3]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[4,5,1,3,2,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,1,3,6,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,1,6,2,3]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[4,5,1,6,3,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,2,1,3,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,2,1,6,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,2,3,1,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,2,3,6,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,2,6,1,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,2,6,3,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,3,1,2,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,3,1,6,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,3,2,1,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[4,5,3,2,6,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[4,5,3,6,1,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,3,6,2,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[4,5,6,1,2,3]=>[3,3]=>[[1,2,3],[4,5,6]]=>00100
[4,5,6,1,3,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,6,2,1,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,6,2,3,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,6,3,1,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,5,6,3,2,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[4,6,1,2,3,5]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[4,6,1,2,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,6,1,3,2,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,6,1,3,5,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,6,1,5,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,6,1,5,3,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,6,2,1,3,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,6,2,1,5,3]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[4,6,2,3,1,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,6,2,3,5,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,6,2,5,1,3]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[4,6,2,5,3,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,6,3,1,2,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,6,3,1,5,2]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[4,6,3,2,1,5]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,6,3,2,5,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,6,3,5,1,2]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[4,6,3,5,2,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,6,5,1,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[4,6,5,1,3,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,6,5,2,1,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,6,5,2,3,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,6,5,3,1,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[4,6,5,3,2,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[5,1,2,3,4,6]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[5,1,2,3,6,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[5,1,2,4,3,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[5,1,2,4,6,3]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[5,1,2,6,3,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[5,1,2,6,4,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,1,3,2,4,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[5,1,3,2,6,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,1,3,4,2,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[5,1,3,4,6,2]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[5,1,3,6,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,1,3,6,4,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,1,4,2,3,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[5,1,4,2,6,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,1,4,3,2,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,1,4,3,6,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,1,4,6,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,1,4,6,3,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,1,6,2,3,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[5,1,6,2,4,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,1,6,3,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,1,6,3,4,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,1,6,4,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,1,6,4,3,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,2,1,3,4,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[5,2,1,3,6,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,2,1,4,3,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,2,1,4,6,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,2,1,6,3,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,2,1,6,4,3]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[5,2,3,1,4,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[5,2,3,1,6,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,2,3,4,1,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[5,2,3,4,6,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[5,2,3,6,1,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,2,3,6,4,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,2,4,1,3,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,2,4,1,6,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,2,4,3,1,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,2,4,3,6,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,2,4,6,1,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,2,4,6,3,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,2,6,1,3,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,2,6,1,4,3]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[5,2,6,3,1,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,2,6,3,4,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,2,6,4,1,3]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[5,2,6,4,3,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,3,1,2,4,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[5,3,1,2,6,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,3,1,4,2,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,3,1,4,6,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,3,1,6,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,3,1,6,4,2]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[5,3,2,1,4,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,3,2,1,6,4]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,3,2,4,1,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,3,2,4,6,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,3,2,6,1,4]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,3,2,6,4,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,3,4,1,2,6]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,3,4,1,6,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,3,4,2,1,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,3,4,2,6,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,3,4,6,1,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,3,4,6,2,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,3,6,1,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,3,6,1,4,2]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[5,3,6,2,1,4]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,3,6,2,4,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,3,6,4,1,2]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[5,3,6,4,2,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,4,1,2,3,6]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[5,4,1,2,6,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,4,1,3,2,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,4,1,3,6,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,4,1,6,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,4,1,6,3,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,4,2,1,3,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,4,2,1,6,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,4,2,3,1,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,4,2,3,6,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,4,2,6,1,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,4,2,6,3,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,4,3,1,2,6]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[5,4,3,1,6,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,4,3,2,1,6]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[5,4,3,2,6,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[5,4,3,6,1,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,4,3,6,2,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[5,4,6,1,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,4,6,1,3,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,4,6,2,1,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,4,6,2,3,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,4,6,3,1,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,4,6,3,2,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[5,6,1,2,3,4]=>[4,2]=>[[1,2,5,6],[3,4]]=>01000
[5,6,1,2,4,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,6,1,3,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,6,1,3,4,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,6,1,4,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,6,1,4,3,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,6,2,1,3,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,6,2,1,4,3]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[5,6,2,3,1,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,6,2,3,4,1]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,6,2,4,1,3]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[5,6,2,4,3,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,6,3,1,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,6,3,1,4,2]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[5,6,3,2,1,4]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,6,3,2,4,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,6,3,4,1,2]=>[2,2,2]=>[[1,2],[3,4],[5,6]]=>01010
[5,6,3,4,2,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,6,4,1,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[5,6,4,1,3,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,6,4,2,1,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,6,4,2,3,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,6,4,3,1,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[5,6,4,3,2,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,1,2,3,4,5]=>[5,1]=>[[1,3,4,5,6],[2]]=>10000
[6,1,2,3,5,4]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,1,2,4,3,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,1,2,4,5,3]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,1,2,5,3,4]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,1,2,5,4,3]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,1,3,2,4,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,1,3,2,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,1,3,4,2,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,1,3,4,5,2]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,1,3,5,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,1,3,5,4,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,1,4,2,3,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,1,4,2,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,1,4,3,2,5]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,1,4,3,5,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,1,4,5,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,1,4,5,3,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,1,5,2,3,4]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,1,5,2,4,3]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,1,5,3,2,4]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,1,5,3,4,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,1,5,4,2,3]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,1,5,4,3,2]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,2,1,3,4,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,2,1,3,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,2,1,4,3,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,2,1,4,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,2,1,5,3,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,2,1,5,4,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,2,3,1,4,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,2,3,1,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,2,3,4,1,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,2,3,4,5,1]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,2,3,5,1,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,2,3,5,4,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,2,4,1,3,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,2,4,1,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,2,4,3,1,5]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,2,4,3,5,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,2,4,5,1,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,2,4,5,3,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,2,5,1,3,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,2,5,1,4,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,2,5,3,1,4]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,2,5,3,4,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,2,5,4,1,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,2,5,4,3,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,3,1,2,4,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,3,1,2,5,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,3,1,4,2,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,3,1,4,5,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,3,1,5,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,3,1,5,4,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,3,2,1,4,5]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,3,2,1,5,4]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,3,2,4,1,5]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,3,2,4,5,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,3,2,5,1,4]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,3,2,5,4,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,3,4,1,2,5]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,3,4,1,5,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,3,4,2,1,5]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,3,4,2,5,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,3,4,5,1,2]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,3,4,5,2,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,3,5,1,2,4]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,3,5,1,4,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,3,5,2,1,4]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,3,5,2,4,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,3,5,4,1,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,3,5,4,2,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,4,1,2,3,5]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,4,1,2,5,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,4,1,3,2,5]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,4,1,3,5,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,4,1,5,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,4,1,5,3,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,4,2,1,3,5]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,4,2,1,5,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,4,2,3,1,5]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,4,2,3,5,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,4,2,5,1,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,4,2,5,3,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,4,3,1,2,5]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,4,3,1,5,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,4,3,2,1,5]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,4,3,2,5,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,4,3,5,1,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,4,3,5,2,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,4,5,1,2,3]=>[3,2,1]=>[[1,3,6],[2,5],[4]]=>10100
[6,4,5,1,3,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,4,5,2,1,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,4,5,2,3,1]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,4,5,3,1,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,4,5,3,2,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,5,1,2,3,4]=>[4,1,1]=>[[1,4,5,6],[2],[3]]=>11000
[6,5,1,2,4,3]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,5,1,3,2,4]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,5,1,3,4,2]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,5,1,4,2,3]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,5,1,4,3,2]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,5,2,1,3,4]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,5,2,1,4,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,5,2,3,1,4]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,5,2,3,4,1]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,5,2,4,1,3]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,5,2,4,3,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,5,3,1,2,4]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,5,3,1,4,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,5,3,2,1,4]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,5,3,2,4,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,5,3,4,1,2]=>[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>11010
[6,5,3,4,2,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,5,4,1,2,3]=>[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>11100
[6,5,4,1,3,2]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,5,4,2,1,3]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,5,4,2,3,1]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,5,4,3,1,2]=>[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>11110
[6,5,4,3,2,1]=>[1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6]]=>11111
[1,2,3,4,5,6,7]=>[7]=>[[1,2,3,4,5,6,7]]=>000000
[1,2,3,4,5,7,6]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,3,4,6,5,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,3,4,6,7,5]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,3,4,7,5,6]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,3,4,7,6,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,3,5,4,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,3,5,4,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,3,5,6,4,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,3,5,6,7,4]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,3,5,7,4,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,3,5,7,6,4]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,3,6,4,5,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,3,6,4,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,3,6,5,4,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,3,6,5,7,4]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,3,6,7,4,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,3,6,7,5,4]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,3,7,4,5,6]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,3,7,4,6,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,3,7,5,4,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,3,7,5,6,4]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,3,7,6,4,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,3,7,6,5,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,4,3,5,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,4,3,5,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,4,3,6,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,4,3,6,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,4,3,7,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,4,3,7,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,4,5,3,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,4,5,3,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,4,5,6,3,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,4,5,6,7,3]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,4,5,7,3,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,4,5,7,6,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,4,6,3,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,4,6,3,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,4,6,5,3,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,4,6,5,7,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,4,6,7,3,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,4,6,7,5,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,4,7,3,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,4,7,3,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,4,7,5,3,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,4,7,5,6,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,4,7,6,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,4,7,6,5,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,5,3,4,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,5,3,4,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,5,3,6,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,5,3,6,7,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,5,3,7,4,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,5,3,7,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,5,4,3,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,5,4,3,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,5,4,6,3,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,5,4,6,7,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,5,4,7,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,5,4,7,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,5,6,3,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,5,6,3,7,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,5,6,4,3,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,5,6,4,7,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,5,6,7,3,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,5,6,7,4,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,5,7,3,4,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,5,7,3,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,5,7,4,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,5,7,4,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,5,7,6,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,5,7,6,4,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,6,3,4,5,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,6,3,4,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,6,3,5,4,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,6,3,5,7,4]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,6,3,7,4,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,6,3,7,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,6,4,3,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,6,4,3,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,6,4,5,3,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,6,4,5,7,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,6,4,7,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,6,4,7,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,6,5,3,4,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,6,5,3,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,6,5,4,3,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,6,5,4,7,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,6,5,7,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,6,5,7,4,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,6,7,3,4,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,2,6,7,3,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,6,7,4,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,6,7,4,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,6,7,5,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,6,7,5,4,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,7,3,4,5,6]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,2,7,3,4,6,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,7,3,5,4,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,7,3,5,6,4]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,7,3,6,4,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,7,3,6,5,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,7,4,3,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,7,4,3,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,7,4,5,3,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,7,4,5,6,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,7,4,6,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,7,4,6,5,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,7,5,3,4,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,7,5,3,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,7,5,4,3,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,7,5,4,6,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,7,5,6,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,2,7,5,6,4,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,7,6,3,4,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,2,7,6,3,5,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,7,6,4,3,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,7,6,4,5,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,7,6,5,3,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,2,7,6,5,4,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,3,2,4,5,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,3,2,4,5,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,2,4,6,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,2,4,6,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,2,4,7,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,2,4,7,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,2,5,4,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,2,5,4,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,3,2,5,6,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,2,5,6,7,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,2,5,7,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,3,2,5,7,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,2,6,4,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,2,6,4,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,3,2,6,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,2,6,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,2,6,7,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,3,2,6,7,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,2,7,4,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,2,7,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,2,7,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,2,7,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,2,7,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,2,7,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,3,4,2,5,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,3,4,2,5,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,4,2,6,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,4,2,6,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,4,2,7,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,4,2,7,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,4,5,2,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,3,4,5,2,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,4,5,6,2,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,3,4,5,6,7,2]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,3,4,5,7,2,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,4,5,7,6,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,4,6,2,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,4,6,2,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,4,6,5,2,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,4,6,5,7,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,4,6,7,2,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,4,6,7,5,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,4,7,2,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,4,7,2,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,4,7,5,2,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,4,7,5,6,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,4,7,6,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,4,7,6,5,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,3,5,2,4,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,5,2,4,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,3,5,2,6,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,5,2,6,7,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,5,2,7,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,3,5,2,7,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,5,4,2,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,5,4,2,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,5,4,6,2,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,5,4,6,7,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,5,4,7,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,5,4,7,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,5,6,2,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,5,6,2,7,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,5,6,4,2,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,5,6,4,7,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,5,6,7,2,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,5,6,7,4,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,5,7,2,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,3,5,7,2,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,5,7,4,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,5,7,4,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,5,7,6,2,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,5,7,6,4,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,3,6,2,4,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,6,2,4,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,3,6,2,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,6,2,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,6,2,7,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,3,6,2,7,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,6,4,2,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,6,4,2,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,6,4,5,2,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,6,4,5,7,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,6,4,7,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,6,4,7,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,6,5,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,6,5,2,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,6,5,4,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,3,6,5,4,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,3,6,5,7,2,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,6,5,7,4,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,3,6,7,2,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,3,6,7,2,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,6,7,4,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,6,7,4,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,6,7,5,2,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,6,7,5,4,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,3,7,2,4,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,3,7,2,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,7,2,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,7,2,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,7,2,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,7,2,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,3,7,4,2,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,7,4,2,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,7,4,5,2,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,7,4,5,6,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,3,7,4,6,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,7,4,6,5,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,3,7,5,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,7,5,2,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,7,5,4,2,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,3,7,5,4,6,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,3,7,5,6,2,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,7,5,6,4,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,3,7,6,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,3,7,6,2,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,3,7,6,4,2,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,3,7,6,4,5,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,3,7,6,5,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,3,7,6,5,4,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,4,2,3,5,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,4,2,3,5,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,2,3,6,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,2,3,6,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,2,3,7,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,2,3,7,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,2,5,3,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,2,5,3,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,4,2,5,6,3,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,2,5,6,7,3]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,2,5,7,3,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,4,2,5,7,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,2,6,3,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,2,6,3,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,4,2,6,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,2,6,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,2,6,7,3,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,4,2,6,7,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,2,7,3,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,2,7,3,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,2,7,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,2,7,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,2,7,6,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,2,7,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,4,3,2,5,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,4,3,2,5,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,2,6,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,2,6,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,2,7,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,2,7,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,4,3,5,2,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,4,3,5,2,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,5,6,2,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,4,3,5,6,7,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,4,3,5,7,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,5,7,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,6,2,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,6,2,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,6,5,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,6,5,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,6,7,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,6,7,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,7,2,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,7,2,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,4,3,7,5,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,7,5,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,3,7,6,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,4,3,7,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,4,5,2,3,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,5,2,3,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,4,5,2,6,3,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,5,2,6,7,3]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,5,2,7,3,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,4,5,2,7,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,5,3,2,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,4,5,3,2,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,5,3,6,2,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,4,5,3,6,7,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,4,5,3,7,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,5,3,7,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,5,6,2,3,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,5,6,2,7,3]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,5,6,3,2,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,4,5,6,3,7,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,4,5,6,7,2,3]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,5,6,7,3,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,4,5,7,2,3,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,4,5,7,2,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,5,7,3,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,5,7,3,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,5,7,6,2,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,5,7,6,3,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,4,6,2,3,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,6,2,3,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,4,6,2,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,2,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,2,7,3,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,4,6,2,7,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,3,2,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,3,2,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,3,5,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,3,5,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,3,7,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,3,7,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,5,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,5,2,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,5,3,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,4,6,5,3,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,4,6,5,7,2,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,5,7,3,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,4,6,7,2,3,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,4,6,7,2,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,7,3,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,7,3,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,7,5,2,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,6,7,5,3,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,4,7,2,3,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,4,7,2,3,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,7,2,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,7,2,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,7,2,6,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,7,2,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,4,7,3,2,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,7,3,2,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,4,7,3,5,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,7,3,5,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,7,3,6,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,4,7,3,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,4,7,5,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,7,5,2,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,7,5,3,2,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,4,7,5,3,6,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,4,7,5,6,2,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,7,5,6,3,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,4,7,6,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,4,7,6,2,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,4,7,6,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,4,7,6,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,4,7,6,5,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,4,7,6,5,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,5,2,3,4,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,5,2,3,4,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,5,2,3,6,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,5,2,3,6,7,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,5,2,3,7,4,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,5,2,3,7,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,2,4,3,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,5,2,4,3,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,2,4,6,3,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,5,2,4,6,7,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,5,2,4,7,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,2,4,7,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,2,6,3,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,5,2,6,3,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,5,2,6,4,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,2,6,4,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,2,6,7,3,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,5,2,6,7,4,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,2,7,3,4,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,5,2,7,3,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,2,7,4,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,2,7,4,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,2,7,6,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,2,7,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,3,2,4,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,5,3,2,4,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,2,6,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,2,6,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,2,7,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,2,7,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,5,3,4,2,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,5,3,4,2,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,4,6,2,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,5,3,4,6,7,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,5,3,4,7,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,4,7,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,6,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,6,2,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,6,4,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,6,4,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,6,7,2,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,6,7,4,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,7,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,7,2,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,5,3,7,4,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,7,4,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,3,7,6,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,5,3,7,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,4,2,3,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,5,4,2,3,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,4,2,6,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,4,2,6,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,4,2,7,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,4,2,7,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,5,4,3,2,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,5,4,3,2,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,4,3,6,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,5,4,3,6,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,5,4,3,7,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,4,3,7,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,4,6,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,4,6,2,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,4,6,3,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,5,4,6,3,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,5,4,6,7,2,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,4,6,7,3,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,5,4,7,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,4,7,2,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,5,4,7,3,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,4,7,3,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,4,7,6,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,5,4,7,6,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,6,2,3,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,5,6,2,3,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,5,6,2,4,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,2,4,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,2,7,3,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,5,6,2,7,4,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,3,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,3,2,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,3,4,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,3,4,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,3,7,2,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,3,7,4,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,4,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,4,2,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,4,3,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,5,6,4,3,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,5,6,4,7,2,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,4,7,3,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,5,6,7,2,3,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[1,5,6,7,2,4,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,7,3,2,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,7,3,4,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,7,4,2,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,6,7,4,3,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,5,7,2,3,4,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,5,7,2,3,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,7,2,4,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,7,2,4,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,7,2,6,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,7,2,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,7,3,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,7,3,2,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,5,7,3,4,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,7,3,4,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,7,3,6,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,5,7,3,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,7,4,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,7,4,2,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,5,7,4,3,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,7,4,3,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,7,4,6,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,5,7,4,6,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,7,6,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,5,7,6,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,7,6,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,7,6,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,7,6,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,5,7,6,4,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,6,2,3,4,5,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,6,2,3,4,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,6,2,3,5,4,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,6,2,3,5,7,4]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,6,2,3,7,4,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,6,2,3,7,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,2,4,3,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,6,2,4,3,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,2,4,5,3,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,6,2,4,5,7,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,6,2,4,7,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,2,4,7,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,2,5,3,4,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,6,2,5,3,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,2,5,4,3,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,2,5,4,7,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,2,5,7,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,2,5,7,4,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,2,7,3,4,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,6,2,7,3,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,2,7,4,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,2,7,4,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,2,7,5,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,2,7,5,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,3,2,4,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,6,3,2,4,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,3,2,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,3,2,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,3,2,7,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,3,2,7,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,6,3,4,2,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,6,3,4,2,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,3,4,5,2,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,6,3,4,5,7,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,6,3,4,7,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,3,4,7,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,3,5,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,3,5,2,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,3,5,4,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,3,5,4,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,3,5,7,2,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,3,5,7,4,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,3,7,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,3,7,2,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,6,3,7,4,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,3,7,4,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,3,7,5,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,6,3,7,5,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,4,2,3,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,6,4,2,3,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,4,2,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,4,2,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,4,2,7,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,4,2,7,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,6,4,3,2,5,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,4,3,2,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,4,3,5,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,4,3,5,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,4,3,7,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,4,3,7,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,4,5,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,4,5,2,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,4,5,3,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,4,5,3,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,4,5,7,2,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,4,5,7,3,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,4,7,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,4,7,2,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,6,4,7,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,4,7,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,4,7,5,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,6,4,7,5,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,5,2,3,4,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,6,5,2,3,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,5,2,4,3,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,5,2,4,7,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,5,2,7,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,5,2,7,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,5,3,2,4,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,5,3,2,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,5,3,4,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,5,3,4,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,5,3,7,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,5,3,7,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,5,4,2,3,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,6,5,4,2,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,5,4,3,2,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,6,5,4,3,7,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,6,5,4,7,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,5,4,7,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,6,5,7,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,5,7,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,5,7,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,5,7,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,5,7,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,5,7,4,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,6,7,2,3,4,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[1,6,7,2,3,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,7,2,4,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,7,2,4,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,7,2,5,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,7,2,5,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,7,3,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,7,3,2,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,6,7,3,4,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,7,3,4,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,7,3,5,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,6,7,3,5,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,7,4,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,7,4,2,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,6,7,4,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,7,4,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,7,4,5,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[1,6,7,4,5,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,7,5,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,6,7,5,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,7,5,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,7,5,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,7,5,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,6,7,5,4,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,2,3,4,5,6]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[1,7,2,3,4,6,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,2,3,5,4,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,2,3,5,6,4]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,2,3,6,4,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,2,3,6,5,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,2,4,3,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,2,4,3,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,2,4,5,3,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,2,4,5,6,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,2,4,6,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,2,4,6,5,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,2,5,3,4,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,2,5,3,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,2,5,4,3,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,2,5,4,6,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,2,5,6,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,2,5,6,4,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,2,6,3,4,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,2,6,3,5,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,2,6,4,3,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,2,6,4,5,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,2,6,5,3,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,2,6,5,4,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,3,2,4,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,3,2,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,3,2,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,3,2,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,3,2,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,3,2,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,3,4,2,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,3,4,2,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,3,4,5,2,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,3,4,5,6,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,3,4,6,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,3,4,6,5,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,3,5,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,3,5,2,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,3,5,4,2,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,3,5,4,6,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,3,5,6,2,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,3,5,6,4,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,3,6,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,3,6,2,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,3,6,4,2,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,3,6,4,5,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,3,6,5,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,3,6,5,4,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,4,2,3,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,4,2,3,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,4,2,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,4,2,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,4,2,6,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,4,2,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,4,3,2,5,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,4,3,2,6,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,4,3,5,2,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,4,3,5,6,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,4,3,6,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,4,3,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,4,5,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,4,5,2,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,4,5,3,2,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,4,5,3,6,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,4,5,6,2,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,4,5,6,3,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,4,6,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,4,6,2,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,4,6,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,4,6,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,4,6,5,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,4,6,5,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,5,2,3,4,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,5,2,3,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,5,2,4,3,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,5,2,4,6,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,5,2,6,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,5,2,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,5,3,2,4,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,5,3,2,6,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,5,3,4,2,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,5,3,4,6,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,5,3,6,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,5,3,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,5,4,2,3,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,5,4,2,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,5,4,3,2,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,5,4,3,6,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,5,4,6,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,5,4,6,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,5,6,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[1,7,5,6,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,5,6,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,5,6,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,5,6,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,5,6,4,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,6,2,3,4,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[1,7,6,2,3,5,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,6,2,4,3,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,6,2,4,5,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,6,2,5,3,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,6,2,5,4,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,6,3,2,4,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,6,3,2,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,6,3,4,2,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,6,3,4,5,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,6,3,5,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,6,3,5,4,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,6,4,2,3,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,6,4,2,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,6,4,3,2,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,6,4,3,5,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,6,4,5,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[1,7,6,4,5,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,6,5,2,3,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[1,7,6,5,2,4,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,6,5,3,2,4]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,6,5,3,4,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,6,5,4,2,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[2,1,3,4,5,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[2,1,3,4,5,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,3,4,6,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,3,4,6,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,3,4,7,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,3,4,7,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,3,5,4,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,3,5,4,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,3,5,6,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,3,5,6,7,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,3,5,7,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,3,5,7,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,3,6,4,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,3,6,4,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,3,6,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,3,6,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,3,6,7,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,3,6,7,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,3,7,4,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,3,7,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,3,7,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,3,7,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,3,7,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,3,7,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,4,3,5,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,4,3,5,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,4,3,6,5,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,4,3,6,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,4,3,7,5,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,4,3,7,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,4,5,3,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,4,5,3,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,4,5,6,3,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,4,5,6,7,3]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,4,5,7,3,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,4,5,7,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,4,6,3,5,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,4,6,3,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,4,6,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,4,6,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,4,6,7,3,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,4,6,7,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,4,7,3,5,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,4,7,3,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,4,7,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,4,7,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,4,7,6,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,4,7,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,5,3,4,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,5,3,4,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,5,3,6,4,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,5,3,6,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,5,3,7,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,5,3,7,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,5,4,3,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,5,4,3,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,5,4,6,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,5,4,6,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,5,4,7,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,5,4,7,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,5,6,3,4,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,5,6,3,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,5,6,4,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,5,6,4,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,5,6,7,3,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,5,6,7,4,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,5,7,3,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,5,7,3,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,5,7,4,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,5,7,4,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,5,7,6,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,5,7,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,6,3,4,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,6,3,4,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,6,3,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,6,3,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,6,3,7,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,6,3,7,5,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,6,4,3,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,6,4,3,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,6,4,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,6,4,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,6,4,7,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,6,4,7,5,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,6,5,3,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,6,5,3,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,6,5,4,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,6,5,4,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,6,5,7,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,6,5,7,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,6,7,3,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,1,6,7,3,5,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,6,7,4,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,6,7,4,5,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,6,7,5,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,6,7,5,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,7,3,4,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,1,7,3,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,7,3,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,7,3,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,7,3,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,7,3,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,7,4,3,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,7,4,3,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,7,4,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,7,4,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,7,4,6,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,7,4,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,7,5,3,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,7,5,3,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,7,5,4,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,7,5,4,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,7,5,6,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,1,7,5,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,7,6,3,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,1,7,6,3,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,7,6,4,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,7,6,4,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,7,6,5,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,1,7,6,5,4,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[2,3,1,4,5,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[2,3,1,4,5,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,1,4,6,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,1,4,6,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,1,4,7,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,1,4,7,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,1,5,4,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,1,5,4,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,3,1,5,6,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,1,5,6,7,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,1,5,7,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,3,1,5,7,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,1,6,4,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,1,6,4,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,3,1,6,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,1,6,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,1,6,7,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,3,1,6,7,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,1,7,4,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,1,7,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,1,7,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,1,7,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,1,7,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,1,7,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,3,4,1,5,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[2,3,4,1,5,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,4,1,6,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,4,1,6,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,4,1,7,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,4,1,7,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,4,5,1,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[2,3,4,5,1,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,4,5,6,1,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[2,3,4,5,6,7,1]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[2,3,4,5,7,1,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,4,5,7,6,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,4,6,1,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,4,6,1,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,4,6,5,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,4,6,5,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,4,6,7,1,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,4,6,7,5,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,4,7,1,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,4,7,1,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,4,7,5,1,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,4,7,5,6,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,4,7,6,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,4,7,6,5,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,3,5,1,4,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,5,1,4,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,3,5,1,6,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,5,1,6,7,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,5,1,7,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,3,5,1,7,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,5,4,1,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,5,4,1,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,5,4,6,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,5,4,6,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,5,4,7,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,5,4,7,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,5,6,1,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,5,6,1,7,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,5,6,4,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,5,6,4,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,5,6,7,1,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,5,6,7,4,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,5,7,1,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,3,5,7,1,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,5,7,4,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,5,7,4,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,5,7,6,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,5,7,6,4,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,3,6,1,4,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,6,1,4,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,3,6,1,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,6,1,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,6,1,7,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,3,6,1,7,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,6,4,1,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,6,4,1,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,6,4,5,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,6,4,5,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,6,4,7,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,6,4,7,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,6,5,1,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,6,5,1,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,6,5,4,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,3,6,5,4,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,3,6,5,7,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,6,5,7,4,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,3,6,7,1,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,3,6,7,1,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,6,7,4,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,6,7,4,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,6,7,5,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,6,7,5,4,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,3,7,1,4,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,3,7,1,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,7,1,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,7,1,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,7,1,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,7,1,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,3,7,4,1,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,7,4,1,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,7,4,5,1,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,7,4,5,6,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,3,7,4,6,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,7,4,6,5,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,3,7,5,1,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,7,5,1,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,7,5,4,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,3,7,5,4,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,3,7,5,6,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,7,5,6,4,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,3,7,6,1,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,3,7,6,1,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,3,7,6,4,1,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,3,7,6,4,5,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,3,7,6,5,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,3,7,6,5,4,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,4,1,3,5,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,4,1,3,5,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,1,3,6,5,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,1,3,6,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,1,3,7,5,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,1,3,7,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,4,1,5,3,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,4,1,5,3,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,1,5,6,3,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,4,1,5,6,7,3]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,4,1,5,7,3,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,1,5,7,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,1,6,3,5,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,1,6,3,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,1,6,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,1,6,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,1,6,7,3,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,1,6,7,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,1,7,3,5,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,1,7,3,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,4,1,7,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,1,7,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,1,7,6,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,4,1,7,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,4,3,1,5,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,4,3,1,5,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,1,6,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,1,6,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,1,7,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,1,7,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,4,3,5,1,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,4,3,5,1,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,5,6,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,4,3,5,6,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,4,3,5,7,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,5,7,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,6,1,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,6,1,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,6,5,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,6,5,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,6,7,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,6,7,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,7,1,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,7,1,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,4,3,7,5,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,7,5,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,3,7,6,1,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,4,3,7,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,4,5,1,3,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,4,5,1,3,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,5,1,6,3,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,4,5,1,6,7,3]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,4,5,1,7,3,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,5,1,7,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,5,3,1,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,4,5,3,1,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,5,3,6,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,4,5,3,6,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,4,5,3,7,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,5,3,7,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,5,6,1,3,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,4,5,6,1,7,3]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,4,5,6,3,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,4,5,6,3,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,4,5,6,7,1,3]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,4,5,6,7,3,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,4,5,7,1,3,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,5,7,1,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,5,7,3,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,5,7,3,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,5,7,6,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,5,7,6,3,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,4,6,1,3,5,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,6,1,3,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,6,1,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,1,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,1,7,3,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,6,1,7,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,3,1,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,3,1,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,3,5,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,3,5,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,3,7,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,3,7,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,5,1,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,5,1,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,5,3,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,4,6,5,3,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,4,6,5,7,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,5,7,3,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,4,6,7,1,3,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,6,7,1,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,7,3,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,7,3,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,7,5,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,6,7,5,3,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,4,7,1,3,5,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,4,7,1,3,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,4,7,1,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,7,1,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,7,1,6,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,4,7,1,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,4,7,3,1,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,7,3,1,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,4,7,3,5,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,7,3,5,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,7,3,6,1,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,4,7,3,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,4,7,5,1,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,7,5,1,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,7,5,3,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,4,7,5,3,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,4,7,5,6,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,4,7,5,6,3,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,4,7,6,1,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,4,7,6,1,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,4,7,6,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,4,7,6,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,4,7,6,5,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,4,7,6,5,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,5,1,3,4,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,5,1,3,4,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,5,1,3,6,4,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,5,1,3,6,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,5,1,3,7,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,5,1,3,7,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,1,4,3,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,1,4,3,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,1,4,6,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,1,4,6,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,1,4,7,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,1,4,7,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,1,6,3,4,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,5,1,6,3,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,5,1,6,4,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,1,6,4,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,1,6,7,3,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,5,1,6,7,4,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,1,7,3,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,5,1,7,3,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,1,7,4,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,1,7,4,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,1,7,6,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,1,7,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,3,1,4,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,5,3,1,4,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,1,6,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,1,6,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,1,7,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,1,7,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,5,3,4,1,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,5,3,4,1,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,4,6,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,5,3,4,6,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,5,3,4,7,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,4,7,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,6,1,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,6,1,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,6,4,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,6,4,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,6,7,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,6,7,4,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,7,1,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,7,1,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,5,3,7,4,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,7,4,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,3,7,6,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,5,3,7,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,4,1,3,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,4,1,3,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,4,1,6,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,4,1,6,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,4,1,7,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,4,1,7,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,5,4,3,1,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,5,4,3,1,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,4,3,6,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,5,4,3,6,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,5,4,3,7,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,4,3,7,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,4,6,1,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,4,6,1,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,4,6,3,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,5,4,6,3,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,5,4,6,7,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,4,6,7,3,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,5,4,7,1,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,4,7,1,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,5,4,7,3,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,4,7,3,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,4,7,6,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,5,4,7,6,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,6,1,3,4,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,5,6,1,3,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,5,6,1,4,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,1,4,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,1,7,3,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,5,6,1,7,4,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,3,1,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,3,1,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,3,4,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,3,4,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,3,7,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,3,7,4,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,4,1,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,4,1,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,4,3,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,5,6,4,3,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,5,6,4,7,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,4,7,3,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,5,6,7,1,3,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,5,6,7,1,4,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,7,3,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,7,3,4,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,7,4,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,6,7,4,3,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,5,7,1,3,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,5,7,1,3,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,7,1,4,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,7,1,4,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,7,1,6,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,7,1,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,7,3,1,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,7,3,1,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,5,7,3,4,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,7,3,4,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,5,7,3,6,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,5,7,3,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,7,4,1,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,7,4,1,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,5,7,4,3,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,7,4,3,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,7,4,6,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,5,7,4,6,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,7,6,1,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,5,7,6,1,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,7,6,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,7,6,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,7,6,4,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,5,7,6,4,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,6,1,3,4,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,6,1,3,4,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,6,1,3,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,1,3,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,1,3,7,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,6,1,3,7,5,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,1,4,3,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,1,4,3,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,1,4,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,1,4,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,1,4,7,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,1,4,7,5,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,1,5,3,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,1,5,3,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,1,5,4,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,1,5,4,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,1,5,7,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,1,5,7,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,1,7,3,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,6,1,7,3,5,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,1,7,4,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,1,7,4,5,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,1,7,5,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,1,7,5,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,3,1,4,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,6,3,1,4,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,3,1,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,3,1,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,3,1,7,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,3,1,7,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,6,3,4,1,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,6,3,4,1,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,3,4,5,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,6,3,4,5,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,6,3,4,7,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,3,4,7,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,3,5,1,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,3,5,1,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,3,5,4,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,6,3,5,4,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,6,3,5,7,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,3,5,7,4,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,6,3,7,1,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,3,7,1,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,6,3,7,4,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,3,7,4,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,3,7,5,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,6,3,7,5,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,4,1,3,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,4,1,3,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,4,1,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,4,1,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,4,1,7,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,4,1,7,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,6,4,3,1,5,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,6,4,3,1,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,4,3,5,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,6,4,3,5,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,6,4,3,7,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,4,3,7,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,4,5,1,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,4,5,1,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,4,5,3,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,6,4,5,3,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,6,4,5,7,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,4,5,7,3,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,6,4,7,1,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,4,7,1,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,6,4,7,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,4,7,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,4,7,5,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,6,4,7,5,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,1,3,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,5,1,3,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,5,1,4,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,1,4,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,1,7,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,5,1,7,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,3,1,4,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,6,5,3,1,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,3,4,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,6,5,3,4,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,6,5,3,7,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,3,7,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,4,1,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,4,1,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,4,3,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,6,5,4,3,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,6,5,4,7,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,4,7,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,6,5,7,1,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,5,7,1,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,7,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,7,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,7,4,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,5,7,4,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,6,7,1,3,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[2,6,7,1,3,5,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,7,1,4,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,7,1,4,5,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,7,1,5,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,7,1,5,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,7,3,1,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,7,3,1,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,6,7,3,4,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,7,3,4,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,6,7,3,5,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,6,7,3,5,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,7,4,1,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,7,4,1,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,6,7,4,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,7,4,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,7,4,5,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[2,6,7,4,5,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,7,5,1,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,6,7,5,1,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,7,5,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,7,5,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,7,5,4,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,6,7,5,4,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,7,1,3,4,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[2,7,1,3,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,1,3,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,1,3,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,1,3,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,1,3,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,1,4,3,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,1,4,3,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,7,1,4,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,1,4,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,1,4,6,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,7,1,4,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,1,5,3,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,1,5,3,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,7,1,5,4,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,1,5,4,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,1,5,6,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,7,1,5,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,1,6,3,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,1,6,3,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,1,6,4,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,1,6,4,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,1,6,5,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,1,6,5,4,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[2,7,3,1,4,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,7,3,1,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,3,1,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,3,1,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,3,1,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,3,1,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,3,4,1,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,7,3,4,1,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,3,4,5,1,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,7,3,4,5,6,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[2,7,3,4,6,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,3,4,6,5,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,3,5,1,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,3,5,1,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,3,5,4,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,3,5,4,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,3,5,6,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,3,5,6,4,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,3,6,1,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,3,6,1,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,3,6,4,1,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,3,6,4,5,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,3,6,5,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,3,6,5,4,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,7,4,1,3,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,4,1,3,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,7,4,1,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,4,1,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,4,1,6,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,7,4,1,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,4,3,1,5,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,4,3,1,6,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,4,3,5,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,4,3,5,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,4,3,6,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,4,3,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,4,5,1,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,4,5,1,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,4,5,3,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,4,5,3,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,4,5,6,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,4,5,6,3,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,4,6,1,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,7,4,6,1,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,4,6,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,4,6,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,4,6,5,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,4,6,5,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,7,5,1,3,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,5,1,3,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,7,5,1,4,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,5,1,4,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,5,1,6,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,7,5,1,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,5,3,1,4,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,5,3,1,6,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,5,3,4,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,5,3,4,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,5,3,6,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,5,3,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,5,4,1,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,5,4,1,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,5,4,3,1,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,7,5,4,3,6,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,7,5,4,6,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,5,4,6,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,7,5,6,1,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[2,7,5,6,1,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,5,6,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,5,6,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,5,6,4,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,5,6,4,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,7,6,1,3,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[2,7,6,1,3,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,6,1,4,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,6,1,4,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,6,1,5,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,6,1,5,4,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[2,7,6,3,1,4,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,6,3,1,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,6,3,4,1,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,6,3,4,5,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[2,7,6,3,5,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,6,3,5,4,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,7,6,4,1,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,6,4,1,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,6,4,3,1,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,7,6,4,3,5,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,7,6,4,5,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,6,4,5,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,7,6,5,1,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[2,7,6,5,1,4,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[2,7,6,5,3,1,4]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,7,6,5,3,4,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[2,7,6,5,4,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[2,7,6,5,4,3,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[3,1,2,4,5,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[3,1,2,4,5,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,2,4,6,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,2,4,6,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,2,4,7,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,2,4,7,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,2,5,4,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,2,5,4,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,2,5,6,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,2,5,6,7,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,2,5,7,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,2,5,7,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,2,6,4,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,2,6,4,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,2,6,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,2,6,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,2,6,7,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,2,6,7,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,2,7,4,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,2,7,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,2,7,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,2,7,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,2,7,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,2,7,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,4,2,5,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,4,2,5,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,4,2,6,5,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,4,2,6,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,4,2,7,5,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,4,2,7,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,4,5,2,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,4,5,2,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,4,5,6,2,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,4,5,6,7,2]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,4,5,7,2,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,4,5,7,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,4,6,2,5,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,4,6,2,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,4,6,5,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,4,6,5,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,4,6,7,2,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,4,6,7,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,4,7,2,5,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,4,7,2,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,4,7,5,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,4,7,5,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,4,7,6,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,4,7,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,5,2,4,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,5,2,4,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,5,2,6,4,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,5,2,6,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,5,2,7,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,5,2,7,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,5,4,2,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,5,4,2,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,5,4,6,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,5,4,6,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,5,4,7,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,5,4,7,6,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,5,6,2,4,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,5,6,2,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,5,6,4,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,5,6,4,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,5,6,7,2,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,5,6,7,4,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,5,7,2,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,5,7,2,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,5,7,4,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,5,7,4,6,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,5,7,6,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,5,7,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,6,2,4,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,6,2,4,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,6,2,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,6,2,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,6,2,7,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,6,2,7,5,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,6,4,2,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,6,4,2,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,6,4,5,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,6,4,5,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,6,4,7,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,6,4,7,5,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,6,5,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,6,5,2,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,6,5,4,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,6,5,4,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,6,5,7,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,6,5,7,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,6,7,2,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,1,6,7,2,5,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,6,7,4,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,6,7,4,5,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,6,7,5,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,6,7,5,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,7,2,4,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,1,7,2,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,7,2,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,7,2,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,7,2,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,7,2,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,7,4,2,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,7,4,2,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,7,4,5,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,7,4,5,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,7,4,6,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,7,4,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,7,5,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,7,5,2,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,7,5,4,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,7,5,4,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,7,5,6,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,1,7,5,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,7,6,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,1,7,6,2,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,7,6,4,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,7,6,4,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,7,6,5,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,1,7,6,5,4,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[3,2,1,4,5,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,2,1,4,5,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,1,4,6,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,1,4,6,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,1,4,7,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,1,4,7,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,1,5,4,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,1,5,4,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,1,5,6,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,1,5,6,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,1,5,7,4,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,1,5,7,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,1,6,4,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,1,6,4,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,1,6,5,4,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,1,6,5,7,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,1,6,7,4,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,1,6,7,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,1,7,4,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,1,7,4,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,1,7,5,4,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,1,7,5,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,1,7,6,4,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,1,7,6,5,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[3,2,4,1,5,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,2,4,1,5,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,1,6,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,1,6,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,1,7,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,1,7,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,4,5,1,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,2,4,5,1,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,5,6,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,2,4,5,6,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,2,4,5,7,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,5,7,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,6,1,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,6,1,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,6,5,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,6,5,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,6,7,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,6,7,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,7,1,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,7,1,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,4,7,5,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,7,5,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,4,7,6,1,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,4,7,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,2,5,1,4,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,5,1,4,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,5,1,6,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,5,1,6,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,5,1,7,4,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,5,1,7,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,5,4,1,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,5,4,1,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,5,4,6,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,5,4,6,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,5,4,7,1,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,5,4,7,6,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,5,6,1,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,5,6,1,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,5,6,4,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,5,6,4,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,5,6,7,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,5,6,7,4,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,5,7,1,4,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,5,7,1,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,5,7,4,1,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,5,7,4,6,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,5,7,6,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,5,7,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,2,6,1,4,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,6,1,4,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,6,1,5,4,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,6,1,5,7,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,6,1,7,4,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,6,1,7,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,6,4,1,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,6,4,1,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,6,4,5,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,6,4,5,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,6,4,7,1,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,6,4,7,5,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,6,5,1,4,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,6,5,1,7,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,6,5,4,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,2,6,5,4,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,2,6,5,7,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,6,5,7,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,2,6,7,1,4,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,6,7,1,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,6,7,4,1,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,6,7,4,5,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,2,6,7,5,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,6,7,5,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,2,7,1,4,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,7,1,4,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,7,1,5,4,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,7,1,5,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,7,1,6,4,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,7,1,6,5,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[3,2,7,4,1,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,7,4,1,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,7,4,5,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,7,4,5,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,2,7,4,6,1,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,7,4,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,2,7,5,1,4,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,7,5,1,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,7,5,4,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,2,7,5,4,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,2,7,5,6,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,7,5,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,2,7,6,1,4,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,2,7,6,1,5,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[3,2,7,6,4,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,2,7,6,4,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,2,7,6,5,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[3,2,7,6,5,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[3,4,1,2,5,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,4,1,2,5,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,1,2,6,5,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,1,2,6,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,1,2,7,5,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,1,2,7,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,4,1,5,2,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,4,1,5,2,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,1,5,6,2,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,4,1,5,6,7,2]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,4,1,5,7,2,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,1,5,7,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,1,6,2,5,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,1,6,2,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,1,6,5,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,1,6,5,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,1,6,7,2,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,1,6,7,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,1,7,2,5,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,1,7,2,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,4,1,7,5,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,1,7,5,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,1,7,6,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,4,1,7,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,4,2,1,5,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,4,2,1,5,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,1,6,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,1,6,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,1,7,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,1,7,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,4,2,5,1,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,4,2,5,1,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,5,6,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,4,2,5,6,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,4,2,5,7,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,5,7,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,6,1,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,6,1,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,6,5,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,6,5,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,6,7,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,6,7,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,7,1,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,7,1,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,4,2,7,5,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,7,5,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,2,7,6,1,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,4,2,7,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,4,5,1,2,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,4,5,1,2,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,5,1,6,2,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,4,5,1,6,7,2]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,4,5,1,7,2,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,5,1,7,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,5,2,1,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,4,5,2,1,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,5,2,6,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,4,5,2,6,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,4,5,2,7,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,5,2,7,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,5,6,1,2,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,4,5,6,1,7,2]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,4,5,6,2,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,4,5,6,2,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,4,5,6,7,1,2]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,4,5,6,7,2,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[3,4,5,7,1,2,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,5,7,1,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,5,7,2,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,5,7,2,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,5,7,6,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,5,7,6,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,4,6,1,2,5,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,6,1,2,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,6,1,5,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,1,5,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,1,7,2,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,6,1,7,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,2,1,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,2,1,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,2,5,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,2,5,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,2,7,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,2,7,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,5,1,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,5,1,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,5,2,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,4,6,5,2,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,4,6,5,7,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,5,7,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,4,6,7,1,2,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,6,7,1,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,7,2,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,7,2,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,7,5,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,6,7,5,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,4,7,1,2,5,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,4,7,1,2,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,4,7,1,5,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,7,1,5,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,7,1,6,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,4,7,1,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,4,7,2,1,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,7,2,1,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,4,7,2,5,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,7,2,5,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,7,2,6,1,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,4,7,2,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,4,7,5,1,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,7,5,1,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,7,5,2,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,4,7,5,2,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,4,7,5,6,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,4,7,5,6,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,4,7,6,1,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,4,7,6,1,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,4,7,6,2,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,4,7,6,2,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,4,7,6,5,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,4,7,6,5,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,5,1,2,4,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,5,1,2,4,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,5,1,2,6,4,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,5,1,2,6,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,5,1,2,7,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,5,1,2,7,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,1,4,2,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,1,4,2,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,1,4,6,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,1,4,6,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,1,4,7,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,1,4,7,6,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,1,6,2,4,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,5,1,6,2,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,5,1,6,4,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,1,6,4,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,1,6,7,2,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,5,1,6,7,4,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,1,7,2,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,5,1,7,2,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,1,7,4,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,1,7,4,6,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,1,7,6,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,1,7,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,2,1,4,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,2,1,4,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,2,1,6,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,2,1,6,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,2,1,7,4,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,2,1,7,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,5,2,4,1,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,2,4,1,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,2,4,6,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,2,4,6,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,2,4,7,1,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,2,4,7,6,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,2,6,1,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,2,6,1,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,2,6,4,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,2,6,4,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,2,6,7,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,2,6,7,4,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,2,7,1,4,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,2,7,1,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,5,2,7,4,1,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,2,7,4,6,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,2,7,6,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,5,2,7,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,4,1,2,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,4,1,2,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,4,1,6,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,4,1,6,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,4,1,7,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,4,1,7,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,5,4,2,1,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,5,4,2,1,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,4,2,6,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,5,4,2,6,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,5,4,2,7,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,4,2,7,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,4,6,1,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,4,6,1,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,4,6,2,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,5,4,6,2,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,5,4,6,7,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,4,6,7,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,5,4,7,1,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,4,7,1,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,5,4,7,2,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,4,7,2,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,4,7,6,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,5,4,7,6,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,6,1,2,4,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,5,6,1,2,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,5,6,1,4,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,1,4,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,1,7,2,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,5,6,1,7,4,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,2,1,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,2,1,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,2,4,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,2,4,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,2,7,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,2,7,4,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,4,1,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,4,1,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,4,2,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,5,6,4,2,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,5,6,4,7,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,4,7,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,5,6,7,1,2,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,5,6,7,1,4,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,7,2,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,7,2,4,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,7,4,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,5,6,7,4,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,5,7,1,2,4,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,5,7,1,2,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,7,1,4,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,7,1,4,6,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,7,1,6,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,7,1,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,7,2,1,4,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,7,2,1,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,5,7,2,4,1,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,7,2,4,6,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,7,2,6,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,5,7,2,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,7,4,1,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,7,4,1,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,5,7,4,2,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,7,4,2,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,7,4,6,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,5,7,4,6,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,7,6,1,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,5,7,6,1,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,7,6,2,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,7,6,2,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,7,6,4,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,5,7,6,4,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,6,1,2,4,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,6,1,2,4,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,6,1,2,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,1,2,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,1,2,7,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,6,1,2,7,5,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,1,4,2,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,1,4,2,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,1,4,5,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,1,4,5,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,1,4,7,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,1,4,7,5,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,1,5,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,1,5,2,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,1,5,4,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,1,5,4,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,1,5,7,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,1,5,7,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,1,7,2,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,6,1,7,2,5,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,1,7,4,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,1,7,4,5,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,1,7,5,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,1,7,5,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,2,1,4,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,2,1,4,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,2,1,5,4,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,2,1,5,7,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,2,1,7,4,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,2,1,7,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,2,4,1,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,2,4,1,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,2,4,5,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,2,4,5,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,2,4,7,1,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,2,4,7,5,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,2,5,1,4,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,2,5,1,7,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,2,5,4,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,2,5,4,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,2,5,7,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,2,5,7,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,2,7,1,4,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,2,7,1,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,2,7,4,1,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,2,7,4,5,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,2,7,5,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,2,7,5,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,4,1,2,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,4,1,2,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,4,1,5,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,4,1,5,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,4,1,7,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,4,1,7,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,4,2,1,5,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,6,4,2,1,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,4,2,5,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,6,4,2,5,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,6,4,2,7,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,4,2,7,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,4,5,1,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,4,5,1,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,4,5,2,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,6,4,5,2,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,6,4,5,7,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,4,5,7,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,6,4,7,1,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,4,7,1,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,4,7,2,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,4,7,2,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,4,7,5,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,4,7,5,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,1,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,6,5,1,2,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,5,1,4,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,1,4,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,1,7,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,5,1,7,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,2,1,4,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,2,1,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,2,4,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,2,4,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,2,7,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,2,7,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,4,1,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,4,1,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,4,2,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,6,5,4,2,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,6,5,4,7,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,4,7,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,6,5,7,1,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,5,7,1,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,7,2,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,7,2,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,7,4,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,5,7,4,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,6,7,1,2,4,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[3,6,7,1,2,5,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,7,1,4,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,7,1,4,5,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,7,1,5,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,7,1,5,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,7,2,1,4,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,7,2,1,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,7,2,4,1,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,7,2,4,5,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,7,2,5,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,7,2,5,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,7,4,1,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,7,4,1,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,7,4,2,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,7,4,2,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,7,4,5,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,6,7,4,5,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,7,5,1,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,6,7,5,1,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,7,5,2,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,7,5,2,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,7,5,4,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,6,7,5,4,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,7,1,2,4,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[3,7,1,2,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,1,2,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,1,2,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,1,2,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,1,2,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,1,4,2,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,1,4,2,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,7,1,4,5,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,1,4,5,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,1,4,6,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,7,1,4,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,1,5,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,1,5,2,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,7,1,5,4,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,1,5,4,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,1,5,6,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,7,1,5,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,1,6,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,1,6,2,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,1,6,4,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,1,6,4,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,1,6,5,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,1,6,5,4,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[3,7,2,1,4,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,2,1,4,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,7,2,1,5,4,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,7,2,1,5,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,7,2,1,6,4,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,7,2,1,6,5,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[3,7,2,4,1,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,2,4,1,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,7,2,4,5,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,2,4,5,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,2,4,6,1,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,7,2,4,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,2,5,1,4,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,7,2,5,1,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,7,2,5,4,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,2,5,4,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,2,5,6,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,7,2,5,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,2,6,1,4,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[3,7,2,6,1,5,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[3,7,2,6,4,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,2,6,4,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,2,6,5,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[3,7,2,6,5,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[3,7,4,1,2,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,4,1,2,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,7,4,1,5,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,4,1,5,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,4,1,6,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,7,4,1,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,4,2,1,5,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,7,4,2,1,6,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,4,2,5,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,7,4,2,5,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,7,4,2,6,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,4,2,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,4,5,1,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,4,5,1,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,4,5,2,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,7,4,5,2,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,7,4,5,6,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,4,5,6,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[3,7,4,6,1,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,7,4,6,1,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,4,6,2,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,4,6,2,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,4,6,5,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,4,6,5,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,7,5,1,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,5,1,2,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,7,5,1,4,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,1,4,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,1,6,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,7,5,1,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,2,1,4,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,2,1,6,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,2,4,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,2,4,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,2,6,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,2,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,4,1,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,4,1,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,4,2,1,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,7,5,4,2,6,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,7,5,4,6,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,4,6,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,7,5,6,1,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[3,7,5,6,1,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,6,2,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,6,2,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,6,4,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,5,6,4,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,7,6,1,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[3,7,6,1,2,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,6,1,4,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,6,1,4,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,6,1,5,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,6,1,5,4,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[3,7,6,2,1,4,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,6,2,1,5,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[3,7,6,2,4,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,6,2,4,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,6,2,5,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[3,7,6,2,5,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[3,7,6,4,1,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,6,4,1,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,6,4,2,1,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,7,6,4,2,5,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,7,6,4,5,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,6,4,5,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[3,7,6,5,1,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[3,7,6,5,1,4,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[3,7,6,5,2,1,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[3,7,6,5,2,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[3,7,6,5,4,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[3,7,6,5,4,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[4,1,2,3,5,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[4,1,2,3,5,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,1,2,3,6,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,1,2,3,6,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,1,2,3,7,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,1,2,3,7,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,2,5,3,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,1,2,5,3,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,2,5,6,3,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,1,2,5,6,7,3]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,1,2,5,7,3,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,2,5,7,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,2,6,3,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,1,2,6,3,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,2,6,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,2,6,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,2,6,7,3,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,2,6,7,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,2,7,3,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,1,2,7,3,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,2,7,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,2,7,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,2,7,6,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,2,7,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,3,2,5,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[4,1,3,2,5,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,2,6,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,2,6,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,2,7,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,2,7,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,1,3,5,2,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[4,1,3,5,2,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,5,6,2,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[4,1,3,5,6,7,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[4,1,3,5,7,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,5,7,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,6,2,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,6,2,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,6,5,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,6,5,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,6,7,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,6,7,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,7,2,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,7,2,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,1,3,7,5,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,7,5,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,3,7,6,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,1,3,7,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,5,2,3,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,1,5,2,3,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,5,2,6,3,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,5,2,6,7,3]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,5,2,7,3,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,5,2,7,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,5,3,2,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,5,3,2,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,5,3,6,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,5,3,6,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,5,3,7,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,5,3,7,6,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,5,6,2,3,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,5,6,2,7,3]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,5,6,3,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,5,6,3,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,5,6,7,2,3]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,5,6,7,3,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,5,7,2,3,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,5,7,2,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,5,7,3,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,5,7,3,6,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,5,7,6,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,5,7,6,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,6,2,3,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,1,6,2,3,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,6,2,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,6,2,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,6,2,7,3,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,6,2,7,5,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,6,3,2,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,6,3,2,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,6,3,5,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,6,3,5,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,6,3,7,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,6,3,7,5,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,6,5,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,6,5,2,7,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,6,5,3,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,6,5,3,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,6,5,7,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,6,5,7,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,6,7,2,3,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,1,6,7,2,5,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,6,7,3,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,6,7,3,5,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,6,7,5,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,6,7,5,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,7,2,3,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,1,7,2,3,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,7,2,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,7,2,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,7,2,6,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,7,2,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,7,3,2,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,7,3,2,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,1,7,3,5,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,7,3,5,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,7,3,6,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,1,7,3,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,7,5,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,7,5,2,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,7,5,3,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,7,5,3,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,7,5,6,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,1,7,5,6,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,7,6,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,1,7,6,2,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,7,6,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,7,6,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,7,6,5,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,1,7,6,5,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,2,1,3,5,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[4,2,1,3,5,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,1,3,6,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,1,3,6,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,1,3,7,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,1,3,7,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,1,5,3,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,1,5,3,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,1,5,6,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,1,5,6,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,1,5,7,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,1,5,7,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,1,6,3,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,1,6,3,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,1,6,5,3,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,1,6,5,7,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,1,6,7,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,1,6,7,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,1,7,3,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,1,7,3,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,1,7,5,3,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,1,7,5,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,1,7,6,3,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,1,7,6,5,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,2,3,1,5,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[4,2,3,1,5,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,1,6,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,1,6,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,1,7,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,1,7,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,3,5,1,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[4,2,3,5,1,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,5,6,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[4,2,3,5,6,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[4,2,3,5,7,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,5,7,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,6,1,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,6,1,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,6,5,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,6,5,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,6,7,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,6,7,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,7,1,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,7,1,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,3,7,5,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,7,5,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,3,7,6,1,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,3,7,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,2,5,1,3,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,5,1,3,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,5,1,6,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,5,1,6,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,5,1,7,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,5,1,7,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,5,3,1,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,5,3,1,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,5,3,6,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,5,3,6,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,5,3,7,1,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,5,3,7,6,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,5,6,1,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,5,6,1,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,5,6,3,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,5,6,3,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,5,6,7,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,5,6,7,3,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,5,7,1,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,5,7,1,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,5,7,3,1,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,5,7,3,6,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,5,7,6,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,5,7,6,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,2,6,1,3,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,6,1,3,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,6,1,5,3,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,6,1,5,7,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,6,1,7,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,6,1,7,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,6,3,1,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,6,3,1,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,6,3,5,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,6,3,5,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,6,3,7,1,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,6,3,7,5,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,6,5,1,3,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,6,5,1,7,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,6,5,3,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,2,6,5,3,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,2,6,5,7,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,6,5,7,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,2,6,7,1,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,6,7,1,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,6,7,3,1,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,6,7,3,5,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,2,6,7,5,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,6,7,5,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,2,7,1,3,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,7,1,3,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,7,1,5,3,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,7,1,5,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,7,1,6,3,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,7,1,6,5,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,2,7,3,1,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,7,3,1,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,7,3,5,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,7,3,5,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,2,7,3,6,1,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,7,3,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,2,7,5,1,3,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,7,5,1,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,7,5,3,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,2,7,5,3,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,2,7,5,6,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,7,5,6,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,2,7,6,1,3,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,2,7,6,1,5,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,2,7,6,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,2,7,6,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,2,7,6,5,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,2,7,6,5,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,3,1,2,5,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[4,3,1,2,5,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,1,2,6,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,1,2,6,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,1,2,7,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,1,2,7,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,1,5,2,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,1,5,2,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,3,1,5,6,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,1,5,6,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,1,5,7,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,3,1,5,7,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,1,6,2,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,1,6,2,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,3,1,6,5,2,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,1,6,5,7,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,1,6,7,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,3,1,6,7,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,1,7,2,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,1,7,2,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,1,7,5,2,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,1,7,5,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,1,7,6,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,1,7,6,5,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,3,2,1,5,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,3,2,1,5,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,1,6,5,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,1,6,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,1,7,5,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,1,7,6,5]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,3,2,5,1,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,3,2,5,1,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,5,6,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,3,2,5,6,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,3,2,5,7,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,5,7,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,6,1,5,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,6,1,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,6,5,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,6,5,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,6,7,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,6,7,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,7,1,5,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,7,1,6,5]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,3,2,7,5,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,7,5,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,2,7,6,1,5]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,3,2,7,6,5,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,3,5,1,2,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,5,1,2,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,3,5,1,6,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,5,1,6,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,5,1,7,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,3,5,1,7,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,5,2,1,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,3,5,2,1,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,5,2,6,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,3,5,2,6,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,3,5,2,7,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,5,2,7,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,5,6,1,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,5,6,1,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,5,6,2,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,3,5,6,2,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,3,5,6,7,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,5,6,7,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,3,5,7,1,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,3,5,7,1,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,5,7,2,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,5,7,2,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,5,7,6,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,5,7,6,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,6,1,2,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,6,1,2,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,3,6,1,5,2,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,6,1,5,7,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,6,1,7,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,3,6,1,7,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,6,2,1,5,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,6,2,1,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,6,2,5,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,6,2,5,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,6,2,7,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,6,2,7,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,6,5,1,2,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,6,5,1,7,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,6,5,2,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,6,5,2,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,6,5,7,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,6,5,7,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,6,7,1,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,3,6,7,1,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,6,7,2,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,6,7,2,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,6,7,5,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,6,7,5,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,7,1,2,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,3,7,1,2,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,7,1,5,2,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,7,1,5,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,7,1,6,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,7,1,6,5,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,3,7,2,1,5,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,7,2,1,6,5]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,3,7,2,5,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,7,2,5,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,7,2,6,1,5]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,3,7,2,6,5,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,3,7,5,1,2,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,7,5,1,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,7,5,2,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,7,5,2,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,7,5,6,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,7,5,6,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,3,7,6,1,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,3,7,6,1,5,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,3,7,6,2,1,5]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,3,7,6,2,5,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,3,7,6,5,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,3,7,6,5,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,5,1,2,3,6,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,5,1,2,3,7,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,5,1,2,6,3,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,5,1,2,6,7,3]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,5,1,2,7,3,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,5,1,2,7,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,1,3,2,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,1,3,2,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,1,3,6,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,1,3,6,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,1,3,7,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,1,3,7,6,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,1,6,2,3,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,5,1,6,2,7,3]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,5,1,6,3,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,1,6,3,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,1,6,7,2,3]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,5,1,6,7,3,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,1,7,2,3,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,5,1,7,2,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,1,7,3,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,1,7,3,6,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,1,7,6,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,1,7,6,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,2,1,3,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,2,1,3,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,2,1,6,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,2,1,6,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,2,1,7,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,2,1,7,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,5,2,3,1,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,2,3,1,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,2,3,6,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,2,3,6,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,2,3,7,1,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,2,3,7,6,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,2,6,1,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,2,6,1,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,2,6,3,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,2,6,3,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,2,6,7,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,2,6,7,3,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,2,7,1,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,2,7,1,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,5,2,7,3,1,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,2,7,3,6,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,2,7,6,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,5,2,7,6,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,3,1,2,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,3,1,2,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,3,1,6,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,3,1,6,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,3,1,7,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,3,1,7,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,5,3,2,1,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,5,3,2,1,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,3,2,6,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,5,3,2,6,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,5,3,2,7,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,3,2,7,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,3,6,1,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,3,6,1,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,3,6,2,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,5,3,6,2,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,5,3,6,7,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,3,6,7,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,5,3,7,1,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,3,7,1,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,5,3,7,2,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,3,7,2,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,3,7,6,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,5,3,7,6,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,6,1,2,3,7]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,5,6,1,2,7,3]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,5,6,1,3,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,1,3,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,1,7,2,3]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,5,6,1,7,3,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,2,1,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,2,1,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,2,3,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,2,3,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,2,7,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,2,7,3,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,3,1,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,3,1,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,3,2,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,5,6,3,2,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,5,6,3,7,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,3,7,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,5,6,7,1,2,3]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,5,6,7,1,3,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,7,2,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,7,2,3,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,7,3,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,5,6,7,3,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[4,5,7,1,2,3,6]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,5,7,1,2,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,7,1,3,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,7,1,3,6,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,7,1,6,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,7,1,6,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,7,2,1,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,7,2,1,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,5,7,2,3,1,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,7,2,3,6,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,7,2,6,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,5,7,2,6,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,7,3,1,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,7,3,1,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,5,7,3,2,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,7,3,2,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,7,3,6,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,5,7,3,6,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,7,6,1,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,5,7,6,1,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,7,6,2,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,7,6,2,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,7,6,3,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,5,7,6,3,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[4,6,1,2,3,5,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,6,1,2,3,7,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,6,1,2,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,6,1,2,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,6,1,2,7,3,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,6,1,2,7,5,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,1,3,2,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,6,1,3,2,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,1,3,5,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,6,1,3,5,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,6,1,3,7,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,1,3,7,5,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,1,5,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,6,1,5,2,7,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,1,5,3,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,1,5,3,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,1,5,7,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,1,5,7,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,1,7,2,3,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,6,1,7,2,5,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,1,7,3,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,1,7,3,5,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,1,7,5,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,1,7,5,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,2,1,3,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,6,2,1,3,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,2,1,5,3,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,2,1,5,7,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,2,1,7,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,2,1,7,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,2,3,1,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,6,2,3,1,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,2,3,5,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,6,2,3,5,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,6,2,3,7,1,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,2,3,7,5,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,2,5,1,3,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,2,5,1,7,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,2,5,3,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,2,5,3,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,2,5,7,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,2,5,7,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,2,7,1,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,2,7,1,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,2,7,3,1,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,2,7,3,5,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,2,7,5,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,2,7,5,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,3,1,2,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,6,3,1,2,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,3,1,5,2,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,3,1,5,7,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,3,1,7,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,3,1,7,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,3,2,1,5,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,3,2,1,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,3,2,5,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,3,2,5,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,3,2,7,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,3,2,7,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,3,5,1,2,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,3,5,1,7,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,3,5,2,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,3,5,2,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,3,5,7,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,3,5,7,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,3,7,1,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,3,7,1,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,3,7,2,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,3,7,2,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,3,7,5,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,3,7,5,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,1,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,6,5,1,2,7,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,5,1,3,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,1,3,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,1,7,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,5,1,7,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,2,1,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,2,1,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,2,3,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,2,3,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,2,7,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,2,7,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,3,1,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,3,1,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,3,2,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[4,6,5,3,2,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[4,6,5,3,7,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,3,7,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[4,6,5,7,1,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,5,7,1,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,7,2,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,7,2,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,7,3,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,5,7,3,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[4,6,7,1,2,3,5]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[4,6,7,1,2,5,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,7,1,3,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,7,1,3,5,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,7,1,5,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,7,1,5,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,7,2,1,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,7,2,1,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,7,2,3,1,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,7,2,3,5,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,7,2,5,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,7,2,5,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,7,3,1,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,7,3,1,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,7,3,2,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,7,3,2,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,7,3,5,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,6,7,3,5,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,7,5,1,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,6,7,5,1,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,7,5,2,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,7,5,2,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,7,5,3,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,6,7,5,3,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[4,7,1,2,3,5,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[4,7,1,2,3,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,1,2,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,1,2,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,1,2,6,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,1,2,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,1,3,2,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,1,3,2,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,1,3,5,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,1,3,5,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,1,3,6,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,1,3,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,1,5,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,1,5,2,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,7,1,5,3,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,1,5,3,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,1,5,6,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,7,1,5,6,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,1,6,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,1,6,2,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,1,6,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,1,6,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,1,6,5,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,1,6,5,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,7,2,1,3,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,2,1,3,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,2,1,5,3,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,2,1,5,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,2,1,6,3,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,2,1,6,5,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,2,3,1,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,2,3,1,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,2,3,5,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,2,3,5,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,2,3,6,1,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,2,3,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,2,5,1,3,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,2,5,1,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,2,5,3,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,2,5,3,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,2,5,6,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,2,5,6,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,2,6,1,3,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,2,6,1,5,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,2,6,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,2,6,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,2,6,5,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,2,6,5,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,7,3,1,2,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,3,1,2,6,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,3,1,5,2,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,3,1,5,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,3,1,6,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,3,1,6,5,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,3,2,1,5,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,3,2,1,6,5]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,3,2,5,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,3,2,5,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,3,2,6,1,5]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,3,2,6,5,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,3,5,1,2,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,3,5,1,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,3,5,2,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,3,5,2,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,3,5,6,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,3,5,6,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,3,6,1,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[4,7,3,6,1,5,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,3,6,2,1,5]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,3,6,2,5,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,3,6,5,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,3,6,5,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,7,5,1,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,5,1,2,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,7,5,1,3,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,1,3,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,1,6,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,7,5,1,6,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,2,1,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,2,1,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,2,3,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,2,3,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,2,6,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,2,6,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,3,1,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,3,1,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,3,2,1,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[4,7,5,3,2,6,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[4,7,5,3,6,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,3,6,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[4,7,5,6,1,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[4,7,5,6,1,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,6,2,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,6,2,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,6,3,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,5,6,3,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[4,7,6,1,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[4,7,6,1,2,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,6,1,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,6,1,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,6,1,5,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,6,1,5,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,7,6,2,1,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,6,2,1,5,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,6,2,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,6,2,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,6,2,5,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,6,2,5,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,7,6,3,1,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,6,3,1,5,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,6,3,2,1,5]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,7,6,3,2,5,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,7,6,3,5,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[4,7,6,3,5,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,7,6,5,1,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[4,7,6,5,1,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,7,6,5,2,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,7,6,5,2,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,7,6,5,3,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[4,7,6,5,3,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[5,1,2,3,4,6,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[5,1,2,3,4,7,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[5,1,2,3,6,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[5,1,2,3,6,7,4]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[5,1,2,3,7,4,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[5,1,2,3,7,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,2,4,3,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,1,2,4,3,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,2,4,6,3,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,1,2,4,6,7,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,1,2,4,7,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,2,4,7,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,2,6,3,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[5,1,2,6,3,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[5,1,2,6,4,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,2,6,4,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,2,6,7,3,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[5,1,2,6,7,4,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,2,7,3,4,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[5,1,2,7,3,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,2,7,4,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,2,7,4,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,2,7,6,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,2,7,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,3,2,4,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,1,3,2,4,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,2,6,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,2,6,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,2,7,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,2,7,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,1,3,4,2,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,1,3,4,2,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,4,6,2,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,1,3,4,6,7,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,1,3,4,7,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,4,7,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,6,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,6,2,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,6,4,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,6,4,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,6,7,2,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,6,7,4,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,7,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,7,2,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,1,3,7,4,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,7,4,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,3,7,6,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,1,3,7,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,4,2,3,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,1,4,2,3,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,4,2,6,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,4,2,6,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,4,2,7,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,4,2,7,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,1,4,3,2,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,1,4,3,2,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,4,3,6,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,1,4,3,6,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,1,4,3,7,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,4,3,7,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,4,6,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,4,6,2,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,4,6,3,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,1,4,6,3,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,1,4,6,7,2,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,4,6,7,3,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,1,4,7,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,4,7,2,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,1,4,7,3,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,4,7,3,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,4,7,6,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,1,4,7,6,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,6,2,3,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[5,1,6,2,3,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[5,1,6,2,4,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,6,2,4,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,6,2,7,3,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[5,1,6,2,7,4,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,1,6,3,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,6,3,2,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,1,6,3,4,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,6,3,4,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,6,3,7,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,1,6,3,7,4,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,1,6,4,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,6,4,2,7,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,1,6,4,3,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,6,4,3,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,6,4,7,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,1,6,4,7,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,6,7,2,3,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[5,1,6,7,2,4,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,1,6,7,3,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,1,6,7,3,4,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,1,6,7,4,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,1,6,7,4,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,7,2,3,4,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[5,1,7,2,3,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,7,2,4,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,7,2,4,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,7,2,6,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,7,2,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,7,3,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,7,3,2,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,1,7,3,4,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,7,3,4,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,7,3,6,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,1,7,3,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,7,4,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,7,4,2,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,1,7,4,3,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,7,4,3,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,7,4,6,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,1,7,4,6,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,7,6,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,1,7,6,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,7,6,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,7,6,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,7,6,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,1,7,6,4,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,2,1,3,4,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,2,1,3,4,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,1,3,6,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,1,3,6,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,1,3,7,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,1,3,7,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,1,4,3,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,1,4,3,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,1,4,6,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,1,4,6,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,1,4,7,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,1,4,7,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,1,6,3,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,1,6,3,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,1,6,4,3,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,1,6,4,7,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,1,6,7,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,1,6,7,4,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,1,7,3,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,1,7,3,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,1,7,4,3,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,1,7,4,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,1,7,6,3,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,1,7,6,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,2,3,1,4,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,2,3,1,4,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,1,6,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,1,6,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,1,7,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,1,7,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,3,4,1,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,2,3,4,1,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,4,6,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,2,3,4,6,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,2,3,4,7,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,4,7,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,6,1,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,6,1,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,6,4,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,6,4,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,6,7,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,6,7,4,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,7,1,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,7,1,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,3,7,4,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,7,4,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,3,7,6,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,3,7,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,4,1,3,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,4,1,3,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,4,1,6,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,4,1,6,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,4,1,7,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,4,1,7,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,4,3,1,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,2,4,3,1,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,4,3,6,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,2,4,3,6,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,2,4,3,7,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,4,3,7,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,4,6,1,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,4,6,1,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,4,6,3,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,2,4,6,3,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,2,4,6,7,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,4,6,7,3,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,2,4,7,1,3,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,4,7,1,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,4,7,3,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,4,7,3,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,4,7,6,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,4,7,6,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,6,1,3,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,6,1,3,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,6,1,4,3,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,6,1,4,7,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,6,1,7,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,6,1,7,4,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,6,3,1,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,6,3,1,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,6,3,4,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,6,3,4,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,6,3,7,1,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,6,3,7,4,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,6,4,1,3,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,6,4,1,7,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,6,4,3,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,6,4,3,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,6,4,7,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,6,4,7,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,6,7,1,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,6,7,1,4,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,6,7,3,1,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,6,7,3,4,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,2,6,7,4,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,6,7,4,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,7,1,3,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,7,1,3,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,7,1,4,3,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,7,1,4,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,7,1,6,3,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,7,1,6,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,2,7,3,1,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,7,3,1,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,7,3,4,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,7,3,4,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,2,7,3,6,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,7,3,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,7,4,1,3,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,7,4,1,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,7,4,3,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,7,4,3,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,7,4,6,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,7,4,6,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,7,6,1,3,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,2,7,6,1,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,2,7,6,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,7,6,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,2,7,6,4,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,2,7,6,4,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,3,1,2,4,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,3,1,2,4,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,1,2,6,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,1,2,6,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,1,2,7,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,1,2,7,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,1,4,2,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,1,4,2,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,3,1,4,6,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,1,4,6,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,1,4,7,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,3,1,4,7,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,1,6,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,1,6,2,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,3,1,6,4,2,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,1,6,4,7,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,1,6,7,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,3,1,6,7,4,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,1,7,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,1,7,2,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,1,7,4,2,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,1,7,4,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,1,7,6,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,1,7,6,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,3,2,1,4,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,3,2,1,4,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,1,6,4,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,1,6,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,1,7,4,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,1,7,6,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,3,2,4,1,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,3,2,4,1,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,4,6,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,3,2,4,6,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,3,2,4,7,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,4,7,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,6,1,4,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,6,1,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,6,4,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,6,4,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,6,7,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,6,7,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,7,1,4,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,7,1,6,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,3,2,7,4,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,7,4,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,2,7,6,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,3,2,7,6,4,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,3,4,1,2,6,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,4,1,2,7,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,3,4,1,6,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,4,1,6,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,4,1,7,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,3,4,1,7,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,4,2,1,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,3,4,2,1,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,4,2,6,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,3,4,2,6,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,3,4,2,7,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,4,2,7,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,4,6,1,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,4,6,1,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,4,6,2,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,3,4,6,2,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,3,4,6,7,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,4,6,7,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,3,4,7,1,2,6]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,3,4,7,1,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,4,7,2,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,4,7,2,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,4,7,6,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,4,7,6,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,6,1,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,6,1,2,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,3,6,1,4,2,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,6,1,4,7,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,6,1,7,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,3,6,1,7,4,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,6,2,1,4,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,6,2,1,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,6,2,4,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,6,2,4,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,6,2,7,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,6,2,7,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,6,4,1,2,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,6,4,1,7,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,6,4,2,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,6,4,2,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,6,4,7,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,6,4,7,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,6,7,1,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,3,6,7,1,4,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,6,7,2,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,6,7,2,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,6,7,4,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,6,7,4,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,7,1,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,3,7,1,2,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,7,1,4,2,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,7,1,4,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,7,1,6,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,7,1,6,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,3,7,2,1,4,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,7,2,1,6,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,3,7,2,4,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,7,2,4,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,7,2,6,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,3,7,2,6,4,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,3,7,4,1,2,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,7,4,1,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,7,4,2,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,7,4,2,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,7,4,6,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,7,4,6,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,3,7,6,1,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,3,7,6,1,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,3,7,6,2,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,3,7,6,2,4,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,3,7,6,4,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,3,7,6,4,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,4,1,2,3,6,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[5,4,1,2,3,7,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,4,1,2,6,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,4,1,2,6,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,4,1,2,7,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,4,1,2,7,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,4,1,3,2,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,4,1,3,2,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,1,3,6,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,4,1,3,6,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,4,1,3,7,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,1,3,7,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,1,6,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,4,1,6,2,7,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,4,1,6,3,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,1,6,3,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,1,6,7,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,4,1,6,7,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,1,7,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,4,1,7,2,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,4,1,7,3,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,1,7,3,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,1,7,6,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,4,1,7,6,3,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,2,1,3,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,4,2,1,3,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,1,6,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,1,6,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,1,7,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,1,7,6,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,2,3,1,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,4,2,3,1,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,3,6,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,4,2,3,6,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,4,2,3,7,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,3,7,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,6,1,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,6,1,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,6,3,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,6,3,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,6,7,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,6,7,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,7,1,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,7,1,6,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,2,7,3,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,7,3,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,2,7,6,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,2,7,6,3,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,3,1,2,6,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[5,4,3,1,2,7,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,3,1,6,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,3,1,6,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,3,1,7,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,3,1,7,6,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,3,2,1,6,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,4,3,2,1,7,6]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,4,3,2,6,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,4,3,2,6,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,4,3,2,7,1,6]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,4,3,2,7,6,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,4,3,6,1,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,3,6,1,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,3,6,2,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,4,3,6,2,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,4,3,6,7,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,3,6,7,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,4,3,7,1,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,3,7,1,6,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,3,7,2,1,6]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,4,3,7,2,6,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,4,3,7,6,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,3,7,6,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,4,6,1,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,4,6,1,2,7,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,4,6,1,3,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,1,3,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,1,7,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,4,6,1,7,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,2,1,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,2,1,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,2,3,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,2,3,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,2,7,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,2,7,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,3,1,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,3,1,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,3,2,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,4,6,3,2,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,4,6,3,7,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,3,7,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,4,6,7,1,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,4,6,7,1,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,7,2,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,7,2,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,7,3,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,6,7,3,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,4,7,1,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,4,7,1,2,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,4,7,1,3,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,7,1,3,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,7,1,6,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,4,7,1,6,3,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,7,2,1,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,7,2,1,6,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,7,2,3,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,7,2,3,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,7,2,6,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,7,2,6,3,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,7,3,1,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,4,7,3,1,6,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,7,3,2,1,6]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,4,7,3,2,6,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,4,7,3,6,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,7,3,6,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,4,7,6,1,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,4,7,6,1,3,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,7,6,2,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,7,6,2,3,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,7,6,3,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,4,7,6,3,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,6,1,2,3,4,7]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[5,6,1,2,3,7,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[5,6,1,2,4,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,6,1,2,4,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,6,1,2,7,3,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[5,6,1,2,7,4,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,1,3,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,6,1,3,2,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,1,3,4,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,6,1,3,4,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,6,1,3,7,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,1,3,7,4,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,1,4,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,6,1,4,2,7,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,1,4,3,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,1,4,3,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,1,4,7,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,1,4,7,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,1,7,2,3,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[5,6,1,7,2,4,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,1,7,3,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,1,7,3,4,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,1,7,4,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,1,7,4,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,2,1,3,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,6,2,1,3,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,2,1,4,3,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,2,1,4,7,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,2,1,7,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,2,1,7,4,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,2,3,1,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,6,2,3,1,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,2,3,4,1,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,6,2,3,4,7,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,6,2,3,7,1,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,2,3,7,4,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,2,4,1,3,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,2,4,1,7,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,2,4,3,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,2,4,3,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,2,4,7,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,2,4,7,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,2,7,1,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,2,7,1,4,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,2,7,3,1,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,2,7,3,4,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,2,7,4,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,2,7,4,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,3,1,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,6,3,1,2,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,3,1,4,2,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,3,1,4,7,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,3,1,7,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,3,1,7,4,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,3,2,1,4,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,3,2,1,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,3,2,4,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,3,2,4,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,3,2,7,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,3,2,7,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,3,4,1,2,7]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,3,4,1,7,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,3,4,2,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,3,4,2,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,3,4,7,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,3,4,7,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,3,7,1,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,3,7,1,4,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,3,7,2,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,3,7,2,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,3,7,4,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,3,7,4,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,1,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,6,4,1,2,7,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,4,1,3,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,1,3,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,1,7,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,4,1,7,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,2,1,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,2,1,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,2,3,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,2,3,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,2,7,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,2,7,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,3,1,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,3,1,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,3,2,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,6,4,3,2,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,6,4,3,7,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,3,7,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,6,4,7,1,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,4,7,1,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,7,2,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,7,2,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,7,3,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,4,7,3,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,6,7,1,2,3,4]=>[4,3]=>[[1,2,3,7],[4,5,6]]=>001000
[5,6,7,1,2,4,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,7,1,3,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,7,1,3,4,2]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,7,1,4,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,7,1,4,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,7,2,1,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,7,2,1,4,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,7,2,3,1,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,7,2,3,4,1]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,7,2,4,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,7,2,4,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,7,3,1,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,7,3,1,4,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,7,3,2,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,7,3,2,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,7,3,4,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,6,7,3,4,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,7,4,1,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[5,6,7,4,1,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,7,4,2,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,7,4,2,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,7,4,3,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,6,7,4,3,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[5,7,1,2,3,4,6]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[5,7,1,2,3,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,1,2,4,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,1,2,4,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,1,2,6,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,1,2,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,1,3,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,1,3,2,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,1,3,4,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,1,3,4,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,1,3,6,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,1,3,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,1,4,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,1,4,2,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,1,4,3,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,1,4,3,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,1,4,6,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,1,4,6,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,1,6,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,1,6,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,1,6,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,1,6,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,1,6,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,1,6,4,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,2,1,3,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,2,1,3,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,2,1,4,3,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,2,1,4,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,2,1,6,3,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,2,1,6,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,2,3,1,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,2,3,1,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,2,3,4,1,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,2,3,4,6,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,2,3,6,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,2,3,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,2,4,1,3,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,2,4,1,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,2,4,3,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,2,4,3,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,2,4,6,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,2,4,6,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,2,6,1,3,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,2,6,1,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,2,6,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,2,6,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,2,6,4,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,2,6,4,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,3,1,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,3,1,2,6,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,3,1,4,2,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,3,1,4,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,3,1,6,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,3,1,6,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,3,2,1,4,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,3,2,1,6,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,3,2,4,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,3,2,4,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,3,2,6,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,3,2,6,4,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,3,4,1,2,6]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,3,4,1,6,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,3,4,2,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,3,4,2,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,3,4,6,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,3,4,6,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,3,6,1,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,3,6,1,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,3,6,2,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,3,6,2,4,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,3,6,4,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,3,6,4,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,4,1,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,4,1,2,6,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,4,1,3,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,4,1,3,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,4,1,6,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,4,1,6,3,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,4,2,1,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,4,2,1,6,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,4,2,3,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,4,2,3,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,4,2,6,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,4,2,6,3,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,4,3,1,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,4,3,1,6,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,4,3,2,1,6]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,4,3,2,6,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,4,3,6,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,4,3,6,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,4,6,1,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[5,7,4,6,1,3,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,4,6,2,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,4,6,2,3,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,4,6,3,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,4,6,3,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,6,1,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[5,7,6,1,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,6,1,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,6,1,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,6,1,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,6,1,4,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,6,2,1,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,6,2,1,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,6,2,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,6,2,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,6,2,4,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,6,2,4,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,6,3,1,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,6,3,1,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,6,3,2,1,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,6,3,2,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,6,3,4,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[5,7,6,3,4,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,6,4,1,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[5,7,6,4,1,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,6,4,2,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,6,4,2,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,6,4,3,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[5,7,6,4,3,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[6,1,2,3,4,5,7]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[6,1,2,3,4,7,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[6,1,2,3,5,4,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,1,2,3,5,7,4]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,1,2,3,7,4,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[6,1,2,3,7,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,2,4,3,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,1,2,4,3,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,2,4,5,3,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,1,2,4,5,7,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,1,2,4,7,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,2,4,7,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,2,5,3,4,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,1,2,5,3,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,2,5,4,3,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,2,5,4,7,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,2,5,7,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,2,5,7,4,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,2,7,3,4,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[6,1,2,7,3,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,2,7,4,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,2,7,4,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,2,7,5,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,2,7,5,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,3,2,4,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,1,3,2,4,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,3,2,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,3,2,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,3,2,7,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,3,2,7,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,1,3,4,2,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,1,3,4,2,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,3,4,5,2,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,1,3,4,5,7,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,1,3,4,7,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,3,4,7,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,3,5,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,3,5,2,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,3,5,4,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,3,5,4,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,3,5,7,2,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,3,5,7,4,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,3,7,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,3,7,2,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,1,3,7,4,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,3,7,4,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,3,7,5,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,1,3,7,5,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,4,2,3,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,1,4,2,3,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,4,2,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,4,2,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,4,2,7,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,4,2,7,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,1,4,3,2,5,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,4,3,2,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,4,3,5,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,4,3,5,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,4,3,7,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,4,3,7,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,4,5,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,4,5,2,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,4,5,3,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,4,5,3,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,4,5,7,2,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,4,5,7,3,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,4,7,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,4,7,2,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,1,4,7,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,4,7,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,4,7,5,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,1,4,7,5,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,5,2,3,4,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,1,5,2,3,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,5,2,4,3,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,5,2,4,7,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,5,2,7,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,5,2,7,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,5,3,2,4,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,5,3,2,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,5,3,4,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,5,3,4,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,5,3,7,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,5,3,7,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,5,4,2,3,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,1,5,4,2,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,5,4,3,2,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,1,5,4,3,7,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,1,5,4,7,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,5,4,7,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,1,5,7,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,5,7,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,5,7,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,5,7,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,5,7,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,5,7,4,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,1,7,2,3,4,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[6,1,7,2,3,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,7,2,4,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,7,2,4,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,7,2,5,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,7,2,5,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,7,3,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,7,3,2,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,1,7,3,4,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,7,3,4,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,7,3,5,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,1,7,3,5,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,7,4,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,7,4,2,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,1,7,4,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,7,4,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,7,4,5,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,1,7,4,5,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,7,5,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,1,7,5,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,7,5,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,7,5,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,7,5,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,1,7,5,4,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,2,1,3,4,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,2,1,3,4,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,1,3,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,1,3,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,1,3,7,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,1,3,7,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,1,4,3,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,1,4,3,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,2,1,4,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,1,4,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,1,4,7,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,2,1,4,7,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,1,5,3,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,1,5,3,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,2,1,5,4,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,1,5,4,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,1,5,7,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,2,1,5,7,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,1,7,3,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,1,7,3,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,1,7,4,3,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,1,7,4,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,1,7,5,3,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,1,7,5,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,2,3,1,4,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,2,3,1,4,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,3,1,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,3,1,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,3,1,7,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,3,1,7,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,3,4,1,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,2,3,4,1,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,3,4,5,1,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,2,3,4,5,7,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,2,3,4,7,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,3,4,7,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,3,5,1,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,3,5,1,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,3,5,4,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,2,3,5,4,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,2,3,5,7,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,3,5,7,4,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,2,3,7,1,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,3,7,1,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,3,7,4,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,3,7,4,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,3,7,5,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,3,7,5,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,4,1,3,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,4,1,3,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,2,4,1,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,4,1,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,4,1,7,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,2,4,1,7,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,4,3,1,5,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,2,4,3,1,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,4,3,5,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,2,4,3,5,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,2,4,3,7,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,4,3,7,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,4,5,1,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,4,5,1,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,4,5,3,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,2,4,5,3,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,2,4,5,7,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,4,5,7,3,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,2,4,7,1,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,2,4,7,1,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,4,7,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,4,7,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,4,7,5,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,4,7,5,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,1,3,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,5,1,3,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,2,5,1,4,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,1,4,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,1,7,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,2,5,1,7,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,3,1,4,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,2,5,3,1,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,3,4,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,2,5,3,4,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,2,5,3,7,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,3,7,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,4,1,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,4,1,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,4,3,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,2,5,4,3,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,2,5,4,7,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,4,7,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,2,5,7,1,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,2,5,7,1,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,7,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,7,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,7,4,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,5,7,4,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,2,7,1,3,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,7,1,3,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,7,1,4,3,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,7,1,4,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,7,1,5,3,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,7,1,5,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,2,7,3,1,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,7,3,1,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,7,3,4,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,7,3,4,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,2,7,3,5,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,7,3,5,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,7,4,1,3,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,7,4,1,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,7,4,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,7,4,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,7,4,5,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,7,4,5,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,7,5,1,3,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,2,7,5,1,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,2,7,5,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,7,5,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,2,7,5,4,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,2,7,5,4,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,3,1,2,4,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,3,1,2,4,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,1,2,5,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,1,2,5,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,1,2,7,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,1,2,7,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,1,4,2,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,1,4,2,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,3,1,4,5,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,1,4,5,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,1,4,7,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,3,1,4,7,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,1,5,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,1,5,2,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,3,1,5,4,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,1,5,4,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,1,5,7,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,3,1,5,7,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,1,7,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,1,7,2,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,1,7,4,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,1,7,4,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,1,7,5,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,1,7,5,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,3,2,1,4,5,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,3,2,1,4,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,1,5,4,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,1,5,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,1,7,4,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,1,7,5,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,3,2,4,1,5,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,3,2,4,1,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,4,5,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,3,2,4,5,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,3,2,4,7,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,4,7,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,5,1,4,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,5,1,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,5,4,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,5,4,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,5,7,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,5,7,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,7,1,4,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,7,1,5,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,3,2,7,4,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,7,4,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,2,7,5,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,3,2,7,5,4,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,3,4,1,2,5,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,4,1,2,7,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,3,4,1,5,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,4,1,5,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,4,1,7,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,3,4,1,7,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,4,2,1,5,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,3,4,2,1,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,4,2,5,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,3,4,2,5,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,3,4,2,7,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,4,2,7,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,4,5,1,2,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,4,5,1,7,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,4,5,2,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,3,4,5,2,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,3,4,5,7,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,4,5,7,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,3,4,7,1,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,3,4,7,1,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,4,7,2,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,4,7,2,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,4,7,5,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,4,7,5,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,1,2,4,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,5,1,2,7,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,3,5,1,4,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,1,4,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,1,7,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,3,5,1,7,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,2,1,4,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,2,1,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,2,4,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,2,4,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,2,7,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,2,7,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,4,1,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,4,1,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,4,2,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,3,5,4,2,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,3,5,4,7,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,4,7,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,3,5,7,1,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,3,5,7,1,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,7,2,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,7,2,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,7,4,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,5,7,4,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,3,7,1,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,3,7,1,2,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,7,1,4,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,7,1,4,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,7,1,5,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,7,1,5,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,3,7,2,1,4,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,7,2,1,5,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,3,7,2,4,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,7,2,4,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,7,2,5,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,3,7,2,5,4,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,3,7,4,1,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,7,4,1,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,7,4,2,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,7,4,2,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,7,4,5,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,7,4,5,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,3,7,5,1,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,3,7,5,1,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,3,7,5,2,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,3,7,5,2,4,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,3,7,5,4,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,3,7,5,4,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,4,1,2,3,5,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,4,1,2,3,7,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,4,1,2,5,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,4,1,2,5,7,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,4,1,2,7,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,4,1,2,7,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,4,1,3,2,5,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,4,1,3,2,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,1,3,5,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,4,1,3,5,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,4,1,3,7,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,1,3,7,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,1,5,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,4,1,5,2,7,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,4,1,5,3,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,1,5,3,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,1,5,7,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,4,1,5,7,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,1,7,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,4,1,7,2,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,4,1,7,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,1,7,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,1,7,5,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,4,1,7,5,3,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,2,1,3,5,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,4,2,1,3,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,1,5,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,1,5,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,1,7,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,1,7,5,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,2,3,1,5,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,4,2,3,1,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,3,5,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,4,2,3,5,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,4,2,3,7,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,3,7,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,5,1,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,5,1,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,5,3,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,5,3,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,5,7,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,5,7,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,7,1,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,7,1,5,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,2,7,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,7,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,2,7,5,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,2,7,5,3,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,3,1,2,5,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,4,3,1,2,7,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,3,1,5,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,3,1,5,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,3,1,7,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,3,1,7,5,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,3,2,1,5,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,4,3,2,1,7,5]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,4,3,2,5,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,4,3,2,5,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,4,3,2,7,1,5]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,4,3,2,7,5,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,4,3,5,1,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,3,5,1,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,3,5,2,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,4,3,5,2,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,4,3,5,7,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,3,5,7,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,4,3,7,1,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,3,7,1,5,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,3,7,2,1,5]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,4,3,7,2,5,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,4,3,7,5,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,3,7,5,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,4,5,1,2,3,7]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,4,5,1,2,7,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,4,5,1,3,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,1,3,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,1,7,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,4,5,1,7,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,2,1,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,2,1,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,2,3,1,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,2,3,7,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,2,7,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,2,7,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,3,1,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,3,1,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,3,2,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,4,5,3,2,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,4,5,3,7,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,3,7,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,4,5,7,1,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[6,4,5,7,1,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,7,2,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,7,2,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,7,3,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,5,7,3,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,4,7,1,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,4,7,1,2,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,4,7,1,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,7,1,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,7,1,5,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,4,7,1,5,3,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,7,2,1,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,7,2,1,5,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,7,2,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,7,2,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,7,2,5,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,7,2,5,3,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,7,3,1,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,4,7,3,1,5,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,7,3,2,1,5]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,4,7,3,2,5,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,4,7,3,5,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,7,3,5,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,4,7,5,1,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,4,7,5,1,3,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,7,5,2,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,7,5,2,3,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,7,5,3,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,4,7,5,3,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,1,2,3,4,7]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[6,5,1,2,3,7,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,5,1,2,4,3,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,5,1,2,4,7,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,5,1,2,7,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,5,1,2,7,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,1,3,2,4,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,5,1,3,2,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,1,3,4,2,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,5,1,3,4,7,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,5,1,3,7,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,1,3,7,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,1,4,2,3,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,5,1,4,2,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,1,4,3,2,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,1,4,3,7,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,1,4,7,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,1,4,7,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,1,7,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,5,1,7,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,1,7,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,1,7,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,1,7,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,1,7,4,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,2,1,3,4,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,5,2,1,3,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,2,1,4,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,2,1,4,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,2,1,7,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,2,1,7,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,5,2,3,1,4,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,5,2,3,1,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,2,3,4,1,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,5,2,3,4,7,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,5,2,3,7,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,2,3,7,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,2,4,1,3,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,2,4,1,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,2,4,3,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,2,4,3,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,2,4,7,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,2,4,7,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,2,7,1,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,2,7,1,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,5,2,7,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,2,7,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,2,7,4,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,5,2,7,4,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,3,1,2,4,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,5,3,1,2,7,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,3,1,4,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,3,1,4,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,3,1,7,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,3,1,7,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,5,3,2,1,4,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,3,2,1,7,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,3,2,4,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,3,2,4,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,3,2,7,1,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,3,2,7,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,3,4,1,2,7]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,3,4,1,7,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,3,4,2,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,3,4,2,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,3,4,7,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,3,4,7,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,3,7,1,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,3,7,1,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,5,3,7,2,1,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,3,7,2,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,3,7,4,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,5,3,7,4,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,4,1,2,3,7]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[6,5,4,1,2,7,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,4,1,3,2,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,4,1,3,7,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,4,1,7,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,4,1,7,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,4,2,1,3,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,4,2,1,7,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,4,2,3,1,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,4,2,3,7,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,4,2,7,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,4,2,7,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,4,3,1,2,7]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[6,5,4,3,1,7,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,4,3,2,1,7]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[6,5,4,3,2,7,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[6,5,4,3,7,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,4,3,7,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[6,5,4,7,1,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,4,7,1,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,4,7,2,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,4,7,2,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,4,7,3,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,4,7,3,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[6,5,7,1,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,5,7,1,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,7,1,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,7,1,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,7,1,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,7,1,4,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,7,2,1,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,7,2,1,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,5,7,2,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,7,2,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,7,2,4,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,5,7,2,4,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,7,3,1,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,7,3,1,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,5,7,3,2,1,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,7,3,2,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,7,3,4,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,5,7,3,4,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,7,4,1,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,5,7,4,1,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,7,4,2,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,7,4,2,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,7,4,3,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,5,7,4,3,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[6,7,1,2,3,4,5]=>[5,2]=>[[1,2,5,6,7],[3,4]]=>010000
[6,7,1,2,3,5,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,1,2,4,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,1,2,4,5,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,1,2,5,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,1,2,5,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,1,3,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,1,3,2,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,1,3,4,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,1,3,4,5,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,1,3,5,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,1,3,5,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,1,4,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,1,4,2,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,1,4,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,1,4,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,1,4,5,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,1,4,5,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,1,5,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,1,5,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,1,5,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,1,5,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,1,5,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,1,5,4,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,2,1,3,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,2,1,3,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,2,1,4,3,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,2,1,4,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,2,1,5,3,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,2,1,5,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,2,3,1,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,2,3,1,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,2,3,4,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,2,3,4,5,1]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,2,3,5,1,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,2,3,5,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,2,4,1,3,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,2,4,1,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,2,4,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,2,4,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,2,4,5,1,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,2,4,5,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,2,5,1,3,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,2,5,1,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,2,5,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,2,5,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,2,5,4,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,2,5,4,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,3,1,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,3,1,2,5,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,3,1,4,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,3,1,4,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,3,1,5,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,3,1,5,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,3,2,1,4,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,3,2,1,5,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,3,2,4,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,3,2,4,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,3,2,5,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,3,2,5,4,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,3,4,1,2,5]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,3,4,1,5,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,3,4,2,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,3,4,2,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,3,4,5,1,2]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,3,4,5,2,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,3,5,1,2,4]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,3,5,1,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,3,5,2,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,3,5,2,4,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,3,5,4,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,3,5,4,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,4,1,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,4,1,2,5,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,4,1,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,4,1,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,4,1,5,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,4,1,5,3,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,4,2,1,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,4,2,1,5,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,4,2,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,4,2,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,4,2,5,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,4,2,5,3,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,4,3,1,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,4,3,1,5,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,4,3,2,1,5]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,4,3,2,5,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,4,3,5,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,4,3,5,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,4,5,1,2,3]=>[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>010100
[6,7,4,5,1,3,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,4,5,2,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,4,5,2,3,1]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,4,5,3,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,4,5,3,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,5,1,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[6,7,5,1,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,5,1,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,5,1,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,5,1,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,5,1,4,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,5,2,1,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,5,2,1,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,5,2,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,5,2,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,5,2,4,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,5,2,4,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,5,3,1,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,5,3,1,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,5,3,2,1,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,5,3,2,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,5,3,4,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[6,7,5,3,4,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,5,4,1,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[6,7,5,4,1,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,5,4,2,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,5,4,2,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,5,4,3,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,1,2,3,4,5,6]=>[6,1]=>[[1,3,4,5,6,7],[2]]=>100000
[7,1,2,3,4,6,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,2,3,5,4,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,2,3,5,6,4]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,2,3,6,4,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,2,3,6,5,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,2,4,3,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,2,4,3,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,2,4,5,3,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,2,4,5,6,3]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,2,4,6,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,2,4,6,5,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,2,5,3,4,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,2,5,3,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,2,5,4,3,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,2,5,4,6,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,2,5,6,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,2,5,6,4,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,2,6,3,4,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,2,6,3,5,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,2,6,4,3,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,2,6,4,5,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,2,6,5,3,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,2,6,5,4,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,3,2,4,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,3,2,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,3,2,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,3,2,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,3,2,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,3,2,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,3,4,2,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,3,4,2,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,3,4,5,2,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,3,4,5,6,2]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,3,4,6,2,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,3,4,6,5,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,3,5,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,3,5,2,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,3,5,4,2,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,3,5,4,6,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,3,5,6,2,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,3,5,6,4,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,3,6,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,3,6,2,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,3,6,4,2,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,3,6,4,5,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,3,6,5,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,3,6,5,4,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,4,2,3,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,4,2,3,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,4,2,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,4,2,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,4,2,6,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,4,2,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,4,3,2,5,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,4,3,2,6,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,4,3,5,2,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,4,3,5,6,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,4,3,6,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,4,3,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,4,5,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,4,5,2,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,4,5,3,2,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,4,5,3,6,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,4,5,6,2,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,4,5,6,3,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,4,6,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,4,6,2,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,4,6,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,4,6,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,4,6,5,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,4,6,5,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,5,2,3,4,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,5,2,3,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,5,2,4,3,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,5,2,4,6,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,5,2,6,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,5,2,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,5,3,2,4,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,5,3,2,6,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,5,3,4,2,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,5,3,4,6,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,5,3,6,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,5,3,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,5,4,2,3,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,5,4,2,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,5,4,3,2,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,5,4,3,6,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,5,4,6,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,5,4,6,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,5,6,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,1,5,6,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,5,6,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,5,6,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,5,6,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,5,6,4,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,6,2,3,4,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,1,6,2,3,5,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,6,2,4,3,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,6,2,4,5,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,6,2,5,3,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,6,2,5,4,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,6,3,2,4,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,6,3,2,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,6,3,4,2,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,6,3,4,5,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,6,3,5,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,6,3,5,4,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,6,4,2,3,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,6,4,2,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,6,4,3,2,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,6,4,3,5,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,6,4,5,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,1,6,4,5,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,6,5,2,3,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,1,6,5,2,4,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,6,5,3,2,4]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,6,5,3,4,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,6,5,4,2,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,1,6,5,4,3,2]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,2,1,3,4,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,2,1,3,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,1,3,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,1,3,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,1,3,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,1,3,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,1,4,3,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,1,4,3,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,2,1,4,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,1,4,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,1,4,6,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,2,1,4,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,1,5,3,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,1,5,3,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,2,1,5,4,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,1,5,4,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,1,5,6,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,2,1,5,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,1,6,3,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,1,6,3,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,1,6,4,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,1,6,4,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,1,6,5,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,1,6,5,4,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,2,3,1,4,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,2,3,1,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,3,1,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,3,1,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,3,1,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,3,1,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,3,4,1,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,2,3,4,1,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,3,4,5,1,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,2,3,4,5,6,1]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,2,3,4,6,1,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,3,4,6,5,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,3,5,1,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,3,5,1,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,3,5,4,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,3,5,4,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,3,5,6,1,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,3,5,6,4,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,3,6,1,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,3,6,1,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,3,6,4,1,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,3,6,4,5,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,3,6,5,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,3,6,5,4,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,2,4,1,3,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,4,1,3,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,2,4,1,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,4,1,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,4,1,6,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,2,4,1,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,4,3,1,5,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,4,3,1,6,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,4,3,5,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,4,3,5,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,4,3,6,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,4,3,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,4,5,1,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,4,5,1,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,4,5,3,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,4,5,3,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,4,5,6,1,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,4,5,6,3,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,4,6,1,3,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,2,4,6,1,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,4,6,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,4,6,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,4,6,5,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,4,6,5,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,2,5,1,3,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,5,1,3,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,2,5,1,4,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,5,1,4,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,5,1,6,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,2,5,1,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,5,3,1,4,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,5,3,1,6,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,5,3,4,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,5,3,4,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,5,3,6,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,5,3,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,5,4,1,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,5,4,1,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,5,4,3,1,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,2,5,4,3,6,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,2,5,4,6,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,5,4,6,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,2,5,6,1,3,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,2,5,6,1,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,5,6,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,5,6,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,5,6,4,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,5,6,4,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,2,6,1,3,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,2,6,1,3,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,6,1,4,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,6,1,4,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,6,1,5,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,6,1,5,4,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,2,6,3,1,4,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,6,3,1,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,6,3,4,1,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,6,3,4,5,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,2,6,3,5,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,6,3,5,4,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,2,6,4,1,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,6,4,1,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,6,4,3,1,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,2,6,4,3,5,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,2,6,4,5,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,6,4,5,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,2,6,5,1,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,2,6,5,1,4,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,2,6,5,3,1,4]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,2,6,5,3,4,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,2,6,5,4,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,2,6,5,4,3,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,3,1,2,4,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,3,1,2,4,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,1,2,5,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,1,2,5,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,1,2,6,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,1,2,6,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,1,4,2,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,1,4,2,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,3,1,4,5,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,1,4,5,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,1,4,6,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,3,1,4,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,1,5,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,1,5,2,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,3,1,5,4,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,1,5,4,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,1,5,6,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,3,1,5,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,1,6,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,1,6,2,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,1,6,4,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,1,6,4,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,1,6,5,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,1,6,5,4,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,3,2,1,4,5,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,3,2,1,4,6,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,1,5,4,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,1,5,6,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,1,6,4,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,1,6,5,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,3,2,4,1,5,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,3,2,4,1,6,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,4,5,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,3,2,4,5,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,3,2,4,6,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,4,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,5,1,4,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,5,1,6,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,5,4,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,5,4,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,5,6,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,5,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,6,1,4,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,6,1,5,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,3,2,6,4,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,6,4,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,2,6,5,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,3,2,6,5,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,3,4,1,2,5,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,4,1,2,6,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,3,4,1,5,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,4,1,5,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,4,1,6,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,3,4,1,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,4,2,1,5,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,3,4,2,1,6,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,4,2,5,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,3,4,2,5,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,3,4,2,6,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,4,2,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,4,5,1,2,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,4,5,1,6,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,4,5,2,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,3,4,5,2,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,3,4,5,6,1,2]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,4,5,6,2,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,3,4,6,1,2,5]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,3,4,6,1,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,4,6,2,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,4,6,2,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,4,6,5,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,4,6,5,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,3,5,1,2,4,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,5,1,2,6,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,3,5,1,4,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,1,4,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,1,6,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,3,5,1,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,2,1,4,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,2,1,6,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,2,4,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,2,4,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,2,6,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,2,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,4,1,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,4,1,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,4,2,1,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,3,5,4,2,6,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,3,5,4,6,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,4,6,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,3,5,6,1,2,4]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,3,5,6,1,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,6,2,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,6,2,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,6,4,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,5,6,4,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,3,6,1,2,4,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,3,6,1,2,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,6,1,4,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,6,1,4,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,6,1,5,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,6,1,5,4,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,3,6,2,1,4,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,6,2,1,5,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,3,6,2,4,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,6,2,4,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,6,2,5,1,4]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,3,6,2,5,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,3,6,4,1,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,6,4,1,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,6,4,2,1,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,3,6,4,2,5,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,3,6,4,5,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,6,4,5,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,3,6,5,1,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,3,6,5,1,4,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,3,6,5,2,1,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,3,6,5,2,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,3,6,5,4,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,3,6,5,4,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,4,1,2,3,5,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,4,1,2,3,6,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,4,1,2,5,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,4,1,2,5,6,3]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,4,1,2,6,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,4,1,2,6,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,1,3,2,5,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,4,1,3,2,6,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,1,3,5,2,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,4,1,3,5,6,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,4,1,3,6,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,1,3,6,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,1,5,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,4,1,5,2,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,4,1,5,3,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,1,5,3,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,1,5,6,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,4,1,5,6,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,1,6,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,4,1,6,2,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,1,6,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,1,6,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,1,6,5,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,1,6,5,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,2,1,3,5,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,4,2,1,3,6,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,1,5,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,1,5,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,1,6,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,1,6,5,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,4,2,3,1,5,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,4,2,3,1,6,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,3,5,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,4,2,3,5,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,4,2,3,6,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,3,6,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,5,1,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,5,1,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,5,3,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,5,3,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,5,6,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,5,6,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,6,1,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,6,1,5,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,4,2,6,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,6,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,2,6,5,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,4,2,6,5,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,3,1,2,5,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,4,3,1,2,6,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,3,1,5,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,3,1,5,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,3,1,6,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,3,1,6,5,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,4,3,2,1,5,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,4,3,2,1,6,5]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,3,2,5,1,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,4,3,2,5,6,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,4,3,2,6,1,5]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,3,2,6,5,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,3,5,1,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,3,5,1,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,3,5,2,1,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,4,3,5,2,6,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,4,3,5,6,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,3,5,6,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,4,3,6,1,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,3,6,1,5,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,4,3,6,2,1,5]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,3,6,2,5,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,3,6,5,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,4,3,6,5,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,5,1,2,3,6]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,4,5,1,2,6,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,4,5,1,3,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,1,3,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,1,6,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,4,5,1,6,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,2,1,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,2,1,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,2,3,1,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,2,3,6,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,2,6,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,2,6,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,3,1,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,3,1,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,3,2,1,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,4,5,3,2,6,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,4,5,3,6,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,3,6,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,4,5,6,1,2,3]=>[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>100100
[7,4,5,6,1,3,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,6,2,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,6,2,3,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,6,3,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,5,6,3,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,4,6,1,2,3,5]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,4,6,1,2,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,6,1,3,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,6,1,3,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,6,1,5,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,6,1,5,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,6,2,1,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,6,2,1,5,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,4,6,2,3,1,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,6,2,3,5,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,6,2,5,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,4,6,2,5,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,6,3,1,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,6,3,1,5,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,4,6,3,2,1,5]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,6,3,2,5,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,6,3,5,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,4,6,3,5,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,6,5,1,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,4,6,5,1,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,6,5,2,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,6,5,2,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,6,5,3,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,4,6,5,3,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,5,1,2,3,4,6]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,5,1,2,3,6,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,5,1,2,4,3,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,5,1,2,4,6,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,5,1,2,6,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,5,1,2,6,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,1,3,2,4,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,5,1,3,2,6,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,1,3,4,2,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,5,1,3,4,6,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,5,1,3,6,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,1,3,6,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,1,4,2,3,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,5,1,4,2,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,1,4,3,2,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,1,4,3,6,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,1,4,6,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,1,4,6,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,1,6,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,5,1,6,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,1,6,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,1,6,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,1,6,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,1,6,4,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,2,1,3,4,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,5,2,1,3,6,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,2,1,4,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,2,1,4,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,2,1,6,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,2,1,6,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,5,2,3,1,4,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,5,2,3,1,6,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,2,3,4,1,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,5,2,3,4,6,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,5,2,3,6,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,2,3,6,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,2,4,1,3,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,2,4,1,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,2,4,3,1,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,2,4,3,6,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,2,4,6,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,2,4,6,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,2,6,1,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,2,6,1,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,5,2,6,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,2,6,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,2,6,4,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,5,2,6,4,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,3,1,2,4,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,5,3,1,2,6,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,3,1,4,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,3,1,4,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,3,1,6,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,3,1,6,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,5,3,2,1,4,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,3,2,1,6,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,3,2,4,1,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,3,2,4,6,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,3,2,6,1,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,3,2,6,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,3,4,1,2,6]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,3,4,1,6,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,3,4,2,1,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,3,4,2,6,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,3,4,6,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,3,4,6,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,3,6,1,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,3,6,1,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,5,3,6,2,1,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,3,6,2,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,3,6,4,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,5,3,6,4,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,4,1,2,3,6]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,5,4,1,2,6,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,4,1,3,2,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,4,1,3,6,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,4,1,6,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,4,1,6,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,4,2,1,3,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,4,2,1,6,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,4,2,3,1,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,4,2,3,6,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,4,2,6,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,4,2,6,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,4,3,1,2,6]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,5,4,3,1,6,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,4,3,2,1,6]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,5,4,3,2,6,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,5,4,3,6,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,4,3,6,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,5,4,6,1,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,4,6,1,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,4,6,2,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,4,6,2,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,4,6,3,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,4,6,3,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,5,6,1,2,3,4]=>[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>101000
[7,5,6,1,2,4,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,6,1,3,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,6,1,3,4,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,6,1,4,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,6,1,4,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,6,2,1,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,6,2,1,4,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,5,6,2,3,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,6,2,3,4,1]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,6,2,4,1,3]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,5,6,2,4,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,6,3,1,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,6,3,1,4,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,5,6,3,2,1,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,6,3,2,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,6,3,4,1,2]=>[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>101010
[7,5,6,3,4,2,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,6,4,1,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,5,6,4,1,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,6,4,2,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,6,4,2,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,6,4,3,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,5,6,4,3,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,1,2,3,4,5]=>[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>110000
[7,6,1,2,3,5,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,1,2,4,3,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,1,2,4,5,3]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,1,2,5,3,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,1,2,5,4,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,1,3,2,4,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,1,3,2,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,1,3,4,2,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,1,3,4,5,2]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,1,3,5,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,1,3,5,4,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,1,4,2,3,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,1,4,2,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,1,4,3,2,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,1,4,3,5,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,1,4,5,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,1,4,5,3,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,1,5,2,3,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,1,5,2,4,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,1,5,3,2,4]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,1,5,3,4,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,1,5,4,2,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,1,5,4,3,2]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,2,1,3,4,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,2,1,3,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,2,1,4,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,2,1,4,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,2,1,5,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,2,1,5,4,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,2,3,1,4,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,2,3,1,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,2,3,4,1,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,2,3,4,5,1]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,2,3,5,1,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,2,3,5,4,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,2,4,1,3,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,2,4,1,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,2,4,3,1,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,2,4,3,5,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,2,4,5,1,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,2,4,5,3,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,2,5,1,3,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,2,5,1,4,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,2,5,3,1,4]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,2,5,3,4,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,2,5,4,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,2,5,4,3,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,3,1,2,4,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,3,1,2,5,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,3,1,4,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,3,1,4,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,3,1,5,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,3,1,5,4,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,3,2,1,4,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,3,2,1,5,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,3,2,4,1,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,3,2,4,5,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,3,2,5,1,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,3,2,5,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,3,4,1,2,5]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,3,4,1,5,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,3,4,2,1,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,3,4,2,5,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,3,4,5,1,2]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,3,4,5,2,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,3,5,1,2,4]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,3,5,1,4,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,3,5,2,1,4]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,3,5,2,4,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,3,5,4,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,3,5,4,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,4,1,2,3,5]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,4,1,2,5,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,4,1,3,2,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,4,1,3,5,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,4,1,5,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,4,1,5,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,4,2,1,3,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,4,2,1,5,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,4,2,3,1,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,4,2,3,5,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,4,2,5,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,4,2,5,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,4,3,1,2,5]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,4,3,1,5,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,4,3,2,1,5]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,4,3,2,5,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,4,3,5,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,4,3,5,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,4,5,1,2,3]=>[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>110100
[7,6,4,5,1,3,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,4,5,2,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,4,5,2,3,1]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,4,5,3,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,4,5,3,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,5,1,2,3,4]=>[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>111000
[7,6,5,1,2,4,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,5,1,3,2,4]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,5,1,3,4,2]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,5,1,4,2,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,5,1,4,3,2]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,5,2,1,3,4]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,5,2,1,4,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,5,2,3,1,4]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,5,2,3,4,1]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,5,2,4,1,3]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,5,2,4,3,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,5,3,1,2,4]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,5,3,1,4,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,5,3,2,1,4]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,5,3,2,4,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,5,3,4,1,2]=>[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[7,6,5,3,4,2,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,5,4,1,2,3]=>[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[7,6,5,4,1,3,2]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,5,4,2,1,3]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,5,4,2,3,1]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,5,4,3,1,2]=>[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7]]=>111111
[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>1111111
[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,6,7,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[7,6,8,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,7,5,6,4,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[7,8,5,6,4,3,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,6,5,7,4,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,5,6,7,4,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,6,5,8,4,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[6,7,5,8,4,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,5,6,8,4,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,5,7,8,4,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,7,6,4,5,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,6,7,4,5,3,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,5,4,6,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,7,4,5,6,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,5,6,4,7,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,4,5,7,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,4,5,6,7,3,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,6,5,4,8,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[6,7,5,4,8,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,5,6,4,8,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,5,7,4,8,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,6,7,4,8,3,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,6,4,5,8,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,7,4,5,8,3,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,4,6,8,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,4,5,6,8,3,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,5,4,7,8,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,6,4,7,8,3,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,4,5,7,8,3,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,4,6,7,8,3,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,5,6,7,8,3,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,7,6,5,3,4,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[7,8,6,5,3,4,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,6,8,5,3,4,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,5,6,3,4,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,8,5,6,3,4,2,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,6,7,3,4,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,5,8,3,4,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,5,7,8,3,4,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,7,8,3,4,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,6,4,3,5,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[7,8,6,4,3,5,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,6,8,4,3,5,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,7,8,4,3,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,6,3,4,5,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,6,3,4,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,7,3,4,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,8,3,4,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,8,3,4,5,2,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,5,4,3,6,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[7,8,5,4,3,6,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,8,5,3,4,6,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,4,3,5,6,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,7,3,4,5,6,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,3,4,5,6,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,5,4,3,7,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,6,4,3,5,7,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,5,3,4,6,7,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,4,3,5,6,7,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,4,5,6,7,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,6,5,4,3,8,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[6,7,5,4,3,8,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,5,6,4,3,8,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,6,7,4,3,8,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,7,4,5,3,8,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,4,6,3,8,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,4,5,6,3,8,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,4,5,7,3,8,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,4,6,7,3,8,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,5,6,7,3,8,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,6,4,3,5,8,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,5,4,3,6,8,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,5,3,4,6,8,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,3,4,5,6,8,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,5,4,3,7,8,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,5,3,4,7,8,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,3,4,5,7,8,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,4,3,6,7,8,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,3,5,6,7,8,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,4,5,6,7,8,2,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,7,6,5,4,2,3,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[7,8,6,5,4,2,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,6,7,5,4,2,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,6,5,7,4,2,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,5,6,7,4,2,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,6,8,4,2,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,7,8,4,2,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,7,4,5,2,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,6,8,4,5,2,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,7,4,5,6,2,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,4,5,6,2,3,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,6,4,7,2,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,4,5,7,2,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,5,6,7,2,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,6,4,8,2,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,7,4,8,2,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,6,7,8,2,3,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,7,6,5,3,2,4,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[7,8,6,5,3,2,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,6,7,5,3,2,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,7,8,5,3,2,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,5,6,3,2,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,6,5,7,3,2,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,5,6,7,3,2,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,7,8,3,2,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,6,5,2,3,4,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,7,5,2,3,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,8,5,2,3,4,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,5,6,2,3,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,5,6,2,3,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,5,7,2,3,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,6,7,2,3,4,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,5,8,2,3,4,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,7,8,2,3,4,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,7,8,2,3,4,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,6,3,4,2,5,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,6,3,4,2,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,7,3,4,2,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,8,3,4,2,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,8,3,4,2,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,4,2,3,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,8,6,3,2,4,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,7,3,2,4,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,8,3,2,4,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,6,2,3,4,5,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,6,2,3,4,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,7,2,3,4,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,8,2,3,4,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,8,2,3,4,5,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,5,4,3,2,6,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,5,3,4,2,6,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,5,3,4,2,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,5,3,2,4,6,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,4,3,2,5,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,3,4,2,5,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,4,2,3,5,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,3,2,4,5,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,2,3,4,5,6,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,8,2,3,4,5,6,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,6,5,4,3,2,7,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,5,6,3,4,2,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,4,3,5,2,7,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,4,5,3,6,2,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,4,3,5,6,2,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,5,3,2,4,7,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,4,2,3,5,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,2,3,4,5,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,5,4,3,2,6,7,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,5,3,4,2,6,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,4,5,2,6,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,5,4,2,3,6,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,4,3,2,5,6,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,4,2,5,6,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,4,2,3,5,6,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,3,2,4,5,6,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,3,4,5,6,7,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,6,5,4,3,2,8,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[6,7,5,4,3,2,8,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,5,7,4,3,2,8,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,6,4,5,3,2,8,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,7,4,5,3,2,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,5,6,3,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,4,5,7,3,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,5,6,7,3,2,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,5,6,3,4,2,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,7,3,4,2,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,4,3,5,2,8,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,6,3,4,5,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,5,4,3,6,2,8,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,4,5,3,6,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,5,3,4,6,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,5,4,3,7,2,8,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,4,5,3,7,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,4,6,3,7,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,5,6,3,7,2,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,5,3,4,7,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,6,3,4,7,2,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,3,5,7,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,3,4,5,7,2,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,5,3,6,7,2,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,4,5,6,7,2,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,7,5,4,2,3,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,6,4,2,3,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,7,4,2,3,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,7,4,2,3,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,4,5,2,3,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,4,5,2,3,8,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,5,6,2,3,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,4,7,2,3,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,4,7,2,3,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,6,7,2,3,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,6,7,2,3,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,7,5,3,2,4,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,7,3,2,4,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,5,2,3,4,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,5,6,2,3,4,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,2,3,4,8,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,4,3,2,5,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,4,2,3,5,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,6,3,2,4,5,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,7,3,2,4,5,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,2,3,4,5,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,7,2,3,4,5,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,4,3,5,2,6,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,5,4,2,3,6,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,4,5,2,3,6,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,3,2,4,6,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,5,2,3,4,6,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,3,2,4,5,6,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,2,3,4,5,6,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,5,4,3,2,7,8,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,5,6,3,2,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,5,3,4,2,7,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,4,3,6,2,7,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,4,5,6,2,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,4,5,2,3,7,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,6,2,3,7,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,5,2,3,4,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,2,3,4,5,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,4,3,2,6,7,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,5,3,2,6,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,3,5,2,6,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,4,5,2,6,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,4,2,3,6,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,5,2,3,6,7,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,3,4,6,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,3,2,5,6,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,4,2,5,6,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,2,3,5,6,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,2,4,5,6,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,4,5,6,7,8,1]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[8,7,6,5,4,3,1,2]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[7,8,6,5,4,3,1,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,6,7,5,4,3,1,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,6,8,5,4,3,1,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,7,8,5,4,3,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,5,6,4,3,1,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,8,5,6,4,3,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,6,5,8,4,3,1,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,7,5,8,4,3,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,6,8,4,3,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,7,8,4,3,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,7,8,4,3,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,6,4,5,3,1,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,8,6,4,5,3,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,6,7,4,5,3,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,7,8,4,5,3,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,5,4,6,3,1,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,5,6,4,7,3,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,4,5,7,3,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,4,6,7,3,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,5,4,8,3,1,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,5,6,4,8,3,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,7,4,8,3,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,4,5,8,3,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,4,5,8,3,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,4,7,8,3,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,6,7,8,3,1,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,7,6,5,3,4,1,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,8,6,5,3,4,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,6,8,5,3,4,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,7,8,5,3,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,5,6,3,4,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,8,5,6,3,4,1,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[8,6,5,7,3,4,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,6,7,3,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,6,8,3,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,7,8,3,4,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,7,8,4,3,5,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,6,3,4,5,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,7,3,4,5,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,5,4,3,6,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,7,4,5,3,6,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,4,5,3,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,4,3,5,6,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,4,3,5,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,3,4,5,6,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,3,4,5,6,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,5,4,3,6,7,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,3,4,6,7,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,3,5,6,7,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,4,5,6,7,1,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,6,5,4,3,8,1,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,6,7,4,3,8,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,4,5,3,8,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,5,6,7,3,8,1,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,6,5,3,4,8,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,4,3,5,8,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,3,4,5,8,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,4,3,6,8,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,3,4,6,8,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,4,5,6,8,1,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,5,4,3,7,8,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,6,3,7,8,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,3,4,7,8,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,4,3,5,7,8,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,4,5,7,8,1,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,4,3,6,7,8,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,3,6,7,8,1,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,5,6,7,8,1,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,4,5,6,7,8,1,2]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[8,7,6,5,4,2,1,3]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[7,8,6,5,4,2,1,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,6,7,5,4,2,1,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,6,8,5,4,2,1,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,7,8,5,4,2,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,5,6,4,2,1,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,8,5,6,4,2,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,7,5,8,4,2,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,6,8,4,2,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,7,8,4,2,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,7,8,4,2,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,6,4,5,2,1,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,6,8,4,5,2,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,4,5,6,7,2,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,5,4,8,2,1,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,7,5,4,8,2,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,7,4,8,2,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,7,4,8,2,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,4,5,8,2,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,5,6,8,2,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,6,7,8,2,1,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,7,6,5,4,1,2,3]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,6,5,4,1,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,8,5,4,1,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,8,5,4,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,8,5,6,4,1,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,5,7,4,1,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,6,7,4,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,5,8,4,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,6,8,4,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,7,8,4,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,7,8,4,1,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,6,7,4,5,1,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,8,4,5,1,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,7,5,4,6,1,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,5,4,6,1,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,4,5,6,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,6,4,7,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,6,4,5,7,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,5,6,7,1,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,6,5,4,8,1,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,5,4,8,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,7,4,8,1,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,4,5,8,1,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,5,4,6,8,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,4,7,8,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,4,7,8,1,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,6,7,8,1,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,6,7,8,1,2,3]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[8,7,6,5,3,2,1,4]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,6,7,5,3,2,1,4]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,7,8,5,3,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,5,6,3,2,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,6,7,3,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,5,8,3,2,1,4]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,7,5,8,3,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,6,8,3,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,7,8,3,2,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,6,5,2,3,1,4]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,6,5,2,3,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,7,5,2,3,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,8,5,2,3,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,5,6,2,3,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,5,6,2,3,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,6,7,2,3,1,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,6,5,8,2,3,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,6,8,2,3,1,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,7,8,2,3,1,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,6,5,3,1,2,4]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,6,5,3,1,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,7,5,3,1,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,8,5,3,1,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,5,6,3,1,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,5,8,3,1,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,7,8,3,1,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,7,8,3,1,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,6,5,2,1,3,4]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,6,5,2,1,3,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,8,5,2,1,3,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,8,5,2,1,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,5,6,2,1,3,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,5,7,2,1,3,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,6,7,2,1,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,6,5,8,2,1,3,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,5,8,2,1,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,6,8,2,1,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,7,8,2,1,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,7,8,2,1,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,6,5,1,2,3,4]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,6,5,1,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,7,5,1,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,8,5,1,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,8,5,1,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,5,6,1,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,5,6,1,2,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,6,5,7,1,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,6,7,1,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,6,5,8,1,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,5,8,1,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,5,6,8,1,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,5,7,8,1,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,7,8,1,2,3,4]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[8,7,6,4,3,2,1,5]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[7,8,6,4,3,2,1,5]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,6,7,4,3,2,1,5]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,6,8,4,3,2,1,5]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,7,8,4,3,2,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,6,3,4,2,1,5]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,6,3,4,2,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,8,3,4,2,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,6,4,2,3,1,5]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,7,8,4,2,3,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,6,3,2,4,1,5]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,7,3,2,4,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,8,3,2,4,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,6,2,3,4,1,5]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,7,2,3,4,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,8,2,3,4,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,8,2,3,4,1,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,6,4,3,1,2,5]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,7,8,4,3,1,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,6,3,4,1,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,6,3,4,1,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,7,3,4,1,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,8,3,4,1,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,7,6,4,2,1,3,5]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,6,4,2,1,3,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,7,4,2,1,3,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,8,4,2,1,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,6,4,1,2,3,5]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,6,4,1,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,8,4,1,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,8,4,1,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,6,3,2,1,4,5]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,7,3,2,1,4,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,8,3,2,1,4,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,6,2,3,1,4,5]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,6,2,3,1,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,7,2,3,1,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,8,2,3,1,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,6,3,1,2,4,5]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,6,3,1,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,7,3,1,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,8,3,1,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,8,3,1,2,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,6,2,1,3,4,5]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,7,2,1,3,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,8,2,1,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,6,1,2,3,4,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,8,6,1,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,6,7,1,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,6,8,1,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,7,8,1,2,3,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[8,7,5,4,3,2,1,6]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[7,8,5,4,3,2,1,6]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,8,4,5,3,2,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,5,3,4,2,1,6]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,3,4,5,2,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,4,5,2,3,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,4,5,2,3,1,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,5,3,2,4,1,6]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,5,2,3,4,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,4,3,2,5,1,6]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,4,3,2,5,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,3,4,2,5,1,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,3,4,2,5,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,2,3,4,5,1,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,8,2,3,4,5,1,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,7,5,4,3,1,2,6]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,5,4,3,1,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,5,3,4,1,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,3,4,5,1,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,3,4,5,1,2,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,5,4,2,1,3,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,5,4,1,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,4,5,1,2,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,7,5,3,2,1,4,6]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,5,3,2,1,4,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,5,3,1,2,4,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,5,3,1,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,5,2,1,3,4,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,5,2,1,3,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,5,1,2,3,4,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,8,5,1,2,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,8,4,3,2,1,5,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,3,4,2,1,5,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,3,4,2,1,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,4,2,3,1,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,3,2,4,1,5,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,3,2,4,1,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,2,3,4,1,5,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,8,2,3,4,1,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,8,4,3,1,2,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,3,4,1,2,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,3,4,1,2,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,7,4,2,1,3,5,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,4,2,1,3,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,4,1,2,3,5,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,7,3,2,1,4,5,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,3,2,1,4,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,2,3,1,4,5,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,8,2,3,1,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,7,2,1,3,4,5,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,8,2,1,3,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,7,1,2,3,4,5,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,8,1,2,3,4,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[8,6,5,4,3,2,1,7]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,5,6,4,3,2,1,7]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,4,5,3,2,1,7]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,4,5,6,3,2,1,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,5,3,4,2,1,7]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,5,6,3,4,2,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,5,3,6,2,1,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,4,3,5,6,2,1,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,4,5,6,2,1,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,6,5,4,2,3,1,7]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,5,6,4,2,3,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,5,6,2,3,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,5,3,2,4,1,7]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,5,2,3,4,1,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,5,6,2,3,4,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,4,2,3,5,1,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,3,2,4,5,1,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,4,3,5,2,6,1,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,5,4,2,3,6,1,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,4,5,2,3,6,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,3,2,4,6,1,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,5,2,3,4,6,1,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,3,2,4,5,6,1,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,3,4,5,6,1,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,6,5,4,3,1,2,7]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,4,5,3,1,2,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,5,3,4,1,2,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,6,3,4,1,2,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,4,3,6,1,2,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,3,4,6,1,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,3,5,6,1,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,4,5,6,1,2,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,6,5,4,2,1,3,7]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,5,6,4,2,1,3,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,5,6,2,1,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,6,4,1,2,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,4,5,1,2,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,5,6,1,2,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,6,5,3,2,1,4,7]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,5,6,3,2,1,4,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,5,2,3,1,4,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,5,6,2,3,1,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,6,3,1,2,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,5,2,1,3,4,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,5,6,2,1,3,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,5,1,2,3,4,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,5,6,1,2,3,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,6,4,3,2,1,5,7]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,3,4,2,1,5,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,4,2,3,1,5,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,3,2,4,1,5,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,2,3,4,1,5,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,6,4,3,1,2,5,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,3,4,1,2,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,4,2,1,3,5,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,4,1,2,3,5,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,6,3,2,1,4,5,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,1,2,3,4,5,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,5,4,3,2,1,6,7]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,4,5,3,2,1,6,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,4,3,5,2,1,6,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,4,5,2,1,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,4,5,2,3,1,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,2,3,4,1,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,4,2,3,5,1,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,3,4,5,1,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,5,3,4,1,2,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,4,5,1,2,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,5,4,2,1,3,6,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,5,4,1,2,3,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,4,5,1,2,3,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,5,3,2,1,4,6,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,5,3,1,2,4,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,5,1,2,3,4,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,4,3,2,1,5,6,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,4,2,1,5,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,4,2,3,1,5,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,3,4,1,5,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,3,4,1,2,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,4,2,1,3,5,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,4,1,2,3,5,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,3,2,1,4,5,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,3,1,4,5,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,3,1,2,4,5,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,2,1,3,4,5,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,1,2,3,4,5,6,7]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[7,6,5,4,3,2,1,8]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[6,7,5,4,3,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,5,6,4,3,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,5,7,4,3,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,6,7,4,3,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,6,4,5,3,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,7,4,5,3,2,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,4,6,3,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,4,5,6,3,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,5,4,7,3,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,6,4,7,3,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,5,6,7,3,2,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,6,5,3,4,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,7,5,3,4,2,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,6,3,4,2,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,7,3,4,2,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,7,3,4,2,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,4,3,5,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,7,4,3,5,2,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,3,4,5,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,5,4,3,6,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,5,4,3,7,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,6,4,3,7,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,4,6,3,7,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,4,3,6,7,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,4,5,6,7,2,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,7,5,4,2,3,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,6,4,2,3,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,7,4,2,3,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,4,5,2,3,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,4,5,2,3,1,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,4,6,2,3,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,4,7,2,3,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,4,7,2,3,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,6,7,2,3,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,6,7,2,3,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,6,5,3,2,4,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,5,7,3,2,4,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,7,3,2,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,5,2,3,4,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,7,5,2,3,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,6,2,3,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,7,2,3,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,2,3,4,1,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,4,3,2,5,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,4,2,3,5,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,7,4,2,3,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,3,2,4,5,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,7,3,2,4,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,4,3,2,6,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,4,5,3,2,6,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,4,3,5,2,6,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,5,3,2,4,6,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,4,2,3,5,6,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,2,3,4,5,6,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,5,4,3,2,7,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,3,4,5,2,7,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,5,3,6,2,7,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,3,4,6,2,7,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,3,5,6,2,7,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,4,5,6,2,7,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,4,6,2,3,7,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,3,2,4,7,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,4,2,3,5,7,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,4,3,2,6,7,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,5,2,3,6,7,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,3,4,6,7,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,3,2,5,6,7,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,4,2,5,6,7,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,2,3,5,6,7,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,2,4,5,6,7,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,4,5,6,7,1,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[7,6,5,4,3,1,2,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,7,5,4,3,1,2,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,6,4,3,1,2,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,4,5,3,1,2,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,6,7,3,1,2,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,6,7,3,1,2,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,6,5,3,4,1,2,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,4,3,7,1,2,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,4,5,7,1,2,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,5,6,7,1,2,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,4,5,6,7,1,2,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[7,6,5,4,2,1,3,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,5,7,4,2,1,3,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,4,5,2,1,3,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,6,7,2,1,3,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,6,7,2,1,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,6,5,4,1,2,3,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,6,7,4,1,2,3,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,5,6,1,2,3,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,6,7,1,2,3,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,6,7,1,2,3,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[7,6,5,3,2,1,4,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,6,5,2,3,1,4,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,7,5,2,3,1,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,6,2,3,1,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,7,2,3,1,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,2,3,1,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,6,5,2,1,3,4,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,5,6,2,1,3,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,2,1,3,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,6,5,1,2,3,4,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,7,5,1,2,3,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,5,6,1,2,3,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,5,7,1,2,3,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,6,7,1,2,3,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[7,6,4,3,2,1,5,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,7,4,3,2,1,5,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,3,4,2,1,5,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,7,3,4,2,1,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,4,2,3,1,5,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,6,3,2,4,1,5,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,6,2,3,4,1,5,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,7,2,3,4,1,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,6,4,3,1,2,5,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,6,4,2,1,3,5,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,6,3,2,1,4,5,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,7,3,2,1,4,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,2,3,1,4,5,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,7,2,3,1,4,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,7,3,1,2,4,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,7,1,2,3,4,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[7,5,4,3,2,1,6,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,4,5,3,2,1,6,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,4,3,5,2,1,6,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,3,4,5,2,1,6,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,5,4,2,3,1,6,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,5,3,2,4,1,6,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,5,2,3,4,1,6,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,4,2,3,5,1,6,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,2,3,4,5,1,6,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,4,5,1,2,3,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,5,3,2,1,4,6,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,5,2,3,1,4,6,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,5,3,1,2,4,6,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,5,1,2,3,4,6,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,2,3,4,1,5,6,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,4,3,1,2,5,6,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,3,4,1,2,5,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,2,1,4,5,6,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,3,1,2,4,5,6,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,2,1,3,4,5,6,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,1,2,3,4,5,6,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[6,5,4,3,2,1,7,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,6,4,3,2,1,7,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,4,6,3,2,1,7,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,5,6,3,2,1,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,6,3,4,2,1,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,6,2,3,1,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,3,2,4,1,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,2,3,4,1,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,6,2,3,4,1,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,4,3,2,5,1,7,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,2,3,4,5,1,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,4,3,2,6,1,7,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,3,5,2,6,1,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,4,5,2,6,1,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,2,3,4,6,1,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,3,2,5,6,1,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,2,3,5,6,1,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,2,4,5,6,1,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,4,5,6,1,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[6,5,4,3,1,2,7,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,4,5,6,1,2,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[6,5,4,2,1,3,7,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,4,5,2,1,3,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,6,1,2,3,7,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,4,3,2,1,5,7,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,3,4,2,1,5,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,4,3,1,2,5,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,4,2,1,3,5,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,4,1,2,3,5,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,2,3,1,4,5,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,3,1,2,4,5,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,1,2,3,4,5,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[5,4,3,2,1,6,7,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,5,3,2,1,6,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,3,4,2,1,6,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,3,5,2,1,6,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,4,5,2,1,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,4,2,3,1,6,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,5,2,3,1,6,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,3,2,4,1,6,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,2,3,4,1,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,3,2,5,1,6,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,4,2,5,1,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,2,3,5,1,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,2,4,5,1,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,4,5,1,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[3,4,5,1,2,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,5,1,2,3,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,3,2,1,4,6,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,2,3,1,4,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,3,1,2,4,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,1,2,3,4,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[4,3,2,1,5,6,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,4,2,1,5,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,2,3,1,5,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,2,4,1,5,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,4,1,5,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[4,3,1,2,5,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,4,1,2,5,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,2,1,3,5,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,1,2,3,5,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[3,2,1,4,5,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,1,4,5,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[3,1,2,4,5,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[2,1,3,4,5,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,2,3,4,5,6,7,8]=>[8]=>[[1,2,3,4,5,6,7,8]]=>0000000
[6,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[5,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[5,7,8,6,4,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,5,8,7,4,3,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,6,8,7,4,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,7,6,8,4,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[4,7,8,6,5,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,6,8,7,5,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,7,6,8,5,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,5,8,7,6,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,5,6,8,7,3,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,7,6,4,8,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,7,6,5,8,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,6,7,5,8,3,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,4,7,6,8,3,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,7,6,8,3,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,6,5,7,8,3,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[3,7,8,6,5,4,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[3,6,8,7,5,4,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[3,5,8,7,6,4,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[3,5,7,8,6,4,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,5,6,8,7,4,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,7,6,5,8,4,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[3,5,7,6,8,4,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,5,6,7,8,4,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,3,8,7,6,5,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[3,4,6,7,8,5,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,4,3,8,7,6,2,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,4,3,7,8,6,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,4,7,8,6,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,5,7,8,6,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,5,4,3,8,7,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,6,4,3,8,7,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,3,6,5,8,7,2,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,3,6,8,7,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,3,6,8,7,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,5,6,8,7,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,7,6,4,3,8,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,4,7,6,3,8,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,7,6,5,4,8,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[3,5,7,6,4,8,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,5,6,7,4,8,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,3,7,6,5,8,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,4,7,6,5,8,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,4,6,7,5,8,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,5,4,7,6,8,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,5,7,6,8,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,5,6,4,7,8,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,3,6,5,7,8,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,6,5,7,8,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,5,4,6,7,8,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[2,7,8,6,5,4,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,6,8,7,5,4,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,7,6,8,5,4,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,6,7,8,5,4,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,5,8,7,6,4,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,6,7,5,8,4,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,5,6,7,8,4,3,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,8,7,6,5,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,4,7,8,6,5,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,4,6,8,7,5,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,4,6,7,8,5,3,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,5,4,8,7,6,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,5,4,7,8,6,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,5,7,8,6,3,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,6,5,4,8,7,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,5,6,4,8,7,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,6,5,8,7,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,5,6,8,7,3,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,7,6,5,4,8,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,5,6,7,4,8,3,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,6,7,5,8,3,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,5,4,7,6,8,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,5,4,7,8,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,5,6,4,7,8,3,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,6,5,7,8,3,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,5,4,6,7,8,3,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,5,6,7,8,3,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,2,8,7,6,5,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[3,2,6,8,7,5,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,2,5,7,8,6,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,5,7,6,8,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,5,6,7,8,4,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,8,7,6,5,4,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,3,6,7,8,5,4,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,5,7,8,6,4,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,6,5,8,7,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,5,6,8,7,4,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,7,6,5,8,4,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,3,5,7,6,8,4,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,5,6,7,8,4,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,3,2,8,7,6,5,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,3,2,7,8,6,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,4,2,8,7,6,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,4,2,7,8,6,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,3,8,7,6,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,4,3,6,8,7,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,3,6,7,8,5,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,8,7,6,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,3,4,8,7,6,5,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,3,4,6,8,7,5,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,4,7,6,8,5,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,4,6,7,8,5,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,4,3,2,8,7,6,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,4,3,2,7,8,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,4,2,7,8,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,5,2,7,8,6,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,5,4,3,8,7,6,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,4,3,7,8,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,5,3,7,8,6,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,5,4,7,8,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,5,4,7,8,6,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,2,5,8,7,6,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,2,5,7,8,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,2,5,8,7,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,2,5,7,8,6,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,5,7,8,6,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,5,8,7,6,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,4,5,7,8,6,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,5,4,3,2,8,7,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[4,6,5,3,2,8,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,6,3,2,8,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,6,4,2,8,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,6,5,2,8,7,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,3,6,2,8,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,3,6,2,8,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,5,4,3,8,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,4,6,5,3,8,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,5,6,3,8,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,6,5,4,8,7,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,3,5,6,4,8,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,2,6,5,8,7,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,4,3,6,5,8,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,4,6,5,8,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,4,6,5,8,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,4,3,2,6,8,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,4,5,3,6,8,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,5,4,6,8,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,2,5,6,8,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,2,5,6,8,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,3,5,6,8,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,5,6,8,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,5,6,8,7,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,7,6,4,3,2,8,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,7,6,5,3,2,8,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,6,7,5,3,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,6,5,7,3,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,5,7,6,4,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,5,6,7,4,2,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,3,7,6,5,2,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,4,7,6,5,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,4,6,7,5,2,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,4,3,7,6,2,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,4,7,6,2,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,5,7,6,2,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,6,5,3,7,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,6,5,4,7,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,5,6,4,7,2,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,3,6,5,7,2,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,6,5,7,2,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,5,4,6,7,2,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,7,6,5,4,3,8,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,6,5,7,4,3,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,5,6,7,4,3,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,6,7,5,3,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,6,5,7,3,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,5,4,6,7,3,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,5,6,7,3,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,2,7,6,5,4,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,2,6,7,5,4,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,5,7,6,4,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,6,5,7,4,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,5,6,7,4,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,7,6,5,4,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,3,5,7,6,4,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,5,6,7,4,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,3,2,7,6,5,8,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,4,2,6,7,5,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,3,6,7,5,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,7,6,5,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,4,6,7,5,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,4,3,2,7,6,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,4,2,7,6,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,5,2,7,6,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,5,2,7,6,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,5,4,7,6,8,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,5,4,7,6,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,2,5,7,6,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,2,5,7,6,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,5,7,6,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,5,7,6,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,5,6,4,2,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,4,6,5,2,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,5,4,6,2,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,6,5,4,3,7,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,5,6,4,3,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,6,5,3,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,5,6,3,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,2,5,6,4,7,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,6,5,4,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,5,6,4,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,4,2,6,5,7,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,3,6,5,7,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,6,5,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,5,4,2,6,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,5,3,6,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,2,5,4,6,7,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,5,4,6,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,4,3,5,6,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[1,7,8,6,5,4,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,6,8,7,5,4,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,7,6,8,5,4,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,6,7,8,5,4,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,5,8,7,6,4,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,6,5,8,7,4,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,7,6,5,8,4,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,6,7,5,8,4,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,5,7,6,8,4,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,5,6,7,8,4,3,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,4,8,7,6,5,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,4,7,8,6,5,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,4,6,8,7,5,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,4,6,7,8,5,3,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,5,4,7,8,6,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,5,8,7,6,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,4,6,5,8,7,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,6,5,4,8,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,4,7,6,5,8,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,4,6,7,5,8,3,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,6,5,4,7,8,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,4,5,6,7,8,3,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,8,7,6,5,4,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,3,7,8,6,5,4,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,3,6,8,7,5,4,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,3,6,7,8,5,4,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,5,8,7,6,4,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,3,5,7,8,6,4,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,5,6,8,7,4,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,6,7,5,8,4,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,6,5,7,8,4,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,5,6,7,8,4,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,4,3,8,7,6,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,4,3,7,8,6,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,3,6,8,7,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,3,6,7,8,5,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,8,7,6,5,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,3,4,7,6,8,5,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,4,6,7,8,5,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,5,4,3,8,7,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,4,5,3,8,7,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,5,3,7,8,6,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,3,5,7,8,6,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,5,8,7,6,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,4,5,7,8,6,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,6,5,4,3,8,7,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,5,6,4,3,8,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,6,5,3,8,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,5,6,3,8,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,3,6,5,8,7,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,4,3,6,8,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,5,3,6,8,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,5,6,8,7,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,7,6,5,4,3,8,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,6,7,5,4,3,8,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,6,5,7,4,3,8,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,4,6,7,5,3,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,5,6,4,7,3,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,4,6,5,7,3,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,5,4,6,7,3,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,4,5,6,7,3,8,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,6,5,7,4,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,5,6,7,4,8,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,4,6,7,5,8,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,5,4,7,6,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,5,7,6,8,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,5,4,6,3,7,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,4,3,6,5,7,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,6,5,7,8,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,5,4,3,6,7,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,4,5,3,6,7,8,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,4,3,5,6,7,8,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,4,5,6,7,8,2]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[2,1,8,7,6,5,4,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[2,1,7,8,6,5,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,6,8,7,5,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,7,6,8,5,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,6,7,8,5,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,5,8,7,6,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,5,7,8,6,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,6,5,8,7,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,5,6,8,7,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,7,6,5,8,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,6,7,5,8,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,5,7,6,8,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,6,5,7,8,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,5,6,7,8,4,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,4,8,7,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,4,7,8,6,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,4,6,8,7,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,4,6,7,8,5,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,5,4,8,7,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,5,4,7,8,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,5,8,7,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,4,5,7,8,6,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,6,5,4,8,7,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,5,6,4,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,6,5,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,5,4,6,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,5,6,8,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,7,6,5,4,8,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,6,7,5,4,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,5,7,6,4,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,6,5,7,4,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,5,6,7,4,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,4,7,6,5,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,4,6,7,5,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,5,4,7,6,8,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,5,6,4,7,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,5,4,6,7,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,4,5,6,7,8,3]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,2,7,8,6,5,4,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,2,6,7,8,5,4,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,6,5,8,7,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,5,6,8,7,4,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,7,6,5,8,4,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,2,5,7,6,8,4,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,6,5,7,8,4,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,5,6,7,8,4,3]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,4,8,7,6,5,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,2,4,6,8,7,5,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,4,6,7,8,5,3]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,5,4,8,7,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,4,5,8,7,6,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,4,5,7,8,6,3]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,5,4,6,8,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,4,5,6,8,7,3]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,7,6,5,4,8,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,2,5,7,6,4,8,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,5,6,7,4,8,3]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,4,7,6,5,8,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,5,4,7,6,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,6,5,4,7,8,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,5,4,6,7,8,3]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,4,5,6,7,8,3]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[3,2,1,8,7,6,5,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[3,2,1,7,8,6,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,1,6,8,7,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,1,7,6,8,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,1,6,7,8,5,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,5,8,7,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,1,5,7,8,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,6,5,8,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,1,5,6,8,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,7,6,5,8,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,1,6,7,5,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,5,7,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,6,5,7,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,5,6,7,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,8,7,6,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,3,1,6,8,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,1,7,6,8,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,1,6,7,8,5,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,5,7,8,6,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,6,5,8,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,1,7,6,5,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,1,6,7,5,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,5,7,6,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,5,6,7,8,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,8,7,6,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,3,2,6,8,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,2,7,6,8,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,2,6,7,8,5,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,5,8,7,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,2,5,7,8,6,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,6,5,8,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,2,5,6,8,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,7,6,5,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,2,6,7,5,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,6,5,7,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,5,6,7,8,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,3,8,7,6,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,3,7,8,6,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,3,6,8,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,3,6,5,8,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,3,5,6,7,8,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,8,7,6,5,4]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,2,3,7,8,6,5,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,3,6,8,7,5,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,3,7,6,8,5,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,3,6,7,8,5,4]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,5,8,7,6,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,3,5,7,8,6,4]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,6,5,8,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,5,6,8,7,4]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,7,6,5,8,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,3,6,7,5,8,4]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,5,7,6,8,4]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,6,5,7,8,4]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,5,6,7,8,4]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[4,3,2,1,8,7,6,5]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[4,3,2,1,7,8,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,2,1,6,8,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,2,1,7,6,8,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,2,1,6,7,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,2,1,8,7,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,4,2,1,7,8,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,4,2,1,6,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,4,2,1,7,6,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,4,2,1,6,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,3,1,8,7,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,4,3,1,7,8,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,3,1,6,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,3,1,7,6,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,3,1,6,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,1,8,7,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,4,1,7,8,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,4,1,6,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,4,1,7,6,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,4,1,6,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,1,8,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,4,1,7,8,6,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,1,6,8,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,1,7,6,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,1,6,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,3,2,8,7,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,4,3,2,6,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,4,3,2,7,6,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,4,3,2,6,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,2,8,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,4,2,7,8,6,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,2,6,8,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,2,7,6,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,2,6,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,4,3,8,7,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,4,3,7,8,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,3,6,8,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,3,7,6,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,3,6,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,4,3,8,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,4,3,7,8,6,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,4,3,7,6,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,4,3,6,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,2,1,4,8,7,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,1,4,7,8,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,4,6,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,4,7,6,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,4,6,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,4,8,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,1,4,7,8,6,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,4,7,6,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,4,6,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,4,8,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,2,4,6,8,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,4,7,6,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,4,6,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,3,4,8,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,3,4,7,8,6,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,3,4,7,6,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,3,4,6,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,4,8,7,6,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,3,4,7,8,6,5]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,4,6,8,7,5]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,4,7,6,8,5]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,4,6,7,8,5]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[5,4,3,2,1,8,7,6]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,4,3,2,1,7,8,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,3,2,1,8,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,4,2,1,8,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,4,2,1,7,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,5,2,1,8,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,4,5,2,1,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,5,4,3,1,8,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,4,5,3,1,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,5,3,1,7,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,5,4,1,8,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,5,4,1,7,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,5,4,1,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,2,5,1,8,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,2,5,1,7,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,2,5,1,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,4,2,5,1,7,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,3,5,1,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,3,5,1,7,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,5,1,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,3,4,5,1,8,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,5,1,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,4,3,2,8,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,5,4,3,2,7,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,5,3,2,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,4,5,3,2,7,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,5,4,2,7,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,5,2,8,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,5,2,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,4,5,3,8,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,5,4,3,7,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,4,5,3,8,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,4,5,3,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,5,4,8,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,2,5,4,7,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,3,5,4,8,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,3,5,4,7,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,3,5,4,8,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,5,4,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,3,2,1,5,7,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,3,1,5,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,4,1,5,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,4,1,5,7,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,1,5,8,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,1,5,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,3,2,5,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,4,3,2,5,7,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,2,5,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,4,3,5,8,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,3,5,7,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,4,3,5,8,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,4,3,5,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,2,1,4,5,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,4,5,7,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,4,5,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,4,5,8,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,4,5,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,3,4,5,8,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,3,4,5,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,4,5,8,7,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,4,5,7,8,6]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[6,5,4,3,2,1,8,7]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,6,4,3,2,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,6,5,3,2,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,6,3,2,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,6,3,2,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,5,4,2,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,6,4,2,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,6,5,2,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,4,6,5,2,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,3,6,2,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,3,6,2,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,5,6,2,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,5,4,3,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,5,6,4,3,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,6,5,3,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,6,5,4,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,2,5,6,4,1,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,6,5,4,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,5,6,4,1,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,2,6,5,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,4,2,6,5,1,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,3,6,5,1,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,3,2,6,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,3,5,2,6,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,5,2,6,1,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,5,4,3,6,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,5,3,6,1,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,5,4,6,1,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,2,5,6,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,2,5,6,1,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,3,5,6,1,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,5,6,1,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,6,5,4,3,2,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,5,4,6,3,2,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,6,5,4,2,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,4,5,6,2,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,6,5,4,3,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,5,6,4,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,6,5,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,5,4,6,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,5,6,3,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,4,5,6,3,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,1,6,5,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,2,6,5,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,2,5,6,4,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,3,5,6,4,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,3,6,5,4,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,5,6,4,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,3,2,1,6,5,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,4,2,1,6,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,3,1,6,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,4,1,6,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,4,1,6,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,4,2,6,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,4,3,6,5,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[1,2,4,3,6,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,1,4,6,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,4,6,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,3,4,6,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,3,4,6,5,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,4,3,2,1,6,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,3,2,1,6,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,4,2,1,6,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,5,2,1,6,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,5,2,1,6,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,5,4,3,1,6,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,5,3,1,6,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,5,4,1,6,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,5,4,1,6,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,5,1,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,5,3,2,6,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,5,4,2,6,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,4,5,3,6,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,5,4,3,6,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,5,4,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,2,4,1,5,6,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,1,5,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,3,2,5,6,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,2,5,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,3,5,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,2,1,4,5,6,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,4,5,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,4,5,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,3,4,5,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,4,5,6,8,7]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[5,7,6,4,3,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,7,6,5,3,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,4,7,6,3,2,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,7,6,3,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,6,5,7,3,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,5,7,6,4,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,5,6,7,4,2,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,3,7,6,5,2,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,4,7,6,5,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,4,3,7,6,2,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,4,7,6,2,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,5,4,7,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,5,6,4,7,2,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,3,6,5,7,2,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,6,5,4,3,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,6,7,5,4,3,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,5,7,6,4,3,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,5,6,7,4,3,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,6,7,5,3,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,5,6,4,7,3,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,5,4,6,7,3,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,5,6,7,3,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,2,7,6,5,4,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,2,6,7,5,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,5,7,6,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,6,5,7,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,5,6,7,4,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,7,6,5,4,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,3,6,7,5,4,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,5,7,6,4,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,6,5,7,4,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,5,6,7,4,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,3,2,6,7,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,2,6,7,5,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,6,7,5,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,7,6,5,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,4,6,7,5,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,4,3,2,7,6,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,3,2,7,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,4,2,7,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,5,2,7,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,5,2,7,6,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,5,4,7,6,1,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,2,5,7,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,2,5,7,6,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,5,7,6,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,5,6,4,2,7,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,5,4,6,2,7,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,5,4,6,3,7,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,2,6,5,4,7,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,5,6,4,7,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,4,3,6,5,7,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,6,5,7,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,5,4,6,7,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,7,6,5,4,3,2,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,6,7,5,4,3,2,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,6,5,7,4,3,2,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,5,6,7,4,3,2,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,4,7,6,5,3,2,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,4,6,7,5,3,2,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,5,6,4,7,3,2,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,5,4,6,7,3,2,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,6,7,5,4,2,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,5,7,6,4,2,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,6,5,7,4,2,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,5,6,7,4,2,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,4,6,7,5,2,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,5,4,7,6,2,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,3,5,7,6,2,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,5,7,6,2,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,5,4,6,3,7,2,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,6,5,4,7,2,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,5,4,3,6,7,2,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,4,5,3,6,7,2,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,4,5,6,7,2,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[2,1,7,6,5,4,3,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,5,6,7,4,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,4,5,6,7,3,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,7,6,5,4,3,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,2,6,7,5,4,3,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,5,7,6,4,3,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,5,6,7,4,3,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,4,6,7,5,3,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,5,6,4,7,3,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,5,4,6,7,3,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,4,5,6,7,3,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[3,2,1,7,6,5,4,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,1,5,7,6,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,3,1,6,7,5,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,5,6,7,4,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,7,6,5,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,2,6,7,5,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,5,7,6,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,5,6,7,4,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,3,6,7,5,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,7,6,5,4,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,3,6,7,5,4,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,5,7,6,4,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,6,5,7,4,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,5,6,7,4,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[3,2,4,1,7,6,5,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,4,1,6,7,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,1,7,6,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,1,6,7,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,3,2,7,6,5,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,4,3,2,6,7,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,2,6,7,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,3,6,7,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,2,1,4,7,6,5,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,3,1,4,6,7,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,4,7,6,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,4,7,6,5,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,4,6,7,5,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[5,4,3,2,1,7,6,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,3,2,1,7,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,4,2,1,7,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,5,2,1,7,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,5,3,1,7,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,5,4,1,7,6,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,4,5,1,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,4,3,2,7,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,5,3,2,7,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,5,4,2,7,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,5,2,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,5,4,3,7,6,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,4,5,3,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,2,1,5,4,7,6,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,1,5,4,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,5,4,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,3,5,4,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,2,4,1,5,7,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,1,5,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,3,2,5,7,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,2,5,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,3,5,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,1,4,5,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,4,5,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,3,4,5,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,4,5,7,6,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[3,6,5,4,2,1,7,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,3,6,5,2,1,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,6,5,3,1,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,5,6,3,1,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,5,6,4,1,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,3,2,6,5,1,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,3,6,5,1,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,5,4,3,2,7,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,5,6,4,3,2,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,4,6,5,3,2,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,5,4,6,3,2,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,4,5,6,3,2,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,5,6,4,2,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,4,3,6,5,2,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,4,3,6,2,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,4,5,3,6,2,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,4,3,5,6,2,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,4,5,6,2,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[2,1,5,6,4,3,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,4,6,5,3,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,6,5,4,3,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,4,6,5,3,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,4,5,6,3,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[3,2,1,5,6,4,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,6,5,4,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,5,6,4,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,6,5,4,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,5,6,4,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,6,5,4,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,5,6,4,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[2,4,3,1,6,5,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,1,6,5,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,1,6,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,4,3,6,5,7,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,4,3,6,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,4,6,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,3,4,6,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,4,6,5,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[3,5,4,2,1,6,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,5,4,3,1,6,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,4,5,3,1,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,2,5,4,1,6,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,5,4,1,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,4,3,5,1,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,5,4,3,2,6,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,4,5,3,2,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,4,5,2,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[2,1,5,4,3,6,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,4,5,3,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,4,3,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,1,5,4,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,5,4,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,5,4,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[2,4,3,1,5,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,4,3,2,5,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,4,2,5,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[2,1,4,3,5,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,3,5,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,3,2,4,5,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,2,3,4,8,6,7,5]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,5,8,6,7,4]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,7,5,6,4,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,7,5,6,8,4]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,8,5,6,7,4]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,8,5,7,6,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,3,8,6,5,7,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,3,8,6,7,5,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,4,5,8,6,7,3]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,4,7,5,6,8,3]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,4,8,5,6,7,3]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,4,8,6,5,7,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,6,4,5,7,8,3]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,7,4,5,6,8,3]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,8,4,5,6,7,3]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,8,4,6,7,5,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,8,4,7,6,5,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,2,8,5,4,6,7,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,8,5,6,4,7,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,8,5,6,7,4,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,8,6,5,4,7,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,2,8,7,5,6,4,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,3,2,7,5,6,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,8,5,7,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,2,8,6,5,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,2,8,6,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,4,2,8,6,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,4,5,8,6,7,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,4,8,5,6,7,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,6,4,5,2,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,6,4,5,7,8,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,7,4,5,6,2,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,7,4,5,6,8,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,8,4,5,6,7,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,8,4,6,5,7,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,8,5,4,6,7,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,8,5,4,7,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,8,5,6,7,4,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,8,5,7,6,4,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,3,8,6,5,7,4,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,3,8,7,5,6,4,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,4,3,5,8,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,3,8,5,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,3,8,5,7,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,3,8,6,5,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,3,8,6,7,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,3,4,2,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,5,3,4,2,7,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,3,4,2,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,3,4,6,2,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,3,4,6,7,2,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,5,3,4,6,7,8,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,6,3,4,5,8,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,3,4,5,6,8,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,8,3,4,5,6,7,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,8,3,4,6,7,5,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,6,3,5,4,2,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,6,3,5,4,8,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,3,5,4,6,2,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,8,3,5,4,7,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,3,5,6,4,7,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,8,3,5,6,7,4,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,8,3,5,7,6,4,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,7,3,6,5,4,8,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,3,6,5,4,7,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,3,7,5,6,4,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,3,7,6,5,4,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,6,4,3,5,2,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,6,4,3,5,8,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,4,3,5,6,7,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,8,4,3,5,7,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,4,3,6,5,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,4,3,6,5,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,4,3,6,7,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,4,5,3,2,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,6,4,5,3,2,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,4,5,3,8,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,4,5,3,6,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,8,4,5,3,6,7,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,7,4,5,6,3,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,8,4,5,6,7,3,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,7,4,6,5,3,2,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,4,6,5,3,7,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,4,6,5,7,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,4,7,6,5,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,8,5,4,3,6,7,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,5,4,3,7,6,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,5,4,6,3,7,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,5,4,6,7,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,5,4,7,6,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,7,6,4,5,3,2,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,6,4,5,7,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,7,4,5,6,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,7,4,6,5,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,8,6,5,4,3,7,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,8,6,5,4,7,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,8,7,5,4,6,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,8,7,5,6,4,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,1,3,4,8,6,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,3,5,8,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,3,8,5,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,3,8,5,7,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,3,8,6,5,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,3,8,6,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,4,3,8,6,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,5,8,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,4,8,5,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,4,8,5,7,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,4,8,6,5,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,4,8,6,7,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,5,4,8,6,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,4,5,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,4,5,7,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,6,4,5,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,8,4,5,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,8,4,5,7,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,7,4,6,5,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,8,4,6,5,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,8,4,6,7,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,8,4,7,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,5,4,7,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,7,5,6,4,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,8,5,6,4,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,8,5,6,7,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,8,5,7,6,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,6,5,4,7,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,6,5,7,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,7,5,6,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,3,1,7,5,6,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,8,5,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,8,6,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,4,1,8,6,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,5,8,6,7,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,4,7,5,6,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,4,7,5,6,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,4,8,5,6,7,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,4,8,5,7,6,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,4,8,6,5,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,4,8,6,7,5,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,5,4,8,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,6,4,5,1,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,6,4,5,1,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,6,4,5,8,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,7,4,5,6,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,8,4,5,6,7,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,7,4,6,5,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,8,4,6,7,5,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,7,5,4,6,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,7,5,4,6,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,8,5,4,6,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,7,5,6,4,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,7,5,6,4,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,8,5,6,4,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,8,5,6,7,4,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,8,5,7,6,4,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,3,8,6,5,4,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,4,3,5,8,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,3,7,5,6,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,3,8,5,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,3,8,5,7,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,3,8,6,5,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,5,3,4,1,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,5,3,4,1,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,5,3,4,6,7,8,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,5,3,4,6,8,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,5,3,4,7,6,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,5,3,4,8,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,6,3,4,5,1,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,6,3,4,5,8,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,3,4,5,6,1,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,8,3,4,5,6,7,1]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,8,3,4,5,7,6,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,6,3,5,4,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,3,5,4,8,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,3,5,4,6,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,3,5,4,7,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,3,5,6,4,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,3,5,6,7,4,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,3,5,7,6,4,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,7,3,6,5,4,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,8,3,7,5,6,4,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,8,3,7,6,5,4,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,5,4,3,8,6,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,4,3,5,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,4,3,5,8,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,4,3,5,6,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,4,3,5,6,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,4,3,5,7,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,4,3,6,5,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,4,3,6,5,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,4,3,6,7,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,4,3,7,6,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,8,4,5,3,6,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,7,4,5,6,3,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,7,4,5,6,3,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,4,5,6,3,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,4,5,6,7,3,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,7,4,6,5,3,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,7,4,6,5,3,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,8,4,6,5,3,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,8,4,7,6,5,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,7,5,4,3,6,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,8,5,4,3,6,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,8,5,4,3,7,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,7,5,4,6,3,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,8,5,4,6,7,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,8,5,4,7,6,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,7,6,4,5,3,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,8,7,4,5,6,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,8,7,4,6,5,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,8,7,5,4,6,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,8,7,5,6,4,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[3,2,1,4,8,6,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,5,8,6,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,7,5,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,8,5,6,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,8,5,7,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,1,8,6,5,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,1,8,6,7,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,4,1,8,6,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,4,5,8,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,7,5,6,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,8,5,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,8,6,7,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,5,4,8,6,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,6,4,5,1,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,7,4,5,6,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,8,4,5,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,7,4,6,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,7,4,6,5,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,8,4,6,5,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,7,5,4,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,8,5,4,6,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,8,5,4,7,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,2,7,5,6,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,7,5,6,4,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,8,5,6,4,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,8,5,7,6,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,2,8,6,5,7,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,2,8,7,5,6,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,2,3,1,5,7,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,3,1,6,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,3,1,6,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,3,1,6,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,3,1,7,6,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,3,1,8,6,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,3,1,8,7,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,2,3,5,1,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,3,5,6,1,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,3,5,6,8,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,3,5,8,7,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,3,6,5,8,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,3,7,5,6,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,3,8,5,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,3,8,5,7,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,3,7,6,5,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,3,8,7,6,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,2,3,4,1,6,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,3,4,1,7,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,3,4,1,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,3,4,6,1,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,3,4,7,6,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,3,4,8,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,2,3,4,5,1,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,2,3,4,5,8,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,2,3,4,5,7,6,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,3,4,7,6,5,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,2,3,5,4,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,2,3,5,4,7,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,3,5,4,6,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,3,5,4,7,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,3,5,6,4,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,3,5,6,7,4,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,3,5,7,6,4,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,3,7,5,6,4,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,3,7,6,5,4,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,2,4,3,1,6,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,2,4,3,1,6,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,2,4,3,1,7,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,2,4,3,1,8,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,4,3,6,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,2,4,3,7,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,2,4,3,7,6,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,2,4,3,8,7,6,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,4,3,5,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,4,3,6,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,4,3,6,5,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,4,3,6,5,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,4,3,6,7,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,4,3,7,6,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,2,4,5,3,6,1,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,2,4,5,3,6,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,4,5,3,7,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,4,5,6,7,3,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,4,5,7,6,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,2,4,6,5,3,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,2,4,6,5,3,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,4,7,5,6,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,4,7,6,5,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,2,5,4,3,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,2,5,4,3,7,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,2,5,4,3,7,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,2,5,4,3,6,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,5,4,3,6,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,5,4,3,7,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,2,5,4,6,3,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,2,6,4,5,3,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,6,4,5,3,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,6,4,5,7,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,7,4,5,6,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,7,4,6,5,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,2,6,5,4,3,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,2,6,5,4,3,8,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,2,6,5,4,3,7,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,2,6,5,4,7,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,2,7,5,4,6,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,2,7,5,6,4,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,2,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[4,3,2,1,8,6,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,2,7,5,6,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,2,8,5,6,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,2,8,5,7,6,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,2,8,6,7,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,2,4,1,6,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,2,4,1,7,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,2,4,1,8,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,2,4,7,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,4,6,5,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,4,6,7,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,4,7,6,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,2,5,4,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,2,5,4,7,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,2,5,4,7,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,2,5,4,8,7,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,2,5,4,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,5,4,7,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,2,5,6,4,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,5,6,7,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,5,7,6,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,2,6,5,7,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,2,7,5,6,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,2,7,6,5,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,3,4,2,1,6,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,4,2,1,7,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,4,2,1,8,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,4,2,6,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,4,2,7,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,4,2,7,6,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,4,2,8,6,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,4,2,5,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,4,2,6,5,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,4,5,2,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,4,5,2,8,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,4,5,2,7,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,4,5,7,6,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,4,7,6,5,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,3,5,4,2,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,5,4,2,7,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,3,5,4,2,7,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,3,5,4,2,8,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,3,5,4,2,6,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,5,4,2,6,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,5,4,2,7,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,3,5,4,6,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,3,5,4,6,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,5,4,6,7,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,5,4,7,6,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,3,6,4,5,2,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,3,6,4,5,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,6,4,5,2,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,7,4,5,6,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,7,4,6,5,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,3,6,5,4,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,3,6,5,4,2,8,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,3,6,5,4,7,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,3,7,5,4,6,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,3,7,5,6,4,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,3,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[5,4,3,2,8,6,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,3,2,5,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,3,2,5,8,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,3,2,5,7,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,3,2,6,5,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,3,2,6,5,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,3,2,6,5,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,3,2,7,6,5,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,4,3,5,2,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,3,5,2,7,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,3,5,7,6,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,3,6,5,2,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,3,6,5,2,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,3,7,5,6,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,3,7,6,5,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,5,3,4,2,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,3,4,2,7,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,3,4,7,6,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,3,4,6,5,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,6,3,5,4,2,1,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,6,3,5,4,2,8,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,3,5,4,2,7,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,3,5,4,7,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,7,3,5,4,6,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,7,3,5,6,4,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,7,3,6,5,4,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,5,4,3,2,7,6,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,5,4,3,7,6,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,4,3,6,5,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,4,6,5,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[2,4,1,3,6,5,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,4,6,3,5,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,1,6,3,5,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,6,1,3,5,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,4,3,6,8,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,1,3,6,8,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,4,6,3,8,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,1,6,3,8,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,6,1,3,8,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,4,6,8,3,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,1,6,8,3,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,6,1,8,3,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,6,8,1,3,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,1,3,6,5,7,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,4,6,3,5,7,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,6,3,5,7,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,6,1,3,5,7,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,4,6,3,7,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,6,3,7,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,6,7,1,3,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,3,6,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,4,6,3,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,6,3,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,4,6,7,3,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,6,7,3,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,6,1,7,3,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,6,7,1,3,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,4,6,7,8,3,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,6,7,8,3,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,6,7,8,1,3,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,4,3,7,5,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,1,3,7,5,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,4,7,3,5,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,1,7,3,5,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,4,3,7,8,5,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,1,3,7,8,5,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,1,7,3,8,5,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,4,7,8,3,5,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,1,7,8,3,5,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,7,1,8,3,5,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,4,1,5,3,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,5,1,3,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,5,1,7,3,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,5,3,7,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,5,1,3,7,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,4,5,7,3,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,5,7,3,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,5,1,7,3,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,5,1,7,8,3,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,5,7,8,1,3,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,4,3,8,5,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,3,8,5,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,4,8,3,5,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,8,3,5,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,8,1,3,5,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,4,3,5,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,5,3,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,4,5,8,3,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,5,8,3,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,5,1,8,3,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,5,3,6,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,5,6,3,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,5,1,6,3,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,5,6,1,3,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,4,5,6,8,3,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,5,6,8,3,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,5,1,6,8,3,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,5,6,1,8,3,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,5,6,8,1,3,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,4,1,3,5,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,4,1,5,3,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,4,5,1,3,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,4,1,5,6,3,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,4,5,1,6,3,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,4,5,6,1,3,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,4,1,5,6,7,3,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,4,5,6,1,7,3,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,4,5,6,7,1,3,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,4,1,5,6,7,8,3]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,4,5,1,6,7,8,3]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,4,5,6,1,7,8,3]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,4,5,6,7,1,8,3]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,4,5,6,7,8,1,3]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,5,3,6,4,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,1,3,6,4,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,5,6,3,4,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,1,6,3,4,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,6,1,3,4,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,5,3,6,8,4,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,1,3,6,8,4,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,6,1,3,8,4,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,5,6,8,3,4,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,1,6,8,3,4,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,1,3,6,4,7,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,5,3,6,7,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,5,6,3,7,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,5,1,6,3,7,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,5,6,1,3,7,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,5,6,7,3,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,5,3,6,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,5,1,3,6,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,5,6,3,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,5,1,6,3,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,5,6,1,3,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,5,6,7,3,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,5,1,6,7,3,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,5,6,7,1,3,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,5,6,7,8,3,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,5,1,6,7,8,3,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,5,6,1,7,8,3,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,5,6,7,1,8,3,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,5,6,7,8,1,3,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,5,3,7,4,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,1,3,7,4,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,1,7,3,4,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,7,1,3,4,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,5,3,7,8,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,1,3,7,8,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,5,7,3,8,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,5,7,8,3,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,1,7,8,3,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,7,1,8,3,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,5,7,8,1,3,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,3,5,1,4,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,5,7,1,4,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,5,1,7,4,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,1,5,7,8,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,5,7,8,1,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,5,3,8,4,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,5,1,3,8,4,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,5,8,3,4,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,5,1,4,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,3,5,8,4,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,5,1,8,4,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,5,3,4,6,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,5,1,6,4,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,3,5,6,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,1,5,6,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,5,1,6,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,5,6,1,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,5,6,8,1,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,5,3,4,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,5,1,3,4,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,5,1,4,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,5,6,1,4,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,5,6,7,1,4,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,5,1,6,7,8,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,5,6,7,8,1,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,6,3,7,4,8,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,6,1,3,7,4,8,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,6,7,3,4,8,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,6,1,7,3,4,8,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,6,7,1,3,4,8,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,6,3,7,8,4,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,6,1,3,7,8,4,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,6,7,1,3,8,4,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,1,6,7,8,3,4,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,6,1,7,8,3,4,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,6,7,1,8,3,4,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,6,7,8,1,3,4,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[2,6,1,7,3,4,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,6,1,3,4,7,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,1,6,4,7,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,6,3,4,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,6,1,3,4,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,6,1,4,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,3,6,7,4,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,3,6,7,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,1,6,7,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,6,1,7,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,6,7,1,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,6,7,8,1,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,6,3,8,4,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,6,1,3,8,4,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,6,8,3,4,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,6,1,8,3,4,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,6,8,1,3,4,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,6,3,4,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,6,1,3,4,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,1,6,4,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,6,1,4,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,1,6,8,4,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,6,1,8,4,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,6,3,4,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,6,1,3,4,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,3,6,4,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,6,1,4,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,4,1,6,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,4,6,1,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,4,6,8,1,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,6,1,3,4,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,3,6,4,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,1,6,4,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,6,1,4,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,6,1,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,6,7,1,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,6,1,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,6,7,8,1,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,7,3,8,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,7,1,3,8,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,7,8,3,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,7,1,8,3,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,7,8,1,3,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,7,3,4,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,3,7,4,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,1,7,4,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,3,7,8,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,1,7,8,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,7,8,1,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,7,3,4,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,7,1,3,4,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,1,7,4,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,7,1,4,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,3,4,7,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,4,1,7,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,4,7,1,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,3,4,7,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,1,4,7,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,4,1,7,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,4,7,1,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,3,4,7,8,1,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[2,1,7,3,4,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,7,1,3,4,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,7,1,4,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,3,4,7,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,1,7,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,7,1,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,5,7,1,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,5,7,1,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,5,7,8,1,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,8,3,4,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,8,1,3,4,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,3,8,4,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,1,8,4,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,8,1,4,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,3,4,8,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,1,4,8,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,1,8,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,8,1,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,1,3,4,5,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,1,4,5,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,1,5,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,5,1,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,5,8,1,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[2,3,4,5,6,8,1,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,4,2,6,5,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,4,1,2,6,5,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,4,6,2,5,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,4,1,6,2,5,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,4,6,1,2,5,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,4,2,6,8,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,4,1,2,6,8,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,4,6,2,8,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,4,1,6,2,8,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,4,6,8,2,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,4,1,6,8,2,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,4,6,8,1,2,5,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,4,1,2,6,5,7,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,2,6,7,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,2,6,7,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,6,2,7,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,6,7,2,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,6,7,1,2,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,2,6,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,2,6,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,6,2,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,6,2,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,6,1,2,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,6,7,2,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,6,7,2,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,6,1,7,2,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,6,7,8,2,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,6,7,8,2,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,6,1,7,8,2,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,6,7,1,8,2,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,6,7,8,1,2,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,2,7,5,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,4,1,2,7,5,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,4,7,2,5,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,4,7,1,2,5,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,4,2,7,8,5,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,4,1,2,7,8,5,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,4,7,1,8,2,5,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,4,7,8,1,2,5,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,4,2,7,5,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,2,7,5,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,2,5,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,5,2,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,5,2,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,5,7,2,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,5,7,1,2,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,2,5,7,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,2,5,7,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,5,2,7,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,5,1,2,7,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,5,7,2,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,5,7,2,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,5,7,8,2,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,5,7,8,2,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,5,1,7,8,2,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,5,7,8,1,2,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,2,8,5,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,2,8,5,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,8,2,5,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,8,2,5,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,8,1,2,5,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,2,5,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,2,5,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,5,2,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,5,8,2,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,5,8,2,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,5,8,1,2,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,2,5,6,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,5,1,2,6,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,5,6,2,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,5,6,2,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,5,1,6,2,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,5,6,1,2,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,5,6,8,2,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,1,5,6,8,2,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,5,6,1,8,2,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,4,5,6,8,1,2,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,4,2,5,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,4,5,2,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,4,1,5,2,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,4,1,5,6,2,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,4,5,1,6,2,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,4,5,6,7,2,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,4,1,5,6,7,2,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,4,5,1,6,7,2,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,4,5,6,1,7,2,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,4,5,6,7,8,2]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,4,1,5,6,7,8,2]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,4,5,1,6,7,8,2]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,4,5,6,1,7,8,2]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,4,5,6,7,1,8,2]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,5,2,6,4,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,1,2,6,4,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,1,6,2,4,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,6,1,2,4,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,5,2,6,8,4,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,1,2,6,8,4,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,5,6,8,2,4,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,1,6,8,2,4,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,6,1,8,2,4,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,6,8,1,2,4,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,1,6,2,4,7,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,6,1,2,4,7,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,2,6,7,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,6,2,7,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,6,1,2,7,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,6,7,2,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,6,7,1,2,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,5,2,6,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,2,6,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,5,6,2,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,6,2,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,6,1,2,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,5,6,7,2,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,6,7,2,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,6,1,7,2,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,6,7,1,2,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,5,6,7,8,2,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,6,7,8,2,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,6,1,7,8,2,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,6,7,1,8,2,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,6,7,8,1,2,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,5,2,7,4,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,1,2,7,4,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,5,7,2,4,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,7,1,2,4,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,5,2,7,8,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,1,2,7,8,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,5,7,2,8,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,1,7,2,8,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,5,7,8,2,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,1,7,8,2,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,5,7,8,1,2,4,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,5,2,7,4,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,2,7,4,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,5,7,2,4,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,7,2,4,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,7,1,2,4,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,5,2,4,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,2,4,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,5,4,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,2,4,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,5,7,4,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,5,7,4,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,2,7,4,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,7,2,4,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,2,4,7,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,5,7,4,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,2,7,4,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,7,2,4,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,5,7,8,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,2,7,8,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,7,2,8,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,7,8,2,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,5,2,8,4,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,2,8,4,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,5,8,2,4,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,8,2,4,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,5,2,4,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,2,4,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,5,4,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,2,4,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,5,8,4,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,5,8,4,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,2,8,4,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,8,2,4,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,2,4,6,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,5,4,6,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,2,4,6,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,5,6,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,2,6,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,6,2,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,5,6,8,2,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,5,1,2,4,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,5,2,4,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,5,6,2,4,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,2,5,6,7,4,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,5,2,6,7,4,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,5,6,2,7,4,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,5,6,7,2,4,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,2,5,6,7,8,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,5,6,7,2,8,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,5,6,7,8,2,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,6,2,7,4,8,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,6,1,2,7,4,8,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,6,1,7,2,4,8,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,6,7,1,2,4,8,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,6,1,2,7,8,4,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,6,7,2,8,4,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,6,1,7,2,8,4,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,6,7,1,2,8,4,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,6,1,7,8,2,4,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,6,7,8,1,2,4,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[3,1,6,7,2,4,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,6,1,2,4,7,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,6,4,7,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,6,4,7,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,6,7,4,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,6,2,7,4,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,6,2,4,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,6,1,2,4,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,6,4,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,6,7,4,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,6,7,4,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,6,2,7,4,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,6,7,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,6,7,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,6,2,7,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,6,7,8,2,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,6,1,2,8,4,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,6,8,2,4,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,6,1,8,2,4,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,6,8,1,2,4,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,6,2,4,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,6,1,2,4,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,6,4,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,6,2,4,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,6,8,4,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,6,8,4,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,6,2,4,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,6,1,2,4,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,6,4,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,6,2,4,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,4,6,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,4,6,2,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,4,6,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,4,6,8,2,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,6,1,2,4,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,6,4,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,6,2,4,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,4,6,2,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,4,6,2,7,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,4,6,7,2,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,2,4,6,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,4,6,7,2,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,7,2,8,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,7,1,2,8,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,7,8,2,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,7,1,8,2,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,7,8,1,2,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,7,1,2,4,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,7,4,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,7,4,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,7,2,4,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,7,8,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,7,2,8,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,7,8,2,4,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,7,2,4,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,7,1,2,4,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,7,2,4,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,4,7,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,4,7,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,4,2,7,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,2,4,7,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,2,4,7,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,4,2,7,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,3,4,7,8,2,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[3,1,7,2,4,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,7,1,2,4,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,2,7,4,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,7,4,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,7,2,4,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,2,4,7,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,4,7,2,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,2,4,5,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,2,4,5,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,4,5,7,8,2,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,8,2,4,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,8,1,2,4,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,2,8,4,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,8,4,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,8,2,4,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,2,4,8,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,4,8,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,4,2,8,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,4,8,2,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,2,4,5,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,2,4,5,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,4,2,5,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,4,5,2,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,4,5,8,2,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[3,1,2,4,5,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,3,4,5,6,8,2,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,5,2,6,3,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,5,1,2,6,3,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,1,5,6,2,3,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,5,1,6,2,3,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,5,6,1,2,3,8,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,1,5,2,6,8,3,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,5,1,2,6,8,3,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,1,5,6,2,8,3,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,5,6,1,2,8,3,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,1,5,6,8,2,3,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,5,1,6,8,2,3,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,5,6,1,8,2,3,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,5,6,8,1,2,3,7]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,1,5,2,6,3,7,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,5,6,2,3,7,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,1,6,2,3,7,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,1,2,6,7,3,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,1,6,2,7,3,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,6,1,2,7,3,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,6,1,7,2,3,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,5,2,6,7,8,3]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,1,2,6,7,8,3]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,1,6,2,7,8,3]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,6,1,2,7,8,3]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,5,6,7,2,8,3]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,1,6,7,2,8,3]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,6,1,7,2,8,3]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,6,7,1,2,8,3]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,5,6,7,8,2,3]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,1,6,7,8,2,3]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,6,1,7,8,2,3]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,6,7,1,8,2,3]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,5,2,7,3,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,5,1,7,2,3,8,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,1,5,2,7,8,3,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,5,1,2,7,8,3,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,1,5,7,2,8,3,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,5,1,7,2,8,3,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,5,7,1,2,8,3,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,5,7,8,1,2,3,6]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,1,5,2,7,3,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,1,2,7,3,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,5,2,3,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,1,2,3,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,5,3,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,5,3,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,5,2,3,7,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,5,7,3,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,5,2,7,3,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,5,7,2,3,6,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,5,2,3,7,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,5,3,7,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,5,2,3,7,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,5,7,3,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,5,7,3,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,5,2,7,3,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,5,7,2,3,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,5,7,8,3,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,5,7,8,3,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,5,2,7,8,3,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,5,7,8,2,3,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,5,2,8,3,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,1,2,8,3,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,1,8,2,3,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,8,1,2,3,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,5,2,3,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,5,1,2,3,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,5,3,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,5,3,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,5,2,3,8,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,5,8,3,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,5,2,8,3,6,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,5,3,6,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,5,6,3,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,5,2,6,3,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,5,6,8,3,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,5,6,8,3,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,5,2,6,8,3,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,5,6,8,2,3,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,5,2,3,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,5,3,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,5,3,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,5,2,3,6,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,5,6,3,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,5,2,6,3,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,5,6,2,3,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,5,6,7,3,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,5,6,7,3,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,5,2,6,7,3,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,5,6,2,7,3,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,5,6,7,2,3,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,5,6,7,8,3]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,5,6,7,8,3]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,5,2,6,7,8,3]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,5,6,2,7,8,3]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,5,6,7,2,8,3]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,5,6,7,8,2,3]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,6,2,7,3,8,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,1,6,7,2,3,8,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,6,7,1,2,3,8,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,6,1,2,7,8,3,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,6,1,7,2,8,3,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,6,7,1,2,8,3,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,1,6,7,8,2,3,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,6,1,7,8,2,3,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,6,7,1,8,2,3,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,6,7,8,1,2,3,5]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[4,1,6,2,7,3,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,6,7,2,3,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,6,1,7,2,3,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,6,7,1,2,3,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,6,2,3,7,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,6,3,7,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,6,3,7,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,6,7,3,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,6,7,3,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,6,2,7,3,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,6,7,2,3,5,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,6,2,3,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,6,3,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,6,2,3,7,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,6,7,3,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,6,2,7,3,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,6,7,8,3,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,6,2,7,8,3,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,6,7,2,8,3,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,6,7,8,2,3,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,6,2,8,3,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,6,1,2,8,3,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,6,8,2,3,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,6,1,8,2,3,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,6,8,1,2,3,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,6,2,3,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,6,3,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,6,3,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,6,2,3,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,6,8,3,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,6,2,8,3,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,6,8,2,3,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,6,2,3,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,6,1,2,3,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,6,3,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,6,3,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,6,2,3,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,3,6,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,3,6,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,4,6,3,5,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,3,6,8,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,4,6,8,3,5,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,6,2,3,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,6,1,2,3,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,6,3,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,6,2,3,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,3,6,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,3,6,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,6,3,5,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,3,6,7,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,3,6,7,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,3,6,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,3,6,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,7,2,8,3,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,7,1,2,8,3,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,7,8,2,3,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,7,1,8,2,3,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,7,2,3,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,7,1,2,3,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,7,3,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,7,2,3,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,7,8,3,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,7,8,3,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,7,2,8,3,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,7,8,2,3,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,7,2,3,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,7,1,2,3,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,7,3,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,7,3,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,7,2,3,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,3,7,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,3,7,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,4,7,3,5,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,2,3,7,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,4,2,3,7,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,4,3,7,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,4,7,3,8,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,4,7,8,3,5,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[4,1,7,2,3,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,7,1,2,3,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,7,3,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,7,3,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,7,2,3,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,3,7,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,3,7,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,3,7,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,7,3,5,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,3,5,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,3,5,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,5,7,3,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,3,5,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,3,5,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,5,7,8,3,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,8,2,3,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,8,1,2,3,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,8,3,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,8,3,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,8,2,3,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,3,8,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,3,8,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,3,8,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,8,3,5,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,3,5,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,3,5,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,3,5,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,5,3,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,5,8,3,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[4,1,2,3,5,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,3,5,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,4,5,6,8,3,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,4,2,3,5,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[5,1,6,2,7,3,8,4]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[5,6,1,2,7,3,8,4]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[5,1,6,7,2,3,8,4]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[5,6,1,7,2,3,8,4]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[5,6,7,1,2,3,8,4]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[5,6,1,2,7,8,3,4]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[5,1,6,7,2,8,3,4]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[5,6,7,1,2,8,3,4]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[5,1,6,7,8,2,3,4]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[5,6,1,7,8,2,3,4]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[5,6,7,1,8,2,3,4]=>[4,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[5,1,6,2,7,3,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,6,1,7,2,3,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,6,2,3,7,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,2,6,3,7,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,6,3,7,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,2,6,7,3,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,6,7,3,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,6,7,2,3,4,8]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,6,2,3,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,6,1,2,3,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,2,6,3,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,6,3,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,6,2,3,7,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,2,6,7,3,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,6,7,2,3,8,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,2,6,7,8,3,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,6,7,8,3,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,6,2,7,8,3,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,6,7,2,8,3,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,6,7,8,2,3,4]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,6,2,8,3,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,6,1,2,8,3,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,6,1,8,2,3,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,6,8,1,2,3,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,6,2,3,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,6,1,2,3,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,2,6,3,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,6,3,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,6,2,3,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,2,6,8,3,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,6,8,3,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,6,2,8,3,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,6,8,2,3,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,6,2,3,4,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,6,1,2,3,4,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,6,3,4,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,6,2,3,4,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,3,6,4,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,5,3,6,4,8,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,2,3,6,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,3,6,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,5,6,3,8,4,7]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,6,2,3,4,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,1,2,6,3,4,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,2,6,3,4,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,6,2,3,4,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,1,2,3,6,4,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,2,3,6,4,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,3,6,4,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,6,3,4,7,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,1,2,3,6,7,4,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,2,3,6,7,4,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,6,3,7,4,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,1,2,3,6,7,8,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,2,3,6,7,8,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,3,6,7,8,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,6,3,7,8,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,6,7,3,8,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,6,7,8,3,4]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,1,7,2,8,3,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,7,1,2,8,3,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,7,8,2,3,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,7,1,8,2,3,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,7,8,1,2,3,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,2,7,3,8,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,7,3,8,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,7,2,3,8,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,2,7,8,3,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,7,8,3,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,7,2,8,3,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,7,8,2,3,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,7,2,3,4,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,7,1,2,3,4,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,2,7,3,4,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,7,3,4,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,7,2,3,4,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,2,3,7,4,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,3,7,4,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,5,3,7,4,8,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,2,3,7,8,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,5,2,3,7,8,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,5,7,3,8,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,5,7,8,3,4,6]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[5,1,7,2,3,4,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,7,1,2,3,4,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,2,7,3,4,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,2,3,7,4,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,3,7,4,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,7,3,4,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,2,3,4,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,3,4,7,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,5,7,4,6,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,1,2,3,4,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,2,3,4,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,3,4,7,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,5,7,4,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,5,7,8,4,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,8,1,2,3,4,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,1,2,8,3,4,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,2,8,3,4,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,8,2,3,4,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,1,2,3,8,4,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,2,3,8,4,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,3,8,4,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,8,3,4,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,1,2,3,4,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,2,3,4,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,3,4,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,5,4,8,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,5,8,4,6,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[5,1,2,3,4,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,2,3,4,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,5,3,4,6,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,5,6,8,4,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,5,2,3,4,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,2,5,3,4,6,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[6,1,7,2,8,3,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,7,1,2,8,3,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,1,7,8,2,3,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,7,1,8,2,3,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,1,7,2,3,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,7,1,2,3,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,1,2,7,3,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,6,2,7,3,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,6,7,2,3,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,1,2,7,8,3,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,6,2,7,8,3,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,6,7,2,8,3,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,6,7,8,2,3,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,1,7,2,3,4,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,7,1,2,3,4,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,1,2,7,3,4,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,6,2,7,3,4,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,1,2,3,7,4,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,6,2,3,7,4,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,6,3,7,4,8,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,1,2,3,7,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,6,2,3,7,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,6,3,7,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,6,7,3,8,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[1,2,6,7,8,3,4,5]=>[5,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[6,1,7,2,3,4,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[6,1,2,7,3,4,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,6,2,7,3,4,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,6,7,2,3,4,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[6,1,2,3,7,4,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,6,2,3,7,4,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,6,3,7,4,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,6,7,3,4,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[6,1,2,3,4,7,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,6,2,3,4,7,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,6,3,4,7,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,6,4,7,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,6,7,4,5,8]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[6,1,2,3,4,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,6,2,3,4,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,6,3,4,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,6,4,7,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,6,7,4,8,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,6,7,8,4,5]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[6,1,8,2,3,4,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[6,8,1,2,3,4,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[6,1,2,8,3,4,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,6,2,8,3,4,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,6,8,2,3,4,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[6,1,2,3,8,4,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,6,2,3,8,4,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,6,3,8,4,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,6,8,3,4,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[6,1,2,3,4,8,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,6,2,3,4,8,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,6,3,4,8,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,6,4,8,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,6,8,4,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[6,1,2,3,4,5,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,6,2,3,4,5,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,6,3,4,5,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,6,4,5,8,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,4,6,8,5,7]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,6,2,3,4,5,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,2,6,3,4,5,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,2,3,6,4,5,7,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[7,1,8,2,3,4,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[7,1,2,8,3,4,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,7,2,8,3,4,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,7,8,2,3,4,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[7,1,2,3,8,4,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,7,2,3,8,4,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,7,3,8,4,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,7,8,3,4,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[7,1,2,3,4,8,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,7,2,3,4,8,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,7,3,4,8,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,7,4,8,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,7,8,4,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[7,1,2,3,4,5,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,7,2,3,4,5,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,7,3,4,5,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,7,4,5,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,4,7,5,8,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,2,3,4,7,8,5,6]=>[6,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[1,7,2,3,4,5,6,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,2,7,3,4,5,6,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,2,3,7,4,5,6,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,2,3,4,7,5,6,8]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,8,2,3,4,5,6,7]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,2,8,3,4,5,6,7]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,2,3,8,4,5,6,7]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,2,3,4,8,5,6,7]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[1,2,3,4,5,8,6,7]=>[7,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[5,3,2,6,1,4,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,2,5,4,8,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,5,2,3,7,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,5,2,3,8,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,5,2,3,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,6,2,1,3,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,6,1,5,4,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,6,5,1,3,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,4,3,1,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,4,3,2,8,1,6]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,6,4,3,7,2,5,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,6,4,3,8,2,1,5]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,7,4,3,8,1,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,4,3,1,8,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,5,1,3,8,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,1,5,4,8,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,7,5,4,8,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,8,1,5,4,7,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,5,1,3,7,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,4,3,1,7,6,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,8,4,3,7,1,5,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,8,4,3,6,5,1,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,8,5,7,3,1,4,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[5,8,6,7,1,3,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,6,1,7,3,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,8,1,6,7,4,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,8,6,7,4,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,7,6,8,4,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,1,6,8,4,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,6,1,8,3,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,6,8,1,3,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,7,2,1,8,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,7,2,8,1,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,6,2,8,3,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,6,2,7,3,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,2,6,7,4,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,2,6,8,4,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,2,7,8,1,4,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,2,7,1,8,4,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,3,2,1,7,8,5,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,4,1,2,8,7,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,2,8,1,7,6,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,3,2,8,7,1,5,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,3,2,8,6,5,1,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[8,4,7,2,6,5,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,4,8,2,6,5,1,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,4,8,2,7,1,5,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[5,4,8,2,1,7,6,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[4,5,8,1,2,7,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,5,1,8,2,7,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,5,8,3,7,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,6,8,7,3,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,6,1,8,7,2,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,6,8,1,7,2,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,8,7,1,2,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,8,7,2,1,4,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,5,8,6,2,4,1,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[8,5,7,6,2,4,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,7,8,6,1,4,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,8,1,6,5,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,1,8,6,5,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,7,8,6,5,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,8,1,7,6,5,4,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[4,8,7,1,6,5,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,8,7,6,1,4,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,8,7,5,4,1,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[2,1,4,3,6,5,8,7,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,4,1,2,6,5,8,7,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[4,3,2,1,6,5,8,7,10,9]=>[4,4,1,1]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>110001000
[6,3,2,5,4,1,8,7,10,9]=>[4,4,1,1]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>110001000
[8,3,2,5,4,7,6,1,10,9]=>[4,4,1,1]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>110001000
[10,3,2,5,4,7,6,9,8,1]=>[4,4,1,1]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>110001000
[4,5,6,1,2,3,8,7,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,5,1,6,2,4,8,7,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,5,6,3,4,8,7,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,6,5,4,3,8,7,10,9]=>[4,4,1,1]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>110001000
[6,5,4,3,2,1,8,7,10,9]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[8,5,4,3,2,7,6,1,10,9]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[10,5,4,3,2,7,6,9,8,1]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[2,1,8,5,4,7,6,3,10,9]=>[4,4,1,1]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>110001000
[8,7,4,3,6,5,2,1,10,9]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[10,7,4,3,6,5,2,9,8,1]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[2,1,10,5,4,7,6,9,8,3]=>[4,4,1,1]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>110001000
[10,9,4,3,6,5,8,7,2,1]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[5,6,7,8,1,2,3,4,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[4,6,7,1,8,2,3,5,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,6,1,7,8,2,4,5,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,6,7,8,3,4,5,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,5,7,3,8,4,6,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,5,1,7,2,8,4,6,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[4,5,7,1,2,8,3,6,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,4,1,2,7,8,5,6,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,4,3,7,8,5,6,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,4,3,8,7,6,5,10,9]=>[4,4,1,1]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>110001000
[4,3,2,1,8,7,6,5,10,9]=>[3,3,2,2]=>[[1,2,7],[3,4,10],[5,6],[8,9]]=>010100100
[8,3,2,7,6,5,4,1,10,9]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[10,3,2,7,6,5,4,9,8,1]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[2,1,8,7,6,5,4,3,10,9]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[8,7,6,5,4,3,2,1,10,9]=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>111111010
[10,7,6,5,4,3,2,9,8,1]=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>111111010
[2,1,10,7,6,5,4,9,8,3]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[10,9,6,5,4,3,8,7,2,1]=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>111111010
[2,1,4,3,10,7,6,9,8,5]=>[4,4,1,1]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>110001000
[4,3,2,1,10,7,6,9,8,5]=>[3,3,2,2]=>[[1,2,7],[3,4,10],[5,6],[8,9]]=>010100100
[10,3,2,9,6,5,8,7,4,1]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[2,1,10,9,6,5,8,7,4,3]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[10,9,8,5,4,7,6,3,2,1]=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>111111010
[2,1,7,8,9,10,3,4,5,6]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,7,1,8,9,10,2,4,5,6]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[4,7,8,1,9,10,2,3,5,6]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[5,7,8,9,1,10,2,3,4,6]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[6,7,8,9,10,1,2,3,4,5]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[5,6,8,9,1,2,10,3,4,7]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[4,6,8,1,9,2,10,3,5,7]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,6,1,8,9,2,10,4,5,7]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,6,8,9,3,10,4,5,7]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,5,8,3,9,10,4,6,7]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,5,1,8,2,9,10,4,6,7]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[4,5,8,1,2,9,10,3,6,7]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,4,1,2,8,9,10,5,6,7]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,4,3,8,9,10,5,6,7]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,4,3,7,9,5,10,6,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,4,1,2,7,9,5,10,6,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[4,5,7,1,2,9,3,10,6,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,5,1,7,2,9,4,10,6,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,5,7,3,9,4,10,6,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,6,7,9,3,4,10,5,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,6,1,7,9,2,4,10,5,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[4,6,7,1,9,2,3,10,5,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[5,6,7,9,1,2,3,10,4,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,5,6,3,4,9,10,7,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,5,1,6,2,4,9,10,7,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[4,5,6,1,2,3,9,10,7,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[3,4,1,2,6,5,9,10,7,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,4,3,6,5,9,10,7,8]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,1,4,3,6,5,10,9,8,7]=>[4,4,1,1]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>110001000
[4,3,2,1,6,5,10,9,8,7]=>[3,3,2,2]=>[[1,2,7],[3,4,10],[5,6],[8,9]]=>010100100
[6,3,2,5,4,1,10,9,8,7]=>[3,3,2,2]=>[[1,2,7],[3,4,10],[5,6],[8,9]]=>010100100
[10,3,2,5,4,9,8,7,6,1]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[2,1,6,5,4,3,10,9,8,7]=>[3,3,2,2]=>[[1,2,7],[3,4,10],[5,6],[8,9]]=>010100100
[6,5,4,3,2,1,10,9,8,7]=>[2,2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>110101010
[10,5,4,3,2,9,8,7,6,1]=>[2,2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>110101010
[2,1,10,5,4,9,8,7,6,3]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[10,9,4,3,8,7,6,5,2,1]=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>111111010
[2,1,4,3,10,9,8,7,6,5]=>[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100
[4,3,2,1,10,9,8,7,6,5]=>[2,2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>110101010
[10,3,2,9,8,7,6,5,4,1]=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>111111010
[2,1,10,9,8,7,6,5,4,3]=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>111111010
[9,10,8,7,6,5,4,3,1,2]=>[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>111111010
[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>111111111
[4,2,5,1,3,6,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,6,1,3,5,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,3,6,1,2,4,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,2,4,1,3,5,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,3,5,1,2,4,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,3,7,1,2,4,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,4,7,1,2,3,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,2,7,1,3,4,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,3,7,1,2,4,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,4,7,1,2,3,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,5,1,2,4,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,6,1,2,4,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,4,6,1,2,3,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,8,1,4,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,8,1,3,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,4,8,1,2,3,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,2,8,1,3,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,3,8,1,2,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,4,8,1,2,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,5,8,1,2,3,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,2,8,1,3,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,8,1,2,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,4,8,1,2,3,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,5,8,1,2,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,2,4,1,3,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,3,5,1,2,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,3,6,1,2,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,3,7,1,2,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,4,7,1,2,3,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,5,7,1,2,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,5,7,1,4,6,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,5,7,1,3,6,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,4,7,1,3,6,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,7,1,3,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,6,7,1,3,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,5,7,1,3,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,5,8,1,3,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,4,8,1,3,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,8,1,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,6,8,1,3,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,4,8,1,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,4,8,1,2,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,5,8,1,2,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,5,8,1,2,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,7,8,1,4,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,7,8,1,2,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,7,8,1,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,7,8,1,2,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,7,8,1,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,2,4,8,1,3,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,4,8,1,2,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,5,8,1,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,5,8,1,2,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,6,8,1,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,4,6,1,2,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,5,6,1,2,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,5,7,1,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,2,6,7,1,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,6,7,1,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,2,5,1,3,7,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,6,3,5,1,2,7,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,7,2,5,1,4,6,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,7,3,5,1,2,6,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,7,2,6,1,4,5,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,7,3,6,1,2,5,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,7,2,6,1,3,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,7,2,5,1,3,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,8,2,5,1,3,6,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,2,4,1,3,6,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,3,4,1,2,6,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,3,6,1,2,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,4,6,1,2,3,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,8,3,5,1,2,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,8,2,7,1,4,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,8,2,7,1,3,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,8,3,7,1,2,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,2,7,1,3,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,3,7,1,2,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,8,2,7,1,3,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,8,5,7,1,2,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,2,4,1,3,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,2,5,1,3,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,3,5,1,2,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,4,6,1,2,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,2,6,1,5,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,2,6,1,4,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,2,5,1,4,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,2,4,1,3,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,2,7,1,5,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,2,7,1,4,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,2,7,1,4,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,2,7,1,3,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,3,7,1,2,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,2,7,1,3,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,3,7,1,2,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,2,5,1,4,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,2,5,1,3,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,2,6,1,4,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,3,6,1,2,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,2,6,1,3,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,3,6,1,2,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,2,8,1,5,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,2,8,1,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,3,8,1,2,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,2,8,1,3,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,3,8,1,2,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,2,8,1,4,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,2,8,1,3,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,3,8,1,2,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,3,8,1,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,4,8,1,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,2,8,1,3,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,5,1,4,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,2,5,1,3,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,6,1,4,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,2,6,1,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,3,6,1,2,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,2,4,1,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,2,5,1,3,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,7,1,4,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,2,7,1,3,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,3,7,1,2,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,2,7,1,3,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,3,7,1,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,3,7,1,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,2,4,1,3,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,2,5,1,3,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,3,5,1,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,2,6,1,3,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,3,6,1,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,4,6,1,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,2,4,8,1,3,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,2,5,8,1,3,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,3,5,8,1,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,2,4,8,1,3,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,3,4,8,1,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,3,6,8,1,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,2,6,8,1,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,4,6,8,1,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,3,4,8,1,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,3,5,8,1,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,8,2,5,7,1,4,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,8,3,5,7,1,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,8,2,4,7,1,3,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,8,2,6,7,1,4,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,8,2,6,7,1,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,8,3,6,7,1,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,8,2,5,7,1,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,8,2,4,6,1,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,8,2,5,6,1,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,8,3,5,6,1,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,3,2,6,8,1,5,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,2,6,8,1,4,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,3,6,8,1,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,2,5,8,1,4,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,3,5,8,1,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,2,4,8,1,3,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,3,2,7,8,1,5,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,2,7,8,1,4,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,2,7,8,1,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,3,7,8,1,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,2,7,8,1,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,3,7,8,1,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,2,5,8,1,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,3,5,8,1,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,2,6,8,1,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,3,6,8,1,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,6,2,4,8,1,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,2,5,7,1,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,2,4,7,1,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,2,6,7,1,4,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,2,6,7,1,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,3,6,7,1,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,6,2,4,7,1,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,2,4,6,1,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,3,4,6,1,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,2,5,6,1,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,3,7,2,6,1,5,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,8,2,6,1,5,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,8,2,6,1,4,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,8,2,6,1,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,8,3,6,1,2,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,8,2,5,1,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,8,3,5,1,2,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,8,2,4,1,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,8,3,4,1,2,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,8,2,7,1,5,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,8,2,7,1,4,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,8,2,7,1,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,8,3,7,1,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,8,2,7,1,4,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,8,2,7,1,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,8,2,5,1,4,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,8,3,5,1,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,8,2,4,1,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,8,2,6,1,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,8,4,6,1,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,8,2,5,1,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,8,3,5,1,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,6,2,4,1,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,7,3,5,1,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,2,4,1,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,7,2,6,1,4,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,7,2,6,1,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,7,3,6,1,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,2,6,1,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,7,2,4,1,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,7,2,5,1,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,7,3,5,1,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,3,2,7,1,6,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,3,2,7,1,5,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,3,2,7,1,4,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,4,2,7,1,3,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,3,2,6,1,4,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,4,2,6,1,3,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,3,2,8,1,6,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,3,2,8,1,4,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,4,3,8,1,2,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,3,2,8,1,4,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,4,2,8,1,3,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,3,2,8,1,4,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,4,3,8,1,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,5,2,8,1,3,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,3,2,6,1,4,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,4,2,6,1,3,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,5,2,4,1,3,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,3,2,7,1,4,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,3,2,7,1,4,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,4,3,7,1,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,3,2,6,1,4,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,4,2,6,1,3,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,4,3,6,1,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,5,2,6,1,3,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,6,2,4,1,3,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,6,2,5,1,3,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,6,3,5,1,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,8,3,7,2,6,1,5]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[5,8,3,7,2,6,1,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[5,8,4,7,3,6,1,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,8,3,7,2,5,1,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,8,4,7,2,5,1,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,8,5,7,2,4,1,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,8,4,6,3,5,1,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,8,5,6,2,4,1,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[5,4,3,8,2,7,1,6]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,4,3,8,2,7,1,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,3,8,2,7,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,4,8,3,7,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,4,3,8,2,6,1,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,5,3,8,2,6,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,5,4,8,2,6,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,6,3,8,2,5,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,6,4,8,2,5,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,4,3,7,2,6,1,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,3,7,2,6,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,4,7,2,6,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,4,7,3,6,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,6,3,7,2,5,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,6,4,7,2,5,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,6,4,7,3,5,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,6,5,7,2,4,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,7,3,6,2,5,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,7,4,6,2,5,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,7,4,6,3,5,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,7,5,6,2,4,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,4,3,2,8,1,7]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,6,5,4,2,8,1,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,5,4,3,2,7,1,6]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,4,3,2,6,1,5]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,5,3,2,6,1,4]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,5,4,2,6,1,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,6,3,2,5,1,4]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,6,4,2,5,1,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,6,5,2,4,1,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,1,2,3,4,7,5,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,1,2,3,6,4,5,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,1,2,3,7,4,5,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,1,2,3,6,4,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,2,3,8,7,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,2,3,6,7,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,8,3,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,2,5,3,4,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,1,2,5,3,4,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,2,6,3,4,5,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,1,2,6,3,4,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,2,5,3,8,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,2,5,3,7,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,2,6,3,7,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,2,5,3,7,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,8,6,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,8,7,3,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,7,6,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,2,5,6,3,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,2,5,7,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,2,7,6,3,4,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,1,2,5,6,3,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,5,8,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,2,8,6,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,2,5,6,7,3,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,8,2,4,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,8,2,6,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,8,2,7,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,7,2,6,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,5,2,8,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,2,6,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,4,2,3,5,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,1,4,2,3,5,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,4,2,3,8,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,4,2,3,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,4,2,3,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,5,2,3,4,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,1,5,2,3,4,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,7,2,3,4,5,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,1,5,2,3,8,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,5,2,3,7,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,8,2,3,7,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,5,2,3,7,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,4,2,8,3,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,4,2,7,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,4,2,6,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,4,2,7,3,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,4,2,6,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,5,2,6,3,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,5,2,7,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,8,2,6,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,5,2,6,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,4,2,6,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,4,2,8,7,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,1,4,2,6,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,5,2,6,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,4,2,6,7,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,4,8,2,7,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,5,2,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,7,5,2,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,6,2,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,7,6,2,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,5,2,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,5,2,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,6,2,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,5,2,7,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,4,5,2,3,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,4,5,2,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,4,6,2,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,4,8,2,3,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,4,6,2,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,6,5,2,3,4,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,1,8,5,2,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,8,6,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,6,5,2,3,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,4,5,2,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,4,5,2,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,4,6,2,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,6,5,2,7,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,4,5,2,7,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,4,8,6,2,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,4,8,7,2,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,4,7,6,2,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,5,6,2,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,5,7,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,7,6,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,7,5,6,2,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,4,5,6,2,3,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,4,5,7,2,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,4,7,6,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,7,5,6,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,4,5,6,2,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,4,5,8,7,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,4,8,6,7,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,5,6,7,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,4,5,6,7,2,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,1,3,4,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,1,3,6,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,1,3,7,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,1,3,6,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,1,3,8,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,1,3,6,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,8,3,7,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,1,5,3,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,1,5,3,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,1,6,3,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,1,6,3,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,1,5,3,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,1,5,3,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,1,5,3,7,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,8,6,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,8,7,3,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,7,6,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,1,5,6,3,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,1,5,7,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,1,7,6,3,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,1,5,6,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,5,8,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,8,6,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,1,5,6,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,1,2,4,5,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,3,1,2,4,8,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,3,1,2,4,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,3,1,2,4,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,3,1,2,8,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,3,1,2,7,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,1,2,6,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,3,1,2,7,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,1,2,6,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,1,2,6,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,1,2,8,7,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,3,1,2,6,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,1,2,6,7,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,4,1,2,3,5,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,4,1,2,3,8,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,4,1,2,3,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,4,1,2,3,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,6,1,2,3,4,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,8,1,2,3,7,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,6,1,2,3,7,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,4,1,2,8,3,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,4,1,2,7,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,2,6,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,4,1,2,7,3,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,4,1,2,6,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,1,2,6,3,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,8,1,2,7,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,7,1,2,6,3,4,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,7,1,2,6,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,1,2,6,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,1,2,8,7,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,4,1,2,6,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,1,2,6,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,1,2,6,7,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,1,8,2,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,1,7,2,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,1,6,2,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,1,8,2,7,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,1,6,2,7,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,1,5,2,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,1,5,2,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,1,6,2,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,1,8,2,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,1,6,2,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,1,5,2,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,1,5,2,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,1,6,2,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,1,5,2,7,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,5,2,3,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,4,1,5,2,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,6,2,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,4,1,8,2,3,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,4,1,6,2,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,8,1,5,2,3,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,7,1,5,2,3,4,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,7,1,6,2,3,4,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,7,1,5,2,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,1,5,2,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,5,2,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,6,2,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,8,1,5,2,7,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,4,1,5,2,7,8,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,1,5,8,2,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,1,5,7,2,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,1,8,6,2,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,1,8,7,2,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,1,7,6,2,8,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,3,1,5,6,2,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,1,5,7,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,1,7,6,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,1,5,6,2,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,5,6,2,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,5,7,2,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,7,6,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,1,5,6,2,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,4,1,5,6,2,8,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,1,5,6,8,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,1,5,8,7,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,3,1,8,6,7,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,3,1,5,6,7,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,5,6,7,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,1,5,6,7,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,8,1,4,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,8,1,6,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,8,1,7,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,7,1,6,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,5,1,8,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,8,1,6,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,4,1,3,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,4,1,3,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,4,1,3,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,4,1,3,7,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,4,1,3,7,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,5,1,3,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,5,1,3,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,7,1,3,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,6,5,1,3,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,5,1,3,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,8,1,3,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,5,1,3,7,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,4,1,8,3,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,4,1,7,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,4,1,6,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,4,1,7,3,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,4,1,6,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,5,1,6,3,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,5,1,7,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,8,1,6,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,5,1,6,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,4,1,6,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,4,1,8,7,3,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,8,4,1,6,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,5,1,6,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,4,1,6,7,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,4,1,2,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,4,1,2,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,4,1,2,7,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,4,1,2,7,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,5,1,2,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,7,1,2,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,5,1,2,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,5,1,2,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,8,1,2,7,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,5,1,2,7,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,5,4,1,2,3,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,4,1,2,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,7,4,1,2,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,8,5,1,2,3,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,7,5,1,2,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,5,4,1,2,8,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,4,1,2,7,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,4,1,2,7,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,8,5,1,2,7,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,5,4,1,2,7,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,4,1,8,2,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,4,1,7,2,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,4,1,6,2,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,4,1,7,2,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,4,1,6,2,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,5,1,6,2,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,5,1,7,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,8,1,6,2,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,3,5,1,6,2,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,5,4,1,6,2,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,4,1,7,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,4,1,6,2,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,5,1,6,2,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,5,4,1,6,2,8,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,4,1,6,8,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,4,1,8,7,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,3,4,1,6,7,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,5,1,6,7,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,5,4,1,6,7,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,4,1,6,7,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,8,1,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,8,5,1,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,7,5,1,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,8,6,1,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,7,6,1,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,6,5,1,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,8,5,1,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,8,6,1,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,6,5,1,7,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,4,5,1,3,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,4,5,1,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,4,6,1,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,4,8,1,3,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,4,6,1,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,6,5,1,3,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,8,5,1,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,8,6,1,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,6,5,1,3,8,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,6,4,5,1,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,4,5,1,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,4,6,1,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,6,5,1,7,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,6,4,5,1,7,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,4,5,1,2,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,4,6,1,2,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,6,5,1,2,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,8,5,1,2,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,3,8,6,1,2,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,3,6,5,1,2,8,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,6,4,5,1,2,8,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,4,5,1,8,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,4,5,1,7,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,4,6,1,7,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,6,5,1,7,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,6,4,5,1,7,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,4,5,1,7,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,8,6,1,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,8,7,1,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,7,6,1,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,8,5,6,1,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,8,5,7,1,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,8,7,6,1,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,7,5,6,1,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,4,5,6,1,3,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,4,5,7,1,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,4,7,6,1,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,8,7,5,6,1,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,7,4,5,6,1,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,3,4,5,7,1,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,4,7,6,1,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,7,5,6,1,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,4,5,6,1,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,5,8,7,1,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,8,6,7,1,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,8,5,6,7,1,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,4,5,6,7,1,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[9,1,2,3,4,5,6,7,8]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[8,1,2,3,4,5,6,9,7]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[7,1,2,3,4,5,9,6,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[9,1,2,3,4,5,8,6,7]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[7,1,2,3,4,5,8,9,6]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[6,1,2,3,4,9,5,7,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[6,1,2,3,4,8,5,9,7]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[9,1,2,3,4,7,5,6,8]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[9,1,2,3,4,8,5,6,7]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[8,1,2,3,4,7,5,9,6]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[6,1,2,3,4,7,9,5,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[6,1,2,3,4,9,8,5,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,1,2,3,4,7,8,5,6]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[6,1,2,3,4,7,8,9,5]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[5,1,2,3,9,4,6,7,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[5,1,2,3,8,4,6,9,7]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[8,1,2,3,9,4,5,6,7]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[5,1,2,3,9,8,4,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,1,2,3,6,8,4,5,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[5,1,2,3,6,9,8,4,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[5,1,2,3,6,7,8,9,4]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[4,1,2,8,3,5,6,9,7]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[4,1,2,9,3,5,8,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[4,1,2,9,3,8,5,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,1,2,8,3,4,5,6,7]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[7,1,2,8,3,4,5,9,6]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[4,1,2,5,9,3,6,7,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[4,1,2,8,9,3,5,6,7]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[8,1,2,5,9,3,4,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[8,1,2,9,6,3,4,5,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[4,1,2,5,9,8,3,6,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,1,2,8,6,7,3,4,5]=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>11010000
[4,1,2,5,6,7,9,3,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[4,1,2,9,6,7,8,3,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,1,2,5,6,7,8,3,4]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[4,1,2,5,6,7,8,9,3]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[3,1,9,2,4,5,6,7,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[3,1,8,2,4,5,6,9,7]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[3,1,9,2,4,5,8,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[8,1,4,2,3,5,6,9,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,1,4,2,3,5,8,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[6,1,4,2,3,7,8,9,5]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,1,8,2,3,4,5,6,7]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[8,1,7,2,3,4,5,9,6]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[3,1,4,9,2,5,6,7,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[3,1,4,9,2,5,8,6,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[3,1,9,8,2,4,5,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,1,4,5,2,3,6,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[7,1,4,5,2,3,8,9,6]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[7,1,4,9,2,3,5,6,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,1,4,8,2,3,5,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,1,6,5,2,3,4,7,8]=>[6,1,1,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>11100000
[7,1,9,6,2,3,4,5,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,1,8,6,2,3,4,5,7]=>[6,1,1,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>11100000
[7,1,8,9,2,3,4,5,6]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[3,1,4,8,9,2,5,6,7]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[3,1,8,9,7,2,4,5,6]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[8,1,4,5,6,2,3,9,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[8,1,4,9,7,2,3,5,6]=>[5,2,2]=>[[1,2,7,8,9],[3,4],[5,6]]=>01010000
[8,1,9,5,6,2,3,4,7]=>[5,2,2]=>[[1,2,7,8,9],[3,4],[5,6]]=>01010000
[8,1,9,7,6,2,3,4,5]=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>11010000
[7,1,4,5,6,2,8,9,3]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[3,1,4,5,6,9,2,7,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[3,1,4,5,6,8,2,9,7]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[3,1,4,9,8,7,2,5,6]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[3,1,9,8,6,7,2,4,5]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[9,1,4,5,6,7,2,3,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,1,4,8,6,7,2,3,5]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[9,1,8,5,6,7,2,3,4]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[8,1,4,5,6,7,2,9,3]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[3,1,4,5,6,7,9,2,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[3,1,4,9,6,7,8,2,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[3,1,9,5,6,7,8,2,4]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,1,4,5,6,7,8,2,3]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[3,1,4,5,6,7,8,9,2]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,9,1,3,4,5,6,7,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,8,1,3,4,5,6,9,7]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,7,1,3,4,5,9,6,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,9,1,3,4,5,8,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,7,1,3,4,5,8,9,6]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,6,1,3,4,9,5,7,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,9,1,3,4,8,5,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,8,1,3,9,4,5,6,7]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,9,1,3,8,7,4,5,6]=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>11010000
[2,9,1,3,6,7,8,4,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,5,1,3,6,7,8,9,4]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,4,1,6,3,8,5,9,7]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,9,1,8,3,4,5,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,7,1,6,3,4,8,9,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,6,1,5,3,7,8,9,4]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,4,1,5,9,3,6,7,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,4,1,8,9,3,5,6,7]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,8,1,9,7,3,4,5,6]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,9,1,8,6,7,3,4,5]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[2,4,1,5,6,7,9,3,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,4,1,5,6,9,8,3,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,9,1,5,6,7,8,3,4]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,4,1,5,6,7,8,9,3]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[9,3,1,2,4,5,6,7,8]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[8,3,1,2,4,5,6,9,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,3,1,2,4,5,8,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[6,3,1,2,4,7,8,9,5]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,3,1,2,6,7,8,4,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[5,3,1,2,6,7,8,9,4]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,4,1,2,3,5,6,7,8]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[7,4,1,2,3,5,8,9,6]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[6,4,1,2,3,7,8,9,5]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[5,9,1,2,3,4,6,7,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[5,8,1,2,3,4,6,9,7]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[5,7,1,2,3,4,8,9,6]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[9,6,1,2,3,4,5,7,8]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[8,6,1,2,3,4,5,9,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,7,1,2,3,4,5,6,8]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[8,9,1,2,3,4,5,6,7]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[8,7,1,2,3,4,5,9,6]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,6,1,2,3,4,8,5,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,7,1,2,3,4,8,5,6]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[7,6,1,2,3,4,8,9,5]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[5,9,1,2,3,8,4,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,8,1,2,3,7,4,5,6]=>[6,1,1,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>11100000
[8,6,1,2,3,7,4,9,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,6,1,2,3,7,8,4,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[5,6,1,2,3,7,8,9,4]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[5,4,1,2,9,3,6,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[8,4,1,2,9,3,5,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[5,8,1,2,9,3,4,6,7]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[9,7,1,2,6,3,8,4,5]=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>11010000
[9,8,1,2,6,7,3,4,5]=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>11010000
[5,4,1,2,6,7,9,3,8]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[5,4,1,2,6,7,8,9,3]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[4,3,1,9,2,5,6,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,3,1,8,2,4,5,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,4,1,8,2,3,5,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[6,9,1,5,2,3,4,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,7,1,6,2,3,4,5,8]=>[6,1,1,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>11100000
[8,7,1,9,2,3,4,5,6]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[8,7,1,6,2,3,4,9,5]=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>11010000
[9,8,1,6,2,7,3,4,5]=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>11010000
[9,8,1,7,6,2,3,4,5]=>[5,1,1,1,1]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>11110000
[4,3,1,5,6,8,2,9,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[4,3,1,5,9,8,2,6,7]=>[4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>01001000
[4,3,1,5,8,7,2,9,6]=>[4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>01001000
[8,9,1,5,6,7,2,3,4]=>[4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>01001000
[4,3,1,5,6,7,9,2,8]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[4,3,1,5,6,9,8,2,7]=>[4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>01001000
[9,3,1,5,6,7,8,2,4]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,4,1,5,6,7,8,2,3]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[4,3,1,5,6,7,8,9,2]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,9,1,4,5,6,7,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,3,8,1,4,5,6,9,7]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,3,9,1,4,5,8,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,9,1,4,7,8,5,6]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,3,9,1,8,7,4,5,6]=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>11010000
[2,3,8,1,6,7,4,9,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,3,5,1,6,7,9,4,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,3,9,1,6,7,8,4,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,3,5,1,6,7,8,9,4]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,9,4,1,3,5,6,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,6,4,1,3,7,8,9,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,9,5,1,3,4,6,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,6,9,1,3,4,5,7,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,9,7,1,3,4,5,6,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,9,8,1,3,4,5,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,6,7,1,3,4,8,9,5]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,9,4,1,6,3,5,7,8]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,8,4,1,9,3,5,6,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,9,4,1,6,3,8,5,7]=>[4,4,1]=>[[1,3,4,5],[2,7,8,9],[6]]=>10001000
[2,9,8,1,7,3,4,5,6]=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>11010000
[2,9,5,1,6,7,8,3,4]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,3,4,1,2,5,6,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[6,3,4,1,2,7,8,9,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,3,7,1,2,4,5,6,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,3,8,1,2,4,5,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,5,4,1,2,3,6,7,8]=>[6,1,1,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>11100000
[8,5,4,1,2,3,6,9,7]=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>11010000
[6,9,4,1,2,3,5,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[6,8,4,1,2,3,5,9,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,7,4,1,2,3,5,6,8]=>[6,1,1,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>11100000
[9,8,4,1,2,3,5,6,7]=>[6,1,1,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>11100000
[6,9,5,1,2,3,4,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[6,8,5,1,2,3,4,9,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[8,7,5,1,2,3,4,9,6]=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>11010000
[6,7,9,1,2,3,4,5,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[6,9,8,1,2,3,4,5,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,7,8,1,2,3,4,5,6]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[6,7,8,1,2,3,4,9,5]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[6,5,4,1,2,8,3,9,7]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[7,8,9,1,6,2,3,4,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[7,8,5,1,6,2,3,9,4]=>[4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>01001000
[5,3,4,1,6,8,2,9,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,3,4,1,8,7,2,5,6]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[8,3,4,1,6,7,2,9,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[8,5,4,1,6,7,2,9,3]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[5,3,4,1,9,7,8,2,6]=>[4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>01001000
[9,3,5,1,6,7,8,2,4]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,5,4,1,6,7,8,2,3]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[5,3,4,1,6,7,8,9,2]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,4,9,1,5,6,7,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,3,4,9,1,5,8,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,4,9,1,7,8,5,6]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,3,4,6,1,7,8,9,5]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,3,9,5,1,4,6,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,9,6,1,4,5,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,7,9,1,4,5,6,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,3,9,8,1,4,5,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,9,5,1,7,4,6,8]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,3,9,6,1,7,8,4,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,9,4,5,1,3,6,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,7,4,5,1,3,8,9,6]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,9,8,6,1,3,4,5,7]=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>11010000
[2,7,8,9,1,3,4,5,6]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,8,9,6,1,7,3,4,5]=>[4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>01001000
[2,9,6,5,1,7,8,3,4]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[7,3,4,5,1,2,8,9,6]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,3,4,8,1,2,5,6,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[7,3,4,8,1,2,5,9,6]=>[4,4,1]=>[[1,3,4,5],[2,7,8,9],[6]]=>10001000
[7,3,8,9,1,2,4,5,6]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,8,4,5,1,2,3,6,7]=>[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>11010000
[7,8,4,6,1,2,3,9,5]=>[4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>01001000
[9,8,6,5,1,2,3,4,7]=>[5,1,1,1,1]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>11110000
[7,8,9,6,1,2,3,4,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[7,8,6,5,1,2,3,9,4]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[8,3,9,6,1,7,2,4,5]=>[4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>01001000
[8,3,6,5,1,7,2,9,4]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[8,6,4,5,1,7,2,9,3]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[6,3,4,5,1,7,9,2,8]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[6,3,4,5,1,9,8,2,7]=>[4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>01001000
[9,3,4,6,1,7,8,2,5]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[6,3,4,5,1,7,8,9,2]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,4,5,9,1,6,7,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,3,4,5,8,1,6,9,7]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,3,4,5,9,1,8,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,4,5,7,1,8,9,6]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,3,4,9,6,1,5,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,4,9,7,1,5,6,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,4,9,6,1,8,5,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,3,4,9,7,1,8,5,6]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,3,9,5,6,1,4,7,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,8,5,6,1,4,9,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,3,9,5,6,1,8,4,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,8,4,5,6,1,3,9,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,8,9,5,7,1,3,4,6]=>[4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>01001000
[2,8,9,7,6,1,3,4,5]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[2,9,7,5,6,1,8,3,4]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[8,3,4,5,6,1,2,9,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[8,3,4,7,6,1,2,9,5]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[8,3,9,7,6,1,2,4,5]=>[4,2,2,1]=>[[1,3,8,9],[2,5],[4,7],[6]]=>10101000
[8,3,7,5,6,1,2,9,4]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[9,7,4,5,6,1,2,3,8]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[8,9,4,5,6,1,2,3,7]=>[4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>01001000
[8,9,7,5,6,1,2,3,4]=>[4,2,2,1]=>[[1,3,8,9],[2,5],[4,7],[6]]=>10101000
[8,7,4,5,6,1,2,9,3]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[7,3,4,5,6,1,9,2,8]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,3,4,5,6,1,8,2,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,3,7,5,6,1,8,2,4]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[7,3,4,5,6,1,8,9,2]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,4,5,6,9,1,7,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,3,4,5,6,8,1,9,7]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,3,4,5,9,7,1,6,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,4,5,9,8,1,6,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,4,9,6,7,1,5,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,9,5,6,7,1,4,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,9,5,6,8,1,4,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,9,4,5,6,7,1,3,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,9,4,5,6,8,1,3,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[2,9,4,5,8,7,1,3,6]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[2,9,4,8,6,7,1,3,5]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[2,9,8,5,6,7,1,3,4]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[2,8,4,5,6,7,1,9,3]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,3,4,5,6,7,1,2,8]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,3,4,5,6,8,1,2,7]=>[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>10010000
[9,8,4,5,6,7,1,2,3]=>[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>11001000
[8,3,4,5,6,7,1,9,2]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,4,5,6,7,9,1,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,3,4,5,6,9,8,1,7]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,4,5,9,7,8,1,6]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,4,9,6,7,8,1,5]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,9,5,6,7,8,1,4]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,9,4,5,6,7,8,1,3]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[9,3,4,5,6,7,8,1,2]=>[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000
[2,3,4,5,6,7,8,9,1]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[]=>[]=>[]=>
[3,5,2,6,1,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,2,6,4,1,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,2,7,4,8,1,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,2,7,4,8,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,7,2,3,8,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,7,2,3,8,1,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,6,2,3,1,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,6,2,1,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,1,6,4,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,6,1,3,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,6,3,1,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,7,3,2,8,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,7,3,2,8,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,7,3,8,2,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,7,3,8,2,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,7,3,8,1,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,7,3,1,8,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,7,1,3,8,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,1,7,4,8,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,5,7,4,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,5,7,4,8,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,1,7,4,8,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,7,1,3,8,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,7,3,1,8,6,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,6,7,3,8,1,5,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,6,7,3,8,5,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,6,7,3,8,5,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,8,3,1,4,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,6,7,8,1,3,4,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,7,1,8,3,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,1,7,8,4,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,7,8,4,5,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,7,8,4,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,1,7,8,4,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,7,1,8,3,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,7,8,1,3,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,7,2,1,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,7,2,8,1,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,7,2,8,3,1,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,7,2,8,3,5,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,2,7,8,4,5,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,2,7,8,4,1,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,2,7,8,1,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,2,7,1,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,2,1,7,8,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,1,2,7,8,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,2,7,1,8,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,2,7,8,1,5,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,2,7,8,5,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,2,7,8,5,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,7,2,8,5,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,7,2,8,5,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,6,7,2,8,1,5,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,5,7,2,1,8,6,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,5,7,1,2,8,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,1,7,2,8,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,5,7,3,8,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,7,8,3,5,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,1,7,8,2,5,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,7,1,8,2,5,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,7,8,1,2,4,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,7,8,2,1,4,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,6,7,8,2,4,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,6,7,8,2,4,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,8,1,4,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,7,1,8,5,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,1,7,8,5,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,7,8,5,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,1,7,8,5,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,7,1,8,5,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,8,1,4,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,8,4,1,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,2,1,6,5,8,7,10,9]=>[5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000
[3,5,2,6,4,1,8,7,10,9]=>[5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000
[3,5,2,7,4,8,6,1,10,9]=>[5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000
[3,5,2,7,4,9,6,10,8,1]=>[5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000
[2,1,5,6,4,3,8,7,10,9]=>[5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000
[4,5,6,3,2,1,8,7,10,9]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[4,5,7,3,2,8,6,1,10,9]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[4,5,7,3,2,9,6,10,8,1]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[2,1,5,7,4,8,6,3,10,9]=>[5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000
[4,6,7,3,8,5,2,1,10,9]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[4,6,7,3,9,5,2,10,8,1]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[2,1,5,7,4,9,6,10,8,3]=>[5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000
[4,6,8,3,9,5,10,7,2,1]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[2,1,4,3,7,8,6,5,10,9]=>[5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000
[3,4,2,1,7,8,6,5,10,9]=>[5,3,2]=>[[1,2,5,9,10],[3,4,8],[6,7]]=>010010000
[3,6,2,7,8,5,4,1,10,9]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[3,6,2,7,9,5,4,10,8,1]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[2,1,6,7,8,5,4,3,10,9]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[5,6,7,8,4,3,2,1,10,9]=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>111010000
[5,6,7,9,4,3,2,10,8,1]=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>111010000
[2,1,6,7,9,5,4,10,8,3]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[5,6,8,9,4,3,10,7,2,1]=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>111010000
[2,1,4,3,7,9,6,10,8,5]=>[5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000
[3,4,2,1,7,9,6,10,8,5]=>[5,3,2]=>[[1,2,5,9,10],[3,4,8],[6,7]]=>010010000
[3,6,2,8,9,5,10,7,4,1]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[2,1,6,8,9,5,10,7,4,3]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[5,7,8,9,4,10,6,3,2,1]=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>111010000
[6,7,8,9,10,1,4,5,3,2]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[6,7,8,9,10,1,4,5,2,3]=>[5,3,2]=>[[1,2,5,9,10],[3,4,8],[6,7]]=>010010000
[6,7,8,9,10,4,3,2,1,5]=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>111010000
[6,7,8,9,10,1,3,4,5,2]=>[5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000
[6,7,8,9,10,3,4,1,2,5]=>[5,3,2]=>[[1,2,5,9,10],[3,4,8],[6,7]]=>010010000
[6,7,8,9,10,3,4,2,1,5]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[6,7,8,9,10,2,3,4,1,5]=>[5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000
[2,1,4,3,6,5,9,10,8,7]=>[5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000
[3,4,2,1,6,5,9,10,8,7]=>[5,3,2]=>[[1,2,5,9,10],[3,4,8],[6,7]]=>010010000
[3,5,2,6,4,1,9,10,8,7]=>[5,3,2]=>[[1,2,5,9,10],[3,4,8],[6,7]]=>010010000
[3,5,2,8,4,9,10,7,6,1]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[2,1,5,6,4,3,9,10,8,7]=>[5,3,2]=>[[1,2,5,9,10],[3,4,8],[6,7]]=>010010000
[4,5,6,3,2,1,9,10,8,7]=>[5,2,2,1]=>[[1,3,8,9,10],[2,5],[4,7],[6]]=>101010000
[4,5,8,3,2,9,10,7,6,1]=>[5,2,2,1]=>[[1,3,8,9,10],[2,5],[4,7],[6]]=>101010000
[2,1,5,8,4,9,10,7,6,3]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[4,7,8,3,9,10,6,5,2,1]=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>111010000
[2,1,4,3,8,9,10,7,6,5]=>[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000
[3,4,2,1,8,9,10,7,6,5]=>[5,2,2,1]=>[[1,3,8,9,10],[2,5],[4,7],[6]]=>101010000
[3,7,2,8,9,10,6,5,4,1]=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>111010000
[2,1,7,8,9,10,6,5,4,3]=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>111010000
[6,7,8,9,10,1,5,4,3,2]=>[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>111010000
[6,7,8,9,10,5,4,3,2,1]=>[5,1,1,1,1,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>111110000
[6,5,8,7,3,4,1,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[3,6,7,4,5,8,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,7,4,5,2,3,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,4,7,6,2,3,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,5,4,7,6,8,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,5,3,7,8,6,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,4,3,8,7,6,1,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,4,8,3,7,5,1,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,3,8,4,5,7,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,5,6,1,8,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,8,4,5,1,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,1,4,5,2,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,3,2,8,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,8,3,1,5,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,3,8,1,6,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,8,2,1,7,5,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,8,3,2,1,6,5,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,8,4,2,6,1,5,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[5,4,2,8,7,1,6,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[4,5,2,7,8,1,6,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,5,3,7,1,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,3,7,2,6,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,7,3,2,5,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,6,7,3,1,5,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,7,2,1,8,5,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,5,6,2,1,4,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,5,8,7,1,2,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,4,8,1,7,2,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,3,1,2,6,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,1,8,2,7,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,1,2,8,7,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,1,3,8,5,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,1,2,6,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,1,6,2,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,1,5,2,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,1,5,2,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,5,1,2,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,5,1,2,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,5,1,2,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,6,1,2,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,5,3,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,1,5,2,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,5,1,2,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,4,1,2,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,5,4,1,2,3,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,4,1,2,8,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,4,1,7,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,4,1,8,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,4,1,8,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,4,1,2,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,5,1,2,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,1,5,2,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,7,5,3,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,8,5,3,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,8,1,5,2,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,8,5,1,2,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,4,1,2,7,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,8,4,1,7,2,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,7,4,1,6,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,6,7,1,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,8,6,1,7,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,8,1,6,7,2,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,8,6,7,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,7,6,8,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,1,6,8,2,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,6,1,8,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,6,8,1,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,7,1,2,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,7,1,8,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,6,1,8,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,6,1,7,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,1,6,7,2,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,1,6,8,2,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,1,7,8,2,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,1,7,2,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,1,2,7,8,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,3,8,7,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,1,2,8,7,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,1,8,7,2,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,3,1,8,6,2,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,4,7,1,6,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,8,1,6,2,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,4,8,1,2,7,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,5,8,1,2,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,1,8,2,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,5,8,3,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,8,7,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,1,8,7,2,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,8,1,7,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,8,7,1,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,5,8,6,1,2,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,5,7,6,1,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,7,8,6,1,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,8,1,6,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,1,8,6,2,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,7,8,6,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,8,7,6,3,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,1,7,6,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,7,1,6,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,7,6,1,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,7,5,1,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,7,3,8,5,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,7,2,5,1,8,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,3,7,6,8,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,8,3,5,7,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,2,6,7,1,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,2,8,6,1,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,8,2,5,1,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,4,2,5,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,2,1,6,8,5,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,3,2,1,8,6,5,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,2,8,1,6,4,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,3,2,1,5,4,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,3,2,1,5,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,8,2,1,5,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,2,7,1,8,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,2,7,1,6,8,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,7,2,1,8,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,7,2,8,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,7,8,2,1,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,8,7,2,1,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,7,2,1,8,4,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,2,7,1,4,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,8,2,1,7,4,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,2,8,1,7,4,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,2,1,8,7,5,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,2,1,8,5,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,8,2,1,4,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,8,2,1,4,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,2,1,8,5,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,2,1,5,8,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,4,1,6,2,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,1,8,4,7,2,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,6,8,4,7,2,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,1,3,2,6,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,3,4,6,5,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,2,4,6,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,1,2,3,6,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,8,2,3,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,8,2,3,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,2,8,1,3,7,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,8,4,7,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,8,4,7,5,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,6,8,4,7,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,2,5,8,3,7,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,1,3,8,7,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,5,3,8,1,7,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,2,1,3,8,7,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,1,2,3,8,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,1,2,8,7,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,8,1,2,7,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,1,3,8,2,7,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,5,4,8,7,2,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,8,1,7,2,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,8,7,2,1,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,5,1,8,7,2,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,4,5,8,7,2,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,8,2,7,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,8,3,7,5,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,5,2,8,7,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,2,8,1,7,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,1,2,4,8,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,5,8,7,6,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,3,2,6,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,3,2,6,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,3,2,5,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,3,2,5,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,3,2,5,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,4,2,5,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,4,2,5,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,4,2,5,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,4,2,6,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,3,5,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,2,5,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,6,2,5,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,5,1,4,3,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,6,1,4,3,8,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,2,7,1,4,3,8,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,2,8,1,4,3,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,8,1,4,3,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,7,1,4,3,8,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,2,6,1,4,3,8,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,2,5,1,4,3,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,1,7,2,5,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,7,2,5,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,7,3,5,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,8,3,5,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,2,5,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,8,2,5,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,2,5,1,4,3,7,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,2,6,1,4,3,7,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,1,4,3,8,2,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,1,4,3,7,2,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,1,5,3,7,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,5,3,8,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,6,1,5,3,7,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,8,2,6,3,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,8,2,6,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,2,6,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,8,3,6,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,7,3,6,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,7,2,6,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,7,2,6,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,2,6,1,5,3,8,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,2,7,1,5,3,8,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,8,1,5,3,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,1,5,2,6,3,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,5,2,7,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,4,2,7,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,4,2,6,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,3,2,6,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,3,2,6,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,3,2,7,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,3,2,7,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,3,2,7,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,3,8,5,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,4,2,8,5,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,3,2,8,5,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,3,2,8,4,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,1,3,2,8,4,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,4,7,1,3,2,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,8,1,3,2,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,8,1,4,2,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,3,7,1,4,2,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,4,2,8,3,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,4,2,8,3,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,5,2,8,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,5,2,8,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,5,3,8,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,3,8,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,2,8,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,6,2,8,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,6,2,8,3,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,5,2,8,3,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,3,7,1,5,2,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,8,1,5,2,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,7,3,8,1,5,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,8,3,7,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,7,2,6,1,5,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,1,8,3,7,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,1,8,3,7,2,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,1,8,4,7,2,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,8,4,7,3,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,7,4,8,3,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,1,7,4,8,2,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,1,7,3,8,2,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,1,7,3,8,2,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,3,8,2,6,1,5,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[8,2,6,3,7,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,2,6,3,8,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,4,2,6,8,1,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,6,2,8,1,4,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,6,2,4,8,1,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,3,8,2,4,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,3,8,2,4,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,2,5,8,3,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,2,5,8,3,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,5,2,6,3,8,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,2,1,6,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,1,6,8,2,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,2,8,1,3,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,6,1,4,8,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,5,6,3,8,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,1,6,3,8,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,6,3,2,8,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,5,3,8,2,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,5,3,8,2,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,4,8,3,2,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,4,8,3,2,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,4,1,8,3,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,5,3,1,8,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,1,5,8,3,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,7,8,1,4,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,5,8,2,4,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,5,8,1,4,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,5,1,7,8,3,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,1,5,8,3,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,4,3,8,1,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,4,8,3,1,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,4,8,3,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,7,3,8,4,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,3,1,8,4,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,6,1,7,3,8,4,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,6,7,3,8,4,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,7,1,8,3,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,3,1,4,5,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,2,8,4,5,1,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,2,8,4,1,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,1,7,4,8,3,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,6,7,3,2,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,1,7,3,2,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,7,3,2,1,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,3,2,8,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,2,7,3,8,4,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,2,7,3,1,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,2,1,7,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,7,4,2,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,2,1,8,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,5,8,2,1,3,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,7,3,1,8,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,1,5,2,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,2,5,1,8,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,4,2,1,8,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,4,2,8,3,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,4,2,8,3,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,6,7,2,8,4,5,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,7,2,8,4,1,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,7,2,1,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,3,8,2,1,4,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,4,7,8,2,1,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,8,1,4,6,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,4,7,8,2,6,1,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,7,3,8,2,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,6,7,2,8,5,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,7,8,5,2,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,7,8,5,2,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,7,8,2,5,3,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,7,8,2,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,1,5,7,8,2,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,7,8,1,6,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,2,8,5,1,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,4,1,7,8,2,5,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,1,6,2,7,8,4,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,2,1,7,8,4,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,6,2,7,1,8,4,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,6,2,7,8,4,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,2,8,4,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,2,1,8,4,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,6,1,7,2,8,4,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,6,7,2,8,4,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,7,1,8,2,5,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,6,7,1,8,5,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,8,5,2,4,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,8,3,5,1,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,7,8,1,5,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,6,7,8,4,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,1,7,8,4,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,1,8,4,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,1,3,4,2,5,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,3,2,5,1,6,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,3,6,2,4,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,3,2,7,4,1,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,3,8,2,4,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,2,4,5,8,3,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,5,3,7,1,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,2,4,5,6,3,1,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,4,5,6,1,3,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,2,4,5,6,3,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,2,5,1,3,6,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,5,6,2,1,4,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,3,6,4,1,2,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,1,5,6,3,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,4,5,6,3,2,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,5,3,7,2,1,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,5,8,3,2,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,3,6,7,2,8,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,6,7,2,8,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,3,6,7,2,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,3,7,1,8,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,5,3,7,2,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,4,7,1,2,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,5,8,2,1,4,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,8,4,1,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,5,8,3,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,6,7,8,1,5,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,4,7,8,3,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,7,8,3,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,6,7,8,4,1,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,5,6,7,8,4,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,6,1,7,8,3,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,7,1,4,8,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,4,1,7,8,5,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,6,7,1,4,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,6,7,8,1,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,3,6,7,8,2,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,6,7,8,2,1,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,6,7,8,2,4,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,7,1,3,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,1,7,8,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,2,7,8,1,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,7,8,3,1,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,7,8,3,5,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,2,7,4,8,5,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,2,7,4,8,1,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,1,6,4,7,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,4,2,1,5,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,3,4,2,5,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,7,2,1,3,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,4,2,1,3,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,1,3,4,2,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,3,4,2,1,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,2,7,1,8,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,6,2,7,1,8,5,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,7,3,8,2,5,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,7,8,5,2,3,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,6,4,7,8,1,5,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,6,2,7,8,1,5,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,4,5,8,6,2,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,1,5,8,6,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,5,3,8,6,1,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,8,2,1,6,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,7,1,3,8,5,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,3,1,7,8,2,5,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,6,1,7,8,5,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,2,6,7,8,4,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,6,7,8,4,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,6,7,8,4,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,5,6,7,8,4,1,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,2,6,7,8,4,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,4,7,8,5,2,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,6,7,1,3,8,5,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,8,2,1,5,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,3,8,5,1,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,7,8,5,3,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,5,2,3,7,6,1,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,3,7,2,5,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,3,6,5,1,2,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,5,6,3,4,8,7,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,2,7,3,5,1,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,6,7,4,5,1,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,2,6,5,3,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,6,2,4,3,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,7,5,4,8,3,6,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,5,4,1,3,2,6]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,8,5,4,2,1,3,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,6,2,4,1,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,2,6,5,1,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,8,6,5,1,4,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,1,2,6,5,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,6,2,4,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,5,4,2,8,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,5,4,8,2,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,1,5,4,7,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,6,7,4,5,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,6,7,4,5,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,6,8,4,2,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,1,7,8,2,4,5,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,7,2,8,4,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,2,7,8,5,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,1,7,8,5,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,8,7,1,5,4,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,2,7,1,5,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,7,2,1,4,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,7,1,2,4,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,6,1,4,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,6,1,4,3,2,5]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,7,6,8,4,3,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,6,7,8,3,4,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,6,7,1,3,4,2,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,8,1,3,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,7,8,2,1,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,2,8,1,3,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,6,8,4,1,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,2,8,3,1,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,8,2,3,1,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,5,8,3,2,1,4,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,8,3,1,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,7,3,1,4,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,5,7,3,8,4,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,3,7,8,5,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,3,7,1,5,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,3,8,2,1,5,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,2,3,8,1,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,5,4,8,1,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,2,3,1,8,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,4,3,1,2,8,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,3,1,8,2,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,3,1,7,6,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,5,8,3,7,6,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,1,3,7,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,1,3,8,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,1,3,2,8,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,1,2,3,8,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,2,1,3,8,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,6,1,4,8,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,7,1,8,4,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,2,1,8,3,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,1,2,8,3,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,1,8,2,3,5,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,6,1,8,3,2,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,1,7,3,5,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,6,8,7,3,5,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,7,8,6,5,3,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,1,6,5,3,2,4]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,8,1,6,5,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,1,7,2,5,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,1,2,7,6,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,2,1,7,6,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,8,1,7,6,4,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,1,2,8,7,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,1,8,2,7,6,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,1,8,7,2,5,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,1,8,6,5,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,7,6,5,4,2,3]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[3,1,2,6,5,8,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,2,4,8,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,5,2,4,8,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,1,2,3,8,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,1,2,3,8,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,5,3,4,8,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,5,2,4,8,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,1,2,3,8,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,4,1,2,3,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,4,1,2,3,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,4,1,2,7,3,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,4,1,7,2,3,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,4,1,8,2,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,4,1,2,8,3,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,5,1,2,8,3,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,1,5,2,8,4,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,5,3,8,4,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,5,3,7,4,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,5,2,7,4,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,1,2,7,3,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,1,2,7,3,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,1,7,2,3,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,4,1,6,2,3,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,6,1,7,2,3,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,6,7,2,4,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,6,7,3,4,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,6,8,3,4,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,6,8,2,4,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,1,8,2,3,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,1,2,8,3,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,7,2,8,4,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,2,7,8,5,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,3,8,7,5,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,2,8,7,5,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,2,8,7,5,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,8,2,7,4,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,8,7,2,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,7,6,2,4,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,7,1,6,2,3,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,8,1,6,2,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,8,1,7,2,3,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,8,1,2,7,3,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,1,2,7,3,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,8,2,7,4,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,8,3,7,4,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,8,7,3,4,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,8,7,2,4,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,1,7,2,3,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,7,1,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,8,7,1,2,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,8,6,1,2,3,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,7,6,1,2,3,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,8,1,6,2,3,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,8,6,2,4,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,8,6,3,4,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,7,6,3,4,5,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,1,7,6,2,4,5,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,7,1,6,2,3,5,4]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,2,5,1,6,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,5,4,7,1,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,5,3,7,6,8,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,5,3,7,1,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,5,3,6,1,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,5,1,6,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,5,4,6,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,5,3,6,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,5,1,6,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,5,2,7,1,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,6,2,7,5,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,6,2,7,1,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,6,1,7,2,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,5,1,7,2,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,5,4,7,2,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,5,4,7,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,5,4,7,6,8,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,5,3,7,6,8,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,5,1,7,6,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,6,1,7,5,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,6,5,7,1,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,6,4,7,2,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,6,4,7,1,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,6,1,7,4,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,6,3,7,4,8,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,6,3,7,5,8,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,4,7,5,8,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,4,7,5,8,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,4,7,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,4,7,2,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,6,3,7,2,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,6,3,7,2,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,6,1,7,2,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,6,2,7,1,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,6,2,7,4,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,2,6,3,7,4,8,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,6,3,7,1,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,6,1,7,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,5,1,7,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,1,7,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,3,7,1,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,3,7,5,8,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,6,4,7,5,8,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,6,4,7,1,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,6,1,7,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,5,1,7,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,4,1,7,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,4,2,7,6,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,5,1,7,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,6,1,7,5,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,6,5,7,1,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,6,5,7,3,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,6,5,7,1,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,6,1,7,5,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,5,1,7,6,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,5,2,7,6,8,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,5,2,7,6,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,5,3,7,6,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,3,7,5,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,2,7,5,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,6,2,7,5,8,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,6,2,7,4,8,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,6,1,7,4,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,6,4,7,1,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,6,4,7,3,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,6,2,7,3,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,6,2,7,1,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,6,1,7,2,8,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,6,4,7,2,8,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,6,5,7,2,8,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,5,7,2,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,5,7,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,5,7,4,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,6,5,7,3,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,6,4,7,3,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,6,1,7,3,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,6,3,7,1,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,5,2,1,6,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,3,5,2,4,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,7,5,2,4,1,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,7,5,2,4,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,2,4,5,7,3,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,5,7,3,1,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,2,4,6,5,3,1,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,5,4,6,1,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,3,5,1,4,2,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,1,4,5,3,2,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,1,5,6,4,3,2,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,7,4,3,2,1,8,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,7,4,3,2,6,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[4,6,8,3,2,7,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,6,3,2,8,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,4,6,7,3,2,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,4,7,3,1,8,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,7,4,5,3,2,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,7,5,1,4,2,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,4,2,1,3,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,7,4,2,1,6,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,3,7,5,1,4,6,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,1,7,5,3,6,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,6,3,8,7,1,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,7,4,8,6,3,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,7,6,3,5,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[3,6,5,8,7,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,1,5,8,6,7,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,1,6,7,3,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,6,4,1,8,7,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,6,1,4,7,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,7,6,8,1,4,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,1,6,4,8,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,7,3,5,6,8,2,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,6,7,5,8,2,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,7,6,5,8,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,6,8,5,7,2,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,3,5,7,6,8,1,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,6,5,7,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,7,6,8,3,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,2,6,8,7,3,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,8,2,4,6,7,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,7,2,6,4,8,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,2,6,1,4,7,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,7,2,1,8,4,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,3,2,1,5,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,6,1,3,4,2,5]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,5,7,3,2,1,6,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,3,6,7,2,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,7,8,6,2,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,6,3,5,2,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[2,7,4,8,1,6,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,8,2,1,7,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,1,5,7,2,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,3,7,1,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,2,1,3,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,6,7,1,3,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,6,1,7,5,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,6,1,8,7,2,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,2,5,6,7,4,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,6,5,7,4,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,7,8,5,6,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,2,5,7,6,4,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,7,6,8,5,4,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,7,2,5,8,6,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,4,8,2,6,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,7,8,1,6,5,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,7,8,6,1,3,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,6,3,5,1,4,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,4,7,6,5,1,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,1,5,6,4,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,1,6,7,5,4,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,5,3,1,2,4,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,3,5,1,2,8,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,5,3,7,2,1,4,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,8,1,4,5,7,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,2,4,5,1,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,2,4,5,1,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,1,4,5,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,2,4,5,3,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,6,3,2,1,4,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,3,6,1,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,1,4,5,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,4,5,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,7,4,5,1,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,7,4,2,6,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[2,8,7,4,1,6,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,7,4,2,6,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,7,8,4,5,1,2,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,8,7,5,3,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,6,8,5,7,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,3,8,1,7,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,6,1,4,5,8,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,7,6,4,5,8,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,5,7,4,1,6,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,1,8,4,7,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,8,4,7,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,4,8,3,5,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,8,3,5,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,8,4,2,5,6,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,4,1,3,5,6,7,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,5,8,4,3,6,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,3,8,4,1,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,5,8,4,6,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,8,3,6,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,3,8,2,1,7,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,3,8,4,2,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,1,2,5,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,8,2,5,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,8,1,5,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,8,2,5,6,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,2,3,5,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,8,2,1,5,6,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,8,1,3,5,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,2,3,5,6,7,4]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,8,2,4,3,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,3,2,4,1,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,8,3,4,6,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,7,8,5,4,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,3,8,1,4,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,1,8,4,5,3,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,8,4,5,3,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,1,4,3,6,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,8,7,4,2,6,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,8,4,3,6,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,3,8,4,2,7,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,3,6,2,1,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,3,1,4,2,7,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,3,8,2,4,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,4,3,1,8,5,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,3,2,6,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,5,3,6,2,8,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,3,5,1,2,7,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,3,2,6,1,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,5,3,8,6,2,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,8,4,7,6,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,2,4,7,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,5,4,1,6,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,7,6,4,5,8,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,6,4,5,8,2,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,7,3,6,1,8,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,1,7,6,5,8,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,8,5,3,6,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,8,3,5,2,1,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,5,4,2,6,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,1,4,2,5,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,4,1,5,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,8,1,2,5,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,4,8,1,5,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,4,2,8,5,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,1,8,5,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,8,5,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,4,2,1,5,6,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,2,4,8,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,3,2,8,1,7,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[2,1,5,3,8,6,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,3,5,8,1,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,5,4,8,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,4,1,5,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,1,8,5,6,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,1,4,8,5,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,5,3,7,2,8,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,7,4,5,8,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,2,4,5,8,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,7,4,8,6,3,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,5,7,4,8,6,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,3,7,1,8,4,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,8,7,4,5,2,1,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,7,5,4,8,6,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,1,4,8,6,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,3,1,8,2,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,6,3,5,8,2,7,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,6,3,8,1,2,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,7,8,4,1,6,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,5,1,6,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,2,5,4,8,1,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,5,2,4,7,1,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,8,2,4,7,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,2,5,8,3,7,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,2,6,5,3,8,1,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,2,1,6,8,3,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,5,1,4,8,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,6,1,5,3,8,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,6,4,3,8,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,3,2,7,1,8,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,3,8,2,7,6,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,3,6,2,8,7,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,7,6,2,1,8,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,3,1,7,2,8,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,4,3,1,8,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,4,7,5,8,3,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,3,5,8,4,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,5,8,4,1,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,8,5,7,4,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,8,7,1,4,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,4,5,8,7,3,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,4,8,7,3,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,3,8,1,7,5,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[4,3,7,1,8,6,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,3,7,6,5,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,3,8,7,6,4,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,5,3,1,8,6,4,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[1,8,6,5,3,7,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,5,8,6,3,7,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,1,8,7,3,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,8,7,3,1,4,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,8,7,4,5,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,2,8,4,1,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,1,6,8,4,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,7,6,4,8,3,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,1,6,3,2,8,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,7,5,3,2,8,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,6,5,3,2,1,8,4]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,5,3,2,8,7,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,2,6,3,8,7,4,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,7,6,3,1,8,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,2,1,7,3,8,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,7,4,1,8,3,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,2,6,3,1,8,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,4,8,6,3,7,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,6,2,4,7,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,6,2,4,1,8,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,6,7,2,1,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,7,8,2,1,5,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,7,1,4,6,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,8,2,5,7,1,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,6,2,7,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,3,6,2,1,5,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[8,7,3,6,2,5,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[4,7,8,2,1,6,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,2,6,8,1,7,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,8,2,7,1,6,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[4,8,1,5,7,2,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,3,7,1,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,7,2,6,1,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,2,7,5,1,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,6,8,1,7,5,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,6,8,2,7,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,2,8,1,7,4,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[5,2,7,1,8,6,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,2,7,6,4,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,2,8,7,5,4,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,6,2,1,8,5,4,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,1,7,2,8,5,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,1,8,2,6,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,1,8,6,2,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,8,3,1,6,5,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,4,6,1,5,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,5,7,1,6,4,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,8,1,7,5,4,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,1,8,6,5,4,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,4,2,3,7,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,2,7,3,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,2,6,3,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,2,6,3,1,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,7,6,4,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,2,6,3,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,7,6,2,3,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,5,2,3,8,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,5,2,8,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,8,5,2,3,1,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,6,2,3,1,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,2,6,3,1,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,8,6,4,1,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,1,6,4,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,5,2,8,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,5,2,7,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,6,7,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,6,7,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,6,8,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,1,7,8,4,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,8,7,1,4,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,7,2,1,3,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,6,8,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,5,8,2,3,1,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,7,2,1,3,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,2,8,3,1,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,2,3,8,1,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,5,4,1,8,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,2,3,1,8,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,2,3,1,8,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,2,1,3,8,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,2,1,8,3,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,2,1,7,3,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,2,8,7,3,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,8,2,7,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,5,1,2,7,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,5,1,2,8,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,5,1,2,3,8,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,6,2,1,3,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,6,1,4,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,7,1,8,4,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,2,1,8,3,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,6,1,8,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,6,1,7,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,8,7,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,8,6,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,8,1,6,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,8,1,7,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,8,2,1,7,3,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,8,1,7,4,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,8,7,4,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,8,2,7,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,8,7,2,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,7,6,2,3,4,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,8,7,6,2,3,4,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,3,5,1,2,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,5,6,1,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,7,5,2,1,4,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,7,5,1,8,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,2,7,1,8,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,2,7,4,1,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,6,1,5,4,3,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,3,5,1,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,1,4,6,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,4,6,5,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,4,6,2,8,3,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,1,4,7,2,6,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,7,8,5,2,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,8,5,7,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,6,3,5,1,7,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,2,4,6,7,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,8,6,5,7,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,4,8,1,6,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,1,4,6,8,2,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,5,4,6,7,1,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,6,3,7,5,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,6,3,8,5,7,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,4,2,8,6,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,1,3,5,8,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,8,4,1,7,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,3,7,4,1,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,4,8,3,7,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,3,8,2,1,6,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,3,7,4,1,8,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,3,1,2,5,7,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,8,2,7,6,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,3,8,1,6,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,7,2,6,8,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,2,3,8,5,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,8,2,1,7,5,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,1,3,6,5,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,8,5,4,3,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,1,6,3,4,2,5]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,8,6,7,2,4,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,8,7,4,2,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,3,8,7,2,1,6,5]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[8,3,6,1,4,2,7,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,5,8,2,4,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,3,4,1,8,5,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,3,2,6,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,3,5,6,2,7,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,6,1,8,7,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,2,8,7,4,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,5,6,1,4,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,6,5,4,7,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,6,4,5,7,2,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,3,6,1,7,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,1,8,6,5,7,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,7,5,3,6,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,3,5,2,1,8,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,4,2,5,6,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,4,1,6,5,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,1,2,8,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,5,8,7,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,2,5,8,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,4,2,1,5,8,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,2,4,6,1,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,3,2,6,8,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,5,3,6,8,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,5,4,6,1,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,4,1,5,7,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,1,5,7,6,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,1,4,5,6,8,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,2,6,3,1,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,5,2,1,4,3,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,2,7,4,8,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,2,7,4,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,7,5,2,1,6,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,7,5,2,8,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,1,6,5,4,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,3,2,4,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,6,2,4,1,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,1,3,5,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,2,3,4,8,5,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,2,3,4,1,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,7,3,8,4,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,7,3,8,6,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,1,3,5,8,4,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,6,7,4,1,8,5,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,6,3,7,4,8,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,6,7,4,8,5,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,8,7,4,3,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,3,7,4,2,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,8,7,4,1,2,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,8,1,3,5,2,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,7,3,2,6,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[2,8,6,3,1,5,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,6,3,2,5,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,4,1,6,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,8,1,2,7,6,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,4,2,5,7,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,3,5,2,7,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,5,3,8,7,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,3,2,8,7,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,5,2,4,8,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,4,2,8,5,7,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,1,8,7,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,2,1,7,5,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,1,8,6,7,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,1,4,8,6,5,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,6,5,4,8,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,7,5,6,8,4,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,7,1,6,8,2,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,6,2,5,1,7,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,2,1,8,7,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,6,2,5,8,3,7,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,2,6,3,8,1,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,1,2,3,6,8,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,3,1,8,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,5,2,8,3,4,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,2,8,4,3,1,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,2,8,1,5,3,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,7,2,1,4,5,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,8,7,1,5,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,8,6,3,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,8,5,4,3,6,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,7,8,4,5,3,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,7,3,8,1,4,6,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,1,7,8,5,4,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,5,8,4,6,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,5,3,8,4,1,2,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,8,4,3,6,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[2,4,8,3,5,6,1,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,8,3,6,5,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,8,1,7,2,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,3,7,2,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,1,8,2,4,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,8,1,4,6,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,8,2,5,1,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,8,4,2,5,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,3,8,2,5,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,4,8,3,5,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,8,2,4,3,5,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,2,3,5,1,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,8,2,1,4,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,8,1,3,4,5,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,4,1,6,5,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,4,1,6,5,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,7,6,1,4,3,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,8,5,6,7,4,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,5,8,6,1,4,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,7,6,1,4,2,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,7,2,4,1,6,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,5,8,2,4,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,5,3,4,7,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,5,3,4,1,7,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,5,3,4,1,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,7,6,1,4,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,8,5,3,6,1,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,5,6,7,4,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,5,3,4,7,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,5,3,4,6,1,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,5,3,4,6,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,5,7,2,4,6,1,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,5,2,7,3,1,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,2,8,3,1,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,2,8,3,1,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,8,2,4,6,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,8,6,1,4,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,8,2,1,3,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,6,2,1,8,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,5,7,6,1,4,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,7,2,4,1,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,7,2,4,6,8,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,5,2,7,3,1,8,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,5,2,6,3,1,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,3,7,6,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,5,2,7,3,4,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,6,7,4,3,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,2,6,4,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,2,8,6,4,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,6,8,7,3,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,2,8,3,7,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,1,2,3,8,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,3,8,6,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,3,8,6,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,3,7,6,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,3,8,5,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,6,8,4,3,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,1,2,8,4,5,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,6,8,2,3,1,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,5,8,2,4,3,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,8,2,4,3,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,2,8,3,4,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,2,8,3,7,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,2,7,3,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,6,7,4,3,2,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,6,8,7,3,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,1,6,8,4,3,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,8,6,3,4,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,1,8,3,6,5,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,8,3,6,2,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,1,4,8,6,2,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,4,8,6,5,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,6,5,8,3,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,1,6,7,8,3,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,6,5,7,3,2,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,2,6,3,7,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,2,7,3,8,1,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,6,2,4,8,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,6,2,4,8,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,5,6,8,4,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,5,2,8,1,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,1,2,5,8,4,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,6,5,8,3,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,2,6,3,8,4,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,1,2,3,5,8,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,3,7,8,6,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,2,7,3,8,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,6,7,8,3,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,2,6,8,5,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,2,5,6,8,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,2,6,3,7,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,8,5,6,1,4,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,8,4,2,1,5,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,2,1,6,5,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,1,2,5,7,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,8,1,5,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,8,1,7,2,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,3,4,5,1,6,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,3,5,4,2,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,3,6,5,4,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,8,2,6,4,1,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,1,6,5,4,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[2,1,8,7,5,4,3,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,3,8,2,6,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,7,1,6,4,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,6,2,7,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,2,5,8,7,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,1,8,4,2,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,4,2,1,5,3,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,3,7,5,8,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,8,7,5,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,4,7,1,5,3,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,7,6,4,2,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,7,2,8,6,4,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,8,1,7,6,4,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,5,7,3,6,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,7,5,8,3,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,5,6,8,2,4,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,7,3,8,4,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,5,6,7,2,8,1,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,7,6,1,8,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,8,6,2,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,5,8,3,2,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,5,7,1,2,8,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,5,6,3,1,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,6,3,4,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,6,4,3,8,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,4,5,8,7,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,4,1,8,3,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,1,4,2,7,6,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,2,4,7,8,3,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,7,2,4,1,6,3,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,7,6,3,4,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,7,6,2,3,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,8,2,1,5,6,3,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,7,8,1,6,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,1,8,7,6,5,3,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,8,6,3,5,7,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,6,5,2,4,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,3,7,8,2,1,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,8,7,1,6,4,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[3,6,7,8,5,1,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,7,8,5,1,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,8,6,2,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,8,7,6,5,4,1,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[2,8,7,5,1,4,3,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,8,6,7,5,1,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,7,8,6,5,4,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,2,7,1,3,8,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,2,5,1,3,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,3,6,1,7,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,6,2,4,8,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,6,7,1,2,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,7,4,1,2,8,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,1,5,2,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,6,4,2,3,8,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,4,2,3,7,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,7,6,3,8,1,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,4,2,3,8,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,6,1,4,8,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,7,5,2,8,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,8,5,2,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,6,2,4,7,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,6,2,7,1,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,6,5,8,1,3,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,7,4,8,1,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,6,7,2,8,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,7,1,4,8,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,7,2,4,8,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,7,3,8,1,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,6,3,8,1,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,6,3,7,1,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,1,6,7,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,1,6,8,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,5,3,7,1,8,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,1,2,7,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,6,4,7,8,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,7,4,8,5,1,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,1,5,8,6,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,5,1,2,8,6,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,6,1,8,5,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,1,7,5,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,7,2,8,1,6,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,3,7,8,5,1,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,6,8,2,7,1,4,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,4,8,7,1,3,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,8,7,1,2,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,8,7,1,2,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,3,7,6,1,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,7,6,1,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,8,7,1,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,8,7,1,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,8,4,7,5,1,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,7,1,6,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,7,6,1,3,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,7,6,1,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,7,6,1,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,3,1,4,2,8,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,5,3,8,2,1,6,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[3,8,7,4,5,1,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,7,8,5,3,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,3,8,1,2,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,7,1,4,5,3,2,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,7,8,4,1,6,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,8,4,2,6,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,1,4,8,6,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,3,1,8,4,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,3,1,2,5,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,1,4,2,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,3,4,5,6,7,8,1,9]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[2,3,4,5,6,8,9,1,7]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,3,4,5,7,8,9,1,6]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,3,4,6,7,8,9,1,5]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,3,5,6,7,8,9,1,4]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,4,5,6,7,8,9,1,3]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[3,4,5,6,7,8,9,1,2]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,3,4,5,6,7,8,9,10,1]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[2,3,4,5,6,7,8,9,1,10]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[2,3,4,5,6,7,1,8,9]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[2,3,4,5,6,7,8,10,1,9]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[2,3,4,5,6,1,9,7,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,3,4,5,6,7,9,10,1,8]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[2,3,4,5,1,8,9,6,7]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,3,4,5,6,8,9,10,1,7]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[2,3,4,1,7,8,9,5,6]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,3,4,5,7,8,9,10,1,6]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[2,3,1,6,7,8,9,4,5]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,3,4,6,7,8,9,10,1,5]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[2,1,5,6,7,8,9,3,4]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,3,5,6,7,8,9,10,1,4]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[1,4,5,6,7,8,9,2,3]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,4,5,6,7,8,9,10,1,3]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[3,4,5,6,7,8,9,10,1,2]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[3,6,4,5,7,2,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,3,2,7,4,6,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,3,6,2,4,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,3,6,2,7,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,2,6,3,4,7,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,6,3,4,5,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,2,7,3,4,5,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,4,7,6,2,3,8,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,3,5,2,4,8,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,7,6,2,4,5,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,6,3,4,5,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,6,5,2,3,7,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,2,1,7,3,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,2,1,8,3,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,3,2,8,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,4,8,6,2,7,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,3,5,2,7,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,5,2,3,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,2,1,7,3,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,8,6,3,7,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,2,7,3,4,5,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,8,1,7,3,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,8,6,1,7,2,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,8,1,5,7,2,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,8,3,7,1,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,1,2,7,3,4,5,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,6,2,7,1,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,7,1,2,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,2,6,1,8,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,1,5,8,4,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,5,1,6,8,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,6,3,8,7,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,6,4,5,8,7,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,5,3,4,8,7,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,2,8,7,1,4,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,1,8,7,2,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,5,3,7,6,1,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,1,8,3,7,2,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,8,1,7,2,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,6,8,2,3,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,7,8,2,4,6,1,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,3,8,2,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,7,8,2,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,2,5,8,7,1,3,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,3,8,7,1,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,2,8,6,1,3,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,8,7,3,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,2,7,6,1,3,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,8,7,3,4,5,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,8,7,2,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,8,3,6,2,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,5,8,7,2,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,8,7,6,1,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,3,7,5,1,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,6,2,5,1,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,1,6,7,3,2,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,1,6,7,3,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,5,3,7,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,5,3,6,2,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,1,3,6,2,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,8,3,6,2,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,4,8,3,2,6,5,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,4,1,3,2,6,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,4,3,2,6,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,4,3,2,7,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,4,3,2,7,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,1,5,4,6,7,2,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,5,3,6,2,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,4,3,2,6,7,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,4,3,2,5,7,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,4,3,2,5,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,4,1,3,2,5,6,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,4,8,3,2,5,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,3,8,2,5,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,3,1,2,5,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,1,3,2,5,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,1,3,2,6,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,1,3,6,2,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,1,4,6,8,2,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,8,3,6,2,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,4,8,3,2,6,1,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,4,8,3,2,5,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,3,8,2,5,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,3,7,2,5,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,3,2,8,6,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,3,2,8,7,1,6]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,3,8,7,2,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,4,8,7,1,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,4,1,7,8,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,3,1,7,2,8,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,3,1,2,7,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,3,2,1,8,6,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,3,1,8,2,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,4,1,8,7,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,1,4,8,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,1,3,2,8,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,1,3,2,8,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,3,1,2,8,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,3,1,2,7,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,3,8,2,7,5,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,3,8,7,2,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,3,1,7,2,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,3,1,8,2,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,1,3,8,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,1,8,3,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,1,8,4,5,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,8,1,4,5,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,8,1,3,2,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,3,7,8,2,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,3,7,2,8,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,3,7,2,1,5,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,8,3,2,1,5,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,8,3,2,1,6,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,5,8,3,1,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,8,4,1,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,4,8,1,7,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,3,8,1,2,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,3,2,8,1,7,6]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,4,3,7,2,1,8,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,3,7,1,2,8,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,4,7,1,8,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,3,7,8,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,3,7,2,8,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,3,2,7,8,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,3,2,6,8,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,2,1,3,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,6,1,2,5,8,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,7,8,4,3,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,1,2,5,4,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,1,3,7,6,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,2,1,8,7,4,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[4,7,2,8,1,3,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,4,7,1,8,2,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,8,2,4,3,5,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,7,2,4,3,5,6,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,6,2,4,3,5,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,5,2,4,3,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,6,2,5,3,4,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,7,2,5,3,4,6,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,8,2,5,3,4,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,8,2,6,3,4,5,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,7,2,6,3,4,5,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,8,2,7,3,5,4,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,7,2,8,3,5,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,2,8,3,5,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,2,8,3,6,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,2,8,3,6,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,8,4,6,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,8,4,6,5,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,7,4,6,5,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,2,7,4,6,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,2,7,3,6,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,2,7,3,6,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,2,7,3,5,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,2,6,3,5,4,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,8,2,6,3,5,4,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,8,2,5,3,6,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,2,5,3,6,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,2,5,3,7,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,2,4,3,7,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,2,4,3,7,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,2,4,3,6,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,2,4,3,6,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,2,3,4,6,5,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,7,2,3,4,6,5,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,8,2,3,4,7,5,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,8,2,4,3,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,2,4,3,8,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,2,4,3,8,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,2,4,3,8,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,2,5,3,8,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,2,5,3,8,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,2,5,3,7,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,2,6,3,7,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,2,6,3,8,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,8,4,7,5,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,2,8,4,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,2,8,3,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,2,8,3,7,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,2,8,3,7,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,2,8,3,6,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,2,7,3,6,4,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,6,3,7,2,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,3,7,5,2,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,3,8,5,1,7,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,6,3,8,5,1,2,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,8,3,4,1,2,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,8,3,4,1,7,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,6,2,7,5,3,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,7,2,4,3,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,8,4,3,1,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,8,4,3,1,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,8,4,1,6,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,8,4,1,6,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,8,4,1,3,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,8,4,2,1,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,8,2,4,1,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,6,2,8,5,1,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,6,8,5,1,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,6,8,5,1,4,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,6,2,8,5,1,3,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,8,2,4,1,3,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,8,4,2,1,3,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,8,4,1,3,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,8,4,1,2,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,8,4,1,2,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,8,1,5,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,8,1,5,2,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,1,5,3,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,1,3,5,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,8,2,1,6,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,2,8,1,6,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,7,8,1,6,4,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,7,8,1,6,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,2,8,1,6,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,8,2,1,6,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,8,1,3,5,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,1,5,3,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,1,5,4,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,8,1,5,4,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,1,4,5,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,8,1,4,5,3,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,1,4,3,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,1,3,4,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,8,2,1,4,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,2,8,1,5,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,7,8,1,5,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,6,8,4,1,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,6,2,8,3,1,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,8,3,2,1,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,8,3,1,4,6,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,8,3,1,6,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,8,3,1,6,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,3,8,1,6,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,3,8,1,6,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,3,8,1,5,6,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,6,3,8,2,1,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,5,3,2,8,1,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,5,2,3,8,1,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,5,4,8,1,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,5,3,2,8,1,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,3,8,2,1,5,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,3,8,1,5,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,3,8,1,2,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,3,8,1,2,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,8,3,1,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,8,3,1,2,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,8,3,1,4,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,8,3,2,1,4,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,2,7,8,1,5,4,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,8,2,1,4,3,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,8,1,3,4,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,8,1,4,3,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,1,4,2,5,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,8,1,4,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,8,1,2,5,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,8,1,2,5,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,1,2,4,5,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,8,1,3,2,5,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,8,2,1,3,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,7,8,1,4,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,8,1,3,2,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,8,1,2,4,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,8,1,2,3,5,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,2,8,5,1,6,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,3,7,5,2,6,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,7,5,4,2,6,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,2,8,5,4,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,5,4,3,1,7,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,8,4,5,6,1,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,6,5,7,3,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,8,4,5,3,7,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,4,3,5,6,1,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,2,8,4,5,6,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,3,7,5,2,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,3,8,5,1,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,2,8,5,1,4,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,8,2,5,6,3,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,8,5,2,1,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,8,5,1,3,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,7,5,2,1,8,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,7,5,1,2,8,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,3,7,1,5,6,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,1,7,5,2,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,1,2,7,6,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,2,1,7,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,5,7,1,4,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,2,7,4,1,8,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,2,6,4,8,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,1,8,6,4,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,1,8,7,2,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,5,8,2,7,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,8,4,2,3,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,2,5,8,3,7,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,6,5,7,3,4,2,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,2,7,4,6,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,1,8,7,6,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,3,8,4,6,2,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,3,4,8,6,1,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,8,6,5,1,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,7,3,5,8,6,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,4,7,8,6,1,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,4,6,2,7,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,4,7,1,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,6,4,1,8,7,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,3,6,1,4,8,2,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,3,5,6,8,4,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,3,5,1,8,2,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,6,1,5,8,4,7,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,7,6,5,8,3,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,1,6,3,8,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,2,4,1,7,8,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,4,2,7,8,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,4,7,2,8,6,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,4,7,8,2,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,4,6,8,5,7,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,4,5,7,1,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,5,4,6,1,7,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,2,1,4,3,6,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,4,1,2,6,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,6,3,2,5,4,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,3,2,5,4,8,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,3,2,5,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,8,4,5,2,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,5,1,6,2,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,2,1,5,6,3,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,8,5,4,3,2,7,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,6,4,3,7,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,7,4,3,1,8,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,7,5,1,3,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,7,1,5,4,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,8,4,3,1,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,6,8,4,3,7,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,7,8,4,3,6,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,7,4,3,6,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,7,5,6,3,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,7,8,5,6,3,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,6,8,5,7,3,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,8,6,7,1,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,8,6,1,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,1,8,6,7,4,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,3,7,1,6,8,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,7,6,1,8,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,7,5,8,3,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,6,5,7,3,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,5,6,7,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,6,7,1,8,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,6,1,7,8,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,1,6,7,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,1,5,7,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,5,1,7,2,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,8,4,6,2,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,8,3,2,6,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,3,2,6,8,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,3,2,7,8,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,3,2,7,1,8,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,2,1,4,3,7,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,3,2,8,7,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,3,2,8,6,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,3,2,7,6,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,4,7,2,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,6,4,8,2,7,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,4,5,8,1,2,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,5,1,8,2,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,5,6,8,7,1,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,5,8,7,2,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,5,7,6,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,6,7,5,4,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,6,7,8,5,4,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,7,8,1,6,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,1,7,8,6,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,4,8,7,1,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>00000100000
[2,1,4,3,6,5,8,7,12,11,10,9]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[2,1,4,3,6,5,10,9,8,7,12,11]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[2,1,4,3,6,5,12,9,8,11,10,7]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[2,1,4,3,8,7,6,5,10,9,12,11]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[2,1,4,3,8,7,6,5,12,11,10,9]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[2,1,4,3,10,7,6,9,8,5,12,11]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[2,1,4,3,12,7,6,9,8,11,10,5]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[2,1,6,5,4,3,8,7,10,9,12,11]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[2,1,6,5,4,3,8,7,12,11,10,9]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[2,1,6,5,4,3,10,9,8,7,12,11]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[2,1,6,5,4,3,12,9,8,11,10,7]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[2,1,6,5,4,3,12,11,10,9,8,7]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[2,1,8,5,4,7,6,3,10,9,12,11]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[2,1,8,5,4,7,6,3,12,11,10,9]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[2,1,10,5,4,7,6,9,8,3,12,11]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[2,1,12,5,4,7,6,9,8,11,10,3]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[2,1,8,7,6,5,4,3,12,11,10,9]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[2,1,12,7,6,5,4,11,10,9,8,3]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[4,3,2,1,6,5,8,7,10,9,12,11]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[4,3,2,1,6,5,8,7,12,11,10,9]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[4,3,2,1,6,5,10,9,8,7,12,11]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[4,3,2,1,6,5,12,9,8,11,10,7]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[4,3,2,1,6,5,12,11,10,9,8,7]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[4,3,2,1,8,7,6,5,10,9,12,11]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[4,3,2,1,10,7,6,9,8,5,12,11]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[4,3,2,1,12,7,6,9,8,11,10,5]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[4,3,2,1,12,7,6,11,10,9,8,5]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[4,3,2,1,10,9,8,7,6,5,12,11]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[4,3,2,1,12,9,8,7,6,11,10,5]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[4,3,2,1,12,11,8,7,10,9,6,5]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[6,3,2,5,4,1,8,7,10,9,12,11]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[6,3,2,5,4,1,8,7,12,11,10,9]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[6,3,2,5,4,1,10,9,8,7,12,11]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[6,3,2,5,4,1,12,9,8,11,10,7]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[6,3,2,5,4,1,12,11,10,9,8,7]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[8,3,2,5,4,7,6,1,10,9,12,11]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[8,3,2,5,4,7,6,1,12,11,10,9]=>[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000
[10,3,2,5,4,7,6,9,8,1,12,11]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[12,3,2,5,4,7,6,9,8,11,10,1]=>[5,5,1,1]=>[[1,4,5,6,7],[2,9,10,11,12],[3],[8]]=>11000010000
[8,3,2,7,6,5,4,1,12,11,10,9]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[12,3,2,7,6,5,4,11,10,9,8,1]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[6,5,4,3,2,1,8,7,12,11,10,9]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[6,5,4,3,2,1,10,9,8,7,12,11]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[6,5,4,3,2,1,12,9,8,11,10,7]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[6,5,4,3,2,1,12,11,10,9,8,7]=>[2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>01010101010
[8,5,4,3,2,7,6,1,12,11,10,9]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[12,5,4,3,2,7,6,11,10,9,8,1]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[10,5,4,3,2,9,8,7,6,1,12,11]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[12,5,4,3,2,9,8,7,6,11,10,1]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[12,5,4,3,2,11,8,7,10,9,6,1]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[8,7,4,3,6,5,2,1,12,11,10,9]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[12,7,4,3,6,5,2,11,10,9,8,1]=>[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100
[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>11111111111
[7,4,6,1,8,3,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,5,1,7,4,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,4,1,7,5,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,3,1,7,5,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,2,1,7,5,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,4,6,2,7,5,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,5,2,6,8,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,2,1,6,8,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,4,3,1,7,5,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[3,6,8,4,1,7,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,6,7,5,1,8,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,6,1,8,3,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,4,6,5,7,1,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,7,5,6,1,8,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,5,1,8,4,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,8,4,1,7,5,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,7,5,3,1,8,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,2,1,6,7,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,4,2,6,7,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,3,2,7,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,2,1,7,6,8,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,3,1,7,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,8,4,1,6,7,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,5,1,6,8,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,6,1,7,5,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,7,1,6,5,8,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,2,6,5,7,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,1,2,7,5,8,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,5,1,2,6,8,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,1,2,6,7,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,1,2,7,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,2,5,3,7,6,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,1,2,7,6,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,5,1,2,7,6,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,1,5,8,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,6,1,5,8,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,3,5,1,7,6,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,6,1,5,8,3,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,6,7,1,5,8,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,6,5,8,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,1,6,8,4,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,1,6,7,5,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,3,1,7,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,5,2,1,7,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,3,5,2,7,6,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,6,2,5,8,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,2,1,5,8,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,1,5,7,6,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,2,4,1,7,5,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,5,1,7,4,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,6,4,8,2,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,6,4,7,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,1,5,2,7,4,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,2,5,8,3,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,5,7,6,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,3,5,7,6,2,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,2,3,7,6,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,1,3,7,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,5,2,6,8,4,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,2,6,7,5,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,1,4,2,7,5,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,2,6,5,7,1,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,6,8,2,5,7,1,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,3,2,5,7,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,1,3,2,7,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,3,2,7,6,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,1,3,7,6,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,4,2,3,7,6,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,1,3,7,6,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,1,3,7,6,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,3,5,7,6,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,2,3,5,7,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,7,1,3,5,8,2,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,3,5,7,6,1,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,2,3,7,6,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,2,4,7,6,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,5,9,3,6,10,1,2,4,7]=>[4,3,2,1]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>101001000
[8,4,9,2,5,10,1,3,6,7]=>[4,3,2,1]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>101001000
[8,1,2,4,3,6,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,3,5,6,2,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,3,4,2,6,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,3,2,4,5,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,8,3,4,5,6,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,6,3,8,4,5,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,3,2,1,4,5,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,1,4,2,6,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,1,5,6,8,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,8,5,6,1,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,7,8,5,6,2,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,7,8,4,2,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,7,8,2,4,5,1,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,2,8,4,5,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,6,7,4,5,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,2,4,8,6,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,4,2,8,7,1,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,5,8,7,1,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,4,5,1,7,8,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,1,2,3,8,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,2,4,1,3,7,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,4,8,3,7,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,6,5,8,7,3,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,5,1,7,3,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,5,2,1,8,3,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,5,6,7,8,3,4,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,6,7,3,8,5,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,6,7,3,1,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,8,2,3,1,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,8,3,2,1,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,4,8,1,7,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,3,8,1,2,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,5,3,7,1,6,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,6,7,2,1,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,6,7,2,8,1,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,4,5,2,7,8,1,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,4,2,5,6,8,1,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,7,8,6,4,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,1,2,7,8,6,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,1,8,6,5,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,1,2,8,6,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,6,8,1,2,7,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,8,7,1,5,3,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,8,7,3,5,1,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,1,6,3,5,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,1,3,6,5,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,3,6,5,2,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,7,2,8,6,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,7,3,4,8,6,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,7,1,8,6,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,2,3,6,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,1,6,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,7,1,2,6,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,2,7,1,3,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,7,2,5,3,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,2,4,8,7,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,6,8,3,7,4,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,8,3,4,7,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,2,4,8,1,7,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,7,2,3,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,2,1,7,3,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,2,1,6,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,1,2,3,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,6,2,1,4,3,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,7,2,3,1,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,4,2,7,1,6,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[1,8,7,5,3,4,6,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,7,3,5,4,6,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,5,4,7,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,2,7,3,1,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,6,2,4,3,1,5]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,7,6,1,2,4,3,5]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,7,6,1,4,2,3,5]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,7,6,4,1,3,2,5]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,8,4,7,2,1,6,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[1,8,7,5,4,3,6,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,6,8,4,3,7,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,7,3,2,5,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,8,1,7,3,2,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,3,1,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,1,3,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,3,1,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,4,7,1,2,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,4,1,7,2,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,4,7,1,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,1,2,6,5,7,4,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,5,6,7,4,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,5,7,1,6,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,5,7,1,2,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,5,1,7,2,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,3,1,7,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,3,7,1,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,1,3,7,2,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,2,8,1,7,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,6,4,8,3,7,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,7,4,5,3,6,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,8,5,7,2,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,3,7,2,1,6,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,7,6,3,1,4,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,6,1,3,2,4,5]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,5,3,2,7,1,6,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,5,2,7,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,7,4,3,5,6,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,7,3,4,5,6,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,4,5,7,1,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,2,3,7,1,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,1,5,4,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,1,5,2,7,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,4,2,1,7,3,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,4,2,1,7,6,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,4,2,1,3,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,4,2,3,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,2,5,1,4,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,4,3,1,2,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,4,1,3,2,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,4,1,2,7,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,4,1,6,3,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,4,1,6,3,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,4,1,6,5,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,5,4,1,3,7,6,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,4,3,1,7,6,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,3,2,5,1,7,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,8,5,3,7,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,2,5,1,7,4,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,4,3,1,7,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,4,1,3,7,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,4,1,6,5,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,4,1,6,2,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,6,5,2,1,4,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,4,3,6,2,1,5]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,3,2,7,6,4,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,7,6,4,3,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,7,6,4,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,2,7,6,4,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,4,3,6,2,5,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,6,5,2,4,3,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,5,4,2,3,7,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,4,2,6,5,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,4,2,6,3,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,4,2,6,3,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,1,7,6,4,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,1,7,6,4,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,1,7,6,5,4,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,3,1,5,4,7,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,1,5,4,7,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,1,7,6,5,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,1,7,6,2,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,4,2,6,1,5,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,7,4,2,6,5,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,4,2,3,7,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,2,5,4,7,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,8,5,4,7,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,2,7,6,5,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,7,4,3,6,5,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,7,6,5,3,1,4,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,6,5,1,3,2,4]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,7,6,5,1,3,4,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,7,6,5,1,4,3,2]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,7,6,5,4,1,3,2]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,7,4,3,6,1,5,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,3,2,7,6,1,5,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[2,1,8,7,6,3,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,2,7,6,1,4,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,6,5,1,4,2,3]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,7,6,5,1,2,4,3]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,3,5,1,8,4,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,4,1,8,5,6,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,5,6,2,1,8,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,5,2,7,4,3,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,3,1,8,6,5,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,6,5,1,8,4,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,6,4,1,8,5,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,4,2,1,8,7,5,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[1,6,4,2,7,5,3,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,3,2,7,6,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,2,1,8,7,6,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[2,5,3,1,7,8,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,6,4,1,7,8,5,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,6,5,1,7,8,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,7,1,6,8,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,5,1,2,8,4,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,1,2,8,5,3,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,1,2,8,6,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,1,2,8,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,1,2,5,8,3,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,3,4,8,2,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,5,6,8,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,1,5,7,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,1,6,8,5,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,3,1,8,6,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,5,2,1,6,8,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,2,5,7,3,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,2,1,5,8,7,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,3,1,5,8,6,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,4,1,8,5,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,5,1,8,4,7,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,1,4,8,6,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,1,4,8,7,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,6,2,4,7,3,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,1,3,8,7,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,4,1,3,8,5,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,1,3,8,4,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,7,1,4,8,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,6,1,4,8,3,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,2,1,3,8,7,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,6,1,4,7,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,4,6,8,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,3,5,8,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,2,4,8,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,3,1,6,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,5,2,3,1,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,6,7,3,5,2,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,3,5,2,4,1,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,5,2,4,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,4,1,6,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,6,3,5,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,4,1,5,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,6,3,4,1,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,7,3,4,1,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,8,6,7,3,4,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,2,8,5,7,3,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,7,3,4,1,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,4,1,5,2,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,7,3,5,2,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,7,4,5,2,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,7,4,5,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,6,7,4,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,1,8,6,7,3,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,6,7,3,4,1,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,3,4,1,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,6,2,7,3,4,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,7,3,5,1,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,1,8,4,7,3,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,1,8,5,7,3,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,1,8,5,7,4,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,8,5,7,4,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,7,4,6,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,7,4,6,2,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,7,3,6,2,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,7,3,6,2,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,7,3,5,1,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,8,4,7,3,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,7,3,6,2,5,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,3,6,2,5,1,8,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,5,1,7,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,4,1,7,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,4,1,7,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,5,7,3,6,2,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,7,4,6,2,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,4,6,2,3,1,8,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,2,3,1,7,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,3,1,7,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,3,1,7,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,4,2,8,6,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,3,1,8,5,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,5,6,2,3,1,7,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,8,5,6,2,3,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,8,5,6,2,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,6,2,4,1,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,4,1,8,6,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,5,2,8,6,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,5,2,8,6,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,3,8,5,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,2,8,5,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,6,2,8,5,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,6,2,8,4,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,6,2,5,1,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,8,4,6,2,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,7,3,8,4,5,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,5,1,6,2,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,8,4,6,2,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,8,5,6,2,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,5,6,2,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,8,5,6,3,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,7,4,8,5,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,7,4,8,5,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,7,3,8,5,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,8,4,5,1,6,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,4,5,1,7,3,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,6,2,8,4,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,8,5,6,1,3,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,3,8,4,7,2,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,6,1,4,7,2,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,1,2,5,7,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,8,2,5,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,2,4,5,6,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,1,5,4,6,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,2,1,6,3,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,4,5,3,1,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,1,4,3,2,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,6,8,3,7,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,8,5,3,1,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,5,8,4,7,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,6,2,4,7,3,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,7,3,6,1,4,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,6,7,2,1,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,7,5,2,4,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,1,2,4,5,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,7,2,5,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,7,5,8,2,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,6,7,8,1,4,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,6,5,7,8,2,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,2,7,6,1,4,3,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,6,8,4,5,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,1,8,5,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,8,6,3,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,8,6,1,3,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,6,5,8,1,3,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,6,3,4,5,8,1,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,2,1,4,8,3,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,2,7,3,1,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,6,4,1,8,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,1,5,2,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,5,2,8,3,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,7,5,3,8,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,5,3,4,2,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,2,4,3,1,6,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,8,1,3,7,5,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,2,6,5,1,3,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,1,2,3,4,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,8,2,3,7,6,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,5,3,6,8,4,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,7,8,5,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,7,8,1,4,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,7,4,1,6,2,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,8,4,6,1,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,1,8,6,3,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,8,5,7,6,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,4,2,7,5,8,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,8,6,7,5,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,3,8,7,6,2,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,4,7,6,2,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,7,4,3,6,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,4,8,3,1,7,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,3,7,1,6,4,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,7,4,1,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,5,3,1,2,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,5,1,2,7,6,3,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,1,2,6,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,6,1,8,4,7,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,1,7,3,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,3,1,7,6,2,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,5,2,7,8,1,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,1,4,7,5,6,2,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,5,6,1,8,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,5,3,1,6,8,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,7,5,8,6,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,2,7,5,3,8,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,2,7,3,8,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,1,7,5,2,3,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,1,3,7,5,2,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,1,2,6,8,5,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,1,2,5,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,7,2,4,8,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,7,8,6,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,7,5,1,8,6,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,7,4,1,5,8,6,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,3,7,1,5,8,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,8,1,3,7,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,6,8,3,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,8,3,1,5,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,8,6,4,1,5,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,4,8,5,1,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,7,4,5,1,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,6,3,7,5,8,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,1,7,8,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,2,3,6,8,1,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,7,3,6,8,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,7,4,6,2,8,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,3,4,6,1,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,8,4,6,1,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,5,2,4,1,6,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,3,5,1,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,8,3,6,7,1,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,8,1,7,3,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,3,6,2,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,3,1,7,2,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,8,4,7,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,4,7,3,1,6,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[4,6,8,3,1,7,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,8,2,7,1,5,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,3,1,8,2,4,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,8,1,2,6,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,7,4,1,6,2,3,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,5,4,1,2,6,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,8,4,2,7,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,2,8,5,3,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,8,5,3,1,7,4,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[8,4,5,1,2,6,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,3,7,1,2,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,3,7,2,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,2,7,8,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,5,7,8,3,1,6,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,7,2,5,8,1,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,1,3,4,6,2,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,8,2,4,6,7,1,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,5,6,8,2,7,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,5,6,8,1,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,8,3,5,6,1,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,6,2,3,7,8,1,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,7,3,4,1,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,7,3,4,1,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,4,7,1,5,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,8,4,7,2,5,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,4,8,7,2,6,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,4,8,7,1,6,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,3,8,7,6,1,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,8,7,6,1,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,3,7,5,1,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,4,6,5,1,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,4,7,5,1,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,8,7,6,1,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,5,8,7,6,1,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,5,8,7,6,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,5,8,7,1,6,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,8,7,2,6,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,8,2,7,6,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,8,1,7,6,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,5,8,1,7,6,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,5,8,7,1,6,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,4,8,7,1,6,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,8,4,7,1,5,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,4,6,1,5,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,4,6,2,5,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,4,7,2,5,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,8,7,2,6,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,8,7,2,6,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,8,2,7,6,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,5,8,3,7,6,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,4,2,8,7,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,3,8,2,7,6,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,3,2,7,5,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,3,2,6,5,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,3,1,6,5,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,3,1,7,5,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,8,1,7,6,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,1,8,7,6,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,3,1,8,7,6,5,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,2,1,8,7,6,5,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[3,8,2,1,7,5,4,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,2,1,6,5,4,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,2,6,1,5,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,2,8,7,1,6,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,8,7,1,6,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,8,1,7,6,4,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,3,8,1,7,6,4,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,3,8,2,7,6,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,8,3,2,7,5,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,8,3,1,7,5,4,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,8,2,1,7,5,4,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,8,2,7,1,5,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,7,2,1,4,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,6,1,2,4,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,7,1,2,4,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,1,2,7,5,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,8,2,3,7,5,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,2,8,3,7,6,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,1,8,3,7,6,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,1,8,7,2,6,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,8,7,2,6,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,1,7,2,5,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,1,6,2,5,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,1,2,6,5,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,1,2,7,5,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,8,2,7,6,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,2,8,7,6,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,1,3,8,7,6,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,1,4,8,7,6,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,3,7,6,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,1,3,7,5,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,1,3,6,5,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,2,3,6,5,4,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,8,2,3,7,5,4,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,8,3,7,6,4,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,4,3,6,8,2,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,2,5,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,1,8,2,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,5,2,8,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,2,6,5,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,4,2,6,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,5,8,2,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,4,2,5,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,2,6,4,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,6,5,4,8,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,5,4,7,3,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,6,3,8,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,5,4,2,8,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,7,5,2,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,3,5,2,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,2,5,1,8,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,5,2,8,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,4,2,8,3,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,4,2,8,3,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,5,3,8,7,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,8,6,5,3,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,2,8,6,3,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,4,2,8,7,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,1,8,7,3,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,6,2,1,8,3,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,1,6,2,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,6,4,2,8,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,5,2,6,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,2,7,5,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,7,6,5,3,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,6,5,3,8,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,2,6,3,8,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,2,7,6,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,5,2,7,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,7,4,2,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,2,8,6,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,8,6,2,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,7,1,8,2,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,1,6,2,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,8,3,2,4,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,8,7,3,2,4,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,2,8,7,3,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,4,2,8,3,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,1,5,4,2,7,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,8,5,2,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,5,3,1,7,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,2,1,7,3,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,6,4,2,7,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,5,2,6,3,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,2,7,3,8,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,8,5,3,7,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,6,3,8,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,7,6,3,8,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,2,7,3,8,5,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,2,8,5,3,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,7,4,2,8,6,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,1,8,3,2,6,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,2,1,8,6,3,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,8,7,3,2,6,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,2,8,7,6,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,8,7,5,3,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,8,6,3,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,7,3,8,6,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,7,3,6,5,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,8,7,6,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,7,6,3,4,5,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,7,8,6,2,4,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,1,6,2,4,3,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,1,5,2,7,3,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,4,5,3,7,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,4,5,3,8,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,4,5,3,7,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[5,1,7,8,6,2,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,4,8,3,5,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,8,6,3,4,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,4,5,3,8,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,4,5,3,6,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,1,4,5,3,6,7,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,4,1,5,2,6,3,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,5,7,2,1,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,5,8,2,1,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,5,7,2,1,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,5,7,3,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,5,8,3,7,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,7,6,2,4,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,4,8,6,3,1,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,1,8,2,3,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,1,6,2,4,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,1,5,2,6,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,5,8,2,1,4,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,3,4,1,8,6,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,3,5,6,2,1,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,8,5,1,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,8,6,1,5,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,6,7,1,3,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,5,7,2,1,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,3,8,5,6,1,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,4,5,6,3,1,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,5,6,3,1,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,5,6,2,8,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,5,8,2,1,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,5,6,2,1,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,6,5,1,3,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,6,8,1,3,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,7,6,5,8,3,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,5,6,1,4,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,6,4,1,8,5,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,6,1,3,8,5,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,1,3,6,5,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,6,8,4,3,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,7,6,1,8,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,6,1,4,3,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,5,1,2,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,5,2,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,1,6,3,4,2,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,1,8,3,2,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,3,8,6,4,1,7,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,6,7,4,3,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,5,7,2,4,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,3,4,1,8,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,6,1,7,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,8,1,6,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,8,1,4,5,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,6,1,4,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,3,4,5,6,7,9,8]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[2,1,3,4,5,6,7,8,9]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,2,3,4,5,6,7,8,10,9]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[2,1,3,4,5,6,7,8,9,10]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[9,1,2,3,4,5,6,7,10,8]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[1,8,2,3,4,5,6,9,7]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[7,1,2,3,4,5,6,9,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,1,9,3,4,5,6,7,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,8,1,3,4,5,6,7,9]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[2,10,1,3,4,5,6,7,8,9]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[8,4,3,6,5,1,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,6,3,4,1,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,5,4,3,1,7,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[1,7,6,5,4,2,3,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,6,5,2,7,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,5,4,1,6,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,8,5,4,1,3,6,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,8,5,4,2,1,7,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,6,2,4,1,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,2,6,5,1,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,8,6,5,1,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,1,7,6,4,5,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,3,7,6,2,5,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,7,3,6,2,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,1,7,5,3,2,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,6,5,2,4,3,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,1,6,5,2,3,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,7,6,3,4,5,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,8,3,7,4,5,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,1,7,2,6,3,5,4]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,1,8,2,6,4,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,8,2,4,7,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,8,3,2,7,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,3,8,2,7,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,8,4,7,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,8,7,1,6,5,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,2,7,1,6,5,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,7,2,1,6,4,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,8,7,1,3,5,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,6,1,5,3,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,6,1,5,4,3,2]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[1,8,7,2,6,5,3,4]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,7,8,2,5,6,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,6,7,1,4,5,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,8,1,4,3,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,8,3,2,1,7,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,5,8,3,1,4,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,3,1,6,4,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[1,6,8,4,2,7,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,4,8,2,7,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,4,3,7,1,6,5,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,4,3,8,1,5,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,3,1,5,2,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,3,1,2,6,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,3,1,2,5,7,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,4,2,3,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,5,1,4,2,3,7,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,1,4,2,6,3,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,1,4,3,2,7,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,6,1,3,4,2,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,6,2,1,5,3,7,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,6,1,5,4,7,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,7,1,4,6,5,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,7,2,1,3,6,5,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,7,1,3,2,6,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,7,1,2,4,5,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,6,1,2,5,4,3,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,1,2,5,3,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,2,3,6,4,5,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,7,1,2,3,6,5,4]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,8,1,2,3,5,6,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,8,1,2,4,3,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,1,3,2,4,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,8,2,1,3,5,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,8,1,4,5,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,3,2,5,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,1,2,4,3,6,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,1,2,3,5,4,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,1,2,3,4,6,5,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,1,2,3,4,5,7,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,7,3,8,5,1,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,4,5,1,8,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,7,6,8,1,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,3,7,8,6,1,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,8,4,5,7,1,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,8,6,7,1,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,6,7,1,8,3,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,6,2,7,4,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,6,1,7,8,4,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,5,6,1,8,7,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,5,6,8,1,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,2,4,5,1,6,3,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,8,6,2,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,6,8,2,3,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,6,2,8,4,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,6,3,4,7,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,2,6,8,5,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,3,2,5,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,2,3,1,5,6,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,3,1,5,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,6,8,7,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,1,6,7,8,5,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,1,7,6,8,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,7,8,1,6,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,3,7,2,6,4,8,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,3,1,5,8,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,2,1,8,5,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,2,8,1,5,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,8,2,1,4,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,1,2,8,4,5,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,1,3,4,8,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,7,3,4,6,8,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,7,3,4,8,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,7,8,2,3,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,8,7,2,3,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,1,2,7,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,3,7,5,8,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,4,5,7,8,6,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,8,3,4,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,1,3,4,6,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,2,3,4,5,7,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,8,3,4,6,7,5]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,2,1,6,5,8,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,2,6,1,4,8,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,2,6,4,1,8,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,2,7,4,8,1,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,2,7,4,8,6,1,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,2,3,8,6,1,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,2,3,8,1,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,2,3,1,8,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,2,1,3,8,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,1,6,4,2,8,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,1,3,2,8,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,3,1,2,8,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,3,2,1,8,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,3,2,8,1,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,3,2,8,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,3,8,2,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,3,8,1,2,5,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,3,1,8,2,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,1,3,8,2,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,1,7,4,8,2,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,5,7,4,8,3,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,7,4,8,6,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,7,4,8,6,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,1,3,8,6,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,3,1,8,6,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,3,8,1,5,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,3,8,5,2,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,8,3,1,4,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,1,8,3,5,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,1,7,8,4,5,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,6,7,8,4,5,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,7,8,4,3,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,7,8,4,2,5,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,1,8,3,2,5,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,2,1,8,3,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,2,8,1,3,5,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,2,8,3,1,5,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,2,8,3,5,1,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,7,8,4,5,1,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,7,8,4,1,5,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,7,8,1,4,5,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,2,7,1,8,4,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,1,7,8,5,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,1,2,7,8,6,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,2,7,8,1,5,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,7,8,5,1,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,7,8,5,4,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,2,8,5,3,1,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,2,1,8,6,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,1,2,8,6,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,7,2,8,6,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,5,7,3,8,6,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,7,8,3,5,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,7,8,2,5,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,1,8,2,5,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,8,2,4,1,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,8,2,4,3,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,1,8,5,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,7,8,5,2,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,6,7,8,5,3,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,7,8,5,4,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,1,8,5,3,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,4,1,3,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,8,5,2,7,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,4,5,8,7,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,1,4,8,7,3,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,4,8,6,3,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,7,1,8,6,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,8,4,2,7,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,8,5,6,7,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,1,2,7,8,5,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,4,2,8,7,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,7,5,2,8,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,2,7,4,8,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,1,4,8,3,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,8,3,5,1,4,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,1,4,6,7,2,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,5,8,4,3,7,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,3,7,4,2,8,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,1,6,2,4,5,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,8,6,7,1,4,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,8,7,4,1,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,8,7,1,5,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,6,1,2,5,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,1,8,7,3,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,3,6,4,2,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,1,5,3,8,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,2,6,3,4,7,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,6,3,5,4,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,2,7,4,3,5,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,7,6,4,5,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,7,6,5,3,4,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,5,4,2,7,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[1,6,5,3,4,8,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,8,4,2,7,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,2,6,4,7,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,5,3,2,6,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,8,3,1,7,2,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,6,3,7,5,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,5,2,6,4,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,1,6,2,5,4,3]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,8,1,7,3,5,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,8,5,7,3,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,7,6,8,3,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,3,1,8,4,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,7,3,8,4,5,2,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,2,8,5,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,6,1,8,4,3,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,1,7,4,2,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,1,2,7,3,4,6,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,1,2,8,3,5,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,2,6,1,7,3,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,3,1,6,8,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,5,6,8,3,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,5,4,8,2,7,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,1,8,7,4,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,4,7,5,3,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,1,8,3,7,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,8,1,7,2,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,6,8,2,4,7,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,2,8,6,3,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,3,8,7,4,5,6,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,2,8,6,4,3,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,7,5,6,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,2,7,6,3,5,4,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,1,7,6,5,2,4,3]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[7,1,8,6,5,3,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,2,8,7,6,3,4,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,8,7,4,6,2,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,7,2,5,4,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[3,8,7,6,4,5,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,8,7,6,5,3,4,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,8,7,6,5,4,2,3]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[5,8,6,7,3,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,6,7,3,5,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,6,7,4,5,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,5,7,4,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,5,7,3,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,3,8,5,6,1,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,2,8,5,6,1,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,7,1,8,5,6,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,7,2,8,5,6,1,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,7,3,8,5,6,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,7,4,8,5,6,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,2,7,4,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,2,7,4,5,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,2,6,4,5,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,1,7,4,5,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,7,4,8,5,6,2,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,7,3,8,5,6,2,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,8,5,6,2,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,3,8,4,6,2,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,8,1,7,3,6,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,2,6,3,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,2,7,3,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,2,7,3,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,2,7,3,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,7,3,8,4,6,1,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,8,4,7,3,6,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,4,7,2,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,5,7,2,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,5,7,3,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,5,7,3,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,6,7,3,5,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,6,7,3,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,6,7,2,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,5,7,1,4,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,6,7,1,4,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,8,6,7,1,5,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,5,2,8,6,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,1,8,5,7,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,6,2,8,5,7,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,8,4,7,1,5,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,3,7,1,5,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,3,7,1,6,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,4,7,1,6,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,6,2,8,4,7,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,6,1,8,4,7,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,8,1,6,2,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,1,6,2,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,1,5,2,6,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,8,2,5,1,7,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,8,2,6,1,7,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,8,2,6,1,7,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,7,3,6,2,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,3,4,5,6,7,8,9]=>[9]=>[[1,2,3,4,5,6,7,8,9]]=>00000000
[1,2,3,4,5,6,8,9,7]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,2,3,4,5,7,8,9,6]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,2,3,4,6,7,8,9,5]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,2,3,5,6,7,8,9,4]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,2,4,5,6,7,8,9,3]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,3,4,5,6,7,8,9,2]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,2,3,4,5,6,7,8,9,10]=>[10]=>[[1,2,3,4,5,6,7,8,9,10]]=>000000000
[1,2,3,4,5,6,9,8,7]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[1,2,3,4,5,6,7,9,10,8]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[1,2,3,4,5,8,7,9,6]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[1,2,3,4,5,6,8,9,10,7]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[1,2,3,4,7,6,8,9,5]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[1,2,3,4,5,7,8,9,10,6]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[1,2,3,6,5,7,8,9,4]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[1,2,3,4,6,7,8,9,10,5]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[1,2,5,4,6,7,8,9,3]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[1,2,3,5,6,7,8,9,10,4]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[1,4,3,5,6,7,8,9,2]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[1,2,4,5,6,7,8,9,10,3]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[3,2,4,5,6,7,8,9,1]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[1,3,4,5,6,7,8,9,10,2]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[5,7,4,6,2,3,1,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,4,6,3,8,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,4,8,3,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,4,8,3,7,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,3,7,2,8,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,4,5,2,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,4,8,2,3,1,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,3,8,2,4,1,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,6,3,5,2,8,1,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,8,3,5,2,4,1,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,3,8,2,7,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,3,7,2,8,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,7,4,8,2,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,3,6,2,8,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,3,5,2,4,1,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,3,5,2,8,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,5,8,2,4,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,5,7,2,3,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,3,8,2,4,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,3,4,2,8,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,3,4,2,8,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,3,8,2,5,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,3,5,2,8,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,3,5,2,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,3,7,2,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,3,7,2,8,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,3,5,2,7,1,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,3,4,2,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,3,4,2,6,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,3,6,2,8,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,5,2,1,8,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,5,2,1,7,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,5,2,1,3,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,4,2,3,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,5,3,1,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,6,1,3,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,6,8,1,7,3,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,8,1,6,3,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,8,1,6,5,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,4,8,1,3,7,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,5,3,1,7,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,7,1,3,8,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,8,1,7,5,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,8,7,2,1,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,7,6,4,2,1,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,4,6,3,7,2,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,2,8,7,4,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,6,8,7,4,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,7,8,6,4,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,2,8,6,4,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,8,5,2,4,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,7,8,6,2,3,1,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,7,6,3,2,1,4]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,8,7,5,3,2,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,8,4,2,3,7,6,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,4,2,6,5,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,7,2,6,3,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,8,6,2,7,3,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,6,1,8,7,4,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,1,8,6,4,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,8,1,6,7,5,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,1,6,8,2,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,6,2,8,1,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,4,2,8,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,4,2,7,5,1,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[2,1,8,6,7,5,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,2,6,7,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,4,3,7,5,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,6,7,3,1,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,5,8,1,3,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,6,5,8,1,4,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,6,5,7,4,1,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,6,4,3,8,1,5,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,3,2,6,8,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,7,6,8,3,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,6,8,1,4,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,7,8,1,2,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,3,7,4,6,5,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,2,8,7,4,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,6,2,5,4,7,3,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,2,7,5,4,8,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,3,5,4,7,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,5,4,3,8,7,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,1,8,3,4,5,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,5,3,4,8,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,4,3,5,6,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,1,3,4,5,6,7,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,7,2,4,5,6,3,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,3,2,7,5,1,8,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,7,2,5,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,8,2,4,7,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,2,1,4,3,7,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,2,8,4,1,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,2,1,4,8,3,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,6,1,8,5,2,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,6,3,5,4,7,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[3,4,1,2,8,6,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,1,2,6,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,1,6,3,2,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,8,5,2,1,4,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,1,5,2,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,8,2,6,1,5,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,6,7,2,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,6,4,2,1,7,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,2,5,8,3,1,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,7,5,6,3,2,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,2,3,8,5,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,2,3,6,5,8,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,2,1,3,8,6,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,7,3,2,4,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,7,3,1,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,2,4,1,3,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,7,2,6,3,4,1,5]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[4,8,1,6,3,2,7,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,1,8,6,4,2,7,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,6,7,4,3,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,8,7,2,4,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,2,1,3,7,8,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,3,8,7,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,8,3,1,7,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,6,1,3,7,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,1,3,6,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,8,2,3,4,1,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,8,3,2,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>11111111
[8,9,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110
[8,7,9,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110
[8,7,6,9,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110
[8,7,6,5,9,4,3,2,1]=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110
[8,7,6,5,4,9,3,2,1]=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110
[8,7,6,5,4,3,9,2,1]=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110
[8,7,6,5,4,3,2,9,1]=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110
[8,7,6,5,4,3,2,1,9]=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110
[9,10,8,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110
[7,8,9,6,5,4,3,2,1]=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100
[9,8,10,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110
[9,8,7,10,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110
[9,8,7,6,10,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110
[9,8,7,6,5,10,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110
[9,8,7,6,5,4,10,3,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110
[9,8,7,6,5,4,3,10,2,1]=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110
[8,7,6,5,4,3,1,2,9]=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100
[9,8,7,6,5,4,3,2,10,1]=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110
[9,8,7,6,5,4,3,2,1,10]=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110
[1,4,2,7,8,6,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,2,4,8,5,3,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,2,4,7,5,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,3,8,5,2,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,7,3,2,8,6,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,5,7,8,6,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,2,3,1,8,5,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,2,5,1,7,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,1,8,3,4,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,8,3,5,1,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,4,8,5,7,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,3,6,4,8,5,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,6,4,7,5,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,2,4,7,5,8,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,1,3,7,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,2,1,4,3,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,6,4,2,3,1,8,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,2,3,1,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,5,4,2,6,8,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,7,5,3,4,6,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,5,4,6,7,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,2,6,3,1,8,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,2,6,4,3,1,7,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,2,7,4,1,3,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,8,4,3,5,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,7,4,2,3,5,6,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,8,4,1,3,2,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,7,4,3,2,5,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,6,3,8,2,4,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,8,1,2,7,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,8,3,2,6,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,7,3,1,2,6,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,7,5,4,2,6,3,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,8,2,4,6,3,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,8,4,2,7,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,4,6,2,8,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,1,6,7,2,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,6,1,2,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,3,2,7,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,4,5,3,8,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,4,1,2,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,1,4,2,7,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,8,3,2,4,5,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,6,3,2,4,1,7,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,3,2,6,7,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,2,6,8,1,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,5,6,7,8,1,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,3,6,7,1,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,2,3,4,1,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,2,3,1,4,5,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,6,1,4,3,2,5,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,1,6,5,2,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,7,5,1,8,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,5,2,8,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,2,4,6,5,3,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,1,2,5,4,6,3,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,2,6,5,1,3,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,1,6,2,5,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,2,6,4,5,3,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,1,2,5,6,4,3,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,1,2,6,5,4,3,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,7,5,4,2,8,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,4,8,2,7,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,4,6,8,2,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,7,6,2,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,4,7,2,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,4,5,2,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,5,1,2,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,2,8,1,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,8,7,1,3,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,5,8,2,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,6,2,8,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,2,8,6,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,2,6,4,8,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,7,6,3,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,2,7,4,6,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,7,2,6,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,3,6,8,5,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,4,2,7,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,2,7,6,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,2,6,8,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,2,8,4,6,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,2,7,6,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,7,1,8,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,4,3,2,5,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,7,2,1,3,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,7,3,4,2,5,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,1,7,8,2,6,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,2,7,8,3,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,8,1,3,4,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,8,6,3,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,2,6,8,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,3,7,8,5,6,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,7,5,8,6,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,2,7,3,8,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,7,2,8,6,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,7,8,3,4,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,3,8,7,5,6,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[10,1,2,3,4,5,6,7,8,9]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[10,1,2,3,4,5,6,9,7,8]=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000
[10,1,2,3,4,5,9,6,7,8]=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000
[9,1,2,3,4,10,5,6,7,8]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[10,1,2,3,9,4,5,6,7,8]=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000
[10,1,2,9,3,4,5,6,7,8]=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000
[9,1,10,2,3,4,5,6,7,8]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[10,9,1,2,3,4,5,6,7,8]=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000
[8,1,2,3,4,5,6,9,10,7]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[7,1,2,3,4,5,10,9,6,8]=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>101000000
[6,1,2,3,4,10,9,5,7,8]=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>101000000
[5,1,2,3,9,10,4,6,7,8]=>[7,3]=>[[1,2,3,7,8,9,10],[4,5,6]]=>001000000
[4,1,2,10,9,3,5,6,7,8]=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>101000000
[3,1,10,9,2,4,5,6,7,8]=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>101000000
[2,9,10,1,3,4,5,6,7,8]=>[7,3]=>[[1,2,3,7,8,9,10],[4,5,6]]=>001000000
[4,7,8,5,6,2,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,8,4,2,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,3,7,2,1,5,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,6,3,8,2,1,5,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,7,8,3,2,1,5,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,8,3,2,1,4,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,6,3,7,2,1,4,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,6,4,7,3,5,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,3,2,1,6,5,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,3,2,1,8,6,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,4,3,2,1,8,7,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,4,2,6,7,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,3,2,6,1,7,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,3,2,6,1,8,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,6,4,7,3,8,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,4,2,7,8,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,3,4,1,2,8,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,5,3,7,2,6,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,7,4,2,6,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,5,8,4,2,6,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[2,1,7,8,5,6,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,8,3,7,5,1,4,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,7,3,8,1,6,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,6,4,8,5,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,2,4,1,7,6,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,5,8,3,1,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,5,4,2,8,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,5,8,3,2,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,8,5,2,1,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,6,2,5,1,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,3,2,5,1,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,6,1,5,2,7,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,6,3,1,5,2,7,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,6,4,1,2,7,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,6,1,7,2,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,4,1,3,7,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,3,1,7,2,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,2,7,1,3,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,2,7,3,1,6,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,6,1,4,7,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,2,7,4,6,1,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,2,4,8,5,1,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,1,4,6,8,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,6,1,5,7,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,2,1,5,7,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,2,1,5,3,7,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,6,1,5,3,7,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,1,7,5,3,6,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,4,1,5,6,2,3,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,1,5,2,6,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,5,1,2,7,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,6,4,1,3,7,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,5,1,2,7,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,1,8,5,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,5,8,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,5,1,2,8,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,5,1,8,2,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,5,8,2,1,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,4,5,2,8,1,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,5,6,2,7,1,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,6,2,7,1,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,4,6,3,7,2,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,6,8,2,7,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,6,2,8,7,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,6,2,7,8,4,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,6,2,7,4,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,6,7,2,8,3,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,6,8,7,2,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,5,8,6,7,3,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,5,8,6,7,3,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,6,8,7,2,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,6,7,2,1,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,5,1,6,7,8,4,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,6,1,7,4,2,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,6,1,7,4,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,6,8,7,1,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,6,7,8,1,3,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,6,7,1,3,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,6,7,1,3,2,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,6,7,3,1,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,6,8,7,4,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,5,8,6,7,4,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,5,6,7,4,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,5,8,6,7,4,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,5,3,7,1,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,4,3,7,1,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,2,4,3,7,1,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,2,5,6,1,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,5,6,1,7,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,5,7,3,2,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,5,8,3,2,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,2,4,7,1,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,8,2,4,7,1,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,3,5,6,7,1,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,7,1,5,6,8,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,1,5,8,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,2,4,6,1,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,2,4,6,1,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,5,1,7,4,6,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,5,1,8,4,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,5,1,7,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,3,2,4,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,1,5,7,8,3,2,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,5,6,1,7,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,7,6,1,8,3,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,6,1,7,3,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,5,8,7,3,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,3,2,4,6,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,2,5,1,8,7,4,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,5,1,6,4,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,1,8,7,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,5,1,6,8,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,8,6,5,1,7,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,7,6,5,1,8,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,1,7,8,4,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,2,5,1,6,7,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,1,8,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,1,7,5,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,1,6,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,4,1,8,5,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,3,2,4,7,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,5,1,8,4,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,5,1,6,7,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,5,1,7,4,2,3,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,1,8,4,2,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,2,3,7,5,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,6,1,8,3,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,2,6,1,8,3,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,4,6,1,7,3,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,6,1,8,4,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,4,2,3,8,5,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,1,6,4,2,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,1,6,4,2,3,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,5,1,7,6,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,5,1,8,6,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,3,2,4,8,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,1,5,7,3,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,2,6,1,8,5,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,5,6,1,7,3,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,6,8,5,1,7,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,1,6,7,4,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,2,5,1,8,6,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,4,1,8,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,4,1,5,8,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,5,1,7,8,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,5,1,6,4,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,5,1,7,6,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,7,5,1,8,6,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,5,1,6,4,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,2,5,1,8,7,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,7,3,1,8,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,3,7,1,8,5,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,6,3,7,5,1,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,6,1,7,5,3,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,5,7,4,1,6,3,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,5,7,4,1,6,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,4,7,3,6,1,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,7,8,3,1,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,7,5,1,8,6,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,4,3,8,5,1,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,4,3,6,1,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,8,3,6,1,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,3,6,7,1,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,5,4,6,1,7,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,5,8,1,6,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,5,4,6,8,1,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,8,4,1,6,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,6,2,1,8,5,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,4,1,7,5,8,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,7,5,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,4,1,8,5,3,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,4,8,2,1,6,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,8,4,1,6,3,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,5,6,1,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,8,3,2,6,1,5,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,2,8,1,6,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,1,6,8,5,4,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,7,1,5,4,8,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,7,1,5,8,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,8,2,5,1,6,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,8,3,2,6,7,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,8,2,6,7,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,2,6,7,8,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,2,6,7,1,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,7,2,6,8,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,7,8,2,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,7,4,8,1,6,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,5,7,8,1,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,5,7,1,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,5,7,1,6,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,2,7,1,5,4,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,2,7,1,5,8,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,2,7,8,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,2,6,1,7,8,5,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,5,2,1,7,8,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,7,5,3,8,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,1,8,5,3,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,3,2,7,1,4,8,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,2,1,4,7,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,2,1,4,7,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,2,1,7,4,6,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,2,1,7,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,4,2,1,7,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,2,1,8,3,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,4,1,7,3,8,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,7,1,4,8,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,5,8,2,1,7,4,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,8,3,7,2,1,5,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,7,2,8,1,5,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,3,7,2,1,5,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,3,2,7,1,5,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,2,8,1,7,4,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,3,2,8,1,4,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,1,4,7,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,2,1,8,4,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,3,2,1,5,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,8,2,1,5,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110
[8,7,6,4,5,3,2,1,9]=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100
[1,9,8,7,5,6,4,3,2]=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100
[1,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110
[9,8,7,5,6,4,3,2,1,10]=>[3,1,1,1,1,1,1,1]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>111111100
[8,7,5,4,6,3,2,1,9]=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100
[8,7,4,6,5,3,2,1,9]=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100
[1,9,8,6,5,7,4,3,2]=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100
[1,9,8,5,7,6,4,3,2]=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100
[1,10,9,8,6,7,5,4,3,2]=>[3,1,1,1,1,1,1,1]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>111111100
[6,2,3,1,5,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,5,2,3,1,7,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,6,7,2,5,3,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,2,5,3,4,1,7,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,2,5,3,4,1,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,5,2,4,3,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,5,1,3,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,5,3,4,2,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,5,1,4,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,5,2,4,1,7,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,7,5,6,2,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,7,2,4,1,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,5,1,4,2,7,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,5,3,4,2,7,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,5,1,3,2,7,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,8,4,5,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,6,7,4,5,1,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,6,7,1,5,3,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,7,3,5,1,4,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,3,7,5,6,1,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,7,3,6,1,4,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,3,7,4,6,2,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,7,4,6,1,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,7,1,6,4,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,7,3,6,4,5,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,1,7,5,6,3,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,7,5,6,1,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,4,7,5,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,7,3,4,2,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,7,3,6,2,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,7,1,6,2,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,7,2,6,4,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,2,7,3,6,4,5,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,7,3,6,1,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,2,7,1,6,3,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,7,2,4,3,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,3,2,7,4,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,8,3,7,4,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,5,2,4,3,7,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,7,1,4,3,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,2,7,3,4,1,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,7,5,6,3,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,7,5,6,2,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,7,2,3,1,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,3,1,7,4,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,3,1,5,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,3,1,8,5,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,3,2,8,6,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,6,7,2,3,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,3,1,7,5,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,7,2,6,3,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,7,2,6,1,4,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,2,7,5,6,1,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,7,2,5,1,4,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,6,7,1,5,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,7,1,3,2,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,8,6,7,3,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,8,3,7,5,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,3,2,7,5,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,7,5,6,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,7,2,6,4,5,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,7,1,6,4,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,2,7,4,6,1,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,2,7,4,6,3,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,7,2,6,3,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,7,2,6,1,5,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,4,7,1,6,2,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,7,4,6,2,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,7,1,6,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,5,7,3,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,7,4,6,1,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,7,1,6,3,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,7,4,6,3,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,7,1,6,3,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,7,3,6,1,5,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[2,4,8,3,6,1,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,5,8,1,3,2,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,5,8,6,3,2,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,5,8,7,3,1,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,5,8,7,3,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,7,2,8,4,6,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,2,8,4,1,5,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,6,2,8,4,5,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,1,8,4,5,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,4,6,1,5,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,1,8,4,5,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,1,6,8,4,5,7,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,6,8,4,5,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,3,7,8,4,1,5,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,3,7,8,4,6,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,7,8,2,4,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,7,8,2,4,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,7,8,4,2,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,1,8,4,2,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,8,7,3,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,8,3,7,1,6,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,2,8,7,3,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,2,1,8,4,6,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,7,8,4,6,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,7,8,1,4,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,2,7,8,5,4,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,1,3,8,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,2,5,8,3,4,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,2,8,5,4,3,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,8,3,5,4,1,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,4,5,3,1,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,4,8,5,2,3,1,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,5,8,2,4,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,3,1,2,8,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,4,2,1,8,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,6,8,4,3,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,1,8,3,4,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,5,8,1,4,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,7,5,8,3,4,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,8,5,4,3,2,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,6,8,5,1,3,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,8,1,4,3,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,8,6,3,4,2,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[2,4,8,3,6,5,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,4,1,5,6,3,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,8,3,5,6,2,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,6,8,4,1,3,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,6,8,1,5,3,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,6,8,4,5,3,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,3,8,5,4,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,7,1,8,5,4,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,7,3,8,4,6,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,3,8,4,6,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,7,8,4,3,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,7,4,1,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,8,5,4,3,1,6,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,5,8,4,2,3,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,1,3,2,8,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,3,2,8,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,2,8,5,4,6,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,8,2,5,3,1,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,4,3,5,1,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,3,4,5,1,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,2,8,4,5,3,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,3,8,5,4,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,3,1,8,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,1,4,8,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,3,2,4,8,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,1,5,3,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,8,4,5,3,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,2,8,5,3,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,4,2,5,3,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,5,3,2,4,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,8,1,5,2,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,1,4,8,2,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,2,8,4,3,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,8,5,4,3,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,5,4,3,8,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,4,8,5,3,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,7,4,8,5,3,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,2,7,8,4,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,2,7,4,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,5,1,4,7,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,8,1,5,4,7,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,2,8,5,7,4,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,4,8,7,5,3,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,1,4,3,7,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,2,8,7,4,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,1,2,8,7,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,4,8,1,7,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,6,1,4,2,8,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,6,2,8,4,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,7,2,8,4,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,1,4,2,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,7,1,4,8,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,7,8,1,5,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,2,8,5,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,2,8,4,5,3,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,2,7,8,5,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,2,8,4,3,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,4,1,2,8,3,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,6,1,3,2,4,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,1,3,2,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,7,3,5,8,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,7,5,8,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,8,1,3,7,2,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,2,5,8,7,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,5,8,3,7,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,1,7,3,5,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,1,3,2,4,7,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,8,1,7,3,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,1,7,4,3,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,1,2,8,4,3,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,2,8,4,7,5,3,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,8,7,4,5,3,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,8,1,7,5,3,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,7,1,5,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,6,1,4,7,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,6,1,4,2,7,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,6,2,7,4,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,2,8,6,4,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,1,2,8,6,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,7,4,8,1,6,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,4,8,7,1,6,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,2,8,1,7,6,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,1,7,6,4,3,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,3,4,1,6,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,3,4,1,8,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,8,3,4,1,7,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,3,4,1,5,2,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,7,3,4,1,6,2,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,6,2,7,3,4,1,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,2,8,3,5,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,8,3,5,1,6,2,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,6,2,4,1,7,3,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,5,1,7,3,8,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,2,7,3,8,1,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,2,7,3,8,1,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,2,7,4,8,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,6,2,8,3,7,1,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[9,2,1,3,4,5,6,7,8]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[10,2,1,3,4,5,6,7,8,9]=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000
[9,2,3,1,4,5,6,7,8]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[4,2,3,5,6,7,8,9,1]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[3,4,2,5,6,7,8,9,1]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[3,2,4,5,6,7,8,9,10,1]=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000
[6,5,3,2,1,4,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,6,3,5,2,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,3,5,2,4,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,8,2,4,5,7,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,2,4,5,3,1,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,6,1,4,5,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,7,4,5,2,1,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,3,8,4,5,7,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,7,4,3,6,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[2,8,7,4,3,6,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,7,4,3,6,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,3,5,1,4,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,6,8,5,7,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,8,3,5,1,7,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,1,8,4,7,6,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,5,8,4,7,6,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,3,8,1,5,6,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,8,1,3,5,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,8,7,4,1,6,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,3,6,1,4,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,3,6,1,2,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,8,7,4,1,6,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,8,1,2,5,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,7,1,4,2,6,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,3,1,2,4,7,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,7,4,5,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,7,4,5,1,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,2,4,1,6,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,3,6,2,4,7,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,3,2,1,4,7,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,3,5,2,1,4,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,3,6,2,1,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,7,4,2,6,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[2,6,8,4,5,7,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,1,8,4,5,7,2,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,8,3,5,1,7,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,1,5,8,3,6,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,3,6,1,2,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,1,8,2,5,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,8,1,5,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,8,2,1,5,6,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,4,8,2,5,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,8,1,4,7,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,3,1,6,2,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,5,3,8,6,1,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,4,1,8,5,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,6,8,10,1,3,5,7,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,7,8,9,10,1,3,4,5,6]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[5,6,7,8,10,1,2,3,4,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,4,6,8,10,12,1,3,5,7,9,11]=>[6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>00000100000
[7,8,9,10,11,12,1,2,3,4,5,6]=>[6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>00000100000
[4,5,7,6,2,3,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,7,2,6,4,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,3,7,6,1,5,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,2,4,7,1,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,1,3,5,8,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,3,7,6,1,5,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[3,8,4,7,6,1,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,8,4,7,1,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,4,7,2,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,3,2,7,6,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,8,2,1,7,6,5,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,7,1,2,8,5,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,2,1,7,6,5,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[1,4,2,7,8,6,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,2,7,1,6,5,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,7,2,1,6,4,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[1,5,7,2,8,6,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,7,6,8,1,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,4,8,7,2,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,3,8,7,6,1,5,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,7,2,8,1,5,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,7,8,1,6,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,2,8,7,1,6,5,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[3,2,8,1,7,6,5,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[1,3,8,2,7,6,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,3,7,6,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,1,7,8,2,6,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,1,7,2,6,5,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,8,1,2,7,6,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,2,3,7,6,5,4]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,1,4,5,6,7,8,9,10,2]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[10,3,4,5,6,7,8,1,2,9]=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>101000000
[10,1,4,5,6,7,8,9,2,3]=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>101000000
[2,10,4,5,6,7,8,1,3,9]=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>101000000
[8,3,4,5,6,7,1,10,2,9]=>[6,3,1]=>[[1,3,4,8,9,10],[2,6,7],[5]]=>100100000
[3,1,10,5,6,7,8,9,2,4]=>[6,3,1]=>[[1,3,4,8,9,10],[2,6,7],[5]]=>100100000
[9,1,4,5,6,7,8,2,10,3]=>[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>101000000
[6,7,1,8,4,5,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,7,1,5,8,2,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,7,1,5,8,3,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,6,5,1,8,3,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,6,5,1,8,2,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,6,5,1,8,7,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,4,1,8,7,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,1,4,5,7,6,2,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,5,1,8,7,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,4,6,1,8,7,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,5,6,1,8,7,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,6,1,8,2,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,6,1,8,3,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,1,3,8,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,6,1,2,8,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,6,1,2,8,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,3,6,1,8,2,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,3,1,5,8,2,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,1,3,5,7,2,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,2,5,7,3,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,1,5,8,3,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,5,1,8,3,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,6,1,3,8,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,3,6,1,4,8,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,5,3,1,8,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,4,1,3,8,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,2,1,4,3,8,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,1,2,4,3,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,3,4,2,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,1,4,2,8,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,3,4,1,2,8,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,6,3,1,2,8,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,6,4,1,2,8,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,6,4,1,3,8,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,7,1,4,3,8,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,7,1,4,2,8,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,1,3,2,8,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,1,6,7,2,3,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,1,2,3,8,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,1,2,4,8,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,1,3,4,8,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,3,1,4,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,2,1,4,8,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,2,1,8,3,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,5,2,1,8,3,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,1,5,2,7,3,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,4,2,3,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,1,2,3,8,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,4,2,1,3,8,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,2,3,1,8,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,2,4,1,8,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,3,2,1,4,8,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,1,2,4,8,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,1,3,2,4,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,2,3,4,7,6,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,2,1,3,4,8,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,3,1,4,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,3,6,1,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,3,6,5,8,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,3,5,8,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,3,5,8,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,1,5,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,5,3,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,2,6,5,1,8,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,6,5,8,1,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,6,5,8,3,1,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,4,6,1,5,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,6,5,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,6,5,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,1,5,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,4,3,8,7,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,4,6,8,1,5,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,1,8,5,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,6,8,5,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,6,8,5,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,6,8,5,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,1,8,5,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,8,1,5,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,8,3,5,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,8,3,5,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,8,3,1,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,3,1,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,3,8,1,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,3,8,5,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,3,8,5,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,3,6,8,5,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,3,6,8,5,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,3,6,8,1,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,3,1,6,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,3,6,8,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,3,6,1,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,3,6,8,1,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,6,3,8,1,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,4,6,8,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,6,8,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,1,8,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,8,1,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,8,3,1,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,6,2,8,5,7,1,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,4,8,7,1,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,4,2,8,7,5,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[2,6,4,8,1,7,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,6,4,8,7,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,6,1,4,8,7,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,4,2,8,7,5,1,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[1,6,4,7,3,8,2,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,7,4,5,8,2,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,4,7,3,6,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,6,3,4,8,2,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,6,3,7,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,6,3,8,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,7,4,8,3,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,7,3,4,8,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,7,4,5,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,4,7,3,8,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,1,7,5,8,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,8,6,3,7,1,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,1,3,7,2,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,2,1,7,3,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,7,2,1,8,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,1,3,8,2,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,2,4,8,3,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,6,1,5,8,2,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,6,1,4,5,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,5,1,3,4,8,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,2,4,8,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,5,1,3,7,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,3,2,8,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,4,2,1,5,8,3,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,5,3,4,1,8,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,5,2,1,8,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,4,8,7,1,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,6,4,8,7,2,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,7,8,3,6,1,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,2,8,7,1,5,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,4,8,7,1,3,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,8,3,7,1,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,4,8,7,2,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,8,2,5,1,3,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,2,5,1,3,8,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,7,2,1,5,4,8,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,8,2,1,5,4,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,3,2,1,5,4,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,1,6,4,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,2,5,1,6,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,1,5,6,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,1,4,6,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,2,1,4,5,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,7,2,1,4,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,7,1,4,6,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,8,1,4,6,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,8,1,4,7,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,2,1,4,7,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,8,2,1,5,7,4,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,8,2,5,1,7,3,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,2,5,1,8,3,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,7,2,1,5,8,4,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,7,2,1,4,8,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,1,7,5,8,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,7,1,6,8,4,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,7,6,1,8,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,3,7,6,8,1,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,3,8,6,7,1,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,8,6,1,7,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,8,1,6,7,4,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,1,8,7,5,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,2,1,7,4,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,8,1,7,4,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,8,1,6,4,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,7,1,6,4,8,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,7,6,1,3,8,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,8,6,1,3,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,8,7,1,3,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,8,3,4,1,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,7,8,1,3,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,6,8,1,3,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,6,7,1,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,6,1,8,4,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,7,2,1,8,4,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,2,1,8,5,4,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,3,8,5,1,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,3,7,8,6,1,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,7,1,8,6,4,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,1,6,8,5,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,6,1,8,7,4,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,6,8,1,7,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,3,6,8,7,1,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,6,7,1,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,2,6,1,7,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,6,4,8,7,1,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,4,6,2,7,8,5,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,8,5,4,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,7,5,4,6,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,8,3,5,4,7,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,6,2,5,4,8,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,6,2,8,7,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,8,1,2,4,6,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,6,1,8,2,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,3,8,5,4,1,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,8,1,5,2,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,4,1,5,3,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,5,1,6,3,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,1,7,6,4,3,2,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,1,7,8,4,3,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,1,8,6,4,3,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,7,6,4,3,2,5]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[3,1,6,7,5,8,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,2,1,4,5,6,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,1,2,5,7,3,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,1,5,6,3,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,6,1,5,7,2,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,3,6,8,5,7,2,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,4,1,5,2,3,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,7,5,2,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,3,8,1,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,8,2,3,4,1,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,1,6,4,7,8,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,8,5,7,4,3,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,1,5,8,4,3,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,1,8,7,4,3,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,7,1,4,3,2,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,8,1,4,3,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,7,1,4,3,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,5,4,1,3,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,6,4,1,8,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,8,5,1,4,3,2,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,5,1,4,3,2,8]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,2,3,4,5,6,9,7,8]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,2,3,4,5,8,6,9,7]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[1,2,3,4,7,5,8,9,6]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[1,2,3,6,4,7,8,9,5]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[1,2,5,3,6,7,8,9,4]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[1,4,2,5,6,7,8,9,3]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[9,8,1,2,3,4,5,6,7]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[7,8,9,1,2,3,4,5,6]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[6,7,8,9,1,2,3,4,5]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[9,8,7,6,5,4,3,1,2]=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110
[9,10,1,2,3,4,5,6,7,8]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[8,9,10,1,2,3,4,5,6,7]=>[7,3]=>[[1,2,3,7,8,9,10],[4,5,6]]=>001000000
[10,9,8,1,2,3,4,5,6,7]=>[7,1,1,1]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>111000000
[7,8,9,10,1,2,3,4,5,6]=>[6,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>000100000
[10,9,8,7,6,5,4,3,1,2]=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110
[3,4,6,2,7,1,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,7,5,4,1,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,6,2,8,1,5,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,2,5,4,7,8,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,4,6,3,7,5,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,6,7,2,5,8,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,6,1,7,5,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,5,4,6,2,8,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,4,6,3,5,8,7,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,3,2,7,1,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,3,2,7,1,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,1,7,8,5,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,4,1,6,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,2,1,6,4,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,8,4,3,2,1,5,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,3,8,2,1,6,4,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,7,5,8,2,1,4,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,6,4,3,2,1,7,5]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,3,7,2,5,1,8,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,6,7,2,8,1,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,7,2,8,1,4,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,5,2,1,4,7,6,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,5,2,1,8,4,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,5,4,1,3,7,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,2,8,6,1,4,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,3,8,2,1,4,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,7,3,2,1,5,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,7,3,2,1,5,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,5,2,1,4,7,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,2,8,6,1,4,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,6,5,4,3,2,1,9]=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100
[8,9,7,6,5,4,3,2,1,10]=>[3,1,1,1,1,1,1,1]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>111111100
[7,6,8,5,4,3,2,1,9]=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100
[7,8,3,5,4,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,3,7,5,2,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,4,1,6,3,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,1,6,2,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,1,6,2,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,1,6,2,8,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,7,6,5,1,8,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,7,6,5,1,8,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,3,6,5,1,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,6,4,1,5,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,6,1,5,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,6,1,4,8,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,7,6,1,4,8,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,5,1,8,4,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,5,1,8,6,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,7,6,1,5,8,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,7,6,4,1,8,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,7,6,3,8,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,7,6,3,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,3,6,2,8,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,7,6,4,1,8,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,5,1,8,6,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,3,5,1,8,2,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,4,8,7,6,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,4,8,5,7,1,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,5,4,8,1,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,3,5,8,7,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,4,5,8,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,3,5,8,7,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,5,4,8,1,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,3,4,8,7,5,6,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,4,8,7,5,1,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,7,6,5,4,8,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,3,5,6,8,4,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,5,6,8,1,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,5,6,8,1,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,1,5,8,7,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,4,1,5,8,7,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,1,5,8,3,7,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,1,6,3,8,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,1,5,8,3,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,1,5,8,2,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,1,5,8,2,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,3,5,7,8,2,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,5,7,8,2,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,6,4,5,8,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,7,3,6,1,8,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,4,5,8,6,3,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,5,4,8,6,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,3,4,8,5,6,1,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,4,8,7,1,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,4,8,1,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,4,8,1,6,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,8,5,1,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,3,5,4,8,2,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,3,5,8,2,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,4,5,8,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,3,5,8,2,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,5,4,8,2,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,3,4,8,5,1,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,3,4,8,1,6,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,4,8,1,5,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,8,2,6,1,5,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,6,7,2,5,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,1,7,2,6,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,1,7,5,6,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,8,2,7,5,6,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,2,7,4,6,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,4,7,1,6,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,2,7,1,6,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,1,7,2,6,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,4,7,2,6,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,3,7,5,6,2,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,1,7,4,6,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,8,2,7,5,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,4,7,5,6,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,4,7,5,6,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,3,7,5,6,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,3,7,1,6,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,1,7,3,6,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,2,8,6,4,1,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,5,1,8,6,2,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,7,4,2,8,5,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,7,3,8,5,2,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,1,8,3,5,6,2,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,3,8,6,2,5,1,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,4,2,8,6,1,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,1,8,4,2,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,7,8,2,6,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,3,7,8,5,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,3,7,8,4,5,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,3,7,8,1,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,1,5,4,7,8,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,1,4,8,2,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,4,8,6,1,3,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,3,8,4,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,8,1,3,6,7,2,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,4,2,8,1,3,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,8,1,4,7,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,8,1,3,6,2,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,7,4,2,6,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,5,1,2,8,7,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,5,3,1,4,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,1,6,4,2,7,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,4,5,8,2,7,1,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,4,6,2,8,1,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,2,6,8,1,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,5,6,1,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,6,8,4,7,2,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,2,5,4,8,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,1,6,5,4,8,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,1,6,5,8,3,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,6,8,4,3,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,4,7,6,3,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[2,7,1,5,4,3,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,2,1,5,4,3,7,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,1,5,7,3,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,6,1,4,7,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,7,6,1,4,3,8,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,5,1,3,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,8,2,4,3,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,6,2,4,8,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,3,8,4,6,2,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,3,5,8,6,2,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,2,1,4,3,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,3,1,4,6,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,6,3,2,5,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,3,5,1,6,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,6,5,7,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,6,5,1,8,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,2,3,4,5,6,7,9]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,9,2,3,4,5,6,7,8]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[9,1,2,3,4,5,6,7,8,10]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[7,8,1,2,3,4,5,6,9]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[1,8,9,2,3,4,5,6,7]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[1,10,2,3,4,5,6,7,8,9]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[8,9,1,2,3,4,5,6,7,10]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[7,1,8,2,3,4,5,6,9]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[6,8,1,2,3,4,5,7,9]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[1,8,2,9,3,4,5,6,7]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[1,7,9,2,3,4,5,6,8]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[1,9,10,2,3,4,5,6,7,8]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[3,6,4,8,7,5,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,4,3,8,7,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,6,2,4,7,8,5,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,6,2,4,8,1,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,7,2,8,1,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,3,8,4,5,6,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,5,6,4,8,7,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,6,8,5,3,7,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,6,5,4,2,8,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,5,2,7,3,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,1,3,4,2,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,5,3,2,8,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,6,8,7,4,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,8,6,3,4,2,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,1,4,5,6,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,8,3,6,5,7,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,1,3,2,7,5,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,3,8,5,7,2,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,6,5,8,1,4,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,6,7,3,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,6,4,3,7,2,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,3,5,4,2,7,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,5,7,4,3,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,3,8,7,1,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,3,8,2,1,7,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[3,5,7,8,4,1,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,4,6,3,1,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,5,4,3,1,2,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,1,4,2,8,5,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,8,6,5,3,2,7,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,5,1,2,4,7,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,7,5,8,2,1,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,7,5,8,2,6,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,3,8,5,7,6,2,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,8,5,7,1,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,3,1,5,6,2,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,8,5,2,1,4,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,2,5,6,1,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,8,1,5,6,3,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,2,5,6,3,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,2,5,7,6,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,8,6,2,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,8,6,1,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,6,1,5,7,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,6,5,7,1,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,6,5,8,1,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,1,7,6,8,4,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,3,7,8,6,2,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,2,5,8,1,6,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,8,5,7,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,1,5,7,6,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,8,6,1,7,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,2,8,6,5,7,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,1,3,6,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,2,5,6,3,7,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,6,5,4,1,8,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,1,3,5,4,7,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,1,5,3,4,7,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,5,6,2,4,1,8,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,2,6,3,7,1,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,3,1,2,6,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,6,5,7,3,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,8,6,2,7,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,1,6,3,7,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,8,5,6,3,7,2,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,6,5,4,2,8,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,6,1,4,2,8,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,1,4,2,6,5,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,7,3,5,6,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,4,1,5,6,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,7,6,4,1,2,8,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,6,1,5,2,8,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,7,6,4,5,2,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,3,6,5,7,2,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,1,6,5,7,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,3,5,7,6,2,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,5,4,1,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,1,5,4,3,7,8,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,5,6,4,2,1,8,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,2,6,5,7,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,6,2,5,1,8,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,1,4,3,5,7,8,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,1,3,4,5,7,8,2]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,2,6,4,5,1,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,3,6,5,7,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,7,8,5,6,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,4,7,2,5,1,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,7,2,5,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,2,4,7,1,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,6,7,5,8,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,7,5,8,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,2,6,1,5,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,6,2,5,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,8,1,2,5,6,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,6,2,5,7,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,8,6,4,7,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,8,3,6,7,4,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,5,8,3,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,1,6,4,7,2,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,8,5,1,3,4,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,3,4,5,1,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,2,4,3,1,5,7,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,7,4,8,2,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,3,7,4,1,6,2,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,7,6,3,1,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,2,7,8,5,4,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,1,2,8,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,1,3,6,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,2,1,4,5,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,4,1,5,3,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,1,6,4,3,8,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,1,8,2,7,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,1,7,5,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,1,7,4,8,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,7,5,6,4,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,8,6,5,4,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,6,5,7,3,4,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,4,7,5,8,2,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,5,3,6,2,7,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,3,7,4,6,8,2,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,7,5,6,3,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,7,6,5,4,8,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,6,5,7,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,2,7,6,8,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,7,5,3,8,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,7,5,6,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,1,7,6,8,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,8,5,6,2,7,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,6,4,2,7,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,5,2,4,6,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,8,6,3,7,4,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,1,6,2,4,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,1,4,7,2,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,4,1,7,2,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,7,1,8,3,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,4,1,8,5,2,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,7,1,4,8,3,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,7,1,8,4,5,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,2,8,4,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,5,1,4,3,8,2,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,6,2,5,8,3,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,5,1,3,7,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,2,1,7,3,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,2,1,8,5,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,5,4,2,8,3,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,4,3,1,5,8,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,6,8,4,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,7,6,8,5,3,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,7,6,8,5,4,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,4,8,6,7,5,2,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,8,6,7,3,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,8,5,4,6,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,4,8,5,6,7,2,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,3,5,8,4,7,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,3,8,6,7,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,2,8,7,3,6,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,5,8,7,3,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,8,5,7,4,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,3,8,7,5,6,2,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,8,7,4,6,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,1,8,5,7,6,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,5,8,7,4,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,1,8,7,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,6,7,4,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,8,7,5,6,3,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,2,1,6,3,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,1,4,3,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,1,4,3,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,2,1,4,3,6,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,4,1,3,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,4,3,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,1,4,3,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,4,1,3,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,2,1,3,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,2,1,3,5,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,2,1,3,6,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,2,1,6,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,2,1,8,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,1,4,3,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,4,3,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,8,4,3,6,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,1,4,3,6,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,4,1,3,6,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,8,2,1,3,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,8,2,1,4,3,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,6,2,1,4,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,1,4,6,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,1,4,8,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,4,1,8,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,2,8,1,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,1,8,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,4,1,8,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,1,6,8,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,1,6,3,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,1,3,6,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,3,8,6,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,3,8,6,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,1,3,8,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,1,8,3,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,1,8,6,3,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,2,1,6,4,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,6,1,4,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,8,1,3,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,8,1,3,6,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,8,3,6,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,8,3,6,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,8,6,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,8,1,6,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,8,6,1,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,8,6,1,3,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,4,6,2,1,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,8,2,1,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,8,4,1,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,8,1,4,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,1,8,4,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,6,8,4,3,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,8,6,4,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,6,4,1,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,6,2,1,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,4,2,1,3,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,6,1,5,4,8,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,2,4,3,8,1,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,4,1,5,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,6,1,5,2,8,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,3,5,2,8,1,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,7,2,6,5,8,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,8,2,6,1,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,8,1,7,2,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,8,1,5,2,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,1,8,3,4,2,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,4,8,1,3,2,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,5,4,8,3,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,1,7,6,8,3,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,3,7,6,8,1,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,7,1,8,5,6,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,3,6,5,8,1,7,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,3,5,4,7,2,8,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,3,5,4,8,1,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,6,3,8,4,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,6,5,8,1,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,4,6,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,6,1,3,2,7,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,6,3,4,2,7,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,6,3,7,2,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,5,1,7,2,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,5,2,6,1,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,5,2,6,4,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,6,3,5,1,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,7,1,5,3,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,2,4,1,5,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,2,4,1,7,3,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,2,4,3,6,1,7,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,8,4,6,1,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,8,1,5,4,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,7,6,8,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,7,1,8,5,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,6,5,8,1,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,5,7,2,4,3,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,8,2,4,1,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,2,4,1,8,5,6,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,6,8,2,4,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,8,1,5,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,7,3,8,5,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,3,2,8,5,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,1,8,5,6,2,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,8,2,6,4,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,8,1,5,4,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,7,4,5,3,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,7,2,6,3,8,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,8,2,6,1,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,8,1,7,2,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,6,5,8,3,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,5,7,4,8,1,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,7,1,8,3,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,7,4,8,3,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,7,1,8,3,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,6,3,8,1,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,4,3,7,8,6,5,11,12,10,9]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[2,1,5,6,4,3,8,7,11,12,10,9]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[2,1,5,6,4,3,9,10,8,7,12,11]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[2,1,5,6,4,3,9,11,8,12,10,7]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[2,1,5,7,4,8,6,3,11,12,10,9]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[3,4,2,1,6,5,8,7,11,12,10,9]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[3,4,2,1,6,5,9,10,8,7,12,11]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[3,4,2,1,6,5,9,11,8,12,10,7]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[3,4,2,1,7,8,6,5,10,9,12,11]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[3,4,2,1,7,9,6,10,8,5,12,11]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[3,4,2,1,7,9,6,11,8,12,10,5]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[3,5,2,6,4,1,8,7,11,12,10,9]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[3,5,2,6,4,1,9,10,8,7,12,11]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[3,5,2,6,4,1,9,11,8,12,10,7]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[3,5,2,7,4,8,6,1,11,12,10,9]=>[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000
[2,8,3,1,5,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,5,3,4,7,1,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,8,3,5,7,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,5,3,1,8,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,1,8,5,3,6,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,4,1,3,8,2,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,4,8,3,2,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,8,4,3,2,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,5,4,3,2,6,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,7,4,3,8,5,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,7,3,8,4,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,4,7,8,3,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,1,5,7,3,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,5,3,7,4,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,4,7,6,5,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,6,8,5,3,7,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,1,7,4,3,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,8,1,7,3,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,8,7,1,5,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,4,1,3,8,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,7,5,6,3,2,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,1,7,8,5,3,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,7,4,6,3,1,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,8,4,3,7,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,4,8,3,7,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,2,6,3,4,1,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,7,3,1,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,1,8,3,5,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,7,3,5,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,1,3,6,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,1,7,3,5,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,2,6,3,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,2,6,3,5,4,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,2,8,7,4,5,6,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,3,7,1,5,6,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,6,1,2,7,5,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,6,2,7,4,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,5,2,6,7,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,2,1,8,6,7,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,5,7,6,4,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,7,8,5,2,6,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,1,6,4,2,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,6,1,5,3,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,3,8,6,1,5,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,6,1,5,3,4,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,7,1,6,4,5,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,1,7,5,6,4,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[1,8,6,7,5,4,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,3,5,2,1,4,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,5,7,2,8,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,2,7,4,3,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,3,6,1,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,1,4,6,2,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,4,5,7,2,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,7,4,6,3,8,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,8,4,6,3,7,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,4,7,3,6,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,4,7,5,1,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,1,4,7,3,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,3,7,1,4,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,8,5,7,4,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,3,7,1,8,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,1,4,7,8,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,3,4,7,5,8,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,4,6,8,3,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,1,3,5,8,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,8,3,7,1,2,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,6,4,1,7,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,8,1,2,5,7,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,7,5,4,1,3,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,2,6,4,1,3,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,8,6,7,4,2,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,6,8,4,2,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,3,7,8,2,4,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,6,2,1,4,7,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,7,6,2,1,8,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,6,2,8,7,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,8,6,4,2,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,6,7,5,4,8,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,7,4,5,8,2,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,7,3,5,1,8,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,1,6,7,5,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,5,7,3,6,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,3,6,1,2,8,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,1,7,2,5,6,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,7,1,6,5,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,2,1,8,7,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,4,6,2,7,8,5,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,6,1,2,5,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,1,4,8,2,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,3,1,8,7,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,5,6,4,7,1,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,4,6,1,5,7,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,4,1,5,7,6,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,8,2,7,1,6,5,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[3,8,2,7,6,1,5,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[3,8,2,7,6,5,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[3,8,2,7,6,5,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[4,8,7,2,6,5,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[4,8,7,2,6,5,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,7,2,6,1,5,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,7,2,1,6,5,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,7,3,1,6,5,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,7,3,2,1,6,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,7,3,2,6,1,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,7,3,2,6,5,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,7,3,6,2,5,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,7,3,6,2,1,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,7,3,6,1,5,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,7,3,6,5,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,8,7,3,6,5,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,8,7,6,3,4,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,8,7,6,3,1,4,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,7,6,3,2,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,8,7,6,2,4,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,8,7,6,2,1,4,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,7,6,4,2,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,8,7,6,4,2,1,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,8,7,6,4,1,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,8,7,6,4,3,1,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,2,1,5,6,4,3,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,6,7,3,8,2,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,4,5,7,1,3,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,5,1,7,4,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,2,1,5,7,4,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,1,5,7,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,7,3,8,1,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,6,7,3,8,5,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,6,7,8,3,4,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,5,6,7,8,3,1,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,1,6,7,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,1,6,7,8,4,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,6,1,7,8,4,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,6,7,8,3,2,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,4,5,7,2,1,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,6,7,2,8,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,4,2,1,7,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,6,2,7,8,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,6,7,2,8,5,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,1,5,7,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,6,7,8,2,4,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,6,7,8,4,2,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,4,6,7,1,8,5,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,6,1,7,8,5,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,4,3,6,5,8,7,9]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,4,1,3,6,5,8,7,9]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,4,1,6,3,5,8,7,9]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,4,1,6,3,8,5,7,9]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,4,1,6,3,7,5,9,8]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,4,1,5,3,7,6,9,8]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,3,1,5,4,7,6,9,8]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[1,3,2,5,4,7,6,9,8]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,4,1,3,6,5,8,7,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,4,6,1,3,5,8,7,9]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,4,1,6,3,5,8,7,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,4,1,6,8,3,5,7,9]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,4,1,6,3,8,5,7,10,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,4,1,6,3,8,9,5,7]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,4,1,6,3,8,5,10,7,9]=>[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[2,4,1,6,3,7,5,8,9]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[2,4,1,6,3,8,5,9,7,10]=>[6,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>000100000
[2,4,1,5,3,8,6,9,7]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,4,1,6,3,7,5,9,8,10]=>[6,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>000100000
[2,3,1,6,4,7,5,9,8]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,4,1,5,3,7,6,9,8,10]=>[6,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>000100000
[1,4,2,5,3,7,6,9,8]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[2,3,1,5,4,7,6,9,8,10]=>[6,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>000100000
[1,3,2,5,4,7,6,9,8,10]=>[6,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>000100000
[7,1,2,3,4,5,6,8,9]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,4,3,6,2,5,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,3,7,2,5,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,3,7,6,8,2,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,4,3,7,5,8,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,3,7,2,6,5,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,3,7,4,8,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,2,6,5,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,4,8,2,6,3,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,4,8,3,7,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,2,3,6,5,8,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,8,2,4,5,7,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,7,8,4,5,2,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,1,4,5,3,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,7,4,1,6,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,8,3,6,1,5,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,3,1,6,4,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,1,4,7,6,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,1,8,6,2,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,1,8,2,6,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,1,8,4,2,6,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,3,8,5,2,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,1,3,8,5,2,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,2,8,4,1,6,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,2,8,3,6,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,2,8,3,6,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,8,2,3,6,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,2,3,8,4,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,2,3,8,4,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,2,8,1,3,5,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,6,3,8,7,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,1,3,8,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,8,1,3,7,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,4,8,3,7,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,4,1,3,8,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,4,8,2,3,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,8,1,5,2,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,8,1,2,4,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,4,8,2,7,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,1,2,8,7,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,1,6,4,2,8,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,1,6,2,8,7,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,4,2,5,8,7,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,2,8,7,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,2,6,1,8,7,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,3,1,5,8,2,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,4,8,7,1,2,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,4,8,1,7,2,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,3,4,8,7,2,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,3,5,4,1,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,7,5,8,6,1,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,7,1,8,3,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,7,6,5,3,8,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,7,6,5,3,8,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,7,6,5,2,4,8,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,7,6,4,8,5,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,6,3,8,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,1,6,2,4,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,6,5,1,2,8,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,3,5,4,8,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,6,3,4,8,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,4,2,8,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,7,1,6,2,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,6,7,4,8,5,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,6,7,4,2,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,6,8,3,5,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,7,6,5,1,4,3,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,2,1,7,4,8,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,2,1,7,3,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,5,2,7,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,2,5,1,3,7,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,2,5,3,1,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,4,3,2,1,8,6]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,7,4,3,2,8,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,7,6,2,4,8,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,3,6,4,8,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,2,7,5,3,8,1,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,1,8,5,3,6,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,3,2,7,1,6,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[8,7,2,6,1,5,4,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[1,8,5,7,4,3,6,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,5,7,2,4,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,6,1,7,2,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,2,8,5,6,1,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,7,5,8,2,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,7,2,6,8,4,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,6,5,8,1,4,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,6,5,8,4,1,3,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,4,8,3,2,1,7]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,3,5,1,8,4,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,1,5,7,3,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,7,4,8,5,2,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,2,5,8,6,3,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,1,8,4,7,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,3,8,7,4,1,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[5,4,8,1,7,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,8,1,7,3,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,7,8,1,5,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,8,7,1,3,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,8,7,2,1,6,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[8,3,7,6,1,5,4,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,2,7,6,5,1,4,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[4,3,8,7,6,2,1,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[2,4,8,7,6,1,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,5,8,7,2,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,3,8,6,5,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,8,6,4,3,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,8,7,3,6,4,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[4,8,7,6,2,5,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[3,8,7,6,5,1,4,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[2,8,7,6,5,4,1,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[3,4,1,2,5,6,7,8,9]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[3,2,1,4,5,6,7,8,9]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[4,3,2,1,5,6,7,8,9]=>[6,1,1,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>11100000
[5,6,7,8,1,2,3,4,9]=>[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000
[5,4,3,2,1,6,7,8,9]=>[5,1,1,1,1]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>11110000
[6,5,4,3,2,1,7,8,9]=>[4,1,1,1,1,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>11111000
[7,6,5,4,3,2,1,8,9]=>[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100
[3,2,1,4,5,6,7,8,9,10]=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000
[4,3,2,1,5,6,7,8,9,10]=>[7,1,1,1]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>111000000
[5,4,3,2,1,6,7,8,9,10]=>[6,1,1,1,1]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>111100000
[6,5,4,3,2,1,7,8,9,10]=>[5,1,1,1,1,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>111110000
[7,6,5,4,3,2,1,8,9,10]=>[4,1,1,1,1,1,1]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>111111000
[8,7,6,5,4,3,2,1,9,10]=>[3,1,1,1,1,1,1,1]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>111111100
[3,6,5,1,2,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,5,8,2,4,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,8,5,7,2,4,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,7,8,4,3,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,2,6,4,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,2,5,4,3,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,2,4,6,3,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,2,6,5,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,5,7,8,3,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,5,8,7,3,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,1,8,3,6,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,1,7,8,5,2,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,7,4,8,2,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,5,3,8,1,4,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,5,8,7,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,8,4,7,2,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,8,7,5,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,1,6,3,2,8,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,2,3,7,5,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,2,3,8,6,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,2,3,5,8,6,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,8,1,4,3,7,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,3,2,4,1,6,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,7,3,4,8,6,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,3,2,4,1,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,1,4,3,8,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,2,3,5,7,6,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,1,2,3,6,7,5,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,1,2,3,6,8,5,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,1,2,3,8,5,6,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,2,3,7,5,6,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,1,2,3,6,5,7,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,1,8,5,4,3,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,2,6,3,4,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,2,7,3,4,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,2,8,3,4,1,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,8,7,1,4,2,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,8,1,4,2,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,6,8,1,4,2,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,5,7,8,2,4,1,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,7,1,4,2,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,6,2,8,3,1,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,2,7,3,1,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,7,5,4,3,2,6]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,1,7,4,5,3,2,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,8,3,7,1,4,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,7,3,4,6,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,7,3,2,4,1,8,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,2,4,3,6,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,1,2,3,5,6,8,4]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[6,1,2,3,8,7,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,2,3,7,8,6,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,2,3,8,7,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,2,3,8,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,2,3,5,8,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,6,2,4,3,1,7,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,3,2,4,8,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,6,3,4,8,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,6,3,2,4,7,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,2,4,3,1,8,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,1,2,3,5,7,8,4]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,1,2,3,6,8,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,8,5,4,2,7,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,8,1,7,3,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,4,8,5,7,6,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,4,2,6,3,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,8,1,4,7,2,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,4,2,8,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,3,8,5,4,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,1,7,3,5,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,1,3,6,5,4,2,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,3,1,6,5,4,2,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,1,2,3,6,5,4,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,8,1,2,7,3,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,8,2,7,6,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,8,2,7,6,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,2,7,6,3,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,8,2,1,7,4,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,6,3,8,5,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,3,8,7,4,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,8,7,1,4,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,8,4,1,7,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,2,8,7,6,3,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,2,8,7,6,5,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[4,1,8,7,6,5,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[4,3,8,7,6,5,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,7,4,6,1,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,3,1,2,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,1,2,4,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,8,1,7,2,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,2,5,8,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,1,8,7,4,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,5,1,8,7,2,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,5,8,3,1,7,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,4,8,7,6,2,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,1,4,8,7,6,2,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,4,8,7,6,5,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,2,7,5,8,6,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,4,8,2,6,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,1,3,7,5,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,7,8,1,2,6,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,3,7,8,2,6,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,7,8,1,6,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,8,1,3,6,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,2,6,7,3,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,2,6,7,5,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,5,7,1,3,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,8,1,6,7,3,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,6,8,3,7,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,6,4,7,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,3,4,1,7,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,3,7,4,1,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,6,8,3,7,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,1,6,7,5,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,2,5,7,1,6,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,7,2,3,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,4,2,6,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,3,5,7,4,1,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,2,4,7,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,3,5,7,1,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,4,7,3,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,7,1,4,6,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,1,2,4,6,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,1,4,6,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,7,1,3,6,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,6,8,3,7,2,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,5,7,1,2,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,7,1,3,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,4,7,1,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,4,7,1,2,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,1,4,7,2,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,4,6,8,2,7,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,5,8,2,7,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,6,3,1,7,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,2,8,1,7,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,4,5,7,2,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,7,3,6,1,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,5,7,1,6,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,6,8,3,7,5,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,8,2,7,5,1,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,8,4,2,7,1,5,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[8,6,4,7,3,1,5,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,4,5,7,3,1,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,2,5,7,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,4,7,2,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,1,3,4,6,2,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,7,2,4,6,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,4,5,7,1,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,3,4,5,1,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,4,5,2,6,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,7,2,3,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,2,3,4,6,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,2,3,6,1,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,2,8,5,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,8,5,3,7,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,1,8,4,3,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,8,4,3,7,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,2,8,4,3,1,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,4,8,2,1,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,4,8,2,7,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,4,1,8,2,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,1,4,5,2,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,5,4,3,2,7,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,4,2,8,1,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,5,3,2,8,7,1,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,3,2,8,7,5,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,3,2,1,7,8,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,6,3,2,7,8,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,6,3,2,7,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,4,2,7,8,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,6,4,3,7,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,7,4,3,6,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,7,4,1,3,6,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,4,2,6,1,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,7,3,2,6,5,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,7,3,2,6,4,8,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,3,2,5,4,1,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,3,2,1,5,4,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,7,5,6,2,3,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,7,5,6,2,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,5,6,1,3,4,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,5,7,1,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,5,7,2,8,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,4,7,2,8,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,4,1,7,2,8,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,4,6,2,1,8,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,5,7,1,8,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,6,1,7,8,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,5,6,7,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,4,6,8,7,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,6,8,7,1,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,1,6,8,7,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,3,6,8,7,2,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,5,1,8,7,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,3,5,8,6,2,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,2,8,5,6,3,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,8,5,1,7,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,1,8,6,7,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,3,2,8,6,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,8,6,7,1,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,3,2,6,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,8,7,1,6,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,2,8,7,6,1,5,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,2,8,7,6,4,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,2,1,8,6,5,4,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,3,6,1,8,5,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,7,8,5,4,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,3,7,8,6,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,1,7,8,6,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,4,7,8,6,1,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,5,7,6,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,7,6,8,1,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,7,6,8,3,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,1,7,6,8,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,7,5,8,3,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,6,5,1,8,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,6,4,3,1,8,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,1,7,4,3,8,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,6,7,5,3,8,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,7,5,1,4,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,6,7,5,4,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[2,7,6,1,5,4,3,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,7,6,5,1,4,2,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,7,6,5,3,1,2,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,4,3,1,5,7,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,4,1,5,2,7,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,6,5,1,3,2,7,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,3,1,7,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,3,1,5,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,1,7,2,4,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,7,1,2,4,5,3,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,6,1,2,4,7,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,1,2,6,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,5,1,6,4,2,7,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,5,1,3,6,4,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,1,5,3,4,7,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,1,5,2,4,7,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,1,2,5,7,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,1,2,7,4,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,1,2,5,4,3,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,1,4,2,3,8,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,4,2,7,3,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,5,8,2,6,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,7,8,1,2,4,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,8,1,3,4,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,1,7,3,4,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,5,7,2,4,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,1,2,7,6,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,2,3,8,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,2,7,6,3,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,2,8,7,5,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,2,4,8,7,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,8,4,6,7,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,7,6,4,8,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,1,2,4,6,8,5,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,1,2,6,8,5,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,2,7,8,5,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,2,7,4,8,5,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,4,7,8,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,1,3,8,4,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,1,8,4,2,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,1,5,3,2,8,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,4,5,2,8,6,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,7,3,1,5,8,6,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,8,7,3,1,5,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,1,7,4,5,2,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,7,5,3,2,6,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,7,1,2,6,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,2,8,4,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,2,8,6,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,7,2,6,4,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,2,3,8,6,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,2,3,8,5,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,8,1,7,2,4,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,1,3,4,7,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,8,6,4,7,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,2,6,7,4,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,2,8,7,3,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,3,5,8,4,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,5,8,6,4,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[7,1,2,8,3,6,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,2,8,6,4,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,7,8,4,6,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,1,8,7,6,4,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,2,7,4,6,5,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,1,2,7,3,6,5,4]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,2,3,5,8,7,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,6,8,5,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,5,6,3,1,4,2,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,8,3,1,4,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,5,3,1,4,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,5,3,1,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,5,3,1,6,4,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,5,8,3,4,1,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,6,3,4,1,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,6,3,1,2,8,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,3,6,1,2,8,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,3,1,4,2,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,3,1,6,4,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,6,4,1,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,6,4,8,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,8,4,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,1,8,4,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,1,8,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,1,6,4,2,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,1,8,4,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,1,8,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,8,6,1,4,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,5,3,8,6,4,1,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,5,8,3,6,1,4,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,5,8,3,1,6,4,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,5,3,6,1,4,2,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,8,4,1,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,8,6,3,1,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,8,6,3,4,1,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,5,6,8,3,1,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,4,1,8,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,6,3,1,8,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,6,3,1,8,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,6,3,8,1,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,6,3,8,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,6,1,8,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,1,2,8,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,3,1,2,8,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,1,4,8,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,4,8,1,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,3,4,1,6,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,3,1,4,6,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,2,5,4,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,5,2,8,4,7,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,4,7,3,2,8,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,8,3,2,7,6,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,4,5,3,2,1,8,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,3,2,6,4,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,5,8,3,2,7,6,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,6,3,8,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,8,6,3,7,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,8,5,3,2,7,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,4,3,2,7,6,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,3,2,8,4,7,6,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,5,8,4,7,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,2,7,4,8,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,4,3,2,8,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,7,5,3,2,8,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,7,8,3,6,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,6,8,3,7,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,4,3,8,5,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,3,2,6,8,5,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,6,7,5,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,2,6,7,5,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,4,3,7,5,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,5,7,6,4,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,4,5,3,2,7,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,7,3,6,5,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,4,6,3,7,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,6,3,8,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,7,2,6,8,5,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,8,2,6,7,5,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,8,2,5,4,7,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,2,8,6,5,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,6,2,8,7,5,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,7,3,8,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,8,3,7,5,2,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,4,8,3,6,5,2,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,4,5,3,2,8,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,4,3,2,8,6,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,3,2,5,4,8,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,7,5,4,8,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,2,8,6,5,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,8,4,3,6,5,2,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,8,5,7,4,3,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,8,4,3,7,5,2,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,3,2,8,7,5,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,3,2,7,8,5,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,4,3,8,5,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,3,1,4,5,6,7,8,9]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[2,3,4,1,5,6,7,8,9]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[2,3,4,5,1,6,7,8,9]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[2,3,4,5,6,1,7,8,9]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[2,3,1,4,5,6,7,8,9,10]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[2,4,3,1,5,6,7,8,9]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[2,3,4,1,5,6,7,8,9,10]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[2,3,4,5,1,6,7,8,9,10]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[2,3,4,5,6,1,7,8,9,10]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[2,3,4,5,6,7,1,8,9,10]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[2,3,4,5,6,8,7,1,9]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[2,3,4,5,6,7,8,1,9,10]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[2,3,4,5,6,7,9,8,1]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[4,6,8,3,5,7,1,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,8,1,2,4,5,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,8,2,4,7,1,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,3,5,2,4,1,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,5,7,3,6,1,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,2,8,3,1,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,5,8,3,7,1,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,1,6,8,4,7,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,2,5,8,3,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,3,6,8,4,7,1,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,6,5,8,2,4,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,2,6,8,5,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,3,8,2,6,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,4,8,3,2,1,6,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,3,7,2,6,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,3,6,2,7,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,3,2,1,8,5,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,1,7,3,2,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,1,7,8,2,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,5,1,2,7,8,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,5,1,4,8,2,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,7,3,8,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,4,7,6,3,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,7,1,4,2,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,5,1,2,7,6,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,3,1,7,2,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,4,3,5,2,7,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,3,1,5,2,8,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,3,6,5,2,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,3,7,6,4,2,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,6,3,4,2,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,8,3,6,2,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,8,7,4,2,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,8,7,5,3,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,6,4,3,8,5,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[1,7,6,2,8,4,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,3,2,6,8,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,3,2,7,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,2,1,8,5,4,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,3,2,7,4,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,2,6,3,7,4,1,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,5,3,1,6,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,7,3,8,5,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,2,3,7,8,5,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,7,2,8,4,5,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,1,8,2,4,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,2,7,8,3,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,7,8,6,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,1,7,3,8,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,8,4,3,1,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,2,1,8,4,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,3,2,5,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,8,2,4,5,6,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,7,6,1,2,4,5,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,3,7,6,2,1,4,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,2,8,7,5,1,4,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,6,5,2,1,4,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,3,5,2,4,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,6,2,5,3,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,2,4,1,6,5,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,8,1,7,5,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,4,1,7,6,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,1,5,6,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,7,3,6,4,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,8,3,7,5,4,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,1,6,7,5,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,2,6,4,3,7,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,1,7,5,4,3,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,5,1,8,6,4,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,7,2,6,4,3,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,2,7,5,4,3,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,8,6,5,4,3,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,2,7,5,4,3,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,2,4,3,8,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,7,2,8,3,6,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,8,6,5,2,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,3,8,6,5,4,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[1,8,7,6,5,2,4,3]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,1,7,3,2,6,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,1,4,3,2,8,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,5,3,2,1,7,4]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,6,3,2,1,7,4,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,5,4,1,7,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,5,1,7,3,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,1,7,4,3,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,6,3,2,7,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,3,7,2,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,8,3,1,6,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,5,8,3,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,4,1,8,2,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,4,3,1,8,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,7,2,5,4,6,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,5,3,7,2,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,1,8,7,5,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,4,8,6,3,5,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,6,3,5,2,1,8]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,3,5,6,8,4,2,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,4,8,7,1,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,1,4,6,8,7,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,3,8,7,2,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,6,2,4,8,7,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,1,6,7,5,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,1,6,4,8,5,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,6,8,5,1,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,3,7,2,6,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,5,2,8,1,4,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,6,5,7,2,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,6,3,8,1,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,7,3,5,1,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,2,4,7,5,1,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,2,4,1,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,3,8,2,1,6,4,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,5,2,1,8,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,6,4,3,1,5,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,6,4,1,5,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,8,7,2,1,4,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,2,7,1,5,4,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,6,8,2,1,5,4,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,4,8,1,6,5,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,8,1,5,7,3,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,5,7,6,1,4,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,1,7,3,5,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,1,7,5,4,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,6,2,8,7,3,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,2,4,6,7,3,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,5,4,7,1,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,5,8,6,4,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,5,6,4,3,1,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,2,5,7,8,4,3,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,7,4,8,6,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,2,7,8,3,6,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,8,6,3,5,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,7,6,3,5,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,7,4,6,3,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,1,6,4,2,3,5,8]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,6,2,4,7,3,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,2,4,5,7,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,1,4,6,5,8,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,1,2,3,8,5,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,5,4,3,8,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,1,5,4,6,2,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,8,7,2,3,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,7,8,2,4,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,4,7,2,5,8,1,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,8,1,2,7,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,8,3,1,5,6,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,8,7,1,5,4,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,4,1,5,7,6,2,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,6,1,5,3,7,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,6,5,1,3,8,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,5,2,1,3,8,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,5,2,8,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,8,4,1,5,2,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,2,3,4,1,6,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,8,3,6,1,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,8,5,7,2,1,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,5,2,7,1,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,5,2,1,7,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,5,4,2,8,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,6,4,7,2,5,3,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,4,8,2,5,3,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,5,8,2,4,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,8,2,4,3,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,2,4,3,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,6,2,4,7,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,6,2,4,7,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,8,2,4,7,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,7,2,4,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,5,7,2,4,3,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,7,2,4,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,6,7,2,4,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,8,2,4,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,7,2,4,6,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,7,8,3,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,8,3,2,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,6,2,4,8,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,6,2,8,3,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,3,4,2,8,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,2,4,3,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,6,2,4,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,8,7,3,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,2,3,5,8,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,2,3,4,8,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,5,2,3,8,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,7,4,2,8,6,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,7,6,5,2,8,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,6,7,5,2,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,5,2,8,4,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,5,6,2,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,7,6,2,4,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,8,3,2,4,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,5,2,3,7,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,5,2,3,7,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,8,4,2,3,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,7,4,6,2,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,3,5,2,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,8,5,2,3,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,4,2,3,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,4,2,3,7,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,8,6,2,4,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,7,3,2,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,3,4,2,8,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,4,2,8,5,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,7,4,2,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,4,2,3,8,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,6,4,2,8,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,7,5,2,8,6,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,6,4,2,3,8,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,7,5,6,1,4,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,4,1,6,7,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,6,4,3,5,8,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,4,1,3,7,2,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,1,3,8,2,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,8,1,2,6,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,8,6,4,2,7,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,1,3,6,2,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,4,3,7,2,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,3,7,8,6,1,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,7,6,8,3,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,4,3,7,2,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,3,4,7,6,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,3,8,5,6,1,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,2,3,7,5,6,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,7,4,8,5,2,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,8,3,6,2,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,5,8,6,3,2,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,8,7,3,2,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[2,5,3,8,7,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,7,3,6,2,5,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,8,7,5,3,2,1,4]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,7,6,8,3,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,7,4,6,5,8,2,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,2,7,5,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,8,4,6,5,7,2,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,1,5,2,4,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,2,8,5,6,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,7,6,8,1,4,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,8,5,6,1,3,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,3,2,7,6,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,6,8,2,4,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,1,6,2,4,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,1,4,2,6,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,1,4,2,5,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,2,1,4,3,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,3,6,5,8,7,1,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,4,1,5,6,7,8,9,2]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[3,4,5,1,6,7,8,9,2]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[3,4,5,6,7,1,8,9,2]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[3,4,5,6,7,8,1,9,2]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[3,1,2,5,6,7,8,9,4]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[3,4,1,5,6,7,8,9,10,2]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[3,4,5,6,1,7,8,9,10,2]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[3,4,5,6,7,1,2,9,8]=>[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000
[3,4,5,6,7,8,1,2,9]=>[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000
[3,4,5,6,7,8,9,1,10,2]=>[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000
[1,6,2,3,8,7,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,4,3,2,8,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,4,7,6,2,5,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,6,5,3,7,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,6,5,3,7,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,7,5,2,6,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,7,4,2,6,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,6,4,3,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,6,4,3,7,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,7,3,2,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,3,2,5,8,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,3,2,4,8,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,5,3,2,8,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,5,3,2,4,8,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,6,5,4,3,1,8,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,8,5,4,3,2,1,7]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,1,5,4,3,8,6,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,8,5,4,3,7,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,7,6,5,4,3,10,9,2]=>[3,2,1,1,1,1,1]=>[[1,7,10],[2,9],[3],[4],[5],[6],[8]]=>111110100
[7,6,1,4,3,8,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,8,5,4,7,2,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,5,1,3,8,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,3,4,7,2,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,8,4,3,2,1,6]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,4,7,5,2,6,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,6,8,2,1,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,6,5,2,1,7,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,8,7,5,6,1,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,7,5,1,8,4,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,8,7,4,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,6,7,4,3,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,6,5,2,4,1,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,3,6,4,1,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,4,5,3,2,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,7,1,4,6,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,1,2,4,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,7,6,8,2,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,6,8,1,7,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,6,8,5,7,1,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,3,7,2,4,8,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,8,6,5,2,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,1,8,2,5,4,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,5,3,7,4,1,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,4,7,5,1,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,4,7,6,2,3,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,4,7,1,2,5,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,8,7,3,5,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,7,4,2,5,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,3,8,2,5,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,1,5,8,2,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,5,8,7,3,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,5,8,7,4,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,5,6,7,4,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,3,2,8,5,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,2,7,1,8,5,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,1,7,2,8,5,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,8,7,3,5,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,8,3,1,5,6,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,4,7,2,8,5,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,1,4,8,5,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,2,3,4,8,5,6,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,8,5,2,7,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,7,4,5,8,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,8,3,6,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,1,6,4,7,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,8,2,6,4,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,6,3,5,8,7,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,6,2,1,5,8,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,2,7,6,1,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,6,8,4,7,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,6,8,7,5,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,8,6,5,2,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,1,6,4,7,3,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,4,1,2,3,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,4,8,5,3,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,5,8,4,2,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,2,5,8,4,1,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,4,7,1,5,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,7,5,6,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,4,8,7,3,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,2,8,4,3,5,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,8,1,3,5,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,3,4,1,5,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,2,7,3,5,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,1,8,7,2,5,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,1,7,2,5,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,3,7,1,5,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,8,7,1,3,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,4,6,7,3,1,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,8,2,7,6,1,5]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,8,4,2,1,3,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,2,4,3,5,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,3,7,1,5,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,2,7,3,5,6,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,4,1,3,2,8,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,8,6,2,1,4,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,5,2,8,3,1,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,3,7,5,1,8,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,8,5,2,7,4,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,2,5,4,3,8,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,6,8,1,4,5,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,8,1,2,4,5,3,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,6,2,4,5,3,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,8,6,1,2,5,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,1,6,2,3,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,6,5,8,2,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,8,6,2,5,1,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,6,1,4,5,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,6,8,4,5,1,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,5,4,3,8,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,8,7,4,2,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,4,3,7,6,1,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[8,7,4,3,1,6,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,7,4,3,8,6,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,5,3,4,8,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,6,1,7,4,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,6,5,7,2,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,7,6,8,2,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,1,8,7,4,3,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,4,3,1,6,7,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,5,8,6,3,4,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,5,8,6,3,4,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,3,8,5,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,5,8,4,3,1,7,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,6,5,2,8,1,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,2,8,1,3,6,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,8,5,2,3,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,3,2,5,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,8,3,1,5,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,8,3,2,5,6,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,3,1,5,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,8,3,5,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,8,2,3,6,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,2,7,8,6,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,5,1,8,2,4,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,8,1,2,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,8,1,2,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,7,1,8,6,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,8,4,1,2,6,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,8,2,3,6,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,3,6,7,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,3,1,6,8,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,3,7,1,8,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,7,3,2,8,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,1,4,3,8,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,1,8,6,3,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,3,6,2,7,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,5,1,7,2,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,3,6,5,8,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,3,5,8,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,8,7,3,6,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,2,8,6,1,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,2,5,6,1,4,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,5,4,1,2,7,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,6,1,8,3,7,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,1,6,2,8,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,5,3,8,7,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,6,3,7,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,1,5,8,2,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,8,5,1,2,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,5,2,4,8,1,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,1,4,8,2,6,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,8,2,5,1,6,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,4,8,5,2,6,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,2,1,8,5,6,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,4,8,2,6,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,2,1,5,8,6,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,8,4,5,1,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,4,8,3,7,6,1,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[3,1,5,8,6,2,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,4,8,5,1,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,4,8,1,6,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,6,1,2,8,3,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,8,4,1,2,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,8,4,6,1,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,4,8,7,1,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,4,8,1,2,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,1,6,2,3,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,5,1,6,8,2,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,4,1,8,2,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,4,7,1,2,8,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,4,7,8,1,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,3,7,1,4,2,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,3,1,8,4,2,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,1,4,8,3,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,6,4,7,3,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,1,4,8,3,6,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,3,7,1,4,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,3,1,5,8,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,1,5,3,8,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,5,4,3,7,6,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,5,4,3,7,2,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,1,5,3,8,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,1,5,3,2,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,5,4,3,2,6,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,1,6,4,2,5,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,3,1,2,7,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,3,8,1,4,2,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,8,1,4,3,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,1,7,2,5,4,3,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,1,7,2,5,4,6,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,6,1,2,5,4,8,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,5,3,8,1,4,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,3,1,2,7,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,1,4,2,6,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,6,4,2,5,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,1,5,3,2,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,3,1,5,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,3,1,5,7,2,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,1,5,3,6,2,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,5,4,3,6,2,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,1,5,4,3,6,7,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[7,4,1,5,3,6,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,3,1,5,7,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,3,8,4,5,1,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,5,6,1,8,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,5,6,3,8,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,3,6,5,7,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,4,7,1,8,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,1,8,4,7,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,6,4,5,1,8,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,3,6,1,5,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,1,5,3,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,3,6,2,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,3,6,4,8,2,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,1,5,3,8,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,5,8,1,4,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,6,7,2,3,1,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,2,8,1,4,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,4,2,7,5,6,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,1,8,4,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,8,2,6,1,4,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,6,7,1,4,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,8,1,4,3,7,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,2,5,4,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,2,7,3,6,1,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,1,8,2,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,1,8,6,7,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,2,5,1,8,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,2,8,1,6,3,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,5,3,6,1,8,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,6,3,7,5,1,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,2,8,3,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,2,3,8,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,2,1,7,6,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,2,1,4,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,7,3,1,4,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,7,3,1,4,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,7,2,1,4,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,2,1,3,7,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,3,1,7,2,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,1,3,2,7,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,8,6,4,1,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,7,5,1,6,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,7,5,1,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,6,5,1,4,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,6,3,5,1,2,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,7,3,1,5,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,3,1,4,2,6,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,7,3,1,2,6,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,3,1,2,4,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,2,1,4,7,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,2,1,7,4,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,7,2,1,5,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,2,1,6,3,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,5,4,1,2,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,8,5,6,7,4,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,5,8,6,2,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,7,8,6,3,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,5,7,6,3,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,6,3,2,1,5,8,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,2,1,5,3,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,1,3,7,6,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,7,2,3,6,1,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,7,4,2,8,1,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,6,8,5,7,3,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,2,7,3,8,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,6,7,5,3,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,1,5,8,7,6,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,4,7,6,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,4,7,8,5,3,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,1,3,7,6,2,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,5,1,6,3,2,7,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,7,1,5,2,8,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,6,8,4,7,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,4,6,1,3,2,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,8,6,7,3,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,4,3,8,2,1,5,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,7,5,8,1,6,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,3,2,7,8,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,2,5,1,6,7,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,8,5,7,1,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,1,4,6,8,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,2,5,6,1,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,4,3,8,7,5,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,7,3,5,1,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,6,8,4,2,5,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,7,1,6,3,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,7,2,8,4,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,4,8,6,5,2,1,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,7,6,1,4,5,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,8,2,1,7,3,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,3,5,1,6,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,6,3,5,8,7,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,5,8,4,3,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,7,1,5,4,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[2,1,6,5,8,4,7,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,6,8,5,4,3,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,1,8,5,6,2,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,4,8,7,3,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,8,4,3,5,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,2,7,6,1,3,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,1,8,2,7,5,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,1,2,6,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,4,3,2,7,1,6]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,4,8,6,3,2,5,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,4,7,2,1,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,8,4,3,7,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,8,2,4,5,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,4,2,3,6,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,2,4,3,1,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,3,1,6,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,2,1,3,4,7,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,8,2,6,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,7,3,5,4,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,8,4,5,7,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,8,3,4,5,7,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,3,8,2,6,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,7,2,3,6,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,2,3,5,4,8,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,8,2,4,5,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,8,4,6,7,5]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,8,2,3,5,4,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,7,8,2,3,6,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,7,8,2,3,5,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,8,2,5,3,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,7,8,2,4,5,3,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,8,3,6,4,5,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,8,2,3,6,4,5,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,8,3,5,4,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,7,8,3,6,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,2,7,8,3,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,2,8,4,6,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,2,3,4,6,7,5]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,7,8,2,4,3,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,7,3,1,5,2,8,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,8,3,1,5,2,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,4,5,1,2,8,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,5,4,1,2,8,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,7,5,1,2,8,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,3,8,1,5,2,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,8,4,1,7,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,6,8,5,7,1,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,5,8,6,7,1,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,8,6,1,7,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,3,8,1,6,7,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,4,7,6,1,8,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,8,6,5,7,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,6,5,7,8,1,2,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,4,6,1,8,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,8,4,6,1,7,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,8,3,1,6,7,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,7,3,1,6,8,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,3,1,7,8,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,3,1,7,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,4,8,1,6,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,4,6,8,1,7,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,8,6,7,5,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,1,7,8,6,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,3,8,1,7,6,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,8,7,1,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,8,7,5,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,8,6,5,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,7,6,5,1,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,5,4,7,3,6,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,6,3,7,5,1,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,7,3,6,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,6,3,1,5,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,3,1,6,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,3,7,6,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,5,3,7,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,7,6,3,5,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,5,3,6,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,3,7,5,4,1,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,5,2,3,8,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,3,7,5,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,1,8,6,5,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,5,3,1,8,6,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,8,3,1,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,3,2,6,4,1,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,8,2,1,4,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,2,8,3,4,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,6,3,8,7,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,8,3,6,4,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,7,6,3,4,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,3,8,7,5,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,3,8,6,4,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,7,4,8,6,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,7,6,3,8,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,6,4,8,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,7,6,4,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,6,3,1,8,5,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,3,8,5,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,8,4,2,3,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,8,4,3,5,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,3,1,8,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,2,8,3,1,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,8,2,4,1,6,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,4,8,3,1,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,2,1,8,3,5,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,8,7,4,2,3,5,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,5,2,8,7,3,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,7,3,6,4,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,8,6,3,7,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,7,3,8,6,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,8,4,7,6,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,7,3,4,8,6,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,6,3,8,4,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,2,3,8,7,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,1,8,3,7,5,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,3,2,1,7,4,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,4,2,7,3,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,8,6,3,4,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,7,3,8,4,6,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,8,7,4,6,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,3,8,7,6,4,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,8,5,7,2,6,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,4,8,6,1,2,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,8,1,5,7,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,8,1,3,5,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,7,6,2,4,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,6,7,1,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,8,5,7,1,6,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,4,8,6,2,1,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,6,7,3,4,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,6,7,2,1,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,6,7,2,1,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,1,7,5,2,8,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,3,8,5,1,6,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,8,6,7,1,5,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,6,7,1,4,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,2,3,8,5,1,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,4,8,6,1,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,5,7,6,1,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,8,5,2,6,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,4,7,2,5,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,2,6,7,5,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,7,5,2,8,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,8,6,7,4,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,6,7,4,1,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,6,7,3,1,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,6,7,3,1,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,1,6,7,5,3,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,6,7,4,2,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,6,7,4,3,1,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,8,7,6,1,4,2,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,1,8,3,6,7,2,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,1,4,7,8,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,8,4,7,5,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,1,3,5,7,2,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,8,1,6,5,4,2,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,1,7,3,8,4,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,7,6,5,8,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,1,6,8,2,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,3,2,7,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,8,6,2,5,3,4,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,7,2,6,8,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,3,6,4,5,2,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,7,4,1,6,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,8,6,4,5,2,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,1,2,7,5,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,7,8,5,1,6,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,4,8,2,7,6,1,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[5,8,2,6,3,4,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,7,5,8,6,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,1,7,8,4,3,6,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,4,3,5,7,8,2,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,2,7,4,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,5,6,4,3,1,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,6,5,4,3,2,7]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[6,1,5,2,8,4,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,1,8,5,7,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,1,2,8,5,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,7,2,8,5,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,3,5,8,6,2,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,3,5,8,6,1,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,6,8,1,5,7,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,4,6,5,8,1,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,8,1,5,7,2,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,1,2,5,8,6,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,7,2,5,8,6,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,7,6,8,2,3,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,8,1,2,3,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,1,5,8,6,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,4,7,1,8,5,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,5,8,3,1,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,2,1,8,5,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,6,8,2,1,3,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,2,7,6,8,3,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,7,6,8,2,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,2,1,6,8,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,4,1,8,5,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,4,3,1,8,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,7,4,1,6,8,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,7,6,8,1,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,2,6,8,5,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,2,5,8,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,1,7,6,8,2,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,6,8,1,2,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,3,7,6,8,2,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,4,2,6,8,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,1,2,6,8,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,4,2,8,5,6,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,1,8,2,5,4,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,8,4,6,1,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,2,8,1,6,4,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,6,8,5,4,2,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,1,2,6,8,5,4,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,7,2,6,8,5,4,3]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,7,6,8,3,2,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,8,3,1,2,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,5,8,6,3,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,2,5,8,6,3,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,6,7,1,8,5,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,6,8,5,4,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,8,2,3,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,7,6,8,3,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,7,1,6,8,5,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,3,1,8,5,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,1,8,5,4,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,2,1,6,8,5,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,8,3,2,1,5,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,7,8,5,6,1,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,5,8,7,1,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,4,8,1,2,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,1,5,6,7,2,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,5,1,8,2,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,4,6,7,1,2,8,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,6,7,2,1,5,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,6,7,1,4,2,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,1,4,6,7,3,2,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,3,6,7,4,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,1,6,8,4,5,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,6,7,1,4,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,6,7,3,1,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,4,1,5,8,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,2,1,5,4,8,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,4,5,3,7,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,1,5,4,8,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,4,1,5,8,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,4,2,1,8,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,5,2,7,1,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,3,8,1,4,2,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,1,7,2,4,5,6,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[7,6,1,2,4,5,8,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,7,8,2,3,1,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,6,2,8,1,4,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,5,2,1,3,7,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,1,3,2,6,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,6,3,2,5,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,1,3,5,2,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,2,3,1,6,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,1,4,5,6,2,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,4,3,5,6,2,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[6,2,3,1,5,7,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,8,4,2,1,6,5,3]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[7,8,4,2,1,5,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,3,4,6,2,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,3,8,7,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,3,7,8,5,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,6,3,8,1,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,4,3,8,7,5,1,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,2,4,1,7,3,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,6,8,3,2,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,1,4,2,3,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,6,8,4,3,7,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,5,8,3,2,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,2,3,4,5,8,1,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,4,3,6,2,8,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,4,3,7,2,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,4,3,8,2,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,2,4,1,7,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,7,2,4,1,8,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,1,4,2,7,8,5,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,7,4,1,6,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,6,3,4,2,7,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,8,6,5,3,2,1,7]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[4,8,5,6,3,2,1,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,4,7,8,3,2,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,8,7,3,2,1,6]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,7,6,8,3,2,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,1,8,4,2,3,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,7,4,2,3,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,8,1,3,4,2,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,8,7,6,3,2,1,5]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[4,8,2,6,3,7,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,3,8,1,6,2,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,8,7,2,5,1,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,4,3,7,1,6,2]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[6,8,1,2,4,3,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,8,7,1,3,4,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,3,8,2,7,5,6,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,4,3,8,2,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,2,8,1,6,5,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,1,3,8,2,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,7,8,1,5,4,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,8,1,5,4,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,4,8,1,6,2,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,2,1,8,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,7,8,4,1,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,7,8,5,3,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,3,1,8,2,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,6,8,4,7,3,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,2,8,3,5,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,2,4,8,1,6,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,8,3,6,1,5,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,4,1,8,5,2,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,3,2,4,8,6,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,2,4,8,6,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,4,8,2,6,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,4,8,5,1,2,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,7,2,8,3,5,4,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,3,4,8,6,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,4,8,6,5,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,8,3,6,2,1,5,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,8,2,6,1,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,5,8,2,4,1,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,8,7,2,4,6,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,4,5,7,3,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,5,7,3,8,1,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,2,4,5,8,3,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,1,2,5,6,3,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,3,5,2,6,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,1,6,3,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,5,1,8,4,3,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,6,1,5,8,4,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,4,5,8,3,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,4,8,1,3,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,5,4,3,8,2,1,7]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,4,3,7,2,8,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,4,3,7,2,6,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,6,8,3,7,2,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,4,6,3,2,8,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,4,3,6,2,7,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,5,4,3,7,2,8,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,8,5,3,1,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,3,4,1,2,8,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,5,4,7,6,2,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,5,7,4,3,6,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,3,8,1,6,7,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,8,3,6,1,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,8,6,7,4,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,3,8,6,4,7,5,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,2,7,4,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,2,1,4,3,8,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,6,1,3,4,2,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,7,3,2,6,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,7,3,2,5,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,6,8,5,7,4,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,2,3,6,7,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,5,2,3,1,6,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,4,7,2,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,7,5,2,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,7,4,1,8,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,6,1,7,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,7,6,3,8,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,8,7,2,3,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,6,8,7,4,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,2,7,4,1,6,8,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,2,1,7,8,4,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,1,8,4,2,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,1,3,7,5,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,1,3,7,4,2,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,3,7,6,2,1,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,3,5,2,7,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,6,2,8,7,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,3,2,8,1,6,5,4]=>[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[3,8,7,2,6,5,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[4,2,7,8,6,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,2,4,7,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,1,8,7,3,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,1,6,3,7,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,8,3,1,7,5,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,1,6,7,2,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,2,8,1,5,7,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,8,2,6,1,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,2,5,6,4,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,7,5,2,4,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,2,6,8,1,5,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,2,7,8,5,6,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,4,8,1,6,2,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,7,1,8,2,6,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,7,3,8,6,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,2,1,7,6,5,4,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,1,4,7,6,5,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,6,7,5,1,4,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[7,8,6,5,4,1,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,8,4,3,2,1,6,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,7,3,2,1,8,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,3,6,2,1,4,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,7,6,2,1,4,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,4,2,6,1,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,7,2,5,1,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,3,2,5,1,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,7,2,5,1,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,2,7,5,1,3,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,7,8,5,1,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,2,7,6,8,1,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,2,7,6,5,1,3,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,8,7,6,5,1,3,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,5,4,3,1,7,8,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,7,3,1,5,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,7,3,1,8,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,3,6,1,8,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,7,6,1,4,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,7,6,1,5,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,7,6,1,4,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,8,7,2,1,5,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,3,2,1,4,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,7,2,1,4,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,2,6,1,4,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,2,7,1,5,3,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,7,6,1,4,5,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,4,1,6,7,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,7,1,5,8,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,7,1,5,6,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,8,3,1,5,6,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,2,1,6,4,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,2,1,5,4,6,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,7,1,5,4,3,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,7,1,6,4,3,8]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,2,7,1,5,4,6,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,8,7,1,5,4,3,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,1,7,5,8,3,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,1,6,7,8,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,1,7,5,4,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,1,6,7,4,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,1,6,5,7,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,8,1,6,5,4,3,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,1,7,8,5,4,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,1,7,6,5,8,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,8,1,2,6,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,5,7,2,6,3,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,3,5,6,2,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,1,3,5,7,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,8,1,7,2,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,5,6,8,1,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,8,2,6,7,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,2,3,5,6,7,1,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,2,3,5,4,6,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,1,2,3,5,4,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,7,8,1,3,5,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,8,3,5,6,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,5,7,8,1,6,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,8,1,7,6,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,5,8,7,2,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,7,3,5,6,2,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,7,2,1,3,5,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,8,7,2,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,4,1,7,5,3,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,6,4,3,1,8,5,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[2,3,6,7,8,1,5,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,6,8,1,2,5,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,6,7,2,5,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,4,1,8,5,2,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,1,4,2,8,3,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,1,8,2,5,3,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,1,7,5,4,2,3,6]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,7,2,6,5,4,3,8]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,7,6,3,2,5,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,3,1,2,5,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,7,6,3,2,4,5]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,2,5,7,6,3,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,6,8,1,7,5,4,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,2,6,7,5,4,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,7,8,6,3,1,5,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,7,8,1,6,5,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,3,1,8,6,5,4,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,7,2,1,6,5,4,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,7,6,3,2,1,5,4]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[2,1,8,6,3,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,6,1,5,2,7,4,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,5,1,7,4,2,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,7,5,4,3,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,7,8,3,6,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,1,4,8,5,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,5,3,1,6,2,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,1,5,2,3,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,7,5,2,6,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,3,7,4,6,8,1,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,3,7,6,2,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[4,2,6,3,8,5,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,2,1,7,6,4,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,3,2,4,1,7,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,8,1,4,6,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,1,4,5,3,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,6,1,4,7,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,5,6,1,7,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,3,6,5,1,4,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[2,7,4,3,6,1,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,7,2,8,1,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,3,5,8,1,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,8,4,7,1,6,5,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,4,5,7,6,1,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,4,5,6,8,1,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,6,8,1,4,2,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,5,7,8,4,6,2,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,3,5,7,8,6,2,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,7,8,6,1,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,1,6,8,2,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,5,6,8,2,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,5,6,8,1,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,6,4,8,2,1,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,1,6,3,8,4,7,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,1,6,8,3,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,2,6,8,3,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,1,8,6,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,2,7,8,6,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,7,5,2,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,1,7,5,2,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,7,5,1,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,2,8,6,1,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,5,7,8,6,2,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,7,8,6,3,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,3,7,8,6,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,2,7,8,4,6,1,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,5,7,8,6,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,7,5,1,8,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,2,6,7,5,8,3,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,2,7,5,4,1,8,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,5,2,4,1,8,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,2,5,3,8,1,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,4,5,2,1,8,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,1,7,8,6,4,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,5,7,8,6,3,1,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,7,8,6,3,2,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,7,5,1,8,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,6,7,5,3,8,2,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,7,5,4,2,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,7,5,1,4,2,8,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,8,6,4,1,2,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,1,7,2,6,5,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,7,1,5,6,8,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,7,4,1,5,2,8,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,6,7,4,5,2,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,3,7,5,8,2,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,1,7,5,8,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,5,3,7,8,6,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,7,5,4,2,1,8,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,2,7,5,8,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,4,2,5,1,8,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,7,4,5,1,8,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,2,3,7,5,8,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,7,6,1,3,8,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,5,1,8,2,6,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[7,3,5,1,8,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,5,1,8,6,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,6,7,4,1,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,5,1,8,4,7,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,6,5,1,8,4,2,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,6,1,5,8,7,3,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,1,6,2,8,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,3,4,7,8,1,6,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,8,5,4,3,2,7,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,9,6,5,4,3,2,1,7]=>[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>11111010
[6,8,5,4,3,7,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[5,8,4,3,2,1,7,6]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,5,4,3,1,8,7,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[8,7,5,4,3,1,6,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,3,4,6,2,1,5,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,6,2,1,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,2,6,8,4,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,5,3,2,8,4,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,3,2,8,4,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,4,5,7,3,8,6,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,5,6,8,3,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,8,1,5,6,3,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,5,6,1,8,4,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,6,8,1,4,2,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,5,6,8,1,3,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,5,6,8,3,2,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,6,3,8,2,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,3,7,2,8,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,4,7,3,2,8,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,1,4,7,3,2,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,8,4,5,3,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,7,3,8,4,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,1,7,4,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,7,4,1,8,6,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,7,1,4,8,6,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,4,3,1,7,8,5,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,1,7,3,8,5,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,3,7,8,4,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,6,3,7,8,4,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,1,3,7,8,4,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,1,7,8,3,4,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,3,7,4,8,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,2,4,1,8,5,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,7,2,1,4,3,8,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,4,7,3,1,2,8,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,6,3,1,2,7,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,1,3,2,7,8,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,3,2,1,7,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,5,6,3,7,8,4,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,5,6,3,1,7,8,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,6,4,7,3,1,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,7,2,8,4,5,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,7,2,8,4,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,2,7,1,8,4,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,5,3,2,1,8,4,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,3,8,4,2,1,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,2,1,3,8,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,3,7,8,6,4,2,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,8,4,6,2,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,3,8,2,1,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,7,8,5,2,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,2,7,8,5,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,2,1,7,8,5,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,4,5,8,1,2,6,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,5,1,7,3,8,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,2,1,3,8,5,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,1,6,7,8,2,4,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,3,7,1,8,5,2,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,1,7,3,8,5,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,7,1,8,5,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,1,7,8,5,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,1,3,6,8,2,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,2,3,6,8,1,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,3,2,1,8,4,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,6,5,8,2,1,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,5,2,1,3,8,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,6,4,5,8,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,4,6,5,8,1,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,2,4,5,8,3,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,3,2,1,6,8,4,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,2,4,5,8,1,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,4,6,5,8,2,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,3,4,5,8,2,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,4,1,8,5,2,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,4,1,7,6,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,1,4,2,7,3,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,5,3,2,8,7,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,2,1,7,5,3,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,6,4,5,8,3,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,8,7,4,1,2,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,7,4,6,2,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[3,4,2,5,8,6,7,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,3,5,6,8,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,4,8,6,7,1,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,6,2,8,1,7,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,7,4,8,2,1,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,3,5,8,6,7,1,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,5,6,8,7,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,8,5,6,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,8,3,5,6,7,4]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[4,2,3,7,1,8,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,6,4,8,1,7,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[8,2,1,6,7,3,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,8,5,4,1,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,7,5,3,8,4,2,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,5,3,1,2,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,2,4,8,5,3,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,3,1,2,7,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,2,7,4,1,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,2,3,7,1,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,4,7,1,3,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,2,4,6,7,1,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,8,2,3,6,7,1,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,5,2,7,6,1,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,3,2,5,8,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,3,2,1,6,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,7,3,4,6,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,2,7,4,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,1,4,2,8,7,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,6,5,8,2,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,3,7,1,6,2,8,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,2,6,8,7,1,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,3,2,1,8,5,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,7,5,4,1,8,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,2,5,6,8,7,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,8,4,2,5,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,8,4,1,5,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,8,5,6,7,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,4,7,1,8,6,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,4,7,1,8,6,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,6,4,1,3,2,5,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,1,3,6,5,2,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,4,3,6,5,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,5,2,1,8,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,3,2,4,6,5,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,2,1,6,5,3,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,1,2,6,5,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,4,2,1,5,3,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,6,4,1,5,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,6,3,4,5,1,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,3,4,8,5,7,2,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,8,4,7,6,2,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[1,3,4,7,5,8,2,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,5,2,4,8,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,5,1,3,8,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,1,6,5,8,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,4,8,7,6,3,1,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[2,8,5,1,4,7,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,3,1,5,8,6,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,3,5,8,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,5,3,8,4,7,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,2,1,6,8,7,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,4,3,2,7,1,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[3,4,7,8,2,1,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,3,2,8,6,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,1,2,8,6,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,2,3,1,6,8,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,2,1,8,6,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,1,3,6,8,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,4,7,3,8,1,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,8,2,7,4,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,1,3,6,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,1,7,8,4,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,4,5,8,3,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,4,3,7,2,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,4,8,7,2,1,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,4,7,8,3,6,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,3,8,7,2,1,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,3,8,7,4,1,2,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,5,7,2,4,8,1,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,7,2,3,1,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,7,1,3,2,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,7,2,1,3,5,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,4,2,1,3,7,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,4,1,3,2,7,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,6,4,2,3,1,7,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,7,2,6,1,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,1,3,8,5,7,2,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,3,2,6,7,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,8,5,3,6,2,7,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,8,1,5,4,7,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,5,8,7,4,6,2,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,1,7,6,4,5,8,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,2,4,6,5,8,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,5,1,7,6,8,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,2,6,1,3,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,3,5,8,7,2,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,7,8,4,1,6,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,8,1,5,6,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,5,2,6,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,5,1,6,8,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,2,8,5,1,6,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,8,5,2,6,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,1,8,5,4,6,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,6,2,1,3,7,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,2,4,1,5,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,6,3,5,8,1,7,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,7,8,3,5,4,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,5,1,8,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,8,1,4,5,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,4,5,7,8,2,6,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,4,6,2,8,5,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,6,8,1,5,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,7,2,1,8,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,4,8,2,1,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,2,7,8,4,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,6,2,8,4,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,6,8,4,1,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,7,2,4,8,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,7,2,8,4,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,7,8,4,1,6,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,2,1,8,5,4,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,6,7,2,8,5,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,8,2,4,5,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,7,2,1,4,8,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,7,2,8,4,5,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,8,2,1,4,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,5,6,7,8,3,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,6,3,7,8,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,6,3,8,5,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,6,7,3,8,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,1,7,3,2,8,6,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,1,8,3,2,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,5,2,6,8,1,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,5,7,3,8,1,6,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,5,8,3,2,1,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,2,7,8,5,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,6,7,3,2,8,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,7,2,8,3,5,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,8,3,2,5,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,2,3,1,5,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,2,6,8,4,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,2,3,8,4,1,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,2,7,8,4,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,6,8,3,4,2,1,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,7,2,3,4,8,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,8,3,4,2,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,8,2,3,4,1,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,2,3,7,8,5,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,2,3,8,5,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,2,7,8,5,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,7,3,8,5,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,7,8,4,5,3,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,1,8,3,4,5,2,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,7,2,3,8,5,4,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,2,8,4,5,3,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,1,2,3,4,8,6,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,2,8,4,5,6,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,1,8,3,4,5,6,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,4,1,8,2,3,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,8,1,2,4,3,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,3,5,7,2,6,4,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,5,8,6,1,2,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,1,6,8,2,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,2,8,1,5,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,6,1,3,8,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,7,5,2,3,4,6,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,7,5,1,3,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,2,5,7,4,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,1,3,7,6,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,5,1,3,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,2,7,5,3,1,6,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,2,6,5,4,7,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,5,2,4,8,1,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,8,2,5,3,1,6,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,1,8,6,3,2,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,1,5,3,2,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,7,5,3,2,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,1,2,4,8,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,1,6,4,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,4,1,2,5,6,3,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,3,6,5,2,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,3,7,2,6,4,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,2,6,5,1,8,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,8,4,2,5,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,7,4,5,6,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,3,6,5,1,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110
[1,8,7,6,5,3,2,4]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[2,8,7,6,3,4,5,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[1,8,7,6,5,2,3,4]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[2,10,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110
[7,2,8,6,5,4,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,2,8,5,4,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,2,8,5,1,7,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,7,2,5,6,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,8,5,4,3,1,7,2]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,6,4,1,3,7,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,8,6,1,5,3,7,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,6,1,8,5,2,7,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,4,1,2,8,6,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,8,3,5,4,1,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,2,5,8,3,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,7,5,6,3,4,2,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,6,8,5,3,1,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,3,8,5,2,1,4]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[7,2,6,4,8,3,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,5,7,4,2,6,3,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,2,3,1,7,8,5,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,8,4,1,7,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,6,3,4,7,2,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,8,3,4,5,1,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,3,2,5,8,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,2,1,5,4,7,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,3,7,1,5,8,4,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,1,8,4,3,7,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,5,4,8,1,3,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,3,1,6,5,8,2,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,3,5,4,6,8,2,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,1,3,4,5,8,2,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,3,4,1,5,2,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,5,4,2,6,8,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,2,6,4,1,7,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,8,4,5,2,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,5,1,8,4,3,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,7,3,2,5,4,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,2,1,5,3,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,1,5,8,7,4,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,3,6,4,5,1,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,6,8,1,2,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,4,7,2,3,5,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,4,1,3,5,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,4,7,8,6,2,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,1,3,5,7,8,6,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,5,1,8,4,7,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,3,1,8,4,7,6,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,7,4,6,1,3,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,7,3,2,8,1,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,3,1,4,7,2,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,7,3,6,1,5,2,4]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,4,3,6,8,2,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,4,7,3,8,5,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,6,1,5,7,3,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,8,2,5,4,3,1,6]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,8,3,4,2,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,5,3,7,4,2,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,7,3,2,4,1,8,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,8,3,4,7,1,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,3,6,7,8,2,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,6,3,2,5,8,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,8,1,5,6,2,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,2,5,6,1,7,4,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,5,2,8,6,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,5,4,8,7,2,1,3]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[1,8,6,4,5,2,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,8,5,3,6,2,7,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,6,2,1,7,5,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,5,4,1,8,7,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,2,6,5,8,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,1,4,2,7,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,4,7,1,8,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,4,7,8,2,5,6,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,8,2,4,5,6,7,3]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[5,2,4,1,6,8,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,2,5,7,6,1,8,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,5,6,1,8,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,4,1,7,6,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,1,4,6,5,7,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,7,3,5,6,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,2,7,5,8,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,2,7,5,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,2,8,5,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,2,4,8,7,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,2,6,4,8,7,3,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,2,7,8,5,6,3,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,3,8,2,6,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,7,8,2,5,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,7,8,2,3,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,2,7,8,4,6,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,6,2,4,8,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,7,3,4,8,5,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,3,7,4,8,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,8,4,1,5,3,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,8,4,2,7,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,7,4,8,3,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,2,6,4,8,3,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,5,2,4,8,3,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,8,3,5,2,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,8,6,2,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,6,8,5,3,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,6,7,8,5,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,7,8,6,2,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,7,6,8,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,7,8,6,5,3,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,2,6,7,3,4,8,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,4,7,6,3,8,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,6,2,1,7,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,2,1,4,8,7,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,6,1,4,5,8,7,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,2,7,6,3,8,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,3,7,6,4,5,8,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,6,1,7,5,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,1,7,4,8,5,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,2,7,8,4,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,1,7,4,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,4,1,7,8,2,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,6,1,3,8,7,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,6,4,1,5,8,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,6,1,5,4,8,7,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,6,1,4,7,8,5,3]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,1,2,4,8,6,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,2,4,8,7,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,2,4,8,7,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,3,8,5,4,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,3,1,2,8,5,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,5,3,8,6,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,3,8,5,6,4,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,8,6,4,5,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,8,6,5,4,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,3,8,5,4,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,6,1,5,4,8,3,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,1,2,4,8,6,3,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,1,2,4,8,3,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,6,3,1,4,8,2,7]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,5,4,3,1,8,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,6,3,1,8,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,6,4,5,1,8,7,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,6,5,4,1,8,7,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,6,1,7,8,4,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,6,2,8,7,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,3,7,8,6,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,1,3,7,8,5,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,4,1,7,8,6,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,3,1,2,8,6,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,1,4,2,8,6,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,3,6,8,5,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,3,8,6,7,4,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,3,8,7,5,4,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,2,3,8,7,4,5,6]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,3,8,5,7,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,1,3,6,8,7,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,4,1,2,8,7,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,1,6,2,8,7,5,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[1,2,3,4,5,9,6,7,8]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,2,3,4,9,5,6,7,8]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,2,3,9,4,5,6,7,8]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,2,9,3,4,5,6,7,8]=>[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[1,2,3,4,5,6,7,10,8,9]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[1,2,3,4,5,9,7,6,8]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[1,2,3,4,5,6,10,7,8,9]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[1,2,3,4,9,6,5,7,8]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[1,2,3,4,5,10,6,7,8,9]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[1,2,3,9,5,4,6,7,8]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[1,2,3,4,10,5,6,7,8,9]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[1,8,3,4,2,5,6,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,2,9,4,3,5,6,7,8]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[1,2,3,10,4,5,6,7,8,9]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[1,8,4,3,2,5,6,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,9,3,2,4,5,6,7,8]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[1,2,10,3,4,5,6,7,8,9]=>[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[8,4,7,6,5,3,2,1]=>[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[8,5,7,4,6,3,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,5,7,3,6,4,2,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,1,7,4,6,5,3,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,2,7,3,6,5,4,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,5,7,2,6,4,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,4,7,1,6,5,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,3,7,1,6,5,4,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,2,7,1,6,5,4,3]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,1,7,6,5,3,4,2]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[8,3,7,6,5,2,4,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,4,7,6,5,2,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,5,7,6,4,2,3,1]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,6,7,5,4,1,3,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[8,3,7,6,5,1,4,2]=>[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[6,8,1,4,2,5,3,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,8,2,5,3,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,2,5,4,7,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,5,3,7,6,8,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,6,1,4,3,7,5,8]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,6,3,7,4,8,1,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,8,2,6,3,7,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[4,8,1,5,2,6,3,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,8,3,7,1,5,2,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,5,7,1,3,2,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,1,3,2,6,5,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,7,5,8,1,4,2,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[3,7,6,8,2,5,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,5,8,2,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,7,5,8,2,6,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,6,5,8,4,7,1,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,6,5,8,3,7,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,6,3,7,1,5,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,6,4,2,8,5,3,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,8,4,3,7,2,1,5]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[6,7,4,3,5,1,8,2]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,7,3,5,4,8,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,3,5,8,2,4,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,4,2,5,1,8,3]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,6,3,8,2,4,1,5]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,8,4,7,2,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,8,4,1,7,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,2,7,4,1,5,3,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,3,4,7,5,8,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,3,5,7,8,4,2,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,6,8,3,7,2,1,4]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,6,8,3,5,7,2,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,8,2,4,1,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,3,6,2,5,7,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,8,3,5,6,2,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,3,5,8,2,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,5,8,7,2,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,8,3,7,2,6,4,1]=>[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[5,8,4,2,3,1,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,8,4,2,3,1,7,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,4,5,3,8,2,1,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,8,5,3,7,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,3,8,5,7,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,2,8,5,3,1,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,6,3,4,8,2,1,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,2,5,1,7,3,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,7,2,4,1,6,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,8,3,6,7,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,8,3,7,2,6,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,3,6,8,2,1,4,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,3,6,7,1,8,2,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,6,3,5,7,8,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,7,3,6,8,2,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,7,4,8,6,3,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,5,6,7,2,8,4,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,2,5,4,7,6,9,8,1]=>[4,4,1]=>[[1,3,4,5],[2,7,8,9],[6]]=>10001000
[3,4,5,6,7,8,9,2,1]=>[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000
[5,4,3,2,1,10,9,8,7,6]=>[2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>010101010
[3,4,5,6,7,8,9,10,2,1]=>[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000
[1,6,2,5,3,4,8,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,8,2,4,6,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,2,3,6,4,8,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,8,2,5,3,7,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,8,2,5,3,4,7,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,8,2,3,6,4,7,5]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,3,5,2,8,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,7,3,5,4,6,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,8,2,7,3,4,6,5]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,5,8,2,3,7,4,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,6,8,2,3,5,4,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,3,6,1,2,4,8,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,5,8,4,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,5,7,4,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,4,5,8,2,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,1,6,2,8,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,4,1,7,2,6,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,4,7,5,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,5,4,7,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,7,5,8,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,5,4,8,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,4,8,5,2,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,4,1,7,2,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,8,3,1,2,4,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,7,1,6,4,2,3,5]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[8,6,1,7,4,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,6,1,8,4,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,8,1,2,4,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,3,7,1,2,4,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,3,6,1,2,4,7,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[8,3,7,5,1,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,6,1,2,4,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,1,8,4,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,8,1,7,4,2,3,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,8,5,4,2,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,8,4,5,2,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,7,8,5,3,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,6,3,1,2,4,8,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,2,3,8,7,5,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,1,4,2,3,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,8,3,1,2,7,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,7,3,1,2,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,7,1,4,2,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,3,6,8,5,7,1,2]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[1,3,6,8,7,4,2,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,1,5,8,3,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,1,6,8,4,3,2]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[8,3,6,4,7,2,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,7,8,4,6,2,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,7,3,1,5,8,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,4,6,8,1,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,7,5,8,6,4,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,6,7,5,4,3,1]=>[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[3,4,2,7,8,1,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,7,3,8,5,2,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,1,4,5,8,2,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,7,4,5,3,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,1,7,3,5,4,8,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,7,2,8,5,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,6,8,7,2,4,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[6,8,5,7,1,2,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,2,4,3,7,5,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,8,2,1,5,7,3,4]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[2,7,8,1,4,6,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,8,2,5,7,1,6,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,1,6,8,5,3,7,2]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[5,2,6,4,8,3,1,7]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,7,1,3,4,5,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,3,2,4,8,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,3,4,2,8,7,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,3,8,7,5,2,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,8,7,4,2,3,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,6,4,5,2,8,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,6,1,3,5,4,2,7]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,3,8,6,1,2,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,5,6,3,4,8,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,5,3,6,8,7,4,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,8,7,3,5,2,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[3,8,7,2,6,4,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,3,5,4,8,7,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,3,8,6,1,5,2,7]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[4,7,6,2,5,3,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,2,6,8,1,4,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,2,7,1,4,3,6]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,8,5,3,6,2,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,7,2,4,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,3,4,8,6,2,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,4,1,3,8,6,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,8,6,3,4,2,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,5,2,8,3,7,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,2,3,7,6,4,5,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[5,8,2,4,7,6,3,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,8,2,5,3,4,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,5,6,4,8,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,7,4,8,2,3,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,1,3,5,8,2,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,2,1,3,5,6,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,3,1,4,7,5,8,2]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,1,3,8,2,6,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,8,3,6,7,5,4,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,1,7,2,8,5,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,6,1,4,7,2,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,5,8,4,7,2,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,1,3,6,2,8,4,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,7,4,5,8,1,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,1,8,4,5,7,3,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,8,5,7,3,2,4,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,1,8,5,4,3,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,7,4,1,5,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,4,8,6,2,3,1,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[2,7,1,4,6,3,8,5]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[4,7,5,6,8,1,3,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,1,3,2,8,5,4,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[2,8,5,4,1,3,6,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,1,7,4,2,3,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,8,6,5,1,4,2,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,3,4,8,6,5,2,7]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[4,1,8,6,5,3,2,7]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[4,8,5,2,7,3,6,1]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,2,8,5,3,6,4,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,2,8,4,3,7,6,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,4,7,5,2,3,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,5,2,8,4,6,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,4,3,6,2,8,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,7,5,1,2,8,3,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,2,6,8,3,4,7,1]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[7,6,2,4,5,8,3,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,6,8,4,7,2,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,6,3,8,4,2,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[2,6,3,8,4,7,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,3,6,5,8,4,1]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[6,2,7,5,8,3,1,4]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[2,8,3,6,4,5,7,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,1,5,6,8,3,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,8,1,2,6,4,7,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,6,8,3,2,7,4,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,5,7,2,8,4,1,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[7,5,1,2,8,4,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,4,8,3,6,2,7,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[5,8,2,7,4,3,6,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[6,4,5,8,2,7,3,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[5,7,3,6,4,8,2,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[1,5,6,4,8,2,7,3]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[3,1,5,6,4,8,7,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[3,5,1,6,4,7,8,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,6,4,3,8,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,6,3,5,8,7,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,3,5,1,8,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[2,3,6,1,8,5,4,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,7,3,6,8,5,4]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[2,3,6,1,8,5,7,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,5,8,4,7,3,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,2,6,8,5,4,3,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,5,8,2,4,7,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,4,6,8,3,2,5,7]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,7,5,6,8,2,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,2,6,7,3,8,5,4]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,1,5,7,6,8,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,4,6,8,2,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,3,6,5,8,7,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,2,7,5,6,8,4,3]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,1,6,7,5,8,4,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,2,7,5,8,3,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,5,7,4,8,2,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,4,7,6,8,3,5,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,4,6,8,3,5,7,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,3,5,8,2,7,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,5,8,4,7,6,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,2,5,8,7,4,3,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,3,5,8,7,2,4,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[5,7,1,2,8,6,4,3]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[6,4,5,7,2,8,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,4,7,2,8,1,6]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[3,2,7,4,6,8,1,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,6,2,7,1,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,6,3,4,7,1,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,3,4,5,8,1,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,7,4,5,6,8,1,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,5,7,3,6,8,1,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,7,6,2,3,8,1,5]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,3,5,2,4,8,1,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[7,6,2,4,5,8,1,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,5,2,3,4,8,1,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,1,2,8,4,7,6]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,5,2,3,7,1,4,8]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,2,1,7,3,4,6,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[5,2,1,8,3,4,6,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,3,2,8,4,5,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,3,1,2,8,4,6,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[6,4,1,3,8,5,7,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[6,2,3,1,8,4,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[8,3,5,2,7,1,4,6]=>[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[8,6,2,4,7,1,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[8,5,2,3,6,1,4,7]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,2,1,7,3,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[8,6,3,7,2,4,5,1]=>[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[7,1,6,2,3,4,5,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,2,7,3,4,5,6,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,1,6,2,3,4,5,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[8,1,7,3,4,5,6,2]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[8,6,1,7,2,4,5,3]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,1,5,7,2,3,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[1,7,5,8,2,3,6,4]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[7,2,1,8,3,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[7,3,8,2,4,5,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,2,8,3,4,5,6,1]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,8,3,4,5,6,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,4,5,8,3,6,7,2]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,5,7,1,8,3,6,4]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[6,2,7,1,8,4,5,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[4,7,1,3,8,5,6,2]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,6,2,8,4,5,7,3]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[4,1,3,6,8,2,7,5]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[5,3,4,6,8,2,7,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[4,6,3,8,7,1,2,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,4,5,8,7,1,2,3]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[5,3,4,8,7,1,2,6]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[3,2,8,7,1,4,6,5]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,1,8,7,2,4,6,5]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[5,3,7,6,1,2,4,8]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[1,8,3,7,2,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[3,8,1,7,2,4,5,6]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[6,8,2,3,5,1,4,7]=>[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[4,7,8,2,6,1,3,5]=>[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[6,2,8,7,1,4,5,3]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[3,8,7,1,4,5,6,2]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[2,8,6,1,3,4,5,7]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[2,7,6,1,3,4,5,8]=>[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[1,7,6,2,3,4,5,8]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[1,8,6,2,3,4,5,7]=>[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[2,8,7,3,4,5,6,1]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[3,8,7,2,4,5,6,1]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[7,8,3,6,2,4,5,1]=>[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[1,5,8,7,2,3,6,4]=>[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[8,7,6,1,3,4,5,2]=>[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[3,4,7,2,5,1,8,6]=>[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[1,2,8,3,7,5,4,6]=>[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[1,6,3,8,7,4,2,5]=