Identifier
Mp00151:
Permutations
—to cycle type⟶
Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
=>
Cc0009;cc-rep-1
[1]=>{{1}}=>[1]=>
[1,2]=>{{1},{2}}=>[1,2]=>1
[2,1]=>{{1,2}}=>[2,1]=>0
[1,2,3]=>{{1},{2},{3}}=>[1,2,3]=>11
[1,3,2]=>{{1},{2,3}}=>[1,3,2]=>10
[2,1,3]=>{{1,2},{3}}=>[2,1,3]=>01
[2,3,1]=>{{1,2,3}}=>[2,3,1]=>00
[3,1,2]=>{{1,2,3}}=>[2,3,1]=>00
[3,2,1]=>{{1,3},{2}}=>[3,2,1]=>00
[1,2,3,4]=>{{1},{2},{3},{4}}=>[1,2,3,4]=>111
[1,2,4,3]=>{{1},{2},{3,4}}=>[1,2,4,3]=>110
[1,3,2,4]=>{{1},{2,3},{4}}=>[1,3,2,4]=>101
[1,3,4,2]=>{{1},{2,3,4}}=>[1,3,4,2]=>100
[1,4,2,3]=>{{1},{2,3,4}}=>[1,3,4,2]=>100
[1,4,3,2]=>{{1},{2,4},{3}}=>[1,4,3,2]=>100
[2,1,3,4]=>{{1,2},{3},{4}}=>[2,1,3,4]=>011
[2,1,4,3]=>{{1,2},{3,4}}=>[2,1,4,3]=>010
[2,3,1,4]=>{{1,2,3},{4}}=>[2,3,1,4]=>001
[2,3,4,1]=>{{1,2,3,4}}=>[2,3,4,1]=>000
[2,4,1,3]=>{{1,2,3,4}}=>[2,3,4,1]=>000
[2,4,3,1]=>{{1,2,4},{3}}=>[2,4,3,1]=>000
[3,1,2,4]=>{{1,2,3},{4}}=>[2,3,1,4]=>001
[3,1,4,2]=>{{1,2,3,4}}=>[2,3,4,1]=>000
[3,2,1,4]=>{{1,3},{2},{4}}=>[3,2,1,4]=>001
[3,2,4,1]=>{{1,3,4},{2}}=>[3,2,4,1]=>000
[3,4,1,2]=>{{1,3},{2,4}}=>[3,4,1,2]=>000
[3,4,2,1]=>{{1,2,3,4}}=>[2,3,4,1]=>000
[4,1,2,3]=>{{1,2,3,4}}=>[2,3,4,1]=>000
[4,1,3,2]=>{{1,2,4},{3}}=>[2,4,3,1]=>000
[4,2,1,3]=>{{1,3,4},{2}}=>[3,2,4,1]=>000
[4,2,3,1]=>{{1,4},{2},{3}}=>[4,2,3,1]=>000
[4,3,1,2]=>{{1,2,3,4}}=>[2,3,4,1]=>000
[4,3,2,1]=>{{1,4},{2,3}}=>[4,3,2,1]=>000
[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}=>[1,2,3,4,5]=>1111
[1,2,3,5,4]=>{{1},{2},{3},{4,5}}=>[1,2,3,5,4]=>1110
[1,2,4,3,5]=>{{1},{2},{3,4},{5}}=>[1,2,4,3,5]=>1101
[1,2,4,5,3]=>{{1},{2},{3,4,5}}=>[1,2,4,5,3]=>1100
[1,2,5,3,4]=>{{1},{2},{3,4,5}}=>[1,2,4,5,3]=>1100
[1,2,5,4,3]=>{{1},{2},{3,5},{4}}=>[1,2,5,4,3]=>1100
[1,3,2,4,5]=>{{1},{2,3},{4},{5}}=>[1,3,2,4,5]=>1011
[1,3,2,5,4]=>{{1},{2,3},{4,5}}=>[1,3,2,5,4]=>1010
[1,3,4,2,5]=>{{1},{2,3,4},{5}}=>[1,3,4,2,5]=>1001
[1,3,4,5,2]=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>1000
[1,3,5,2,4]=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>1000
[1,3,5,4,2]=>{{1},{2,3,5},{4}}=>[1,3,5,4,2]=>1000
[1,4,2,3,5]=>{{1},{2,3,4},{5}}=>[1,3,4,2,5]=>1001
[1,4,2,5,3]=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>1000
[1,4,3,2,5]=>{{1},{2,4},{3},{5}}=>[1,4,3,2,5]=>1001
[1,4,3,5,2]=>{{1},{2,4,5},{3}}=>[1,4,3,5,2]=>1000
[1,4,5,2,3]=>{{1},{2,4},{3,5}}=>[1,4,5,2,3]=>1000
[1,4,5,3,2]=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>1000
[1,5,2,3,4]=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>1000
[1,5,2,4,3]=>{{1},{2,3,5},{4}}=>[1,3,5,4,2]=>1000
[1,5,3,2,4]=>{{1},{2,4,5},{3}}=>[1,4,3,5,2]=>1000
[1,5,3,4,2]=>{{1},{2,5},{3},{4}}=>[1,5,3,4,2]=>1000
[1,5,4,2,3]=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>1000
[1,5,4,3,2]=>{{1},{2,5},{3,4}}=>[1,5,4,3,2]=>1000
[2,1,3,4,5]=>{{1,2},{3},{4},{5}}=>[2,1,3,4,5]=>0111
[2,1,3,5,4]=>{{1,2},{3},{4,5}}=>[2,1,3,5,4]=>0110
[2,1,4,3,5]=>{{1,2},{3,4},{5}}=>[2,1,4,3,5]=>0101
[2,1,4,5,3]=>{{1,2},{3,4,5}}=>[2,1,4,5,3]=>0100
[2,1,5,3,4]=>{{1,2},{3,4,5}}=>[2,1,4,5,3]=>0100
[2,1,5,4,3]=>{{1,2},{3,5},{4}}=>[2,1,5,4,3]=>0100
[2,3,1,4,5]=>{{1,2,3},{4},{5}}=>[2,3,1,4,5]=>0011
[2,3,1,5,4]=>{{1,2,3},{4,5}}=>[2,3,1,5,4]=>0010
[2,3,4,1,5]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>0001
[2,3,4,5,1]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[2,3,5,1,4]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[2,3,5,4,1]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>0000
[2,4,1,3,5]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>0001
[2,4,1,5,3]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[2,4,3,1,5]=>{{1,2,4},{3},{5}}=>[2,4,3,1,5]=>0001
[2,4,3,5,1]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>0000
[2,4,5,1,3]=>{{1,2,4},{3,5}}=>[2,4,5,1,3]=>0000
[2,4,5,3,1]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[2,5,1,3,4]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[2,5,1,4,3]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>0000
[2,5,3,1,4]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>0000
[2,5,3,4,1]=>{{1,2,5},{3},{4}}=>[2,5,3,4,1]=>0000
[2,5,4,1,3]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[2,5,4,3,1]=>{{1,2,5},{3,4}}=>[2,5,4,3,1]=>0000
[3,1,2,4,5]=>{{1,2,3},{4},{5}}=>[2,3,1,4,5]=>0011
[3,1,2,5,4]=>{{1,2,3},{4,5}}=>[2,3,1,5,4]=>0010
[3,1,4,2,5]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>0001
[3,1,4,5,2]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[3,1,5,2,4]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[3,1,5,4,2]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>0000
[3,2,1,4,5]=>{{1,3},{2},{4},{5}}=>[3,2,1,4,5]=>0011
[3,2,1,5,4]=>{{1,3},{2},{4,5}}=>[3,2,1,5,4]=>0010
[3,2,4,1,5]=>{{1,3,4},{2},{5}}=>[3,2,4,1,5]=>0001
[3,2,4,5,1]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>0000
[3,2,5,1,4]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>0000
[3,2,5,4,1]=>{{1,3,5},{2},{4}}=>[3,2,5,4,1]=>0000
[3,4,1,2,5]=>{{1,3},{2,4},{5}}=>[3,4,1,2,5]=>0001
[3,4,1,5,2]=>{{1,3},{2,4,5}}=>[3,4,1,5,2]=>0000
[3,4,2,1,5]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>0001
[3,4,2,5,1]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[3,4,5,1,2]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[3,4,5,2,1]=>{{1,3,5},{2,4}}=>[3,4,5,2,1]=>0000
[3,5,1,2,4]=>{{1,3},{2,4,5}}=>[3,4,1,5,2]=>0000
[3,5,1,4,2]=>{{1,3},{2,5},{4}}=>[3,5,1,4,2]=>0000
[3,5,2,1,4]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[3,5,2,4,1]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>0000
[3,5,4,1,2]=>{{1,3,4},{2,5}}=>[3,5,4,1,2]=>0000
[3,5,4,2,1]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[4,1,2,3,5]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>0001
[4,1,2,5,3]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[4,1,3,2,5]=>{{1,2,4},{3},{5}}=>[2,4,3,1,5]=>0001
[4,1,3,5,2]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>0000
[4,1,5,2,3]=>{{1,2,4},{3,5}}=>[2,4,5,1,3]=>0000
[4,1,5,3,2]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[4,2,1,3,5]=>{{1,3,4},{2},{5}}=>[3,2,4,1,5]=>0001
[4,2,1,5,3]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>0000
[4,2,3,1,5]=>{{1,4},{2},{3},{5}}=>[4,2,3,1,5]=>0001
[4,2,3,5,1]=>{{1,4,5},{2},{3}}=>[4,2,3,5,1]=>0000
[4,2,5,1,3]=>{{1,4},{2},{3,5}}=>[4,2,5,1,3]=>0000
[4,2,5,3,1]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>0000
[4,3,1,2,5]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>0001
[4,3,1,5,2]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[4,3,2,1,5]=>{{1,4},{2,3},{5}}=>[4,3,2,1,5]=>0001
[4,3,2,5,1]=>{{1,4,5},{2,3}}=>[4,3,2,5,1]=>0000
[4,3,5,1,2]=>{{1,4},{2,3,5}}=>[4,3,5,1,2]=>0000
[4,3,5,2,1]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[4,5,1,2,3]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[4,5,1,3,2]=>{{1,3,4},{2,5}}=>[3,5,4,1,2]=>0000
[4,5,2,1,3]=>{{1,4},{2,3,5}}=>[4,3,5,1,2]=>0000
[4,5,2,3,1]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[4,5,3,1,2]=>{{1,4},{2,5},{3}}=>[4,5,3,1,2]=>0000
[4,5,3,2,1]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>0000
[5,1,2,3,4]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[5,1,2,4,3]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>0000
[5,1,3,2,4]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>0000
[5,1,3,4,2]=>{{1,2,5},{3},{4}}=>[2,5,3,4,1]=>0000
[5,1,4,2,3]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[5,1,4,3,2]=>{{1,2,5},{3,4}}=>[2,5,4,3,1]=>0000
[5,2,1,3,4]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>0000
[5,2,1,4,3]=>{{1,3,5},{2},{4}}=>[3,2,5,4,1]=>0000
[5,2,3,1,4]=>{{1,4,5},{2},{3}}=>[4,2,3,5,1]=>0000
[5,2,3,4,1]=>{{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>0000
[5,2,4,1,3]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>0000
[5,2,4,3,1]=>{{1,5},{2},{3,4}}=>[5,2,4,3,1]=>0000
[5,3,1,2,4]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[5,3,1,4,2]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>0000
[5,3,2,1,4]=>{{1,4,5},{2,3}}=>[4,3,2,5,1]=>0000
[5,3,2,4,1]=>{{1,5},{2,3},{4}}=>[5,3,2,4,1]=>0000
[5,3,4,1,2]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[5,3,4,2,1]=>{{1,5},{2,3,4}}=>[5,3,4,2,1]=>0000
[5,4,1,2,3]=>{{1,3,5},{2,4}}=>[3,4,5,2,1]=>0000
[5,4,1,3,2]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[5,4,2,1,3]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
[5,4,2,3,1]=>{{1,5},{2,3,4}}=>[5,3,4,2,1]=>0000
[5,4,3,1,2]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>0000
[5,4,3,2,1]=>{{1,5},{2,4},{3}}=>[5,4,3,2,1]=>0000
[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}=>[1,2,3,4,5,6]=>11111
[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}=>[1,2,3,4,6,5]=>11110
[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}=>[1,2,3,5,4,6]=>11101
[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}=>[1,2,3,5,6,4]=>11100
[1,2,3,6,4,5]=>{{1},{2},{3},{4,5,6}}=>[1,2,3,5,6,4]=>11100
[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}=>[1,2,3,6,5,4]=>11100
[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}=>[1,2,4,3,5,6]=>11011
[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}=>[1,2,4,3,6,5]=>11010
[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}=>[1,2,4,5,3,6]=>11001
[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>11000
[1,2,4,6,3,5]=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>11000
[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}=>[1,2,4,6,5,3]=>11000
[1,2,5,3,4,6]=>{{1},{2},{3,4,5},{6}}=>[1,2,4,5,3,6]=>11001
[1,2,5,3,6,4]=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>11000
[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}=>[1,2,5,4,3,6]=>11001
[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}=>[1,2,5,4,6,3]=>11000
[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}=>[1,2,5,6,3,4]=>11000
[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>11000
[1,2,6,3,4,5]=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>11000
[1,2,6,3,5,4]=>{{1},{2},{3,4,6},{5}}=>[1,2,4,6,5,3]=>11000
[1,2,6,4,3,5]=>{{1},{2},{3,5,6},{4}}=>[1,2,5,4,6,3]=>11000
[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}}=>[1,2,6,4,5,3]=>11000
[1,2,6,5,3,4]=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>11000
[1,2,6,5,4,3]=>{{1},{2},{3,6},{4,5}}=>[1,2,6,5,4,3]=>11000
[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}=>[1,3,2,4,5,6]=>10111
[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}=>[1,3,2,4,6,5]=>10110
[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}=>[1,3,2,5,4,6]=>10101
[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}=>[1,3,2,5,6,4]=>10100
[1,3,2,6,4,5]=>{{1},{2,3},{4,5,6}}=>[1,3,2,5,6,4]=>10100
[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}}=>[1,3,2,6,5,4]=>10100
[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}=>[1,3,4,2,5,6]=>10011
[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}=>[1,3,4,2,6,5]=>10010
[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>10001
[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,3,4,6,2,5]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>10000
[1,3,5,2,4,6]=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>10001
[1,3,5,2,6,4]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}=>[1,3,5,4,2,6]=>10001
[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>10000
[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}=>[1,3,5,6,2,4]=>10000
[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,3,6,2,4,5]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,3,6,2,5,4]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>10000
[1,3,6,4,2,5]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>10000
[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}=>[1,3,6,4,5,2]=>10000
[1,3,6,5,2,4]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,3,6,5,4,2]=>{{1},{2,3,6},{4,5}}=>[1,3,6,5,4,2]=>10000
[1,4,2,3,5,6]=>{{1},{2,3,4},{5},{6}}=>[1,3,4,2,5,6]=>10011
[1,4,2,3,6,5]=>{{1},{2,3,4},{5,6}}=>[1,3,4,2,6,5]=>10010
[1,4,2,5,3,6]=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>10001
[1,4,2,5,6,3]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,4,2,6,3,5]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,4,2,6,5,3]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>10000
[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}=>[1,4,3,2,5,6]=>10011
[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}}=>[1,4,3,2,6,5]=>10010
[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}=>[1,4,3,5,2,6]=>10001
[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>10000
[1,4,3,6,2,5]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>10000
[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}=>[1,4,3,6,5,2]=>10000
[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}=>[1,4,5,2,3,6]=>10001
[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}=>[1,4,5,2,6,3]=>10000
[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>10001
[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,4,5,6,2,3]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,4,5,6,3,2]=>{{1},{2,4,6},{3,5}}=>[1,4,5,6,3,2]=>10000
[1,4,6,2,3,5]=>{{1},{2,4},{3,5,6}}=>[1,4,5,2,6,3]=>10000
[1,4,6,2,5,3]=>{{1},{2,4},{3,6},{5}}=>[1,4,6,2,5,3]=>10000
[1,4,6,3,2,5]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,4,6,3,5,2]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>10000
[1,4,6,5,2,3]=>{{1},{2,4,5},{3,6}}=>[1,4,6,5,2,3]=>10000
[1,4,6,5,3,2]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,5,2,3,4,6]=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>10001
[1,5,2,3,6,4]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,5,2,4,3,6]=>{{1},{2,3,5},{4},{6}}=>[1,3,5,4,2,6]=>10001
[1,5,2,4,6,3]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>10000
[1,5,2,6,3,4]=>{{1},{2,3,5},{4,6}}=>[1,3,5,6,2,4]=>10000
[1,5,2,6,4,3]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,5,3,2,4,6]=>{{1},{2,4,5},{3},{6}}=>[1,4,3,5,2,6]=>10001
[1,5,3,2,6,4]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>10000
[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}}=>[1,5,3,4,2,6]=>10001
[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}=>[1,5,3,4,6,2]=>10000
[1,5,3,6,2,4]=>{{1},{2,5},{3},{4,6}}=>[1,5,3,6,2,4]=>10000
[1,5,3,6,4,2]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>10000
[1,5,4,2,3,6]=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>10001
[1,5,4,2,6,3]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,5,4,3,2,6]=>{{1},{2,5},{3,4},{6}}=>[1,5,4,3,2,6]=>10001
[1,5,4,3,6,2]=>{{1},{2,5,6},{3,4}}=>[1,5,4,3,6,2]=>10000
[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}=>[1,5,4,6,2,3]=>10000
[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,5,6,2,3,4]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,5,6,2,4,3]=>{{1},{2,4,5},{3,6}}=>[1,4,6,5,2,3]=>10000
[1,5,6,3,2,4]=>{{1},{2,5},{3,4,6}}=>[1,5,4,6,2,3]=>10000
[1,5,6,3,4,2]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,5,6,4,2,3]=>{{1},{2,5},{3,6},{4}}=>[1,5,6,4,2,3]=>10000
[1,5,6,4,3,2]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>10000
[1,6,2,3,4,5]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,6,2,3,5,4]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>10000
[1,6,2,4,3,5]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>10000
[1,6,2,4,5,3]=>{{1},{2,3,6},{4},{5}}=>[1,3,6,4,5,2]=>10000
[1,6,2,5,3,4]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,6,2,5,4,3]=>{{1},{2,3,6},{4,5}}=>[1,3,6,5,4,2]=>10000
[1,6,3,2,4,5]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>10000
[1,6,3,2,5,4]=>{{1},{2,4,6},{3},{5}}=>[1,4,3,6,5,2]=>10000
[1,6,3,4,2,5]=>{{1},{2,5,6},{3},{4}}=>[1,5,3,4,6,2]=>10000
[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}}=>[1,6,3,4,5,2]=>10000
[1,6,3,5,2,4]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>10000
[1,6,3,5,4,2]=>{{1},{2,6},{3},{4,5}}=>[1,6,3,5,4,2]=>10000
[1,6,4,2,3,5]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,6,4,2,5,3]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>10000
[1,6,4,3,2,5]=>{{1},{2,5,6},{3,4}}=>[1,5,4,3,6,2]=>10000
[1,6,4,3,5,2]=>{{1},{2,6},{3,4},{5}}=>[1,6,4,3,5,2]=>10000
[1,6,4,5,2,3]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,6,4,5,3,2]=>{{1},{2,6},{3,4,5}}=>[1,6,4,5,3,2]=>10000
[1,6,5,2,3,4]=>{{1},{2,4,6},{3,5}}=>[1,4,5,6,3,2]=>10000
[1,6,5,2,4,3]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,6,5,3,2,4]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
[1,6,5,3,4,2]=>{{1},{2,6},{3,4,5}}=>[1,6,4,5,3,2]=>10000
[1,6,5,4,2,3]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>10000
[1,6,5,4,3,2]=>{{1},{2,6},{3,5},{4}}=>[1,6,5,4,3,2]=>10000
[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}}=>[2,1,3,4,5,6]=>01111
[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}}=>[2,1,3,4,6,5]=>01110
[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}}=>[2,1,3,5,4,6]=>01101
[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}}=>[2,1,3,5,6,4]=>01100
[2,1,3,6,4,5]=>{{1,2},{3},{4,5,6}}=>[2,1,3,5,6,4]=>01100
[2,1,3,6,5,4]=>{{1,2},{3},{4,6},{5}}=>[2,1,3,6,5,4]=>01100
[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}}=>[2,1,4,3,5,6]=>01011
[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}=>[2,1,4,3,6,5]=>01010
[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}}=>[2,1,4,5,3,6]=>01001
[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>01000
[2,1,4,6,3,5]=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>01000
[2,1,4,6,5,3]=>{{1,2},{3,4,6},{5}}=>[2,1,4,6,5,3]=>01000
[2,1,5,3,4,6]=>{{1,2},{3,4,5},{6}}=>[2,1,4,5,3,6]=>01001
[2,1,5,3,6,4]=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>01000
[2,1,5,4,3,6]=>{{1,2},{3,5},{4},{6}}=>[2,1,5,4,3,6]=>01001
[2,1,5,4,6,3]=>{{1,2},{3,5,6},{4}}=>[2,1,5,4,6,3]=>01000
[2,1,5,6,3,4]=>{{1,2},{3,5},{4,6}}=>[2,1,5,6,3,4]=>01000
[2,1,5,6,4,3]=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>01000
[2,1,6,3,4,5]=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>01000
[2,1,6,3,5,4]=>{{1,2},{3,4,6},{5}}=>[2,1,4,6,5,3]=>01000
[2,1,6,4,3,5]=>{{1,2},{3,5,6},{4}}=>[2,1,5,4,6,3]=>01000
[2,1,6,4,5,3]=>{{1,2},{3,6},{4},{5}}=>[2,1,6,4,5,3]=>01000
[2,1,6,5,3,4]=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>01000
[2,1,6,5,4,3]=>{{1,2},{3,6},{4,5}}=>[2,1,6,5,4,3]=>01000
[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}=>[2,3,1,4,5,6]=>00111
[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}}=>[2,3,1,4,6,5]=>00110
[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}}=>[2,3,1,5,4,6]=>00101
[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}}=>[2,3,1,5,6,4]=>00100
[2,3,1,6,4,5]=>{{1,2,3},{4,5,6}}=>[2,3,1,5,6,4]=>00100
[2,3,1,6,5,4]=>{{1,2,3},{4,6},{5}}=>[2,3,1,6,5,4]=>00100
[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>00011
[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>00010
[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,3,4,6,1,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[2,3,5,1,4,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[2,3,5,1,6,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,3,5,4,1,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>00001
[2,3,5,4,6,1]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[2,3,5,6,1,4]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>00000
[2,3,5,6,4,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,3,6,1,4,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,3,6,1,5,4]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[2,3,6,4,1,5]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[2,3,6,4,5,1]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>00000
[2,3,6,5,1,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>00000
[2,4,1,3,5,6]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>00011
[2,4,1,3,6,5]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>00010
[2,4,1,5,3,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[2,4,1,5,6,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,4,1,6,3,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,4,1,6,5,3]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[2,4,3,1,5,6]=>{{1,2,4},{3},{5},{6}}=>[2,4,3,1,5,6]=>00011
[2,4,3,1,6,5]=>{{1,2,4},{3},{5,6}}=>[2,4,3,1,6,5]=>00010
[2,4,3,5,1,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>00001
[2,4,3,5,6,1]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[2,4,3,6,1,5]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[2,4,3,6,5,1]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>00000
[2,4,5,1,3,6]=>{{1,2,4},{3,5},{6}}=>[2,4,5,1,3,6]=>00001
[2,4,5,1,6,3]=>{{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>00000
[2,4,5,3,1,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[2,4,5,3,6,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,4,5,6,1,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,4,5,6,3,1]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>00000
[2,4,6,1,3,5]=>{{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>00000
[2,4,6,1,5,3]=>{{1,2,4},{3,6},{5}}=>[2,4,6,1,5,3]=>00000
[2,4,6,3,1,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,4,6,3,5,1]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[2,4,6,5,1,3]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>00000
[2,4,6,5,3,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,5,1,3,4,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[2,5,1,3,6,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,5,1,4,3,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>00001
[2,5,1,4,6,3]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[2,5,1,6,3,4]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>00000
[2,5,1,6,4,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,5,3,1,4,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>00001
[2,5,3,1,6,4]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[2,5,3,4,1,6]=>{{1,2,5},{3},{4},{6}}=>[2,5,3,4,1,6]=>00001
[2,5,3,4,6,1]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>00000
[2,5,3,6,1,4]=>{{1,2,5},{3},{4,6}}=>[2,5,3,6,1,4]=>00000
[2,5,3,6,4,1]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[2,5,4,1,3,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[2,5,4,1,6,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,5,4,3,1,6]=>{{1,2,5},{3,4},{6}}=>[2,5,4,3,1,6]=>00001
[2,5,4,3,6,1]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>00000
[2,5,4,6,1,3]=>{{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>00000
[2,5,4,6,3,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,5,6,1,3,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,5,6,1,4,3]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>00000
[2,5,6,3,1,4]=>{{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>00000
[2,5,6,3,4,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,5,6,4,1,3]=>{{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>00000
[2,5,6,4,3,1]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[2,6,1,3,4,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,6,1,3,5,4]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[2,6,1,4,3,5]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[2,6,1,4,5,3]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>00000
[2,6,1,5,3,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,6,1,5,4,3]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>00000
[2,6,3,1,4,5]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[2,6,3,1,5,4]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>00000
[2,6,3,4,1,5]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>00000
[2,6,3,4,5,1]=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>00000
[2,6,3,5,1,4]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[2,6,3,5,4,1]=>{{1,2,6},{3},{4,5}}=>[2,6,3,5,4,1]=>00000
[2,6,4,1,3,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,6,4,1,5,3]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[2,6,4,3,1,5]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>00000
[2,6,4,3,5,1]=>{{1,2,6},{3,4},{5}}=>[2,6,4,3,5,1]=>00000
[2,6,4,5,1,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,6,4,5,3,1]=>{{1,2,6},{3,4,5}}=>[2,6,4,5,3,1]=>00000
[2,6,5,1,3,4]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>00000
[2,6,5,1,4,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,6,5,3,1,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[2,6,5,3,4,1]=>{{1,2,6},{3,4,5}}=>[2,6,4,5,3,1]=>00000
[2,6,5,4,1,3]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[2,6,5,4,3,1]=>{{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>00000
[3,1,2,4,5,6]=>{{1,2,3},{4},{5},{6}}=>[2,3,1,4,5,6]=>00111
[3,1,2,4,6,5]=>{{1,2,3},{4},{5,6}}=>[2,3,1,4,6,5]=>00110
[3,1,2,5,4,6]=>{{1,2,3},{4,5},{6}}=>[2,3,1,5,4,6]=>00101
[3,1,2,5,6,4]=>{{1,2,3},{4,5,6}}=>[2,3,1,5,6,4]=>00100
[3,1,2,6,4,5]=>{{1,2,3},{4,5,6}}=>[2,3,1,5,6,4]=>00100
[3,1,2,6,5,4]=>{{1,2,3},{4,6},{5}}=>[2,3,1,6,5,4]=>00100
[3,1,4,2,5,6]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>00011
[3,1,4,2,6,5]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>00010
[3,1,4,5,2,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[3,1,4,5,6,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,1,4,6,2,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,1,4,6,5,2]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[3,1,5,2,4,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[3,1,5,2,6,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,1,5,4,2,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>00001
[3,1,5,4,6,2]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[3,1,5,6,2,4]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>00000
[3,1,5,6,4,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,1,6,2,4,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,1,6,2,5,4]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[3,1,6,4,2,5]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[3,1,6,4,5,2]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>00000
[3,1,6,5,2,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,1,6,5,4,2]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>00000
[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}}=>[3,2,1,4,5,6]=>00111
[3,2,1,4,6,5]=>{{1,3},{2},{4},{5,6}}=>[3,2,1,4,6,5]=>00110
[3,2,1,5,4,6]=>{{1,3},{2},{4,5},{6}}=>[3,2,1,5,4,6]=>00101
[3,2,1,5,6,4]=>{{1,3},{2},{4,5,6}}=>[3,2,1,5,6,4]=>00100
[3,2,1,6,4,5]=>{{1,3},{2},{4,5,6}}=>[3,2,1,5,6,4]=>00100
[3,2,1,6,5,4]=>{{1,3},{2},{4,6},{5}}=>[3,2,1,6,5,4]=>00100
[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}}=>[3,2,4,1,5,6]=>00011
[3,2,4,1,6,5]=>{{1,3,4},{2},{5,6}}=>[3,2,4,1,6,5]=>00010
[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>00001
[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[3,2,4,6,1,5]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[3,2,4,6,5,1]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>00000
[3,2,5,1,4,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>00001
[3,2,5,1,6,4]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[3,2,5,4,1,6]=>{{1,3,5},{2},{4},{6}}=>[3,2,5,4,1,6]=>00001
[3,2,5,4,6,1]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>00000
[3,2,5,6,1,4]=>{{1,3,5},{2},{4,6}}=>[3,2,5,6,1,4]=>00000
[3,2,5,6,4,1]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[3,2,6,1,4,5]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[3,2,6,1,5,4]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>00000
[3,2,6,4,1,5]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>00000
[3,2,6,4,5,1]=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>00000
[3,2,6,5,1,4]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[3,2,6,5,4,1]=>{{1,3,6},{2},{4,5}}=>[3,2,6,5,4,1]=>00000
[3,4,1,2,5,6]=>{{1,3},{2,4},{5},{6}}=>[3,4,1,2,5,6]=>00011
[3,4,1,2,6,5]=>{{1,3},{2,4},{5,6}}=>[3,4,1,2,6,5]=>00010
[3,4,1,5,2,6]=>{{1,3},{2,4,5},{6}}=>[3,4,1,5,2,6]=>00001
[3,4,1,5,6,2]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>00000
[3,4,1,6,2,5]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>00000
[3,4,1,6,5,2]=>{{1,3},{2,4,6},{5}}=>[3,4,1,6,5,2]=>00000
[3,4,2,1,5,6]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>00011
[3,4,2,1,6,5]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>00010
[3,4,2,5,1,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[3,4,2,5,6,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,4,2,6,1,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,4,2,6,5,1]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[3,4,5,1,2,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[3,4,5,1,6,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,4,5,2,1,6]=>{{1,3,5},{2,4},{6}}=>[3,4,5,2,1,6]=>00001
[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>00000
[3,4,5,6,1,2]=>{{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>00000
[3,4,5,6,2,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,4,6,1,2,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,4,6,1,5,2]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[3,4,6,2,1,5]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>00000
[3,4,6,2,5,1]=>{{1,3,6},{2,4},{5}}=>[3,4,6,2,5,1]=>00000
[3,4,6,5,1,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,4,6,5,2,1]=>{{1,3,6},{2,4,5}}=>[3,4,6,5,2,1]=>00000
[3,5,1,2,4,6]=>{{1,3},{2,4,5},{6}}=>[3,4,1,5,2,6]=>00001
[3,5,1,2,6,4]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>00000
[3,5,1,4,2,6]=>{{1,3},{2,5},{4},{6}}=>[3,5,1,4,2,6]=>00001
[3,5,1,4,6,2]=>{{1,3},{2,5,6},{4}}=>[3,5,1,4,6,2]=>00000
[3,5,1,6,2,4]=>{{1,3},{2,5},{4,6}}=>[3,5,1,6,2,4]=>00000
[3,5,1,6,4,2]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>00000
[3,5,2,1,4,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[3,5,2,1,6,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,5,2,4,1,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>00001
[3,5,2,4,6,1]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[3,5,2,6,1,4]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>00000
[3,5,2,6,4,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,5,4,1,2,6]=>{{1,3,4},{2,5},{6}}=>[3,5,4,1,2,6]=>00001
[3,5,4,1,6,2]=>{{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>00000
[3,5,4,2,1,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[3,5,4,2,6,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,5,4,6,1,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,5,4,6,2,1]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>00000
[3,5,6,1,2,4]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>00000
[3,5,6,1,4,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,5,6,2,1,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,5,6,2,4,1]=>{{1,3,6},{2,4,5}}=>[3,4,6,5,2,1]=>00000
[3,5,6,4,1,2]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[3,5,6,4,2,1]=>{{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>00000
[3,6,1,2,4,5]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>00000
[3,6,1,2,5,4]=>{{1,3},{2,4,6},{5}}=>[3,4,1,6,5,2]=>00000
[3,6,1,4,2,5]=>{{1,3},{2,5,6},{4}}=>[3,5,1,4,6,2]=>00000
[3,6,1,4,5,2]=>{{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>00000
[3,6,1,5,2,4]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>00000
[3,6,1,5,4,2]=>{{1,3},{2,6},{4,5}}=>[3,6,1,5,4,2]=>00000
[3,6,2,1,4,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,6,2,1,5,4]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[3,6,2,4,1,5]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[3,6,2,4,5,1]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>00000
[3,6,2,5,1,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,6,2,5,4,1]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>00000
[3,6,4,1,2,5]=>{{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>00000
[3,6,4,1,5,2]=>{{1,3,4},{2,6},{5}}=>[3,6,4,1,5,2]=>00000
[3,6,4,2,1,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,6,4,2,5,1]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[3,6,4,5,1,2]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>00000
[3,6,4,5,2,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,6,5,1,2,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,6,5,1,4,2]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>00000
[3,6,5,2,1,4]=>{{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>00000
[3,6,5,2,4,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[3,6,5,4,1,2]=>{{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>00000
[3,6,5,4,2,1]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[4,1,2,3,5,6]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>00011
[4,1,2,3,6,5]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>00010
[4,1,2,5,3,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[4,1,2,5,6,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,1,2,6,3,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,1,2,6,5,3]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[4,1,3,2,5,6]=>{{1,2,4},{3},{5},{6}}=>[2,4,3,1,5,6]=>00011
[4,1,3,2,6,5]=>{{1,2,4},{3},{5,6}}=>[2,4,3,1,6,5]=>00010
[4,1,3,5,2,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>00001
[4,1,3,5,6,2]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[4,1,3,6,2,5]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[4,1,3,6,5,2]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>00000
[4,1,5,2,3,6]=>{{1,2,4},{3,5},{6}}=>[2,4,5,1,3,6]=>00001
[4,1,5,2,6,3]=>{{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>00000
[4,1,5,3,2,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[4,1,5,3,6,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,1,5,6,2,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,1,5,6,3,2]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>00000
[4,1,6,2,3,5]=>{{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>00000
[4,1,6,2,5,3]=>{{1,2,4},{3,6},{5}}=>[2,4,6,1,5,3]=>00000
[4,1,6,3,2,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,1,6,3,5,2]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[4,1,6,5,2,3]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>00000
[4,1,6,5,3,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,2,1,3,5,6]=>{{1,3,4},{2},{5},{6}}=>[3,2,4,1,5,6]=>00011
[4,2,1,3,6,5]=>{{1,3,4},{2},{5,6}}=>[3,2,4,1,6,5]=>00010
[4,2,1,5,3,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>00001
[4,2,1,5,6,3]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[4,2,1,6,3,5]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[4,2,1,6,5,3]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>00000
[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}}=>[4,2,3,1,5,6]=>00011
[4,2,3,1,6,5]=>{{1,4},{2},{3},{5,6}}=>[4,2,3,1,6,5]=>00010
[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}}=>[4,2,3,5,1,6]=>00001
[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>00000
[4,2,3,6,1,5]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>00000
[4,2,3,6,5,1]=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>00000
[4,2,5,1,3,6]=>{{1,4},{2},{3,5},{6}}=>[4,2,5,1,3,6]=>00001
[4,2,5,1,6,3]=>{{1,4},{2},{3,5,6}}=>[4,2,5,1,6,3]=>00000
[4,2,5,3,1,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>00001
[4,2,5,3,6,1]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[4,2,5,6,1,3]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[4,2,5,6,3,1]=>{{1,4,6},{2},{3,5}}=>[4,2,5,6,3,1]=>00000
[4,2,6,1,3,5]=>{{1,4},{2},{3,5,6}}=>[4,2,5,1,6,3]=>00000
[4,2,6,1,5,3]=>{{1,4},{2},{3,6},{5}}=>[4,2,6,1,5,3]=>00000
[4,2,6,3,1,5]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[4,2,6,3,5,1]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>00000
[4,2,6,5,1,3]=>{{1,4,5},{2},{3,6}}=>[4,2,6,5,1,3]=>00000
[4,2,6,5,3,1]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[4,3,1,2,5,6]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>00011
[4,3,1,2,6,5]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>00010
[4,3,1,5,2,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[4,3,1,5,6,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,3,1,6,2,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,3,1,6,5,2]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}}=>[4,3,2,1,5,6]=>00011
[4,3,2,1,6,5]=>{{1,4},{2,3},{5,6}}=>[4,3,2,1,6,5]=>00010
[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}}=>[4,3,2,5,1,6]=>00001
[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>00000
[4,3,2,6,1,5]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>00000
[4,3,2,6,5,1]=>{{1,4,6},{2,3},{5}}=>[4,3,2,6,5,1]=>00000
[4,3,5,1,2,6]=>{{1,4},{2,3,5},{6}}=>[4,3,5,1,2,6]=>00001
[4,3,5,1,6,2]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>00000
[4,3,5,2,1,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[4,3,5,2,6,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,3,5,6,1,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,3,5,6,2,1]=>{{1,4,6},{2,3,5}}=>[4,3,5,6,2,1]=>00000
[4,3,6,1,2,5]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>00000
[4,3,6,1,5,2]=>{{1,4},{2,3,6},{5}}=>[4,3,6,1,5,2]=>00000
[4,3,6,2,1,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,3,6,2,5,1]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[4,3,6,5,1,2]=>{{1,4,5},{2,3,6}}=>[4,3,6,5,1,2]=>00000
[4,3,6,5,2,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,5,1,2,3,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[4,5,1,2,6,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,5,1,3,2,6]=>{{1,3,4},{2,5},{6}}=>[3,5,4,1,2,6]=>00001
[4,5,1,3,6,2]=>{{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>00000
[4,5,1,6,2,3]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>00000
[4,5,1,6,3,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,5,2,1,3,6]=>{{1,4},{2,3,5},{6}}=>[4,3,5,1,2,6]=>00001
[4,5,2,1,6,3]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>00000
[4,5,2,3,1,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[4,5,2,3,6,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,5,2,6,1,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,5,2,6,3,1]=>{{1,4,6},{2,3,5}}=>[4,3,5,6,2,1]=>00000
[4,5,3,1,2,6]=>{{1,4},{2,5},{3},{6}}=>[4,5,3,1,2,6]=>00001
[4,5,3,1,6,2]=>{{1,4},{2,5,6},{3}}=>[4,5,3,1,6,2]=>00000
[4,5,3,2,1,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>00001
[4,5,3,2,6,1]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[4,5,3,6,1,2]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[4,5,3,6,2,1]=>{{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>00000
[4,5,6,1,2,3]=>{{1,4},{2,5},{3,6}}=>[4,5,6,1,2,3]=>00000
[4,5,6,1,3,2]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>00000
[4,5,6,2,1,3]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>00000
[4,5,6,2,3,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,5,6,3,1,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,5,6,3,2,1]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>00000
[4,6,1,2,3,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,6,1,2,5,3]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[4,6,1,3,2,5]=>{{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>00000
[4,6,1,3,5,2]=>{{1,3,4},{2,6},{5}}=>[3,6,4,1,5,2]=>00000
[4,6,1,5,2,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,6,1,5,3,2]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>00000
[4,6,2,1,3,5]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>00000
[4,6,2,1,5,3]=>{{1,4},{2,3,6},{5}}=>[4,3,6,1,5,2]=>00000
[4,6,2,3,1,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,6,2,3,5,1]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[4,6,2,5,1,3]=>{{1,4,5},{2,3,6}}=>[4,3,6,5,1,2]=>00000
[4,6,2,5,3,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,6,3,1,2,5]=>{{1,4},{2,5,6},{3}}=>[4,5,3,1,6,2]=>00000
[4,6,3,1,5,2]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>00000
[4,6,3,2,1,5]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[4,6,3,2,5,1]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>00000
[4,6,3,5,1,2]=>{{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>00000
[4,6,3,5,2,1]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[4,6,5,1,2,3]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>00000
[4,6,5,1,3,2]=>{{1,4},{2,6},{3,5}}=>[4,6,5,1,3,2]=>00000
[4,6,5,2,1,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[4,6,5,2,3,1]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>00000
[4,6,5,3,1,2]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>00000
[4,6,5,3,2,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,1,2,3,4,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[5,1,2,3,6,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,1,2,4,3,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>00001
[5,1,2,4,6,3]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[5,1,2,6,3,4]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>00000
[5,1,2,6,4,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,1,3,2,4,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>00001
[5,1,3,2,6,4]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[5,1,3,4,2,6]=>{{1,2,5},{3},{4},{6}}=>[2,5,3,4,1,6]=>00001
[5,1,3,4,6,2]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>00000
[5,1,3,6,2,4]=>{{1,2,5},{3},{4,6}}=>[2,5,3,6,1,4]=>00000
[5,1,3,6,4,2]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[5,1,4,2,3,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[5,1,4,2,6,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,1,4,3,2,6]=>{{1,2,5},{3,4},{6}}=>[2,5,4,3,1,6]=>00001
[5,1,4,3,6,2]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>00000
[5,1,4,6,2,3]=>{{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>00000
[5,1,4,6,3,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,1,6,2,3,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,1,6,2,4,3]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>00000
[5,1,6,3,2,4]=>{{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>00000
[5,1,6,3,4,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,1,6,4,2,3]=>{{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>00000
[5,1,6,4,3,2]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[5,2,1,3,4,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>00001
[5,2,1,3,6,4]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[5,2,1,4,3,6]=>{{1,3,5},{2},{4},{6}}=>[3,2,5,4,1,6]=>00001
[5,2,1,4,6,3]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>00000
[5,2,1,6,3,4]=>{{1,3,5},{2},{4,6}}=>[3,2,5,6,1,4]=>00000
[5,2,1,6,4,3]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[5,2,3,1,4,6]=>{{1,4,5},{2},{3},{6}}=>[4,2,3,5,1,6]=>00001
[5,2,3,1,6,4]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>00000
[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>00001
[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>00000
[5,2,3,6,1,4]=>{{1,5},{2},{3},{4,6}}=>[5,2,3,6,1,4]=>00000
[5,2,3,6,4,1]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>00000
[5,2,4,1,3,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>00001
[5,2,4,1,6,3]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[5,2,4,3,1,6]=>{{1,5},{2},{3,4},{6}}=>[5,2,4,3,1,6]=>00001
[5,2,4,3,6,1]=>{{1,5,6},{2},{3,4}}=>[5,2,4,3,6,1]=>00000
[5,2,4,6,1,3]=>{{1,5},{2},{3,4,6}}=>[5,2,4,6,1,3]=>00000
[5,2,4,6,3,1]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[5,2,6,1,3,4]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[5,2,6,1,4,3]=>{{1,4,5},{2},{3,6}}=>[4,2,6,5,1,3]=>00000
[5,2,6,3,1,4]=>{{1,5},{2},{3,4,6}}=>[5,2,4,6,1,3]=>00000
[5,2,6,3,4,1]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[5,2,6,4,1,3]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>00000
[5,2,6,4,3,1]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>00000
[5,3,1,2,4,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[5,3,1,2,6,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,3,1,4,2,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>00001
[5,3,1,4,6,2]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[5,3,1,6,2,4]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>00000
[5,3,1,6,4,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,3,2,1,4,6]=>{{1,4,5},{2,3},{6}}=>[4,3,2,5,1,6]=>00001
[5,3,2,1,6,4]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>00000
[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}}=>[5,3,2,4,1,6]=>00001
[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}}=>[5,3,2,4,6,1]=>00000
[5,3,2,6,1,4]=>{{1,5},{2,3},{4,6}}=>[5,3,2,6,1,4]=>00000
[5,3,2,6,4,1]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>00000
[5,3,4,1,2,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[5,3,4,1,6,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}}=>[5,3,4,2,1,6]=>00001
[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}}=>[5,3,4,2,6,1]=>00000
[5,3,4,6,1,2]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>00000
[5,3,4,6,2,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,3,6,1,2,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,3,6,1,4,2]=>{{1,4,5},{2,3,6}}=>[4,3,6,5,1,2]=>00000
[5,3,6,2,1,4]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>00000
[5,3,6,2,4,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,3,6,4,1,2]=>{{1,5},{2,3,6},{4}}=>[5,3,6,4,1,2]=>00000
[5,3,6,4,2,1]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[5,4,1,2,3,6]=>{{1,3,5},{2,4},{6}}=>[3,4,5,2,1,6]=>00001
[5,4,1,2,6,3]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>00000
[5,4,1,3,2,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[5,4,1,3,6,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,4,1,6,2,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,4,1,6,3,2]=>{{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>00000
[5,4,2,1,3,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
[5,4,2,1,6,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,4,2,3,1,6]=>{{1,5},{2,3,4},{6}}=>[5,3,4,2,1,6]=>00001
[5,4,2,3,6,1]=>{{1,5,6},{2,3,4}}=>[5,3,4,2,6,1]=>00000
[5,4,2,6,1,3]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>00000
[5,4,2,6,3,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,4,3,1,2,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>00001
[5,4,3,1,6,2]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}}=>[5,4,3,2,1,6]=>00001
[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}}=>[5,4,3,2,6,1]=>00000
[5,4,3,6,1,2]=>{{1,5},{2,4,6},{3}}=>[5,4,3,6,1,2]=>00000
[5,4,3,6,2,1]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[5,4,6,1,2,3]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>00000
[5,4,6,1,3,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,4,6,2,1,3]=>{{1,5},{2,4},{3,6}}=>[5,4,6,2,1,3]=>00000
[5,4,6,2,3,1]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>00000
[5,4,6,3,1,2]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>00000
[5,4,6,3,2,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,6,1,2,3,4]=>{{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>00000
[5,6,1,2,4,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,6,1,3,2,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,6,1,3,4,2]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>00000
[5,6,1,4,2,3]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[5,6,1,4,3,2]=>{{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>00000
[5,6,2,1,3,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,6,2,1,4,3]=>{{1,4,5},{2,3,6}}=>[4,3,6,5,1,2]=>00000
[5,6,2,3,1,4]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>00000
[5,6,2,3,4,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,6,2,4,1,3]=>{{1,5},{2,3,6},{4}}=>[5,3,6,4,1,2]=>00000
[5,6,2,4,3,1]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[5,6,3,1,2,4]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[5,6,3,1,4,2]=>{{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>00000
[5,6,3,2,1,4]=>{{1,5},{2,4,6},{3}}=>[5,4,3,6,1,2]=>00000
[5,6,3,2,4,1]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[5,6,3,4,1,2]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>00000
[5,6,3,4,2,1]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>00000
[5,6,4,1,2,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,6,4,1,3,2]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>00000
[5,6,4,2,1,3]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>00000
[5,6,4,2,3,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[5,6,4,3,1,2]=>{{1,5},{2,6},{3,4}}=>[5,6,4,3,1,2]=>00000
[5,6,4,3,2,1]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>00000
[6,1,2,3,4,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,1,2,3,5,4]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[6,1,2,4,3,5]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[6,1,2,4,5,3]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>00000
[6,1,2,5,3,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,1,2,5,4,3]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>00000
[6,1,3,2,4,5]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[6,1,3,2,5,4]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>00000
[6,1,3,4,2,5]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>00000
[6,1,3,4,5,2]=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>00000
[6,1,3,5,2,4]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[6,1,3,5,4,2]=>{{1,2,6},{3},{4,5}}=>[2,6,3,5,4,1]=>00000
[6,1,4,2,3,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,1,4,2,5,3]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[6,1,4,3,2,5]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>00000
[6,1,4,3,5,2]=>{{1,2,6},{3,4},{5}}=>[2,6,4,3,5,1]=>00000
[6,1,4,5,2,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,1,4,5,3,2]=>{{1,2,6},{3,4,5}}=>[2,6,4,5,3,1]=>00000
[6,1,5,2,3,4]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>00000
[6,1,5,2,4,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,1,5,3,2,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,1,5,3,4,2]=>{{1,2,6},{3,4,5}}=>[2,6,4,5,3,1]=>00000
[6,1,5,4,2,3]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[6,1,5,4,3,2]=>{{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>00000
[6,2,1,3,4,5]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[6,2,1,3,5,4]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>00000
[6,2,1,4,3,5]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>00000
[6,2,1,4,5,3]=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>00000
[6,2,1,5,3,4]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[6,2,1,5,4,3]=>{{1,3,6},{2},{4,5}}=>[3,2,6,5,4,1]=>00000
[6,2,3,1,4,5]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>00000
[6,2,3,1,5,4]=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>00000
[6,2,3,4,1,5]=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>00000
[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>00000
[6,2,3,5,1,4]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>00000
[6,2,3,5,4,1]=>{{1,6},{2},{3},{4,5}}=>[6,2,3,5,4,1]=>00000
[6,2,4,1,3,5]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[6,2,4,1,5,3]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>00000
[6,2,4,3,1,5]=>{{1,5,6},{2},{3,4}}=>[5,2,4,3,6,1]=>00000
[6,2,4,3,5,1]=>{{1,6},{2},{3,4},{5}}=>[6,2,4,3,5,1]=>00000
[6,2,4,5,1,3]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[6,2,4,5,3,1]=>{{1,6},{2},{3,4,5}}=>[6,2,4,5,3,1]=>00000
[6,2,5,1,3,4]=>{{1,4,6},{2},{3,5}}=>[4,2,5,6,3,1]=>00000
[6,2,5,1,4,3]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[6,2,5,3,1,4]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
[6,2,5,3,4,1]=>{{1,6},{2},{3,4,5}}=>[6,2,4,5,3,1]=>00000
[6,2,5,4,1,3]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>00000
[6,2,5,4,3,1]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>00000
[6,3,1,2,4,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,3,1,2,5,4]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[6,3,1,4,2,5]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[6,3,1,4,5,2]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>00000
[6,3,1,5,2,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,3,1,5,4,2]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>00000
[6,3,2,1,4,5]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>00000
[6,3,2,1,5,4]=>{{1,4,6},{2,3},{5}}=>[4,3,2,6,5,1]=>00000
[6,3,2,4,1,5]=>{{1,5,6},{2,3},{4}}=>[5,3,2,4,6,1]=>00000
[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}}=>[6,3,2,4,5,1]=>00000
[6,3,2,5,1,4]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>00000
[6,3,2,5,4,1]=>{{1,6},{2,3},{4,5}}=>[6,3,2,5,4,1]=>00000
[6,3,4,1,2,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,3,4,1,5,2]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[6,3,4,2,1,5]=>{{1,5,6},{2,3,4}}=>[5,3,4,2,6,1]=>00000
[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}}=>[6,3,4,2,5,1]=>00000
[6,3,4,5,1,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>00000
[6,3,5,1,2,4]=>{{1,4,6},{2,3,5}}=>[4,3,5,6,2,1]=>00000
[6,3,5,1,4,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,3,5,2,1,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,3,5,2,4,1]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>00000
[6,3,5,4,1,2]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[6,3,5,4,2,1]=>{{1,6},{2,3,5},{4}}=>[6,3,5,4,2,1]=>00000
[6,4,1,2,3,5]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>00000
[6,4,1,2,5,3]=>{{1,3,6},{2,4},{5}}=>[3,4,6,2,5,1]=>00000
[6,4,1,3,2,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,4,1,3,5,2]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[6,4,1,5,2,3]=>{{1,3,6},{2,4,5}}=>[3,4,6,5,2,1]=>00000
[6,4,1,5,3,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,4,2,1,3,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,4,2,1,5,3]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
[6,4,2,3,1,5]=>{{1,5,6},{2,3,4}}=>[5,3,4,2,6,1]=>00000
[6,4,2,3,5,1]=>{{1,6},{2,3,4},{5}}=>[6,3,4,2,5,1]=>00000
[6,4,2,5,1,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,4,2,5,3,1]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>00000
[6,4,3,1,2,5]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[6,4,3,1,5,2]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>00000
[6,4,3,2,1,5]=>{{1,5,6},{2,4},{3}}=>[5,4,3,2,6,1]=>00000
[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>00000
[6,4,3,5,1,2]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}}=>[6,4,3,5,2,1]=>00000
[6,4,5,1,2,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,4,5,1,3,2]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>00000
[6,4,5,2,1,3]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>00000
[6,4,5,2,3,1]=>{{1,6},{2,4},{3,5}}=>[6,4,5,2,3,1]=>00000
[6,4,5,3,1,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,4,5,3,2,1]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>00000
[6,5,1,2,3,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,5,1,2,4,3]=>{{1,3,6},{2,4,5}}=>[3,4,6,5,2,1]=>00000
[6,5,1,3,2,4]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>00000
[6,5,1,3,4,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,5,1,4,2,3]=>{{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>00000
[6,5,1,4,3,2]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[6,5,2,1,3,4]=>{{1,4,6},{2,3,5}}=>[4,3,5,6,2,1]=>00000
[6,5,2,1,4,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,5,2,3,1,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,5,2,3,4,1]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>00000
[6,5,2,4,1,3]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
[6,5,2,4,3,1]=>{{1,6},{2,3,5},{4}}=>[6,3,5,4,2,1]=>00000
[6,5,3,1,2,4]=>{{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>00000
[6,5,3,1,4,2]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[6,5,3,2,1,4]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
[6,5,3,2,4,1]=>{{1,6},{2,4,5},{3}}=>[6,4,3,5,2,1]=>00000
[6,5,3,4,1,2]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>00000
[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>00000
[6,5,4,1,2,3]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>00000
[6,5,4,1,3,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,5,4,2,1,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
[6,5,4,2,3,1]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>00000
[6,5,4,3,1,2]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>00000
[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}}=>[6,5,4,3,2,1]=>00000
[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}=>[1,2,3,4,5,6,7]=>111111
[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}=>[1,2,3,4,5,7,6]=>111110
[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}=>[1,2,3,4,6,5,7]=>111101
[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}=>[1,2,3,4,6,7,5]=>111100
[1,2,3,4,7,5,6]=>{{1},{2},{3},{4},{5,6,7}}=>[1,2,3,4,6,7,5]=>111100
[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}=>[1,2,3,4,7,6,5]=>111100
[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}=>[1,2,3,5,4,6,7]=>111011
[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}=>[1,2,3,5,4,7,6]=>111010
[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}=>[1,2,3,5,6,4,7]=>111001
[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}=>[1,2,3,5,6,7,4]=>111000
[1,2,3,5,7,4,6]=>{{1},{2},{3},{4,5,6,7}}=>[1,2,3,5,6,7,4]=>111000
[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}=>[1,2,3,5,7,6,4]=>111000
[1,2,3,6,4,5,7]=>{{1},{2},{3},{4,5,6},{7}}=>[1,2,3,5,6,4,7]=>111001
[1,2,3,6,4,7,5]=>{{1},{2},{3},{4,5,6,7}}=>[1,2,3,5,6,7,4]=>111000
[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}=>[1,2,3,6,5,4,7]=>111001
[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}=>[1,2,3,6,5,7,4]=>111000
[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}=>[1,2,3,6,7,4,5]=>111000
[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}=>[1,2,3,5,6,7,4]=>111000
[1,2,3,7,4,5,6]=>{{1},{2},{3},{4,5,6,7}}=>[1,2,3,5,6,7,4]=>111000
[1,2,3,7,4,6,5]=>{{1},{2},{3},{4,5,7},{6}}=>[1,2,3,5,7,6,4]=>111000
[1,2,3,7,5,4,6]=>{{1},{2},{3},{4,6,7},{5}}=>[1,2,3,6,5,7,4]=>111000
[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}=>[1,2,3,7,5,6,4]=>111000
[1,2,3,7,6,4,5]=>{{1},{2},{3},{4,5,6,7}}=>[1,2,3,5,6,7,4]=>111000
[1,2,3,7,6,5,4]=>{{1},{2},{3},{4,7},{5,6}}=>[1,2,3,7,6,5,4]=>111000
[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}=>[1,2,4,3,5,6,7]=>110111
[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}=>[1,2,4,3,5,7,6]=>110110
[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}=>[1,2,4,3,6,5,7]=>110101
[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}=>[1,2,4,3,6,7,5]=>110100
[1,2,4,3,7,5,6]=>{{1},{2},{3,4},{5,6,7}}=>[1,2,4,3,6,7,5]=>110100
[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}=>[1,2,4,3,7,6,5]=>110100
[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}=>[1,2,4,5,3,6,7]=>110011
[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}=>[1,2,4,5,3,7,6]=>110010
[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}=>[1,2,4,5,6,3,7]=>110001
[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,4,5,7,3,6]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}=>[1,2,4,5,7,6,3]=>110000
[1,2,4,6,3,5,7]=>{{1},{2},{3,4,5,6},{7}}=>[1,2,4,5,6,3,7]=>110001
[1,2,4,6,3,7,5]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}=>[1,2,4,6,5,3,7]=>110001
[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}=>[1,2,4,6,5,7,3]=>110000
[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}=>[1,2,4,6,7,3,5]=>110000
[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,4,7,3,5,6]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,4,7,3,6,5]=>{{1},{2},{3,4,5,7},{6}}=>[1,2,4,5,7,6,3]=>110000
[1,2,4,7,5,3,6]=>{{1},{2},{3,4,6,7},{5}}=>[1,2,4,6,5,7,3]=>110000
[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}=>[1,2,4,7,5,6,3]=>110000
[1,2,4,7,6,3,5]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,4,7,6,5,3]=>{{1},{2},{3,4,7},{5,6}}=>[1,2,4,7,6,5,3]=>110000
[1,2,5,3,4,6,7]=>{{1},{2},{3,4,5},{6},{7}}=>[1,2,4,5,3,6,7]=>110011
[1,2,5,3,4,7,6]=>{{1},{2},{3,4,5},{6,7}}=>[1,2,4,5,3,7,6]=>110010
[1,2,5,3,6,4,7]=>{{1},{2},{3,4,5,6},{7}}=>[1,2,4,5,6,3,7]=>110001
[1,2,5,3,6,7,4]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,5,3,7,4,6]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,5,3,7,6,4]=>{{1},{2},{3,4,5,7},{6}}=>[1,2,4,5,7,6,3]=>110000
[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}=>[1,2,5,4,3,6,7]=>110011
[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}=>[1,2,5,4,3,7,6]=>110010
[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}=>[1,2,5,4,6,3,7]=>110001
[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}=>[1,2,5,4,6,7,3]=>110000
[1,2,5,4,7,3,6]=>{{1},{2},{3,5,6,7},{4}}=>[1,2,5,4,6,7,3]=>110000
[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}=>[1,2,5,4,7,6,3]=>110000
[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}=>[1,2,5,6,3,4,7]=>110001
[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}=>[1,2,5,6,3,7,4]=>110000
[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}=>[1,2,4,5,6,3,7]=>110001
[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,5,6,7,3,4]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,5,6,7,4,3]=>{{1},{2},{3,5,7},{4,6}}=>[1,2,5,6,7,4,3]=>110000
[1,2,5,7,3,4,6]=>{{1},{2},{3,5},{4,6,7}}=>[1,2,5,6,3,7,4]=>110000
[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}=>[1,2,5,7,3,6,4]=>110000
[1,2,5,7,4,3,6]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}=>[1,2,4,5,7,6,3]=>110000
[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}=>[1,2,5,7,6,3,4]=>110000
[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,6,3,4,5,7]=>{{1},{2},{3,4,5,6},{7}}=>[1,2,4,5,6,3,7]=>110001
[1,2,6,3,4,7,5]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,6,3,5,4,7]=>{{1},{2},{3,4,6},{5},{7}}=>[1,2,4,6,5,3,7]=>110001
[1,2,6,3,5,7,4]=>{{1},{2},{3,4,6,7},{5}}=>[1,2,4,6,5,7,3]=>110000
[1,2,6,3,7,4,5]=>{{1},{2},{3,4,6},{5,7}}=>[1,2,4,6,7,3,5]=>110000
[1,2,6,3,7,5,4]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,6,4,3,5,7]=>{{1},{2},{3,5,6},{4},{7}}=>[1,2,5,4,6,3,7]=>110001
[1,2,6,4,3,7,5]=>{{1},{2},{3,5,6,7},{4}}=>[1,2,5,4,6,7,3]=>110000
[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}=>[1,2,6,4,5,3,7]=>110001
[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}=>[1,2,6,4,5,7,3]=>110000
[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}=>[1,2,6,4,7,3,5]=>110000
[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}=>[1,2,5,4,6,7,3]=>110000
[1,2,6,5,3,4,7]=>{{1},{2},{3,4,5,6},{7}}=>[1,2,4,5,6,3,7]=>110001
[1,2,6,5,3,7,4]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,6,5,4,3,7]=>{{1},{2},{3,6},{4,5},{7}}=>[1,2,6,5,4,3,7]=>110001
[1,2,6,5,4,7,3]=>{{1},{2},{3,6,7},{4,5}}=>[1,2,6,5,4,7,3]=>110000
[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}=>[1,2,6,5,7,3,4]=>110000
[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,6,7,3,4,5]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,6,7,3,5,4]=>{{1},{2},{3,5,6},{4,7}}=>[1,2,5,7,6,3,4]=>110000
[1,2,6,7,4,3,5]=>{{1},{2},{3,6},{4,5,7}}=>[1,2,6,5,7,3,4]=>110000
[1,2,6,7,4,5,3]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}=>[1,2,6,7,5,3,4]=>110000
[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}=>[1,2,4,6,5,7,3]=>110000
[1,2,7,3,4,5,6]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,7,3,4,6,5]=>{{1},{2},{3,4,5,7},{6}}=>[1,2,4,5,7,6,3]=>110000
[1,2,7,3,5,4,6]=>{{1},{2},{3,4,6,7},{5}}=>[1,2,4,6,5,7,3]=>110000
[1,2,7,3,5,6,4]=>{{1},{2},{3,4,7},{5},{6}}=>[1,2,4,7,5,6,3]=>110000
[1,2,7,3,6,4,5]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,7,3,6,5,4]=>{{1},{2},{3,4,7},{5,6}}=>[1,2,4,7,6,5,3]=>110000
[1,2,7,4,3,5,6]=>{{1},{2},{3,5,6,7},{4}}=>[1,2,5,4,6,7,3]=>110000
[1,2,7,4,3,6,5]=>{{1},{2},{3,5,7},{4},{6}}=>[1,2,5,4,7,6,3]=>110000
[1,2,7,4,5,3,6]=>{{1},{2},{3,6,7},{4},{5}}=>[1,2,6,4,5,7,3]=>110000
[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}}=>[1,2,7,4,5,6,3]=>110000
[1,2,7,4,6,3,5]=>{{1},{2},{3,5,6,7},{4}}=>[1,2,5,4,6,7,3]=>110000
[1,2,7,4,6,5,3]=>{{1},{2},{3,7},{4},{5,6}}=>[1,2,7,4,6,5,3]=>110000
[1,2,7,5,3,4,6]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,7,5,3,6,4]=>{{1},{2},{3,4,5,7},{6}}=>[1,2,4,5,7,6,3]=>110000
[1,2,7,5,4,3,6]=>{{1},{2},{3,6,7},{4,5}}=>[1,2,6,5,4,7,3]=>110000
[1,2,7,5,4,6,3]=>{{1},{2},{3,7},{4,5},{6}}=>[1,2,7,5,4,6,3]=>110000
[1,2,7,5,6,3,4]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,7,5,6,4,3]=>{{1},{2},{3,7},{4,5,6}}=>[1,2,7,5,6,4,3]=>110000
[1,2,7,6,3,4,5]=>{{1},{2},{3,5,7},{4,6}}=>[1,2,5,6,7,4,3]=>110000
[1,2,7,6,3,5,4]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,7,6,4,3,5]=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
[1,2,7,6,4,5,3]=>{{1},{2},{3,7},{4,5,6}}=>[1,2,7,5,6,4,3]=>110000
[1,2,7,6,5,3,4]=>{{1},{2},{3,4,6,7},{5}}=>[1,2,4,6,5,7,3]=>110000
[1,2,7,6,5,4,3]=>{{1},{2},{3,7},{4,6},{5}}=>[1,2,7,6,5,4,3]=>110000
[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}=>[1,3,2,4,5,6,7]=>101111
[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}=>[1,3,2,4,5,7,6]=>101110
[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}=>[1,3,2,4,6,5,7]=>101101
[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}=>[1,3,2,4,6,7,5]=>101100
[1,3,2,4,7,5,6]=>{{1},{2,3},{4},{5,6,7}}=>[1,3,2,4,6,7,5]=>101100
[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}=>[1,3,2,4,7,6,5]=>101100
[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}=>[1,3,2,5,4,6,7]=>101011
[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}=>[1,3,2,5,4,7,6]=>101010
[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}=>[1,3,2,5,6,4,7]=>101001
[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}=>[1,3,2,5,6,7,4]=>101000
[1,3,2,5,7,4,6]=>{{1},{2,3},{4,5,6,7}}=>[1,3,2,5,6,7,4]=>101000
[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}=>[1,3,2,5,7,6,4]=>101000
[1,3,2,6,4,5,7]=>{{1},{2,3},{4,5,6},{7}}=>[1,3,2,5,6,4,7]=>101001
[1,3,2,6,4,7,5]=>{{1},{2,3},{4,5,6,7}}=>[1,3,2,5,6,7,4]=>101000
[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}=>[1,3,2,6,5,4,7]=>101001
[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}=>[1,3,2,6,5,7,4]=>101000
[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}=>[1,3,2,6,7,4,5]=>101000
[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}=>[1,3,2,5,6,7,4]=>101000
[1,3,2,7,4,5,6]=>{{1},{2,3},{4,5,6,7}}=>[1,3,2,5,6,7,4]=>101000
[1,3,2,7,4,6,5]=>{{1},{2,3},{4,5,7},{6}}=>[1,3,2,5,7,6,4]=>101000
[1,3,2,7,5,4,6]=>{{1},{2,3},{4,6,7},{5}}=>[1,3,2,6,5,7,4]=>101000
[1,3,2,7,5,6,4]=>{{1},{2,3},{4,7},{5},{6}}=>[1,3,2,7,5,6,4]=>101000
[1,3,2,7,6,4,5]=>{{1},{2,3},{4,5,6,7}}=>[1,3,2,5,6,7,4]=>101000
[1,3,2,7,6,5,4]=>{{1},{2,3},{4,7},{5,6}}=>[1,3,2,7,6,5,4]=>101000
[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}=>[1,3,4,2,5,6,7]=>100111
[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}=>[1,3,4,2,5,7,6]=>100110
[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}=>[1,3,4,2,6,5,7]=>100101
[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}=>[1,3,4,2,6,7,5]=>100100
[1,3,4,2,7,5,6]=>{{1},{2,3,4},{5,6,7}}=>[1,3,4,2,6,7,5]=>100100
[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}=>[1,3,4,2,7,6,5]=>100100
[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}=>[1,3,4,5,2,6,7]=>100011
[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>100010
[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,4,5,7,2,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,3,4,6,2,5,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,3,4,6,2,7,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}=>[1,3,4,6,5,2,7]=>100001
[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>100000
[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,4,7,2,5,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,4,7,2,6,5]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,3,4,7,5,2,6]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>100000
[1,3,4,7,6,2,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,4,7,6,5,2]=>{{1},{2,3,4,7},{5,6}}=>[1,3,4,7,6,5,2]=>100000
[1,3,5,2,4,6,7]=>{{1},{2,3,4,5},{6},{7}}=>[1,3,4,5,2,6,7]=>100011
[1,3,5,2,4,7,6]=>{{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>100010
[1,3,5,2,6,4,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,3,5,2,6,7,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,5,2,7,4,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,5,2,7,6,4]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}=>[1,3,5,4,2,6,7]=>100011
[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}=>[1,3,5,4,2,7,6]=>100010
[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}=>[1,3,5,4,6,2,7]=>100001
[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,3,5,4,7,2,6]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>100000
[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}=>[1,3,5,6,2,4,7]=>100001
[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}=>[1,3,5,6,2,7,4]=>100000
[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,5,6,7,2,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,5,6,7,4,2]=>{{1},{2,3,5,7},{4,6}}=>[1,3,5,6,7,4,2]=>100000
[1,3,5,7,2,4,6]=>{{1},{2,3,5},{4,6,7}}=>[1,3,5,6,2,7,4]=>100000
[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}=>[1,3,5,7,2,6,4]=>100000
[1,3,5,7,4,2,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}=>[1,3,5,7,6,2,4]=>100000
[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,6,2,4,5,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,3,6,2,4,7,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,6,2,5,4,7]=>{{1},{2,3,4,6},{5},{7}}=>[1,3,4,6,5,2,7]=>100001
[1,3,6,2,5,7,4]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,3,6,2,7,4,5]=>{{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>100000
[1,3,6,2,7,5,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,6,4,2,5,7]=>{{1},{2,3,5,6},{4},{7}}=>[1,3,5,4,6,2,7]=>100001
[1,3,6,4,2,7,5]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}=>[1,3,6,4,5,2,7]=>100001
[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}=>[1,3,6,4,5,7,2]=>100000
[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}=>[1,3,6,4,7,2,5]=>100000
[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,3,6,5,2,4,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,3,6,5,2,7,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,6,5,4,2,7]=>{{1},{2,3,6},{4,5},{7}}=>[1,3,6,5,4,2,7]=>100001
[1,3,6,5,4,7,2]=>{{1},{2,3,6,7},{4,5}}=>[1,3,6,5,4,7,2]=>100000
[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}=>[1,3,6,5,7,2,4]=>100000
[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,6,7,2,4,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,6,7,2,5,4]=>{{1},{2,3,5,6},{4,7}}=>[1,3,5,7,6,2,4]=>100000
[1,3,6,7,4,2,5]=>{{1},{2,3,6},{4,5,7}}=>[1,3,6,5,7,2,4]=>100000
[1,3,6,7,4,5,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}=>[1,3,6,7,5,2,4]=>100000
[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,3,7,2,4,5,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,7,2,4,6,5]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,3,7,2,5,4,6]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,3,7,2,5,6,4]=>{{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>100000
[1,3,7,2,6,4,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,7,2,6,5,4]=>{{1},{2,3,4,7},{5,6}}=>[1,3,4,7,6,5,2]=>100000
[1,3,7,4,2,5,6]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,3,7,4,2,6,5]=>{{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>100000
[1,3,7,4,5,2,6]=>{{1},{2,3,6,7},{4},{5}}=>[1,3,6,4,5,7,2]=>100000
[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}}=>[1,3,7,4,5,6,2]=>100000
[1,3,7,4,6,2,5]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,3,7,4,6,5,2]=>{{1},{2,3,7},{4},{5,6}}=>[1,3,7,4,6,5,2]=>100000
[1,3,7,5,2,4,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,7,5,2,6,4]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,3,7,5,4,2,6]=>{{1},{2,3,6,7},{4,5}}=>[1,3,6,5,4,7,2]=>100000
[1,3,7,5,4,6,2]=>{{1},{2,3,7},{4,5},{6}}=>[1,3,7,5,4,6,2]=>100000
[1,3,7,5,6,2,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,7,5,6,4,2]=>{{1},{2,3,7},{4,5,6}}=>[1,3,7,5,6,4,2]=>100000
[1,3,7,6,2,4,5]=>{{1},{2,3,5,7},{4,6}}=>[1,3,5,6,7,4,2]=>100000
[1,3,7,6,2,5,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,7,6,4,2,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,3,7,6,4,5,2]=>{{1},{2,3,7},{4,5,6}}=>[1,3,7,5,6,4,2]=>100000
[1,3,7,6,5,2,4]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,3,7,6,5,4,2]=>{{1},{2,3,7},{4,6},{5}}=>[1,3,7,6,5,4,2]=>100000
[1,4,2,3,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}=>[1,3,4,2,5,6,7]=>100111
[1,4,2,3,5,7,6]=>{{1},{2,3,4},{5},{6,7}}=>[1,3,4,2,5,7,6]=>100110
[1,4,2,3,6,5,7]=>{{1},{2,3,4},{5,6},{7}}=>[1,3,4,2,6,5,7]=>100101
[1,4,2,3,6,7,5]=>{{1},{2,3,4},{5,6,7}}=>[1,3,4,2,6,7,5]=>100100
[1,4,2,3,7,5,6]=>{{1},{2,3,4},{5,6,7}}=>[1,3,4,2,6,7,5]=>100100
[1,4,2,3,7,6,5]=>{{1},{2,3,4},{5,7},{6}}=>[1,3,4,2,7,6,5]=>100100
[1,4,2,5,3,6,7]=>{{1},{2,3,4,5},{6},{7}}=>[1,3,4,5,2,6,7]=>100011
[1,4,2,5,3,7,6]=>{{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>100010
[1,4,2,5,6,3,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,4,2,5,6,7,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,2,5,7,3,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,2,5,7,6,3]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,4,2,6,3,5,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,4,2,6,3,7,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,2,6,5,3,7]=>{{1},{2,3,4,6},{5},{7}}=>[1,3,4,6,5,2,7]=>100001
[1,4,2,6,5,7,3]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,4,2,6,7,3,5]=>{{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>100000
[1,4,2,6,7,5,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,2,7,3,5,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,2,7,3,6,5]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,4,2,7,5,3,6]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,4,2,7,5,6,3]=>{{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>100000
[1,4,2,7,6,3,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,2,7,6,5,3]=>{{1},{2,3,4,7},{5,6}}=>[1,3,4,7,6,5,2]=>100000
[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}=>[1,4,3,2,5,6,7]=>100111
[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}=>[1,4,3,2,5,7,6]=>100110
[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}=>[1,4,3,2,6,5,7]=>100101
[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}=>[1,4,3,2,6,7,5]=>100100
[1,4,3,2,7,5,6]=>{{1},{2,4},{3},{5,6,7}}=>[1,4,3,2,6,7,5]=>100100
[1,4,3,2,7,6,5]=>{{1},{2,4},{3},{5,7},{6}}=>[1,4,3,2,7,6,5]=>100100
[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}=>[1,4,3,5,2,6,7]=>100011
[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}=>[1,4,3,5,2,7,6]=>100010
[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}=>[1,4,3,5,6,2,7]=>100001
[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,4,3,5,7,2,6]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}=>[1,4,3,5,7,6,2]=>100000
[1,4,3,6,2,5,7]=>{{1},{2,4,5,6},{3},{7}}=>[1,4,3,5,6,2,7]=>100001
[1,4,3,6,2,7,5]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}=>[1,4,3,6,5,2,7]=>100001
[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}=>[1,4,3,6,5,7,2]=>100000
[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}=>[1,4,3,6,7,2,5]=>100000
[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,4,3,7,2,5,6]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,4,3,7,2,6,5]=>{{1},{2,4,5,7},{3},{6}}=>[1,4,3,5,7,6,2]=>100000
[1,4,3,7,5,2,6]=>{{1},{2,4,6,7},{3},{5}}=>[1,4,3,6,5,7,2]=>100000
[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}}=>[1,4,3,7,5,6,2]=>100000
[1,4,3,7,6,2,5]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,4,3,7,6,5,2]=>{{1},{2,4,7},{3},{5,6}}=>[1,4,3,7,6,5,2]=>100000
[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}=>[1,4,5,2,3,6,7]=>100011
[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}=>[1,4,5,2,3,7,6]=>100010
[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}=>[1,4,5,2,6,3,7]=>100001
[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}=>[1,4,5,2,6,7,3]=>100000
[1,4,5,2,7,3,6]=>{{1},{2,4},{3,5,6,7}}=>[1,4,5,2,6,7,3]=>100000
[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}=>[1,4,5,2,7,6,3]=>100000
[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}=>[1,3,4,5,2,6,7]=>100011
[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>100010
[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,5,3,7,2,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,4,5,6,2,3,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,4,5,6,2,7,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,5,6,3,2,7]=>{{1},{2,4,6},{3,5},{7}}=>[1,4,5,6,3,2,7]=>100001
[1,4,5,6,3,7,2]=>{{1},{2,4,6,7},{3,5}}=>[1,4,5,6,3,7,2]=>100000
[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}=>[1,4,5,6,7,2,3]=>100000
[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,5,7,2,3,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,5,7,2,6,3]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,4,5,7,3,2,6]=>{{1},{2,4,6,7},{3,5}}=>[1,4,5,6,3,7,2]=>100000
[1,4,5,7,3,6,2]=>{{1},{2,4,7},{3,5},{6}}=>[1,4,5,7,3,6,2]=>100000
[1,4,5,7,6,2,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,5,7,6,3,2]=>{{1},{2,4,7},{3,5,6}}=>[1,4,5,7,6,3,2]=>100000
[1,4,6,2,3,5,7]=>{{1},{2,4},{3,5,6},{7}}=>[1,4,5,2,6,3,7]=>100001
[1,4,6,2,3,7,5]=>{{1},{2,4},{3,5,6,7}}=>[1,4,5,2,6,7,3]=>100000
[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}=>[1,4,6,2,5,3,7]=>100001
[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}=>[1,4,6,2,5,7,3]=>100000
[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}=>[1,4,6,2,7,3,5]=>100000
[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}=>[1,4,5,2,6,7,3]=>100000
[1,4,6,3,2,5,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,4,6,3,2,7,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}=>[1,3,4,6,5,2,7]=>100001
[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>100000
[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}=>[1,4,6,5,2,3,7]=>100001
[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}=>[1,4,6,5,2,7,3]=>100000
[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,6,5,7,2,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,6,5,7,3,2]=>{{1},{2,4,5,7},{3,6}}=>[1,4,6,5,7,3,2]=>100000
[1,4,6,7,2,3,5]=>{{1},{2,4,5,7},{3,6}}=>[1,4,6,5,7,3,2]=>100000
[1,4,6,7,2,5,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,6,7,3,2,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,6,7,3,5,2]=>{{1},{2,4,7},{3,5,6}}=>[1,4,5,7,6,3,2]=>100000
[1,4,6,7,5,2,3]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,4,6,7,5,3,2]=>{{1},{2,4,7},{3,6},{5}}=>[1,4,6,7,5,3,2]=>100000
[1,4,7,2,3,5,6]=>{{1},{2,4},{3,5,6,7}}=>[1,4,5,2,6,7,3]=>100000
[1,4,7,2,3,6,5]=>{{1},{2,4},{3,5,7},{6}}=>[1,4,5,2,7,6,3]=>100000
[1,4,7,2,5,3,6]=>{{1},{2,4},{3,6,7},{5}}=>[1,4,6,2,5,7,3]=>100000
[1,4,7,2,5,6,3]=>{{1},{2,4},{3,7},{5},{6}}=>[1,4,7,2,5,6,3]=>100000
[1,4,7,2,6,3,5]=>{{1},{2,4},{3,5,6,7}}=>[1,4,5,2,6,7,3]=>100000
[1,4,7,2,6,5,3]=>{{1},{2,4},{3,7},{5,6}}=>[1,4,7,2,6,5,3]=>100000
[1,4,7,3,2,5,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,7,3,2,6,5]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,4,7,3,5,2,6]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,4,7,3,5,6,2]=>{{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>100000
[1,4,7,3,6,2,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,7,3,6,5,2]=>{{1},{2,3,4,7},{5,6}}=>[1,3,4,7,6,5,2]=>100000
[1,4,7,5,2,3,6]=>{{1},{2,4,5},{3,6,7}}=>[1,4,6,5,2,7,3]=>100000
[1,4,7,5,2,6,3]=>{{1},{2,4,5},{3,7},{6}}=>[1,4,7,5,2,6,3]=>100000
[1,4,7,5,3,2,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,7,5,3,6,2]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,4,7,5,6,2,3]=>{{1},{2,4,5,6},{3,7}}=>[1,4,7,5,6,2,3]=>100000
[1,4,7,5,6,3,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,7,6,2,3,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,7,6,2,5,3]=>{{1},{2,4,5,6},{3,7}}=>[1,4,7,5,6,2,3]=>100000
[1,4,7,6,3,2,5]=>{{1},{2,4,6},{3,5,7}}=>[1,4,5,6,7,2,3]=>100000
[1,4,7,6,3,5,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,4,7,6,5,2,3]=>{{1},{2,4,6},{3,7},{5}}=>[1,4,7,6,5,2,3]=>100000
[1,4,7,6,5,3,2]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,5,2,3,4,6,7]=>{{1},{2,3,4,5},{6},{7}}=>[1,3,4,5,2,6,7]=>100011
[1,5,2,3,4,7,6]=>{{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>100010
[1,5,2,3,6,4,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,5,2,3,6,7,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,2,3,7,4,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,2,3,7,6,4]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,5,2,4,3,6,7]=>{{1},{2,3,5},{4},{6},{7}}=>[1,3,5,4,2,6,7]=>100011
[1,5,2,4,3,7,6]=>{{1},{2,3,5},{4},{6,7}}=>[1,3,5,4,2,7,6]=>100010
[1,5,2,4,6,3,7]=>{{1},{2,3,5,6},{4},{7}}=>[1,3,5,4,6,2,7]=>100001
[1,5,2,4,6,7,3]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,5,2,4,7,3,6]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,5,2,4,7,6,3]=>{{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>100000
[1,5,2,6,3,4,7]=>{{1},{2,3,5},{4,6},{7}}=>[1,3,5,6,2,4,7]=>100001
[1,5,2,6,3,7,4]=>{{1},{2,3,5},{4,6,7}}=>[1,3,5,6,2,7,4]=>100000
[1,5,2,6,4,3,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,5,2,6,4,7,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,2,6,7,3,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,2,6,7,4,3]=>{{1},{2,3,5,7},{4,6}}=>[1,3,5,6,7,4,2]=>100000
[1,5,2,7,3,4,6]=>{{1},{2,3,5},{4,6,7}}=>[1,3,5,6,2,7,4]=>100000
[1,5,2,7,3,6,4]=>{{1},{2,3,5},{4,7},{6}}=>[1,3,5,7,2,6,4]=>100000
[1,5,2,7,4,3,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,2,7,4,6,3]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,5,2,7,6,3,4]=>{{1},{2,3,5,6},{4,7}}=>[1,3,5,7,6,2,4]=>100000
[1,5,2,7,6,4,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,3,2,4,6,7]=>{{1},{2,4,5},{3},{6},{7}}=>[1,4,3,5,2,6,7]=>100011
[1,5,3,2,4,7,6]=>{{1},{2,4,5},{3},{6,7}}=>[1,4,3,5,2,7,6]=>100010
[1,5,3,2,6,4,7]=>{{1},{2,4,5,6},{3},{7}}=>[1,4,3,5,6,2,7]=>100001
[1,5,3,2,6,7,4]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,5,3,2,7,4,6]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,5,3,2,7,6,4]=>{{1},{2,4,5,7},{3},{6}}=>[1,4,3,5,7,6,2]=>100000
[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}=>[1,5,3,4,2,6,7]=>100011
[1,5,3,4,2,7,6]=>{{1},{2,5},{3},{4},{6,7}}=>[1,5,3,4,2,7,6]=>100010
[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}=>[1,5,3,4,6,2,7]=>100001
[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}=>[1,5,3,4,6,7,2]=>100000
[1,5,3,4,7,2,6]=>{{1},{2,5,6,7},{3},{4}}=>[1,5,3,4,6,7,2]=>100000
[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}}=>[1,5,3,4,7,6,2]=>100000
[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}=>[1,5,3,6,2,4,7]=>100001
[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}=>[1,5,3,6,2,7,4]=>100000
[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}=>[1,4,3,5,6,2,7]=>100001
[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,5,3,6,7,2,4]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,5,3,6,7,4,2]=>{{1},{2,5,7},{3},{4,6}}=>[1,5,3,6,7,4,2]=>100000
[1,5,3,7,2,4,6]=>{{1},{2,5},{3},{4,6,7}}=>[1,5,3,6,2,7,4]=>100000
[1,5,3,7,2,6,4]=>{{1},{2,5},{3},{4,7},{6}}=>[1,5,3,7,2,6,4]=>100000
[1,5,3,7,4,2,6]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,5,3,7,4,6,2]=>{{1},{2,4,5,7},{3},{6}}=>[1,4,3,5,7,6,2]=>100000
[1,5,3,7,6,2,4]=>{{1},{2,5,6},{3},{4,7}}=>[1,5,3,7,6,2,4]=>100000
[1,5,3,7,6,4,2]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,5,4,2,3,6,7]=>{{1},{2,3,4,5},{6},{7}}=>[1,3,4,5,2,6,7]=>100011
[1,5,4,2,3,7,6]=>{{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>100010
[1,5,4,2,6,3,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,5,4,2,6,7,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,4,2,7,3,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,4,2,7,6,3]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,5,4,3,2,6,7]=>{{1},{2,5},{3,4},{6},{7}}=>[1,5,4,3,2,6,7]=>100011
[1,5,4,3,2,7,6]=>{{1},{2,5},{3,4},{6,7}}=>[1,5,4,3,2,7,6]=>100010
[1,5,4,3,6,2,7]=>{{1},{2,5,6},{3,4},{7}}=>[1,5,4,3,6,2,7]=>100001
[1,5,4,3,6,7,2]=>{{1},{2,5,6,7},{3,4}}=>[1,5,4,3,6,7,2]=>100000
[1,5,4,3,7,2,6]=>{{1},{2,5,6,7},{3,4}}=>[1,5,4,3,6,7,2]=>100000
[1,5,4,3,7,6,2]=>{{1},{2,5,7},{3,4},{6}}=>[1,5,4,3,7,6,2]=>100000
[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}=>[1,5,4,6,2,3,7]=>100001
[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>100000
[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,4,6,7,2,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,4,6,7,3,2]=>{{1},{2,5,7},{3,4,6}}=>[1,5,4,6,7,3,2]=>100000
[1,5,4,7,2,3,6]=>{{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>100000
[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}=>[1,5,4,7,2,6,3]=>100000
[1,5,4,7,3,2,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}=>[1,5,4,7,6,2,3]=>100000
[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,6,2,3,4,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,5,6,2,3,7,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,6,2,4,3,7]=>{{1},{2,4,5},{3,6},{7}}=>[1,4,6,5,2,3,7]=>100001
[1,5,6,2,4,7,3]=>{{1},{2,4,5},{3,6,7}}=>[1,4,6,5,2,7,3]=>100000
[1,5,6,2,7,3,4]=>{{1},{2,4,5,7},{3,6}}=>[1,4,6,5,7,3,2]=>100000
[1,5,6,2,7,4,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,6,3,2,4,7]=>{{1},{2,5},{3,4,6},{7}}=>[1,5,4,6,2,3,7]=>100001
[1,5,6,3,2,7,4]=>{{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>100000
[1,5,6,3,4,2,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,5,6,3,4,7,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,6,3,7,2,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,6,3,7,4,2]=>{{1},{2,5,7},{3,4,6}}=>[1,5,4,6,7,3,2]=>100000
[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}=>[1,5,6,4,2,3,7]=>100001
[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}=>[1,5,6,4,2,7,3]=>100000
[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}=>[1,3,5,4,6,2,7]=>100001
[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,5,6,4,7,2,3]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,5,6,4,7,3,2]=>{{1},{2,5,7},{3,6},{4}}=>[1,5,6,4,7,3,2]=>100000
[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}=>[1,5,6,7,2,3,4]=>100000
[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>100000
[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}=>[1,3,5,7,6,2,4]=>100000
[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,6,7,4,2,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,6,7,4,3,2]=>{{1},{2,4,5,7},{3,6}}=>[1,4,6,5,7,3,2]=>100000
[1,5,7,2,3,4,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,7,2,3,6,4]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,5,7,2,4,3,6]=>{{1},{2,4,5},{3,6,7}}=>[1,4,6,5,2,7,3]=>100000
[1,5,7,2,4,6,3]=>{{1},{2,4,5},{3,7},{6}}=>[1,4,7,5,2,6,3]=>100000
[1,5,7,2,6,3,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,7,2,6,4,3]=>{{1},{2,4,5,6},{3,7}}=>[1,4,7,5,6,2,3]=>100000
[1,5,7,3,2,4,6]=>{{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>100000
[1,5,7,3,2,6,4]=>{{1},{2,5},{3,4,7},{6}}=>[1,5,4,7,2,6,3]=>100000
[1,5,7,3,4,2,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,7,3,4,6,2]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,5,7,3,6,2,4]=>{{1},{2,5,6},{3,4,7}}=>[1,5,4,7,6,2,3]=>100000
[1,5,7,3,6,4,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,7,4,2,3,6]=>{{1},{2,5},{3,6,7},{4}}=>[1,5,6,4,2,7,3]=>100000
[1,5,7,4,2,6,3]=>{{1},{2,5},{3,7},{4},{6}}=>[1,5,7,4,2,6,3]=>100000
[1,5,7,4,3,2,6]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,5,7,4,3,6,2]=>{{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>100000
[1,5,7,4,6,2,3]=>{{1},{2,5,6},{3,7},{4}}=>[1,5,7,4,6,2,3]=>100000
[1,5,7,4,6,3,2]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,5,7,6,2,3,4]=>{{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>100000
[1,5,7,6,2,4,3]=>{{1},{2,5},{3,7},{4,6}}=>[1,5,7,6,2,4,3]=>100000
[1,5,7,6,3,2,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,5,7,6,3,4,2]=>{{1},{2,3,5,7},{4,6}}=>[1,3,5,6,7,4,2]=>100000
[1,5,7,6,4,2,3]=>{{1},{2,4,5,6},{3,7}}=>[1,4,7,5,6,2,3]=>100000
[1,5,7,6,4,3,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,2,3,4,5,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,6,2,3,4,7,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,2,3,5,4,7]=>{{1},{2,3,4,6},{5},{7}}=>[1,3,4,6,5,2,7]=>100001
[1,6,2,3,5,7,4]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,6,2,3,7,4,5]=>{{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>100000
[1,6,2,3,7,5,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,2,4,3,5,7]=>{{1},{2,3,5,6},{4},{7}}=>[1,3,5,4,6,2,7]=>100001
[1,6,2,4,3,7,5]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,6,2,4,5,3,7]=>{{1},{2,3,6},{4},{5},{7}}=>[1,3,6,4,5,2,7]=>100001
[1,6,2,4,5,7,3]=>{{1},{2,3,6,7},{4},{5}}=>[1,3,6,4,5,7,2]=>100000
[1,6,2,4,7,3,5]=>{{1},{2,3,6},{4},{5,7}}=>[1,3,6,4,7,2,5]=>100000
[1,6,2,4,7,5,3]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,6,2,5,3,4,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,6,2,5,3,7,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,2,5,4,3,7]=>{{1},{2,3,6},{4,5},{7}}=>[1,3,6,5,4,2,7]=>100001
[1,6,2,5,4,7,3]=>{{1},{2,3,6,7},{4,5}}=>[1,3,6,5,4,7,2]=>100000
[1,6,2,5,7,3,4]=>{{1},{2,3,6},{4,5,7}}=>[1,3,6,5,7,2,4]=>100000
[1,6,2,5,7,4,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,2,7,3,4,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,2,7,3,5,4]=>{{1},{2,3,5,6},{4,7}}=>[1,3,5,7,6,2,4]=>100000
[1,6,2,7,4,3,5]=>{{1},{2,3,6},{4,5,7}}=>[1,3,6,5,7,2,4]=>100000
[1,6,2,7,4,5,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,2,7,5,3,4]=>{{1},{2,3,6},{4,7},{5}}=>[1,3,6,7,5,2,4]=>100000
[1,6,2,7,5,4,3]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,6,3,2,4,5,7]=>{{1},{2,4,5,6},{3},{7}}=>[1,4,3,5,6,2,7]=>100001
[1,6,3,2,4,7,5]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,6,3,2,5,4,7]=>{{1},{2,4,6},{3},{5},{7}}=>[1,4,3,6,5,2,7]=>100001
[1,6,3,2,5,7,4]=>{{1},{2,4,6,7},{3},{5}}=>[1,4,3,6,5,7,2]=>100000
[1,6,3,2,7,4,5]=>{{1},{2,4,6},{3},{5,7}}=>[1,4,3,6,7,2,5]=>100000
[1,6,3,2,7,5,4]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,6,3,4,2,5,7]=>{{1},{2,5,6},{3},{4},{7}}=>[1,5,3,4,6,2,7]=>100001
[1,6,3,4,2,7,5]=>{{1},{2,5,6,7},{3},{4}}=>[1,5,3,4,6,7,2]=>100000
[1,6,3,4,5,2,7]=>{{1},{2,6},{3},{4},{5},{7}}=>[1,6,3,4,5,2,7]=>100001
[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}}=>[1,6,3,4,5,7,2]=>100000
[1,6,3,4,7,2,5]=>{{1},{2,6},{3},{4},{5,7}}=>[1,6,3,4,7,2,5]=>100000
[1,6,3,4,7,5,2]=>{{1},{2,5,6,7},{3},{4}}=>[1,5,3,4,6,7,2]=>100000
[1,6,3,5,2,4,7]=>{{1},{2,4,5,6},{3},{7}}=>[1,4,3,5,6,2,7]=>100001
[1,6,3,5,2,7,4]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,6,3,5,4,2,7]=>{{1},{2,6},{3},{4,5},{7}}=>[1,6,3,5,4,2,7]=>100001
[1,6,3,5,4,7,2]=>{{1},{2,6,7},{3},{4,5}}=>[1,6,3,5,4,7,2]=>100000
[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}=>[1,6,3,5,7,2,4]=>100000
[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,6,3,7,2,4,5]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,6,3,7,2,5,4]=>{{1},{2,5,6},{3},{4,7}}=>[1,5,3,7,6,2,4]=>100000
[1,6,3,7,4,2,5]=>{{1},{2,6},{3},{4,5,7}}=>[1,6,3,5,7,2,4]=>100000
[1,6,3,7,4,5,2]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,6,3,7,5,2,4]=>{{1},{2,6},{3},{4,7},{5}}=>[1,6,3,7,5,2,4]=>100000
[1,6,3,7,5,4,2]=>{{1},{2,4,6,7},{3},{5}}=>[1,4,3,6,5,7,2]=>100000
[1,6,4,2,3,5,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,6,4,2,3,7,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,4,2,5,3,7]=>{{1},{2,3,4,6},{5},{7}}=>[1,3,4,6,5,2,7]=>100001
[1,6,4,2,5,7,3]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,6,4,2,7,3,5]=>{{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>100000
[1,6,4,2,7,5,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,4,3,2,5,7]=>{{1},{2,5,6},{3,4},{7}}=>[1,5,4,3,6,2,7]=>100001
[1,6,4,3,2,7,5]=>{{1},{2,5,6,7},{3,4}}=>[1,5,4,3,6,7,2]=>100000
[1,6,4,3,5,2,7]=>{{1},{2,6},{3,4},{5},{7}}=>[1,6,4,3,5,2,7]=>100001
[1,6,4,3,5,7,2]=>{{1},{2,6,7},{3,4},{5}}=>[1,6,4,3,5,7,2]=>100000
[1,6,4,3,7,2,5]=>{{1},{2,6},{3,4},{5,7}}=>[1,6,4,3,7,2,5]=>100000
[1,6,4,3,7,5,2]=>{{1},{2,5,6,7},{3,4}}=>[1,5,4,3,6,7,2]=>100000
[1,6,4,5,2,3,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,6,4,5,2,7,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,4,5,3,2,7]=>{{1},{2,6},{3,4,5},{7}}=>[1,6,4,5,3,2,7]=>100001
[1,6,4,5,3,7,2]=>{{1},{2,6,7},{3,4,5}}=>[1,6,4,5,3,7,2]=>100000
[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>100000
[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,4,7,2,3,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,4,7,2,5,3]=>{{1},{2,5,6},{3,4,7}}=>[1,5,4,7,6,2,3]=>100000
[1,6,4,7,3,2,5]=>{{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>100000
[1,6,4,7,3,5,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}=>[1,6,4,7,5,2,3]=>100000
[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,6,5,2,3,4,7]=>{{1},{2,4,6},{3,5},{7}}=>[1,4,5,6,3,2,7]=>100001
[1,6,5,2,3,7,4]=>{{1},{2,4,6,7},{3,5}}=>[1,4,5,6,3,7,2]=>100000
[1,6,5,2,4,3,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,6,5,2,4,7,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,5,2,7,3,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,5,2,7,4,3]=>{{1},{2,4,6},{3,5,7}}=>[1,4,5,6,7,2,3]=>100000
[1,6,5,3,2,4,7]=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
[1,6,5,3,2,7,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,5,3,4,2,7]=>{{1},{2,6},{3,4,5},{7}}=>[1,6,4,5,3,2,7]=>100001
[1,6,5,3,4,7,2]=>{{1},{2,6,7},{3,4,5}}=>[1,6,4,5,3,7,2]=>100000
[1,6,5,3,7,2,4]=>{{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>100000
[1,6,5,3,7,4,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,5,4,2,3,7]=>{{1},{2,3,5,6},{4},{7}}=>[1,3,5,4,6,2,7]=>100001
[1,6,5,4,2,7,3]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,6,5,4,3,2,7]=>{{1},{2,6},{3,5},{4},{7}}=>[1,6,5,4,3,2,7]=>100001
[1,6,5,4,3,7,2]=>{{1},{2,6,7},{3,5},{4}}=>[1,6,5,4,3,7,2]=>100000
[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}=>[1,6,5,4,7,2,3]=>100000
[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,6,5,7,2,3,4]=>{{1},{2,3,5,6},{4,7}}=>[1,3,5,7,6,2,4]=>100000
[1,6,5,7,2,4,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,5,7,3,2,4]=>{{1},{2,6},{3,5},{4,7}}=>[1,6,5,7,3,2,4]=>100000
[1,6,5,7,3,4,2]=>{{1},{2,4,6,7},{3,5}}=>[1,4,5,6,3,7,2]=>100000
[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>100000
[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,7,2,3,4,5]=>{{1},{2,4,6},{3,5,7}}=>[1,4,5,6,7,2,3]=>100000
[1,6,7,2,3,5,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,7,2,4,3,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,7,2,4,5,3]=>{{1},{2,4,5,6},{3,7}}=>[1,4,7,5,6,2,3]=>100000
[1,6,7,2,5,3,4]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,6,7,2,5,4,3]=>{{1},{2,4,6},{3,7},{5}}=>[1,4,7,6,5,2,3]=>100000
[1,6,7,3,2,4,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,7,3,2,5,4]=>{{1},{2,5,6},{3,4,7}}=>[1,5,4,7,6,2,3]=>100000
[1,6,7,3,4,2,5]=>{{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>100000
[1,6,7,3,4,5,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,7,3,5,2,4]=>{{1},{2,6},{3,4,7},{5}}=>[1,6,4,7,5,2,3]=>100000
[1,6,7,3,5,4,2]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,6,7,4,2,3,5]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,6,7,4,2,5,3]=>{{1},{2,5,6},{3,7},{4}}=>[1,5,7,4,6,2,3]=>100000
[1,6,7,4,3,2,5]=>{{1},{2,6},{3,5,7},{4}}=>[1,6,5,4,7,2,3]=>100000
[1,6,7,4,3,5,2]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,6,7,4,5,2,3]=>{{1},{2,6},{3,7},{4},{5}}=>[1,6,7,4,5,2,3]=>100000
[1,6,7,4,5,3,2]=>{{1},{2,3,6,7},{4},{5}}=>[1,3,6,4,5,7,2]=>100000
[1,6,7,5,2,3,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,7,5,2,4,3]=>{{1},{2,4,5,6},{3,7}}=>[1,4,7,5,6,2,3]=>100000
[1,6,7,5,3,2,4]=>{{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>100000
[1,6,7,5,3,4,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,6,7,5,4,2,3]=>{{1},{2,6},{3,7},{4,5}}=>[1,6,7,5,4,2,3]=>100000
[1,6,7,5,4,3,2]=>{{1},{2,3,6,7},{4,5}}=>[1,3,6,5,4,7,2]=>100000
[1,7,2,3,4,5,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,2,3,4,6,5]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,7,2,3,5,4,6]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,7,2,3,5,6,4]=>{{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>100000
[1,7,2,3,6,4,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,2,3,6,5,4]=>{{1},{2,3,4,7},{5,6}}=>[1,3,4,7,6,5,2]=>100000
[1,7,2,4,3,5,6]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,7,2,4,3,6,5]=>{{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>100000
[1,7,2,4,5,3,6]=>{{1},{2,3,6,7},{4},{5}}=>[1,3,6,4,5,7,2]=>100000
[1,7,2,4,5,6,3]=>{{1},{2,3,7},{4},{5},{6}}=>[1,3,7,4,5,6,2]=>100000
[1,7,2,4,6,3,5]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,7,2,4,6,5,3]=>{{1},{2,3,7},{4},{5,6}}=>[1,3,7,4,6,5,2]=>100000
[1,7,2,5,3,4,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,2,5,3,6,4]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,7,2,5,4,3,6]=>{{1},{2,3,6,7},{4,5}}=>[1,3,6,5,4,7,2]=>100000
[1,7,2,5,4,6,3]=>{{1},{2,3,7},{4,5},{6}}=>[1,3,7,5,4,6,2]=>100000
[1,7,2,5,6,3,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,2,5,6,4,3]=>{{1},{2,3,7},{4,5,6}}=>[1,3,7,5,6,4,2]=>100000
[1,7,2,6,3,4,5]=>{{1},{2,3,5,7},{4,6}}=>[1,3,5,6,7,4,2]=>100000
[1,7,2,6,3,5,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,2,6,4,3,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,2,6,4,5,3]=>{{1},{2,3,7},{4,5,6}}=>[1,3,7,5,6,4,2]=>100000
[1,7,2,6,5,3,4]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,7,2,6,5,4,3]=>{{1},{2,3,7},{4,6},{5}}=>[1,3,7,6,5,4,2]=>100000
[1,7,3,2,4,5,6]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,7,3,2,4,6,5]=>{{1},{2,4,5,7},{3},{6}}=>[1,4,3,5,7,6,2]=>100000
[1,7,3,2,5,4,6]=>{{1},{2,4,6,7},{3},{5}}=>[1,4,3,6,5,7,2]=>100000
[1,7,3,2,5,6,4]=>{{1},{2,4,7},{3},{5},{6}}=>[1,4,3,7,5,6,2]=>100000
[1,7,3,2,6,4,5]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,7,3,2,6,5,4]=>{{1},{2,4,7},{3},{5,6}}=>[1,4,3,7,6,5,2]=>100000
[1,7,3,4,2,5,6]=>{{1},{2,5,6,7},{3},{4}}=>[1,5,3,4,6,7,2]=>100000
[1,7,3,4,2,6,5]=>{{1},{2,5,7},{3},{4},{6}}=>[1,5,3,4,7,6,2]=>100000
[1,7,3,4,5,2,6]=>{{1},{2,6,7},{3},{4},{5}}=>[1,6,3,4,5,7,2]=>100000
[1,7,3,4,5,6,2]=>{{1},{2,7},{3},{4},{5},{6}}=>[1,7,3,4,5,6,2]=>100000
[1,7,3,4,6,2,5]=>{{1},{2,5,6,7},{3},{4}}=>[1,5,3,4,6,7,2]=>100000
[1,7,3,4,6,5,2]=>{{1},{2,7},{3},{4},{5,6}}=>[1,7,3,4,6,5,2]=>100000
[1,7,3,5,2,4,6]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,7,3,5,2,6,4]=>{{1},{2,4,5,7},{3},{6}}=>[1,4,3,5,7,6,2]=>100000
[1,7,3,5,4,2,6]=>{{1},{2,6,7},{3},{4,5}}=>[1,6,3,5,4,7,2]=>100000
[1,7,3,5,4,6,2]=>{{1},{2,7},{3},{4,5},{6}}=>[1,7,3,5,4,6,2]=>100000
[1,7,3,5,6,2,4]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,7,3,5,6,4,2]=>{{1},{2,7},{3},{4,5,6}}=>[1,7,3,5,6,4,2]=>100000
[1,7,3,6,2,4,5]=>{{1},{2,5,7},{3},{4,6}}=>[1,5,3,6,7,4,2]=>100000
[1,7,3,6,2,5,4]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,7,3,6,4,2,5]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
[1,7,3,6,4,5,2]=>{{1},{2,7},{3},{4,5,6}}=>[1,7,3,5,6,4,2]=>100000
[1,7,3,6,5,2,4]=>{{1},{2,4,6,7},{3},{5}}=>[1,4,3,6,5,7,2]=>100000
[1,7,3,6,5,4,2]=>{{1},{2,7},{3},{4,6},{5}}=>[1,7,3,6,5,4,2]=>100000
[1,7,4,2,3,5,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,4,2,3,6,5]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,7,4,2,5,3,6]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,7,4,2,5,6,3]=>{{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>100000
[1,7,4,2,6,3,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,4,2,6,5,3]=>{{1},{2,3,4,7},{5,6}}=>[1,3,4,7,6,5,2]=>100000
[1,7,4,3,2,5,6]=>{{1},{2,5,6,7},{3,4}}=>[1,5,4,3,6,7,2]=>100000
[1,7,4,3,2,6,5]=>{{1},{2,5,7},{3,4},{6}}=>[1,5,4,3,7,6,2]=>100000
[1,7,4,3,5,2,6]=>{{1},{2,6,7},{3,4},{5}}=>[1,6,4,3,5,7,2]=>100000
[1,7,4,3,5,6,2]=>{{1},{2,7},{3,4},{5},{6}}=>[1,7,4,3,5,6,2]=>100000
[1,7,4,3,6,2,5]=>{{1},{2,5,6,7},{3,4}}=>[1,5,4,3,6,7,2]=>100000
[1,7,4,3,6,5,2]=>{{1},{2,7},{3,4},{5,6}}=>[1,7,4,3,6,5,2]=>100000
[1,7,4,5,2,3,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,4,5,2,6,3]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,7,4,5,3,2,6]=>{{1},{2,6,7},{3,4,5}}=>[1,6,4,5,3,7,2]=>100000
[1,7,4,5,3,6,2]=>{{1},{2,7},{3,4,5},{6}}=>[1,7,4,5,3,6,2]=>100000
[1,7,4,5,6,2,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,4,5,6,3,2]=>{{1},{2,7},{3,4,5,6}}=>[1,7,4,5,6,3,2]=>100000
[1,7,4,6,2,3,5]=>{{1},{2,5,7},{3,4,6}}=>[1,5,4,6,7,3,2]=>100000
[1,7,4,6,2,5,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,4,6,3,2,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,4,6,3,5,2]=>{{1},{2,7},{3,4,5,6}}=>[1,7,4,5,6,3,2]=>100000
[1,7,4,6,5,2,3]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,7,4,6,5,3,2]=>{{1},{2,7},{3,4,6},{5}}=>[1,7,4,6,5,3,2]=>100000
[1,7,5,2,3,4,6]=>{{1},{2,4,6,7},{3,5}}=>[1,4,5,6,3,7,2]=>100000
[1,7,5,2,3,6,4]=>{{1},{2,4,7},{3,5},{6}}=>[1,4,5,7,3,6,2]=>100000
[1,7,5,2,4,3,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,5,2,4,6,3]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,7,5,2,6,3,4]=>{{1},{2,4,7},{3,5,6}}=>[1,4,5,7,6,3,2]=>100000
[1,7,5,2,6,4,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,5,3,2,4,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,5,3,2,6,4]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
[1,7,5,3,4,2,6]=>{{1},{2,6,7},{3,4,5}}=>[1,6,4,5,3,7,2]=>100000
[1,7,5,3,4,6,2]=>{{1},{2,7},{3,4,5},{6}}=>[1,7,4,5,3,6,2]=>100000
[1,7,5,3,6,2,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,5,3,6,4,2]=>{{1},{2,7},{3,4,5,6}}=>[1,7,4,5,6,3,2]=>100000
[1,7,5,4,2,3,6]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,7,5,4,2,6,3]=>{{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>100000
[1,7,5,4,3,2,6]=>{{1},{2,6,7},{3,5},{4}}=>[1,6,5,4,3,7,2]=>100000
[1,7,5,4,3,6,2]=>{{1},{2,7},{3,5},{4},{6}}=>[1,7,5,4,3,6,2]=>100000
[1,7,5,4,6,2,3]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,7,5,4,6,3,2]=>{{1},{2,7},{3,5,6},{4}}=>[1,7,5,4,6,3,2]=>100000
[1,7,5,6,2,3,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,5,6,2,4,3]=>{{1},{2,3,5,7},{4,6}}=>[1,3,5,6,7,4,2]=>100000
[1,7,5,6,3,2,4]=>{{1},{2,4,6,7},{3,5}}=>[1,4,5,6,3,7,2]=>100000
[1,7,5,6,3,4,2]=>{{1},{2,7},{3,5},{4,6}}=>[1,7,5,6,3,4,2]=>100000
[1,7,5,6,4,2,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,5,6,4,3,2]=>{{1},{2,7},{3,4,5,6}}=>[1,7,4,5,6,3,2]=>100000
[1,7,6,2,3,4,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,6,2,3,5,4]=>{{1},{2,4,7},{3,5,6}}=>[1,4,5,7,6,3,2]=>100000
[1,7,6,2,4,3,5]=>{{1},{2,4,5,7},{3,6}}=>[1,4,6,5,7,3,2]=>100000
[1,7,6,2,4,5,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,6,2,5,3,4]=>{{1},{2,4,7},{3,6},{5}}=>[1,4,6,7,5,3,2]=>100000
[1,7,6,2,5,4,3]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,7,6,3,2,4,5]=>{{1},{2,5,7},{3,4,6}}=>[1,5,4,6,7,3,2]=>100000
[1,7,6,3,2,5,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,6,3,4,2,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,6,3,4,5,2]=>{{1},{2,7},{3,4,5,6}}=>[1,7,4,5,6,3,2]=>100000
[1,7,6,3,5,2,4]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
[1,7,6,3,5,4,2]=>{{1},{2,7},{3,4,6},{5}}=>[1,7,4,6,5,3,2]=>100000
[1,7,6,4,2,3,5]=>{{1},{2,5,7},{3,6},{4}}=>[1,5,6,4,7,3,2]=>100000
[1,7,6,4,2,5,3]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,7,6,4,3,2,5]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
[1,7,6,4,3,5,2]=>{{1},{2,7},{3,5,6},{4}}=>[1,7,5,4,6,3,2]=>100000
[1,7,6,4,5,2,3]=>{{1},{2,3,6,7},{4},{5}}=>[1,3,6,4,5,7,2]=>100000
[1,7,6,4,5,3,2]=>{{1},{2,7},{3,6},{4},{5}}=>[1,7,6,4,5,3,2]=>100000
[1,7,6,5,2,3,4]=>{{1},{2,4,5,7},{3,6}}=>[1,4,6,5,7,3,2]=>100000
[1,7,6,5,2,4,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,6,5,3,2,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
[1,7,6,5,3,4,2]=>{{1},{2,7},{3,4,5,6}}=>[1,7,4,5,6,3,2]=>100000
[1,7,6,5,4,2,3]=>{{1},{2,3,6,7},{4,5}}=>[1,3,6,5,4,7,2]=>100000
[1,7,6,5,4,3,2]=>{{1},{2,7},{3,6},{4,5}}=>[1,7,6,5,4,3,2]=>100000
[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}}=>[2,1,3,4,5,6,7]=>011111
[2,1,3,4,5,7,6]=>{{1,2},{3},{4},{5},{6,7}}=>[2,1,3,4,5,7,6]=>011110
[2,1,3,4,6,5,7]=>{{1,2},{3},{4},{5,6},{7}}=>[2,1,3,4,6,5,7]=>011101
[2,1,3,4,6,7,5]=>{{1,2},{3},{4},{5,6,7}}=>[2,1,3,4,6,7,5]=>011100
[2,1,3,4,7,5,6]=>{{1,2},{3},{4},{5,6,7}}=>[2,1,3,4,6,7,5]=>011100
[2,1,3,4,7,6,5]=>{{1,2},{3},{4},{5,7},{6}}=>[2,1,3,4,7,6,5]=>011100
[2,1,3,5,4,6,7]=>{{1,2},{3},{4,5},{6},{7}}=>[2,1,3,5,4,6,7]=>011011
[2,1,3,5,4,7,6]=>{{1,2},{3},{4,5},{6,7}}=>[2,1,3,5,4,7,6]=>011010
[2,1,3,5,6,4,7]=>{{1,2},{3},{4,5,6},{7}}=>[2,1,3,5,6,4,7]=>011001
[2,1,3,5,6,7,4]=>{{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>011000
[2,1,3,5,7,4,6]=>{{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>011000
[2,1,3,5,7,6,4]=>{{1,2},{3},{4,5,7},{6}}=>[2,1,3,5,7,6,4]=>011000
[2,1,3,6,4,5,7]=>{{1,2},{3},{4,5,6},{7}}=>[2,1,3,5,6,4,7]=>011001
[2,1,3,6,4,7,5]=>{{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>011000
[2,1,3,6,5,4,7]=>{{1,2},{3},{4,6},{5},{7}}=>[2,1,3,6,5,4,7]=>011001
[2,1,3,6,5,7,4]=>{{1,2},{3},{4,6,7},{5}}=>[2,1,3,6,5,7,4]=>011000
[2,1,3,6,7,4,5]=>{{1,2},{3},{4,6},{5,7}}=>[2,1,3,6,7,4,5]=>011000
[2,1,3,6,7,5,4]=>{{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>011000
[2,1,3,7,4,5,6]=>{{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>011000
[2,1,3,7,4,6,5]=>{{1,2},{3},{4,5,7},{6}}=>[2,1,3,5,7,6,4]=>011000
[2,1,3,7,5,4,6]=>{{1,2},{3},{4,6,7},{5}}=>[2,1,3,6,5,7,4]=>011000
[2,1,3,7,5,6,4]=>{{1,2},{3},{4,7},{5},{6}}=>[2,1,3,7,5,6,4]=>011000
[2,1,3,7,6,4,5]=>{{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>011000
[2,1,3,7,6,5,4]=>{{1,2},{3},{4,7},{5,6}}=>[2,1,3,7,6,5,4]=>011000
[2,1,4,3,5,6,7]=>{{1,2},{3,4},{5},{6},{7}}=>[2,1,4,3,5,6,7]=>010111
[2,1,4,3,5,7,6]=>{{1,2},{3,4},{5},{6,7}}=>[2,1,4,3,5,7,6]=>010110
[2,1,4,3,6,5,7]=>{{1,2},{3,4},{5,6},{7}}=>[2,1,4,3,6,5,7]=>010101
[2,1,4,3,6,7,5]=>{{1,2},{3,4},{5,6,7}}=>[2,1,4,3,6,7,5]=>010100
[2,1,4,3,7,5,6]=>{{1,2},{3,4},{5,6,7}}=>[2,1,4,3,6,7,5]=>010100
[2,1,4,3,7,6,5]=>{{1,2},{3,4},{5,7},{6}}=>[2,1,4,3,7,6,5]=>010100
[2,1,4,5,3,6,7]=>{{1,2},{3,4,5},{6},{7}}=>[2,1,4,5,3,6,7]=>010011
[2,1,4,5,3,7,6]=>{{1,2},{3,4,5},{6,7}}=>[2,1,4,5,3,7,6]=>010010
[2,1,4,5,6,3,7]=>{{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>010001
[2,1,4,5,6,7,3]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,4,5,7,3,6]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,4,5,7,6,3]=>{{1,2},{3,4,5,7},{6}}=>[2,1,4,5,7,6,3]=>010000
[2,1,4,6,3,5,7]=>{{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>010001
[2,1,4,6,3,7,5]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,4,6,5,3,7]=>{{1,2},{3,4,6},{5},{7}}=>[2,1,4,6,5,3,7]=>010001
[2,1,4,6,5,7,3]=>{{1,2},{3,4,6,7},{5}}=>[2,1,4,6,5,7,3]=>010000
[2,1,4,6,7,3,5]=>{{1,2},{3,4,6},{5,7}}=>[2,1,4,6,7,3,5]=>010000
[2,1,4,6,7,5,3]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,4,7,3,5,6]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,4,7,3,6,5]=>{{1,2},{3,4,5,7},{6}}=>[2,1,4,5,7,6,3]=>010000
[2,1,4,7,5,3,6]=>{{1,2},{3,4,6,7},{5}}=>[2,1,4,6,5,7,3]=>010000
[2,1,4,7,5,6,3]=>{{1,2},{3,4,7},{5},{6}}=>[2,1,4,7,5,6,3]=>010000
[2,1,4,7,6,3,5]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,4,7,6,5,3]=>{{1,2},{3,4,7},{5,6}}=>[2,1,4,7,6,5,3]=>010000
[2,1,5,3,4,6,7]=>{{1,2},{3,4,5},{6},{7}}=>[2,1,4,5,3,6,7]=>010011
[2,1,5,3,4,7,6]=>{{1,2},{3,4,5},{6,7}}=>[2,1,4,5,3,7,6]=>010010
[2,1,5,3,6,4,7]=>{{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>010001
[2,1,5,3,6,7,4]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,5,3,7,4,6]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,5,3,7,6,4]=>{{1,2},{3,4,5,7},{6}}=>[2,1,4,5,7,6,3]=>010000
[2,1,5,4,3,6,7]=>{{1,2},{3,5},{4},{6},{7}}=>[2,1,5,4,3,6,7]=>010011
[2,1,5,4,3,7,6]=>{{1,2},{3,5},{4},{6,7}}=>[2,1,5,4,3,7,6]=>010010
[2,1,5,4,6,3,7]=>{{1,2},{3,5,6},{4},{7}}=>[2,1,5,4,6,3,7]=>010001
[2,1,5,4,6,7,3]=>{{1,2},{3,5,6,7},{4}}=>[2,1,5,4,6,7,3]=>010000
[2,1,5,4,7,3,6]=>{{1,2},{3,5,6,7},{4}}=>[2,1,5,4,6,7,3]=>010000
[2,1,5,4,7,6,3]=>{{1,2},{3,5,7},{4},{6}}=>[2,1,5,4,7,6,3]=>010000
[2,1,5,6,3,4,7]=>{{1,2},{3,5},{4,6},{7}}=>[2,1,5,6,3,4,7]=>010001
[2,1,5,6,3,7,4]=>{{1,2},{3,5},{4,6,7}}=>[2,1,5,6,3,7,4]=>010000
[2,1,5,6,4,3,7]=>{{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>010001
[2,1,5,6,4,7,3]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,5,6,7,3,4]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,5,6,7,4,3]=>{{1,2},{3,5,7},{4,6}}=>[2,1,5,6,7,4,3]=>010000
[2,1,5,7,3,4,6]=>{{1,2},{3,5},{4,6,7}}=>[2,1,5,6,3,7,4]=>010000
[2,1,5,7,3,6,4]=>{{1,2},{3,5},{4,7},{6}}=>[2,1,5,7,3,6,4]=>010000
[2,1,5,7,4,3,6]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,5,7,4,6,3]=>{{1,2},{3,4,5,7},{6}}=>[2,1,4,5,7,6,3]=>010000
[2,1,5,7,6,3,4]=>{{1,2},{3,5,6},{4,7}}=>[2,1,5,7,6,3,4]=>010000
[2,1,5,7,6,4,3]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,6,3,4,5,7]=>{{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>010001
[2,1,6,3,4,7,5]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,6,3,5,4,7]=>{{1,2},{3,4,6},{5},{7}}=>[2,1,4,6,5,3,7]=>010001
[2,1,6,3,5,7,4]=>{{1,2},{3,4,6,7},{5}}=>[2,1,4,6,5,7,3]=>010000
[2,1,6,3,7,4,5]=>{{1,2},{3,4,6},{5,7}}=>[2,1,4,6,7,3,5]=>010000
[2,1,6,3,7,5,4]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,6,4,3,5,7]=>{{1,2},{3,5,6},{4},{7}}=>[2,1,5,4,6,3,7]=>010001
[2,1,6,4,3,7,5]=>{{1,2},{3,5,6,7},{4}}=>[2,1,5,4,6,7,3]=>010000
[2,1,6,4,5,3,7]=>{{1,2},{3,6},{4},{5},{7}}=>[2,1,6,4,5,3,7]=>010001
[2,1,6,4,5,7,3]=>{{1,2},{3,6,7},{4},{5}}=>[2,1,6,4,5,7,3]=>010000
[2,1,6,4,7,3,5]=>{{1,2},{3,6},{4},{5,7}}=>[2,1,6,4,7,3,5]=>010000
[2,1,6,4,7,5,3]=>{{1,2},{3,5,6,7},{4}}=>[2,1,5,4,6,7,3]=>010000
[2,1,6,5,3,4,7]=>{{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>010001
[2,1,6,5,3,7,4]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,6,5,4,3,7]=>{{1,2},{3,6},{4,5},{7}}=>[2,1,6,5,4,3,7]=>010001
[2,1,6,5,4,7,3]=>{{1,2},{3,6,7},{4,5}}=>[2,1,6,5,4,7,3]=>010000
[2,1,6,5,7,3,4]=>{{1,2},{3,6},{4,5,7}}=>[2,1,6,5,7,3,4]=>010000
[2,1,6,5,7,4,3]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,6,7,3,4,5]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,6,7,3,5,4]=>{{1,2},{3,5,6},{4,7}}=>[2,1,5,7,6,3,4]=>010000
[2,1,6,7,4,3,5]=>{{1,2},{3,6},{4,5,7}}=>[2,1,6,5,7,3,4]=>010000
[2,1,6,7,4,5,3]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,6,7,5,3,4]=>{{1,2},{3,6},{4,7},{5}}=>[2,1,6,7,5,3,4]=>010000
[2,1,6,7,5,4,3]=>{{1,2},{3,4,6,7},{5}}=>[2,1,4,6,5,7,3]=>010000
[2,1,7,3,4,5,6]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,7,3,4,6,5]=>{{1,2},{3,4,5,7},{6}}=>[2,1,4,5,7,6,3]=>010000
[2,1,7,3,5,4,6]=>{{1,2},{3,4,6,7},{5}}=>[2,1,4,6,5,7,3]=>010000
[2,1,7,3,5,6,4]=>{{1,2},{3,4,7},{5},{6}}=>[2,1,4,7,5,6,3]=>010000
[2,1,7,3,6,4,5]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,7,3,6,5,4]=>{{1,2},{3,4,7},{5,6}}=>[2,1,4,7,6,5,3]=>010000
[2,1,7,4,3,5,6]=>{{1,2},{3,5,6,7},{4}}=>[2,1,5,4,6,7,3]=>010000
[2,1,7,4,3,6,5]=>{{1,2},{3,5,7},{4},{6}}=>[2,1,5,4,7,6,3]=>010000
[2,1,7,4,5,3,6]=>{{1,2},{3,6,7},{4},{5}}=>[2,1,6,4,5,7,3]=>010000
[2,1,7,4,5,6,3]=>{{1,2},{3,7},{4},{5},{6}}=>[2,1,7,4,5,6,3]=>010000
[2,1,7,4,6,3,5]=>{{1,2},{3,5,6,7},{4}}=>[2,1,5,4,6,7,3]=>010000
[2,1,7,4,6,5,3]=>{{1,2},{3,7},{4},{5,6}}=>[2,1,7,4,6,5,3]=>010000
[2,1,7,5,3,4,6]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,7,5,3,6,4]=>{{1,2},{3,4,5,7},{6}}=>[2,1,4,5,7,6,3]=>010000
[2,1,7,5,4,3,6]=>{{1,2},{3,6,7},{4,5}}=>[2,1,6,5,4,7,3]=>010000
[2,1,7,5,4,6,3]=>{{1,2},{3,7},{4,5},{6}}=>[2,1,7,5,4,6,3]=>010000
[2,1,7,5,6,3,4]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,7,5,6,4,3]=>{{1,2},{3,7},{4,5,6}}=>[2,1,7,5,6,4,3]=>010000
[2,1,7,6,3,4,5]=>{{1,2},{3,5,7},{4,6}}=>[2,1,5,6,7,4,3]=>010000
[2,1,7,6,3,5,4]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,7,6,4,3,5]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
[2,1,7,6,4,5,3]=>{{1,2},{3,7},{4,5,6}}=>[2,1,7,5,6,4,3]=>010000
[2,1,7,6,5,3,4]=>{{1,2},{3,4,6,7},{5}}=>[2,1,4,6,5,7,3]=>010000
[2,1,7,6,5,4,3]=>{{1,2},{3,7},{4,6},{5}}=>[2,1,7,6,5,4,3]=>010000
[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}=>[2,3,1,4,5,6,7]=>001111
[2,3,1,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}=>[2,3,1,4,5,7,6]=>001110
[2,3,1,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}}=>[2,3,1,4,6,5,7]=>001101
[2,3,1,4,6,7,5]=>{{1,2,3},{4},{5,6,7}}=>[2,3,1,4,6,7,5]=>001100
[2,3,1,4,7,5,6]=>{{1,2,3},{4},{5,6,7}}=>[2,3,1,4,6,7,5]=>001100
[2,3,1,4,7,6,5]=>{{1,2,3},{4},{5,7},{6}}=>[2,3,1,4,7,6,5]=>001100
[2,3,1,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}}=>[2,3,1,5,4,6,7]=>001011
[2,3,1,5,4,7,6]=>{{1,2,3},{4,5},{6,7}}=>[2,3,1,5,4,7,6]=>001010
[2,3,1,5,6,4,7]=>{{1,2,3},{4,5,6},{7}}=>[2,3,1,5,6,4,7]=>001001
[2,3,1,5,6,7,4]=>{{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000
[2,3,1,5,7,4,6]=>{{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000
[2,3,1,5,7,6,4]=>{{1,2,3},{4,5,7},{6}}=>[2,3,1,5,7,6,4]=>001000
[2,3,1,6,4,5,7]=>{{1,2,3},{4,5,6},{7}}=>[2,3,1,5,6,4,7]=>001001
[2,3,1,6,4,7,5]=>{{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000
[2,3,1,6,5,4,7]=>{{1,2,3},{4,6},{5},{7}}=>[2,3,1,6,5,4,7]=>001001
[2,3,1,6,5,7,4]=>{{1,2,3},{4,6,7},{5}}=>[2,3,1,6,5,7,4]=>001000
[2,3,1,6,7,4,5]=>{{1,2,3},{4,6},{5,7}}=>[2,3,1,6,7,4,5]=>001000
[2,3,1,6,7,5,4]=>{{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000
[2,3,1,7,4,5,6]=>{{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000
[2,3,1,7,4,6,5]=>{{1,2,3},{4,5,7},{6}}=>[2,3,1,5,7,6,4]=>001000
[2,3,1,7,5,4,6]=>{{1,2,3},{4,6,7},{5}}=>[2,3,1,6,5,7,4]=>001000
[2,3,1,7,5,6,4]=>{{1,2,3},{4,7},{5},{6}}=>[2,3,1,7,5,6,4]=>001000
[2,3,1,7,6,4,5]=>{{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000
[2,3,1,7,6,5,4]=>{{1,2,3},{4,7},{5,6}}=>[2,3,1,7,6,5,4]=>001000
[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>000111
[2,3,4,1,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>000110
[2,3,4,1,6,5,7]=>{{1,2,3,4},{5,6},{7}}=>[2,3,4,1,6,5,7]=>000101
[2,3,4,1,6,7,5]=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100
[2,3,4,1,7,5,6]=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100
[2,3,4,1,7,6,5]=>{{1,2,3,4},{5,7},{6}}=>[2,3,4,1,7,6,5]=>000100
[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[2,3,4,5,1,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,4,5,7,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,3,4,6,1,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,4,6,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[2,3,4,6,5,7,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,3,4,6,7,1,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[2,3,4,6,7,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,4,7,1,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,3,4,7,5,1,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,3,4,7,5,6,1]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[2,3,4,7,6,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,4,7,6,5,1]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[2,3,5,1,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[2,3,5,1,4,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[2,3,5,1,6,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,5,1,7,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,3,5,4,1,6,7]=>{{1,2,3,5},{4},{6},{7}}=>[2,3,5,4,1,6,7]=>000011
[2,3,5,4,1,7,6]=>{{1,2,3,5},{4},{6,7}}=>[2,3,5,4,1,7,6]=>000010
[2,3,5,4,6,1,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[2,3,5,4,6,7,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,3,5,4,7,1,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,3,5,4,7,6,1]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[2,3,5,6,1,4,7]=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>000001
[2,3,5,6,1,7,4]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000
[2,3,5,6,4,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,3,5,6,4,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,5,6,7,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,5,6,7,4,1]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[2,3,5,7,1,4,6]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000
[2,3,5,7,1,6,4]=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>000000
[2,3,5,7,4,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,5,7,4,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,3,5,7,6,1,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[2,3,5,7,6,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,6,1,4,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,3,6,1,4,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,6,1,5,4,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[2,3,6,1,5,7,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,3,6,1,7,4,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[2,3,6,1,7,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,6,4,1,5,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[2,3,6,4,1,7,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,3,6,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>000001
[2,3,6,4,5,7,1]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[2,3,6,4,7,1,5]=>{{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>000000
[2,3,6,4,7,5,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,3,6,5,1,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,3,6,5,1,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,6,5,4,1,7]=>{{1,2,3,6},{4,5},{7}}=>[2,3,6,5,4,1,7]=>000001
[2,3,6,5,4,7,1]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[2,3,6,5,7,1,4]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000
[2,3,6,5,7,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,6,7,1,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,6,7,1,5,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[2,3,6,7,4,1,5]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000
[2,3,6,7,4,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,6,7,5,1,4]=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>000000
[2,3,6,7,5,4,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,3,7,1,4,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,7,1,4,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,3,7,1,5,4,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,3,7,1,5,6,4]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[2,3,7,1,6,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,7,1,6,5,4]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[2,3,7,4,1,5,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,3,7,4,1,6,5]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[2,3,7,4,5,1,6]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[2,3,7,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}}=>[2,3,7,4,5,6,1]=>000000
[2,3,7,4,6,1,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,3,7,4,6,5,1]=>{{1,2,3,7},{4},{5,6}}=>[2,3,7,4,6,5,1]=>000000
[2,3,7,5,1,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,7,5,1,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,3,7,5,4,1,6]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[2,3,7,5,4,6,1]=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>000000
[2,3,7,5,6,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,7,5,6,4,1]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000
[2,3,7,6,1,4,5]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[2,3,7,6,1,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,7,6,4,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,3,7,6,4,5,1]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000
[2,3,7,6,5,1,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,3,7,6,5,4,1]=>{{1,2,3,7},{4,6},{5}}=>[2,3,7,6,5,4,1]=>000000
[2,4,1,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>000111
[2,4,1,3,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>000110
[2,4,1,3,6,5,7]=>{{1,2,3,4},{5,6},{7}}=>[2,3,4,1,6,5,7]=>000101
[2,4,1,3,6,7,5]=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100
[2,4,1,3,7,5,6]=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100
[2,4,1,3,7,6,5]=>{{1,2,3,4},{5,7},{6}}=>[2,3,4,1,7,6,5]=>000100
[2,4,1,5,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[2,4,1,5,3,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[2,4,1,5,6,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,1,5,7,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,4,1,6,3,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,1,6,5,3,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[2,4,1,6,5,7,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,4,1,6,7,3,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[2,4,1,6,7,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,1,7,3,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,4,1,7,5,3,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,4,1,7,5,6,3]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,1,7,6,5,3]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[2,4,3,1,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}=>[2,4,3,1,5,6,7]=>000111
[2,4,3,1,5,7,6]=>{{1,2,4},{3},{5},{6,7}}=>[2,4,3,1,5,7,6]=>000110
[2,4,3,1,6,5,7]=>{{1,2,4},{3},{5,6},{7}}=>[2,4,3,1,6,5,7]=>000101
[2,4,3,1,6,7,5]=>{{1,2,4},{3},{5,6,7}}=>[2,4,3,1,6,7,5]=>000100
[2,4,3,1,7,5,6]=>{{1,2,4},{3},{5,6,7}}=>[2,4,3,1,6,7,5]=>000100
[2,4,3,1,7,6,5]=>{{1,2,4},{3},{5,7},{6}}=>[2,4,3,1,7,6,5]=>000100
[2,4,3,5,1,6,7]=>{{1,2,4,5},{3},{6},{7}}=>[2,4,3,5,1,6,7]=>000011
[2,4,3,5,1,7,6]=>{{1,2,4,5},{3},{6,7}}=>[2,4,3,5,1,7,6]=>000010
[2,4,3,5,6,1,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[2,4,3,5,6,7,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,4,3,5,7,1,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,4,3,5,7,6,1]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[2,4,3,6,1,5,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[2,4,3,6,1,7,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,4,3,6,5,1,7]=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>000001
[2,4,3,6,5,7,1]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[2,4,3,6,7,1,5]=>{{1,2,4,6},{3},{5,7}}=>[2,4,3,6,7,1,5]=>000000
[2,4,3,6,7,5,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,4,3,7,1,5,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,4,3,7,1,6,5]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[2,4,3,7,5,1,6]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[2,4,3,7,5,6,1]=>{{1,2,4,7},{3},{5},{6}}=>[2,4,3,7,5,6,1]=>000000
[2,4,3,7,6,1,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,4,3,7,6,5,1]=>{{1,2,4,7},{3},{5,6}}=>[2,4,3,7,6,5,1]=>000000
[2,4,5,1,3,6,7]=>{{1,2,4},{3,5},{6},{7}}=>[2,4,5,1,3,6,7]=>000011
[2,4,5,1,3,7,6]=>{{1,2,4},{3,5},{6,7}}=>[2,4,5,1,3,7,6]=>000010
[2,4,5,1,6,3,7]=>{{1,2,4},{3,5,6},{7}}=>[2,4,5,1,6,3,7]=>000001
[2,4,5,1,6,7,3]=>{{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000
[2,4,5,1,7,3,6]=>{{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000
[2,4,5,1,7,6,3]=>{{1,2,4},{3,5,7},{6}}=>[2,4,5,1,7,6,3]=>000000
[2,4,5,3,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[2,4,5,3,1,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[2,4,5,3,6,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,4,5,3,6,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,5,3,7,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,5,3,7,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,4,5,6,1,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,4,5,6,1,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,5,6,3,1,7]=>{{1,2,4,6},{3,5},{7}}=>[2,4,5,6,3,1,7]=>000001
[2,4,5,6,3,7,1]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[2,4,5,6,7,1,3]=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000
[2,4,5,6,7,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,5,7,1,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,5,7,1,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,4,5,7,3,1,6]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[2,4,5,7,3,6,1]=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>000000
[2,4,5,7,6,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,5,7,6,3,1]=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000
[2,4,6,1,3,5,7]=>{{1,2,4},{3,5,6},{7}}=>[2,4,5,1,6,3,7]=>000001
[2,4,6,1,3,7,5]=>{{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000
[2,4,6,1,5,3,7]=>{{1,2,4},{3,6},{5},{7}}=>[2,4,6,1,5,3,7]=>000001
[2,4,6,1,5,7,3]=>{{1,2,4},{3,6,7},{5}}=>[2,4,6,1,5,7,3]=>000000
[2,4,6,1,7,3,5]=>{{1,2,4},{3,6},{5,7}}=>[2,4,6,1,7,3,5]=>000000
[2,4,6,1,7,5,3]=>{{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000
[2,4,6,3,1,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,4,6,3,1,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,6,3,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[2,4,6,3,5,7,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,4,6,3,7,1,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[2,4,6,3,7,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,6,5,1,3,7]=>{{1,2,4,5},{3,6},{7}}=>[2,4,6,5,1,3,7]=>000001
[2,4,6,5,1,7,3]=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000
[2,4,6,5,3,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,4,6,5,3,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,6,5,7,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,6,5,7,3,1]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[2,4,6,7,1,3,5]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[2,4,6,7,1,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,6,7,3,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,6,7,3,5,1]=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000
[2,4,6,7,5,1,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,4,6,7,5,3,1]=>{{1,2,4,7},{3,6},{5}}=>[2,4,6,7,5,3,1]=>000000
[2,4,7,1,3,5,6]=>{{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000
[2,4,7,1,3,6,5]=>{{1,2,4},{3,5,7},{6}}=>[2,4,5,1,7,6,3]=>000000
[2,4,7,1,5,3,6]=>{{1,2,4},{3,6,7},{5}}=>[2,4,6,1,5,7,3]=>000000
[2,4,7,1,5,6,3]=>{{1,2,4},{3,7},{5},{6}}=>[2,4,7,1,5,6,3]=>000000
[2,4,7,1,6,3,5]=>{{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000
[2,4,7,1,6,5,3]=>{{1,2,4},{3,7},{5,6}}=>[2,4,7,1,6,5,3]=>000000
[2,4,7,3,1,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,7,3,1,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,4,7,3,5,1,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,4,7,3,5,6,1]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[2,4,7,3,6,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,7,3,6,5,1]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[2,4,7,5,1,3,6]=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000
[2,4,7,5,1,6,3]=>{{1,2,4,5},{3,7},{6}}=>[2,4,7,5,1,6,3]=>000000
[2,4,7,5,3,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,7,5,3,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,4,7,5,6,1,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[2,4,7,5,6,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,7,6,1,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,7,6,1,5,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[2,4,7,6,3,1,5]=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000
[2,4,7,6,3,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,4,7,6,5,1,3]=>{{1,2,4,6},{3,7},{5}}=>[2,4,7,6,5,1,3]=>000000
[2,4,7,6,5,3,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,5,1,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[2,5,1,3,4,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[2,5,1,3,6,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,5,1,3,6,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,1,3,7,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,1,3,7,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,5,1,4,3,6,7]=>{{1,2,3,5},{4},{6},{7}}=>[2,3,5,4,1,6,7]=>000011
[2,5,1,4,3,7,6]=>{{1,2,3,5},{4},{6,7}}=>[2,3,5,4,1,7,6]=>000010
[2,5,1,4,6,3,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[2,5,1,4,6,7,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,5,1,4,7,3,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,5,1,4,7,6,3]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[2,5,1,6,3,4,7]=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>000001
[2,5,1,6,3,7,4]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000
[2,5,1,6,4,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,5,1,6,4,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,1,6,7,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,1,6,7,4,3]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[2,5,1,7,3,4,6]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000
[2,5,1,7,3,6,4]=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>000000
[2,5,1,7,4,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,1,7,4,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,5,1,7,6,3,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[2,5,1,7,6,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,3,1,4,6,7]=>{{1,2,4,5},{3},{6},{7}}=>[2,4,3,5,1,6,7]=>000011
[2,5,3,1,4,7,6]=>{{1,2,4,5},{3},{6,7}}=>[2,4,3,5,1,7,6]=>000010
[2,5,3,1,6,4,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[2,5,3,1,6,7,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,5,3,1,7,4,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,5,3,1,7,6,4]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[2,5,3,4,1,6,7]=>{{1,2,5},{3},{4},{6},{7}}=>[2,5,3,4,1,6,7]=>000011
[2,5,3,4,1,7,6]=>{{1,2,5},{3},{4},{6,7}}=>[2,5,3,4,1,7,6]=>000010
[2,5,3,4,6,1,7]=>{{1,2,5,6},{3},{4},{7}}=>[2,5,3,4,6,1,7]=>000001
[2,5,3,4,6,7,1]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[2,5,3,4,7,1,6]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[2,5,3,4,7,6,1]=>{{1,2,5,7},{3},{4},{6}}=>[2,5,3,4,7,6,1]=>000000
[2,5,3,6,1,4,7]=>{{1,2,5},{3},{4,6},{7}}=>[2,5,3,6,1,4,7]=>000001
[2,5,3,6,1,7,4]=>{{1,2,5},{3},{4,6,7}}=>[2,5,3,6,1,7,4]=>000000
[2,5,3,6,4,1,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[2,5,3,6,4,7,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,5,3,6,7,1,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,5,3,6,7,4,1]=>{{1,2,5,7},{3},{4,6}}=>[2,5,3,6,7,4,1]=>000000
[2,5,3,7,1,4,6]=>{{1,2,5},{3},{4,6,7}}=>[2,5,3,6,1,7,4]=>000000
[2,5,3,7,1,6,4]=>{{1,2,5},{3},{4,7},{6}}=>[2,5,3,7,1,6,4]=>000000
[2,5,3,7,4,1,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,5,3,7,4,6,1]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[2,5,3,7,6,1,4]=>{{1,2,5,6},{3},{4,7}}=>[2,5,3,7,6,1,4]=>000000
[2,5,3,7,6,4,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,5,4,1,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[2,5,4,1,3,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[2,5,4,1,6,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,5,4,1,6,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,4,1,7,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,5,4,3,1,6,7]=>{{1,2,5},{3,4},{6},{7}}=>[2,5,4,3,1,6,7]=>000011
[2,5,4,3,1,7,6]=>{{1,2,5},{3,4},{6,7}}=>[2,5,4,3,1,7,6]=>000010
[2,5,4,3,6,1,7]=>{{1,2,5,6},{3,4},{7}}=>[2,5,4,3,6,1,7]=>000001
[2,5,4,3,6,7,1]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[2,5,4,3,7,1,6]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[2,5,4,3,7,6,1]=>{{1,2,5,7},{3,4},{6}}=>[2,5,4,3,7,6,1]=>000000
[2,5,4,6,1,3,7]=>{{1,2,5},{3,4,6},{7}}=>[2,5,4,6,1,3,7]=>000001
[2,5,4,6,1,7,3]=>{{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000
[2,5,4,6,3,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,5,4,6,3,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,4,6,7,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,4,6,7,3,1]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000
[2,5,4,7,1,3,6]=>{{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000
[2,5,4,7,1,6,3]=>{{1,2,5},{3,4,7},{6}}=>[2,5,4,7,1,6,3]=>000000
[2,5,4,7,3,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,4,7,3,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,5,4,7,6,1,3]=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000
[2,5,4,7,6,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,6,1,3,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,5,6,1,3,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,6,1,4,3,7]=>{{1,2,4,5},{3,6},{7}}=>[2,4,6,5,1,3,7]=>000001
[2,5,6,1,4,7,3]=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000
[2,5,6,1,7,3,4]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[2,5,6,1,7,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,6,3,1,4,7]=>{{1,2,5},{3,4,6},{7}}=>[2,5,4,6,1,3,7]=>000001
[2,5,6,3,1,7,4]=>{{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000
[2,5,6,3,4,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,5,6,3,4,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,6,3,7,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,6,3,7,4,1]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000
[2,5,6,4,1,3,7]=>{{1,2,5},{3,6},{4},{7}}=>[2,5,6,4,1,3,7]=>000001
[2,5,6,4,1,7,3]=>{{1,2,5},{3,6,7},{4}}=>[2,5,6,4,1,7,3]=>000000
[2,5,6,4,3,1,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[2,5,6,4,3,7,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,5,6,4,7,1,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,5,6,4,7,3,1]=>{{1,2,5,7},{3,6},{4}}=>[2,5,6,4,7,3,1]=>000000
[2,5,6,7,1,3,4]=>{{1,2,5},{3,6},{4,7}}=>[2,5,6,7,1,3,4]=>000000
[2,5,6,7,1,4,3]=>{{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000
[2,5,6,7,3,1,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[2,5,6,7,3,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,6,7,4,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,6,7,4,3,1]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[2,5,7,1,3,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,7,1,3,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,5,7,1,4,3,6]=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000
[2,5,7,1,4,6,3]=>{{1,2,4,5},{3,7},{6}}=>[2,4,7,5,1,6,3]=>000000
[2,5,7,1,6,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,7,1,6,4,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[2,5,7,3,1,4,6]=>{{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000
[2,5,7,3,1,6,4]=>{{1,2,5},{3,4,7},{6}}=>[2,5,4,7,1,6,3]=>000000
[2,5,7,3,4,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,7,3,4,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,5,7,3,6,1,4]=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000
[2,5,7,3,6,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,7,4,1,3,6]=>{{1,2,5},{3,6,7},{4}}=>[2,5,6,4,1,7,3]=>000000
[2,5,7,4,1,6,3]=>{{1,2,5},{3,7},{4},{6}}=>[2,5,7,4,1,6,3]=>000000
[2,5,7,4,3,1,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,5,7,4,3,6,1]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[2,5,7,4,6,1,3]=>{{1,2,5,6},{3,7},{4}}=>[2,5,7,4,6,1,3]=>000000
[2,5,7,4,6,3,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,5,7,6,1,3,4]=>{{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000
[2,5,7,6,1,4,3]=>{{1,2,5},{3,7},{4,6}}=>[2,5,7,6,1,4,3]=>000000
[2,5,7,6,3,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,5,7,6,3,4,1]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[2,5,7,6,4,1,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[2,5,7,6,4,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,1,3,4,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,6,1,3,4,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,1,3,5,4,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[2,6,1,3,5,7,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,6,1,3,7,4,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[2,6,1,3,7,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,1,4,3,5,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[2,6,1,4,3,7,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,6,1,4,5,3,7]=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>000001
[2,6,1,4,5,7,3]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[2,6,1,4,7,3,5]=>{{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>000000
[2,6,1,4,7,5,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,6,1,5,3,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,6,1,5,3,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,1,5,4,3,7]=>{{1,2,3,6},{4,5},{7}}=>[2,3,6,5,4,1,7]=>000001
[2,6,1,5,4,7,3]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[2,6,1,5,7,3,4]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000
[2,6,1,5,7,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,1,7,3,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,1,7,3,5,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[2,6,1,7,4,3,5]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000
[2,6,1,7,4,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,1,7,5,3,4]=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>000000
[2,6,1,7,5,4,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,6,3,1,4,5,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[2,6,3,1,4,7,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,6,3,1,5,4,7]=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>000001
[2,6,3,1,5,7,4]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[2,6,3,1,7,4,5]=>{{1,2,4,6},{3},{5,7}}=>[2,4,3,6,7,1,5]=>000000
[2,6,3,1,7,5,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,6,3,4,1,5,7]=>{{1,2,5,6},{3},{4},{7}}=>[2,5,3,4,6,1,7]=>000001
[2,6,3,4,1,7,5]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[2,6,3,4,5,1,7]=>{{1,2,6},{3},{4},{5},{7}}=>[2,6,3,4,5,1,7]=>000001
[2,6,3,4,5,7,1]=>{{1,2,6,7},{3},{4},{5}}=>[2,6,3,4,5,7,1]=>000000
[2,6,3,4,7,1,5]=>{{1,2,6},{3},{4},{5,7}}=>[2,6,3,4,7,1,5]=>000000
[2,6,3,4,7,5,1]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[2,6,3,5,1,4,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[2,6,3,5,1,7,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,6,3,5,4,1,7]=>{{1,2,6},{3},{4,5},{7}}=>[2,6,3,5,4,1,7]=>000001
[2,6,3,5,4,7,1]=>{{1,2,6,7},{3},{4,5}}=>[2,6,3,5,4,7,1]=>000000
[2,6,3,5,7,1,4]=>{{1,2,6},{3},{4,5,7}}=>[2,6,3,5,7,1,4]=>000000
[2,6,3,5,7,4,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,6,3,7,1,4,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,6,3,7,1,5,4]=>{{1,2,5,6},{3},{4,7}}=>[2,5,3,7,6,1,4]=>000000
[2,6,3,7,4,1,5]=>{{1,2,6},{3},{4,5,7}}=>[2,6,3,5,7,1,4]=>000000
[2,6,3,7,4,5,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,6,3,7,5,1,4]=>{{1,2,6},{3},{4,7},{5}}=>[2,6,3,7,5,1,4]=>000000
[2,6,3,7,5,4,1]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[2,6,4,1,3,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,6,4,1,3,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,4,1,5,3,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[2,6,4,1,5,7,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,6,4,1,7,3,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[2,6,4,1,7,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,4,3,1,5,7]=>{{1,2,5,6},{3,4},{7}}=>[2,5,4,3,6,1,7]=>000001
[2,6,4,3,1,7,5]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[2,6,4,3,5,1,7]=>{{1,2,6},{3,4},{5},{7}}=>[2,6,4,3,5,1,7]=>000001
[2,6,4,3,5,7,1]=>{{1,2,6,7},{3,4},{5}}=>[2,6,4,3,5,7,1]=>000000
[2,6,4,3,7,1,5]=>{{1,2,6},{3,4},{5,7}}=>[2,6,4,3,7,1,5]=>000000
[2,6,4,3,7,5,1]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[2,6,4,5,1,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,6,4,5,1,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,4,5,3,1,7]=>{{1,2,6},{3,4,5},{7}}=>[2,6,4,5,3,1,7]=>000001
[2,6,4,5,3,7,1]=>{{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000
[2,6,4,5,7,1,3]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000
[2,6,4,5,7,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,4,7,1,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,4,7,1,5,3]=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000
[2,6,4,7,3,1,5]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000
[2,6,4,7,3,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,4,7,5,1,3]=>{{1,2,6},{3,4,7},{5}}=>[2,6,4,7,5,1,3]=>000000
[2,6,4,7,5,3,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,6,5,1,3,4,7]=>{{1,2,4,6},{3,5},{7}}=>[2,4,5,6,3,1,7]=>000001
[2,6,5,1,3,7,4]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[2,6,5,1,4,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,6,5,1,4,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,5,1,7,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,5,1,7,4,3]=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000
[2,6,5,3,1,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[2,6,5,3,1,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,5,3,4,1,7]=>{{1,2,6},{3,4,5},{7}}=>[2,6,4,5,3,1,7]=>000001
[2,6,5,3,4,7,1]=>{{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000
[2,6,5,3,7,1,4]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000
[2,6,5,3,7,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,5,4,1,3,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[2,6,5,4,1,7,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,6,5,4,3,1,7]=>{{1,2,6},{3,5},{4},{7}}=>[2,6,5,4,3,1,7]=>000001
[2,6,5,4,3,7,1]=>{{1,2,6,7},{3,5},{4}}=>[2,6,5,4,3,7,1]=>000000
[2,6,5,4,7,1,3]=>{{1,2,6},{3,5,7},{4}}=>[2,6,5,4,7,1,3]=>000000
[2,6,5,4,7,3,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,6,5,7,1,3,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[2,6,5,7,1,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,5,7,3,1,4]=>{{1,2,6},{3,5},{4,7}}=>[2,6,5,7,3,1,4]=>000000
[2,6,5,7,3,4,1]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[2,6,5,7,4,1,3]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000
[2,6,5,7,4,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,7,1,3,4,5]=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000
[2,6,7,1,3,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,7,1,4,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,7,1,4,5,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[2,6,7,1,5,3,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,6,7,1,5,4,3]=>{{1,2,4,6},{3,7},{5}}=>[2,4,7,6,5,1,3]=>000000
[2,6,7,3,1,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,7,3,1,5,4]=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000
[2,6,7,3,4,1,5]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000
[2,6,7,3,4,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,7,3,5,1,4]=>{{1,2,6},{3,4,7},{5}}=>[2,6,4,7,5,1,3]=>000000
[2,6,7,3,5,4,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,6,7,4,1,3,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,6,7,4,1,5,3]=>{{1,2,5,6},{3,7},{4}}=>[2,5,7,4,6,1,3]=>000000
[2,6,7,4,3,1,5]=>{{1,2,6},{3,5,7},{4}}=>[2,6,5,4,7,1,3]=>000000
[2,6,7,4,3,5,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,6,7,4,5,1,3]=>{{1,2,6},{3,7},{4},{5}}=>[2,6,7,4,5,1,3]=>000000
[2,6,7,4,5,3,1]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[2,6,7,5,1,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,7,5,1,4,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[2,6,7,5,3,1,4]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000
[2,6,7,5,3,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,6,7,5,4,1,3]=>{{1,2,6},{3,7},{4,5}}=>[2,6,7,5,4,1,3]=>000000
[2,6,7,5,4,3,1]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[2,7,1,3,4,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,1,3,4,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,7,1,3,5,4,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,7,1,3,5,6,4]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[2,7,1,3,6,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,1,3,6,5,4]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[2,7,1,4,3,5,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,7,1,4,3,6,5]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[2,7,1,4,5,3,6]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[2,7,1,4,5,6,3]=>{{1,2,3,7},{4},{5},{6}}=>[2,3,7,4,5,6,1]=>000000
[2,7,1,4,6,3,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,7,1,4,6,5,3]=>{{1,2,3,7},{4},{5,6}}=>[2,3,7,4,6,5,1]=>000000
[2,7,1,5,3,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,1,5,3,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,7,1,5,4,3,6]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[2,7,1,5,4,6,3]=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>000000
[2,7,1,5,6,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,1,5,6,4,3]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000
[2,7,1,6,3,4,5]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[2,7,1,6,3,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,1,6,4,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,1,6,4,5,3]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000
[2,7,1,6,5,3,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,7,1,6,5,4,3]=>{{1,2,3,7},{4,6},{5}}=>[2,3,7,6,5,4,1]=>000000
[2,7,3,1,4,5,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,7,3,1,4,6,5]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[2,7,3,1,5,4,6]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[2,7,3,1,5,6,4]=>{{1,2,4,7},{3},{5},{6}}=>[2,4,3,7,5,6,1]=>000000
[2,7,3,1,6,4,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,7,3,1,6,5,4]=>{{1,2,4,7},{3},{5,6}}=>[2,4,3,7,6,5,1]=>000000
[2,7,3,4,1,5,6]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[2,7,3,4,1,6,5]=>{{1,2,5,7},{3},{4},{6}}=>[2,5,3,4,7,6,1]=>000000
[2,7,3,4,5,1,6]=>{{1,2,6,7},{3},{4},{5}}=>[2,6,3,4,5,7,1]=>000000
[2,7,3,4,5,6,1]=>{{1,2,7},{3},{4},{5},{6}}=>[2,7,3,4,5,6,1]=>000000
[2,7,3,4,6,1,5]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[2,7,3,4,6,5,1]=>{{1,2,7},{3},{4},{5,6}}=>[2,7,3,4,6,5,1]=>000000
[2,7,3,5,1,4,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,7,3,5,1,6,4]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[2,7,3,5,4,1,6]=>{{1,2,6,7},{3},{4,5}}=>[2,6,3,5,4,7,1]=>000000
[2,7,3,5,4,6,1]=>{{1,2,7},{3},{4,5},{6}}=>[2,7,3,5,4,6,1]=>000000
[2,7,3,5,6,1,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,7,3,5,6,4,1]=>{{1,2,7},{3},{4,5,6}}=>[2,7,3,5,6,4,1]=>000000
[2,7,3,6,1,4,5]=>{{1,2,5,7},{3},{4,6}}=>[2,5,3,6,7,4,1]=>000000
[2,7,3,6,1,5,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,7,3,6,4,1,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[2,7,3,6,4,5,1]=>{{1,2,7},{3},{4,5,6}}=>[2,7,3,5,6,4,1]=>000000
[2,7,3,6,5,1,4]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[2,7,3,6,5,4,1]=>{{1,2,7},{3},{4,6},{5}}=>[2,7,3,6,5,4,1]=>000000
[2,7,4,1,3,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,4,1,3,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,7,4,1,5,3,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,7,4,1,5,6,3]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[2,7,4,1,6,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,4,1,6,5,3]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[2,7,4,3,1,5,6]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[2,7,4,3,1,6,5]=>{{1,2,5,7},{3,4},{6}}=>[2,5,4,3,7,6,1]=>000000
[2,7,4,3,5,1,6]=>{{1,2,6,7},{3,4},{5}}=>[2,6,4,3,5,7,1]=>000000
[2,7,4,3,5,6,1]=>{{1,2,7},{3,4},{5},{6}}=>[2,7,4,3,5,6,1]=>000000
[2,7,4,3,6,1,5]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[2,7,4,3,6,5,1]=>{{1,2,7},{3,4},{5,6}}=>[2,7,4,3,6,5,1]=>000000
[2,7,4,5,1,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,4,5,1,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,7,4,5,3,1,6]=>{{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000
[2,7,4,5,3,6,1]=>{{1,2,7},{3,4,5},{6}}=>[2,7,4,5,3,6,1]=>000000
[2,7,4,5,6,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,4,5,6,3,1]=>{{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000
[2,7,4,6,1,3,5]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000
[2,7,4,6,1,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,4,6,3,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,4,6,3,5,1]=>{{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000
[2,7,4,6,5,1,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,7,4,6,5,3,1]=>{{1,2,7},{3,4,6},{5}}=>[2,7,4,6,5,3,1]=>000000
[2,7,5,1,3,4,6]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[2,7,5,1,3,6,4]=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>000000
[2,7,5,1,4,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,5,1,4,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,7,5,1,6,3,4]=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000
[2,7,5,1,6,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,5,3,1,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,5,3,1,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[2,7,5,3,4,1,6]=>{{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000
[2,7,5,3,4,6,1]=>{{1,2,7},{3,4,5},{6}}=>[2,7,4,5,3,6,1]=>000000
[2,7,5,3,6,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,5,3,6,4,1]=>{{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000
[2,7,5,4,1,3,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,7,5,4,1,6,3]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[2,7,5,4,3,1,6]=>{{1,2,6,7},{3,5},{4}}=>[2,6,5,4,3,7,1]=>000000
[2,7,5,4,3,6,1]=>{{1,2,7},{3,5},{4},{6}}=>[2,7,5,4,3,6,1]=>000000
[2,7,5,4,6,1,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,7,5,4,6,3,1]=>{{1,2,7},{3,5,6},{4}}=>[2,7,5,4,6,3,1]=>000000
[2,7,5,6,1,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,5,6,1,4,3]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[2,7,5,6,3,1,4]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[2,7,5,6,3,4,1]=>{{1,2,7},{3,5},{4,6}}=>[2,7,5,6,3,4,1]=>000000
[2,7,5,6,4,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,5,6,4,3,1]=>{{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000
[2,7,6,1,3,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,6,1,3,5,4]=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000
[2,7,6,1,4,3,5]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[2,7,6,1,4,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,6,1,5,3,4]=>{{1,2,4,7},{3,6},{5}}=>[2,4,6,7,5,3,1]=>000000
[2,7,6,1,5,4,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,7,6,3,1,4,5]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000
[2,7,6,3,1,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,6,3,4,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,6,3,4,5,1]=>{{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000
[2,7,6,3,5,1,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[2,7,6,3,5,4,1]=>{{1,2,7},{3,4,6},{5}}=>[2,7,4,6,5,3,1]=>000000
[2,7,6,4,1,3,5]=>{{1,2,5,7},{3,6},{4}}=>[2,5,6,4,7,3,1]=>000000
[2,7,6,4,1,5,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,7,6,4,3,1,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[2,7,6,4,3,5,1]=>{{1,2,7},{3,5,6},{4}}=>[2,7,5,4,6,3,1]=>000000
[2,7,6,4,5,1,3]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[2,7,6,4,5,3,1]=>{{1,2,7},{3,6},{4},{5}}=>[2,7,6,4,5,3,1]=>000000
[2,7,6,5,1,3,4]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[2,7,6,5,1,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,6,5,3,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[2,7,6,5,3,4,1]=>{{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000
[2,7,6,5,4,1,3]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[2,7,6,5,4,3,1]=>{{1,2,7},{3,6},{4,5}}=>[2,7,6,5,4,3,1]=>000000
[3,1,2,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}=>[2,3,1,4,5,6,7]=>001111
[3,1,2,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}=>[2,3,1,4,5,7,6]=>001110
[3,1,2,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}}=>[2,3,1,4,6,5,7]=>001101
[3,1,2,4,6,7,5]=>{{1,2,3},{4},{5,6,7}}=>[2,3,1,4,6,7,5]=>001100
[3,1,2,4,7,5,6]=>{{1,2,3},{4},{5,6,7}}=>[2,3,1,4,6,7,5]=>001100
[3,1,2,4,7,6,5]=>{{1,2,3},{4},{5,7},{6}}=>[2,3,1,4,7,6,5]=>001100
[3,1,2,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}}=>[2,3,1,5,4,6,7]=>001011
[3,1,2,5,4,7,6]=>{{1,2,3},{4,5},{6,7}}=>[2,3,1,5,4,7,6]=>001010
[3,1,2,5,6,4,7]=>{{1,2,3},{4,5,6},{7}}=>[2,3,1,5,6,4,7]=>001001
[3,1,2,5,6,7,4]=>{{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000
[3,1,2,5,7,4,6]=>{{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000
[3,1,2,5,7,6,4]=>{{1,2,3},{4,5,7},{6}}=>[2,3,1,5,7,6,4]=>001000
[3,1,2,6,4,5,7]=>{{1,2,3},{4,5,6},{7}}=>[2,3,1,5,6,4,7]=>001001
[3,1,2,6,4,7,5]=>{{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000
[3,1,2,6,5,4,7]=>{{1,2,3},{4,6},{5},{7}}=>[2,3,1,6,5,4,7]=>001001
[3,1,2,6,5,7,4]=>{{1,2,3},{4,6,7},{5}}=>[2,3,1,6,5,7,4]=>001000
[3,1,2,6,7,4,5]=>{{1,2,3},{4,6},{5,7}}=>[2,3,1,6,7,4,5]=>001000
[3,1,2,6,7,5,4]=>{{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000
[3,1,2,7,4,5,6]=>{{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000
[3,1,2,7,4,6,5]=>{{1,2,3},{4,5,7},{6}}=>[2,3,1,5,7,6,4]=>001000
[3,1,2,7,5,4,6]=>{{1,2,3},{4,6,7},{5}}=>[2,3,1,6,5,7,4]=>001000
[3,1,2,7,5,6,4]=>{{1,2,3},{4,7},{5},{6}}=>[2,3,1,7,5,6,4]=>001000
[3,1,2,7,6,4,5]=>{{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000
[3,1,2,7,6,5,4]=>{{1,2,3},{4,7},{5,6}}=>[2,3,1,7,6,5,4]=>001000
[3,1,4,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>000111
[3,1,4,2,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>000110
[3,1,4,2,6,5,7]=>{{1,2,3,4},{5,6},{7}}=>[2,3,4,1,6,5,7]=>000101
[3,1,4,2,6,7,5]=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100
[3,1,4,2,7,5,6]=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100
[3,1,4,2,7,6,5]=>{{1,2,3,4},{5,7},{6}}=>[2,3,4,1,7,6,5]=>000100
[3,1,4,5,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[3,1,4,5,2,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[3,1,4,5,6,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,1,4,5,6,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,4,5,7,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,1,4,6,2,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,4,6,5,2,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[3,1,4,6,5,7,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,1,4,6,7,2,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[3,1,4,6,7,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,4,7,2,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,4,7,2,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,1,4,7,5,2,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,1,4,7,5,6,2]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[3,1,4,7,6,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,4,7,6,5,2]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[3,1,5,2,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[3,1,5,2,4,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[3,1,5,2,6,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,5,2,7,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,1,5,4,2,6,7]=>{{1,2,3,5},{4},{6},{7}}=>[2,3,5,4,1,6,7]=>000011
[3,1,5,4,2,7,6]=>{{1,2,3,5},{4},{6,7}}=>[2,3,5,4,1,7,6]=>000010
[3,1,5,4,6,2,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[3,1,5,4,6,7,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,1,5,4,7,2,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,1,5,4,7,6,2]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[3,1,5,6,2,4,7]=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>000001
[3,1,5,6,2,7,4]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000
[3,1,5,6,4,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,1,5,6,4,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,5,6,7,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,5,6,7,4,2]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[3,1,5,7,2,4,6]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000
[3,1,5,7,2,6,4]=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>000000
[3,1,5,7,4,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,5,7,4,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,1,5,7,6,2,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[3,1,5,7,6,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,6,2,4,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,1,6,2,4,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,6,2,5,4,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[3,1,6,2,5,7,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,1,6,2,7,4,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[3,1,6,2,7,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,6,4,2,5,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[3,1,6,4,2,7,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,1,6,4,5,2,7]=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>000001
[3,1,6,4,5,7,2]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[3,1,6,4,7,2,5]=>{{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>000000
[3,1,6,4,7,5,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,1,6,5,2,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,1,6,5,2,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,6,5,4,2,7]=>{{1,2,3,6},{4,5},{7}}=>[2,3,6,5,4,1,7]=>000001
[3,1,6,5,4,7,2]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[3,1,6,5,7,2,4]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000
[3,1,6,5,7,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,6,7,2,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,6,7,2,5,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[3,1,6,7,4,2,5]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000
[3,1,6,7,4,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,6,7,5,2,4]=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>000000
[3,1,6,7,5,4,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,7,2,4,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,1,7,2,5,4,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,1,7,2,5,6,4]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[3,1,7,2,6,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,7,2,6,5,4]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[3,1,7,4,2,5,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,1,7,4,2,6,5]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[3,1,7,4,5,2,6]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[3,1,7,4,5,6,2]=>{{1,2,3,7},{4},{5},{6}}=>[2,3,7,4,5,6,1]=>000000
[3,1,7,4,6,2,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,1,7,4,6,5,2]=>{{1,2,3,7},{4},{5,6}}=>[2,3,7,4,6,5,1]=>000000
[3,1,7,5,2,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,7,5,2,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,1,7,5,4,2,6]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[3,1,7,5,4,6,2]=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>000000
[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,7,5,6,4,2]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000
[3,1,7,6,2,4,5]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[3,1,7,6,2,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,7,6,4,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,1,7,6,4,5,2]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000
[3,1,7,6,5,2,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,1,7,6,5,4,2]=>{{1,2,3,7},{4,6},{5}}=>[2,3,7,6,5,4,1]=>000000
[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}}=>[3,2,1,4,5,6,7]=>001111
[3,2,1,4,5,7,6]=>{{1,3},{2},{4},{5},{6,7}}=>[3,2,1,4,5,7,6]=>001110
[3,2,1,4,6,5,7]=>{{1,3},{2},{4},{5,6},{7}}=>[3,2,1,4,6,5,7]=>001101
[3,2,1,4,6,7,5]=>{{1,3},{2},{4},{5,6,7}}=>[3,2,1,4,6,7,5]=>001100
[3,2,1,4,7,5,6]=>{{1,3},{2},{4},{5,6,7}}=>[3,2,1,4,6,7,5]=>001100
[3,2,1,4,7,6,5]=>{{1,3},{2},{4},{5,7},{6}}=>[3,2,1,4,7,6,5]=>001100
[3,2,1,5,4,6,7]=>{{1,3},{2},{4,5},{6},{7}}=>[3,2,1,5,4,6,7]=>001011
[3,2,1,5,4,7,6]=>{{1,3},{2},{4,5},{6,7}}=>[3,2,1,5,4,7,6]=>001010
[3,2,1,5,6,4,7]=>{{1,3},{2},{4,5,6},{7}}=>[3,2,1,5,6,4,7]=>001001
[3,2,1,5,6,7,4]=>{{1,3},{2},{4,5,6,7}}=>[3,2,1,5,6,7,4]=>001000
[3,2,1,5,7,4,6]=>{{1,3},{2},{4,5,6,7}}=>[3,2,1,5,6,7,4]=>001000
[3,2,1,5,7,6,4]=>{{1,3},{2},{4,5,7},{6}}=>[3,2,1,5,7,6,4]=>001000
[3,2,1,6,4,5,7]=>{{1,3},{2},{4,5,6},{7}}=>[3,2,1,5,6,4,7]=>001001
[3,2,1,6,4,7,5]=>{{1,3},{2},{4,5,6,7}}=>[3,2,1,5,6,7,4]=>001000
[3,2,1,6,5,4,7]=>{{1,3},{2},{4,6},{5},{7}}=>[3,2,1,6,5,4,7]=>001001
[3,2,1,6,5,7,4]=>{{1,3},{2},{4,6,7},{5}}=>[3,2,1,6,5,7,4]=>001000
[3,2,1,6,7,4,5]=>{{1,3},{2},{4,6},{5,7}}=>[3,2,1,6,7,4,5]=>001000
[3,2,1,6,7,5,4]=>{{1,3},{2},{4,5,6,7}}=>[3,2,1,5,6,7,4]=>001000
[3,2,1,7,4,5,6]=>{{1,3},{2},{4,5,6,7}}=>[3,2,1,5,6,7,4]=>001000
[3,2,1,7,4,6,5]=>{{1,3},{2},{4,5,7},{6}}=>[3,2,1,5,7,6,4]=>001000
[3,2,1,7,5,4,6]=>{{1,3},{2},{4,6,7},{5}}=>[3,2,1,6,5,7,4]=>001000
[3,2,1,7,5,6,4]=>{{1,3},{2},{4,7},{5},{6}}=>[3,2,1,7,5,6,4]=>001000
[3,2,1,7,6,4,5]=>{{1,3},{2},{4,5,6,7}}=>[3,2,1,5,6,7,4]=>001000
[3,2,1,7,6,5,4]=>{{1,3},{2},{4,7},{5,6}}=>[3,2,1,7,6,5,4]=>001000
[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}=>[3,2,4,1,5,6,7]=>000111
[3,2,4,1,5,7,6]=>{{1,3,4},{2},{5},{6,7}}=>[3,2,4,1,5,7,6]=>000110
[3,2,4,1,6,5,7]=>{{1,3,4},{2},{5,6},{7}}=>[3,2,4,1,6,5,7]=>000101
[3,2,4,1,6,7,5]=>{{1,3,4},{2},{5,6,7}}=>[3,2,4,1,6,7,5]=>000100
[3,2,4,1,7,5,6]=>{{1,3,4},{2},{5,6,7}}=>[3,2,4,1,6,7,5]=>000100
[3,2,4,1,7,6,5]=>{{1,3,4},{2},{5,7},{6}}=>[3,2,4,1,7,6,5]=>000100
[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>000011
[3,2,4,5,1,7,6]=>{{1,3,4,5},{2},{6,7}}=>[3,2,4,5,1,7,6]=>000010
[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,4,5,7,1,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,4,5,7,6,1]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[3,2,4,6,1,5,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[3,2,4,6,1,7,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,4,6,5,1,7]=>{{1,3,4,6},{2},{5},{7}}=>[3,2,4,6,5,1,7]=>000001
[3,2,4,6,5,7,1]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[3,2,4,6,7,1,5]=>{{1,3,4,6},{2},{5,7}}=>[3,2,4,6,7,1,5]=>000000
[3,2,4,6,7,5,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,4,7,1,5,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,4,7,1,6,5]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[3,2,4,7,5,1,6]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[3,2,4,7,5,6,1]=>{{1,3,4,7},{2},{5},{6}}=>[3,2,4,7,5,6,1]=>000000
[3,2,4,7,6,1,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,4,7,6,5,1]=>{{1,3,4,7},{2},{5,6}}=>[3,2,4,7,6,5,1]=>000000
[3,2,5,1,4,6,7]=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>000011
[3,2,5,1,4,7,6]=>{{1,3,4,5},{2},{6,7}}=>[3,2,4,5,1,7,6]=>000010
[3,2,5,1,6,4,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[3,2,5,1,6,7,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,5,1,7,4,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,5,1,7,6,4]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[3,2,5,4,1,6,7]=>{{1,3,5},{2},{4},{6},{7}}=>[3,2,5,4,1,6,7]=>000011
[3,2,5,4,1,7,6]=>{{1,3,5},{2},{4},{6,7}}=>[3,2,5,4,1,7,6]=>000010
[3,2,5,4,6,1,7]=>{{1,3,5,6},{2},{4},{7}}=>[3,2,5,4,6,1,7]=>000001
[3,2,5,4,6,7,1]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[3,2,5,4,7,1,6]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[3,2,5,4,7,6,1]=>{{1,3,5,7},{2},{4},{6}}=>[3,2,5,4,7,6,1]=>000000
[3,2,5,6,1,4,7]=>{{1,3,5},{2},{4,6},{7}}=>[3,2,5,6,1,4,7]=>000001
[3,2,5,6,1,7,4]=>{{1,3,5},{2},{4,6,7}}=>[3,2,5,6,1,7,4]=>000000
[3,2,5,6,4,1,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[3,2,5,6,4,7,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,5,6,7,1,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,5,6,7,4,1]=>{{1,3,5,7},{2},{4,6}}=>[3,2,5,6,7,4,1]=>000000
[3,2,5,7,1,4,6]=>{{1,3,5},{2},{4,6,7}}=>[3,2,5,6,1,7,4]=>000000
[3,2,5,7,1,6,4]=>{{1,3,5},{2},{4,7},{6}}=>[3,2,5,7,1,6,4]=>000000
[3,2,5,7,4,1,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,5,7,4,6,1]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[3,2,5,7,6,1,4]=>{{1,3,5,6},{2},{4,7}}=>[3,2,5,7,6,1,4]=>000000
[3,2,5,7,6,4,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,6,1,4,5,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[3,2,6,1,4,7,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,6,1,5,4,7]=>{{1,3,4,6},{2},{5},{7}}=>[3,2,4,6,5,1,7]=>000001
[3,2,6,1,5,7,4]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[3,2,6,1,7,4,5]=>{{1,3,4,6},{2},{5,7}}=>[3,2,4,6,7,1,5]=>000000
[3,2,6,1,7,5,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,6,4,1,5,7]=>{{1,3,5,6},{2},{4},{7}}=>[3,2,5,4,6,1,7]=>000001
[3,2,6,4,1,7,5]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[3,2,6,4,5,1,7]=>{{1,3,6},{2},{4},{5},{7}}=>[3,2,6,4,5,1,7]=>000001
[3,2,6,4,5,7,1]=>{{1,3,6,7},{2},{4},{5}}=>[3,2,6,4,5,7,1]=>000000
[3,2,6,4,7,1,5]=>{{1,3,6},{2},{4},{5,7}}=>[3,2,6,4,7,1,5]=>000000
[3,2,6,4,7,5,1]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[3,2,6,5,1,4,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[3,2,6,5,1,7,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,6,5,4,1,7]=>{{1,3,6},{2},{4,5},{7}}=>[3,2,6,5,4,1,7]=>000001
[3,2,6,5,4,7,1]=>{{1,3,6,7},{2},{4,5}}=>[3,2,6,5,4,7,1]=>000000
[3,2,6,5,7,1,4]=>{{1,3,6},{2},{4,5,7}}=>[3,2,6,5,7,1,4]=>000000
[3,2,6,5,7,4,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,6,7,1,4,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,6,7,1,5,4]=>{{1,3,5,6},{2},{4,7}}=>[3,2,5,7,6,1,4]=>000000
[3,2,6,7,4,1,5]=>{{1,3,6},{2},{4,5,7}}=>[3,2,6,5,7,1,4]=>000000
[3,2,6,7,4,5,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,6,7,5,1,4]=>{{1,3,6},{2},{4,7},{5}}=>[3,2,6,7,5,1,4]=>000000
[3,2,6,7,5,4,1]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[3,2,7,1,4,5,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,7,1,4,6,5]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[3,2,7,1,5,4,6]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[3,2,7,1,5,6,4]=>{{1,3,4,7},{2},{5},{6}}=>[3,2,4,7,5,6,1]=>000000
[3,2,7,1,6,4,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,7,1,6,5,4]=>{{1,3,4,7},{2},{5,6}}=>[3,2,4,7,6,5,1]=>000000
[3,2,7,4,1,5,6]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[3,2,7,4,1,6,5]=>{{1,3,5,7},{2},{4},{6}}=>[3,2,5,4,7,6,1]=>000000
[3,2,7,4,5,1,6]=>{{1,3,6,7},{2},{4},{5}}=>[3,2,6,4,5,7,1]=>000000
[3,2,7,4,5,6,1]=>{{1,3,7},{2},{4},{5},{6}}=>[3,2,7,4,5,6,1]=>000000
[3,2,7,4,6,1,5]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[3,2,7,4,6,5,1]=>{{1,3,7},{2},{4},{5,6}}=>[3,2,7,4,6,5,1]=>000000
[3,2,7,5,1,4,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,7,5,1,6,4]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[3,2,7,5,4,1,6]=>{{1,3,6,7},{2},{4,5}}=>[3,2,6,5,4,7,1]=>000000
[3,2,7,5,4,6,1]=>{{1,3,7},{2},{4,5},{6}}=>[3,2,7,5,4,6,1]=>000000
[3,2,7,5,6,1,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,7,5,6,4,1]=>{{1,3,7},{2},{4,5,6}}=>[3,2,7,5,6,4,1]=>000000
[3,2,7,6,1,4,5]=>{{1,3,5,7},{2},{4,6}}=>[3,2,5,6,7,4,1]=>000000
[3,2,7,6,1,5,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,7,6,4,1,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[3,2,7,6,4,5,1]=>{{1,3,7},{2},{4,5,6}}=>[3,2,7,5,6,4,1]=>000000
[3,2,7,6,5,1,4]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[3,2,7,6,5,4,1]=>{{1,3,7},{2},{4,6},{5}}=>[3,2,7,6,5,4,1]=>000000
[3,4,1,2,5,6,7]=>{{1,3},{2,4},{5},{6},{7}}=>[3,4,1,2,5,6,7]=>000111
[3,4,1,2,5,7,6]=>{{1,3},{2,4},{5},{6,7}}=>[3,4,1,2,5,7,6]=>000110
[3,4,1,2,6,5,7]=>{{1,3},{2,4},{5,6},{7}}=>[3,4,1,2,6,5,7]=>000101
[3,4,1,2,6,7,5]=>{{1,3},{2,4},{5,6,7}}=>[3,4,1,2,6,7,5]=>000100
[3,4,1,2,7,5,6]=>{{1,3},{2,4},{5,6,7}}=>[3,4,1,2,6,7,5]=>000100
[3,4,1,2,7,6,5]=>{{1,3},{2,4},{5,7},{6}}=>[3,4,1,2,7,6,5]=>000100
[3,4,1,5,2,6,7]=>{{1,3},{2,4,5},{6},{7}}=>[3,4,1,5,2,6,7]=>000011
[3,4,1,5,2,7,6]=>{{1,3},{2,4,5},{6,7}}=>[3,4,1,5,2,7,6]=>000010
[3,4,1,5,6,2,7]=>{{1,3},{2,4,5,6},{7}}=>[3,4,1,5,6,2,7]=>000001
[3,4,1,5,6,7,2]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,4,1,5,7,2,6]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,4,1,5,7,6,2]=>{{1,3},{2,4,5,7},{6}}=>[3,4,1,5,7,6,2]=>000000
[3,4,1,6,2,5,7]=>{{1,3},{2,4,5,6},{7}}=>[3,4,1,5,6,2,7]=>000001
[3,4,1,6,2,7,5]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,4,1,6,5,2,7]=>{{1,3},{2,4,6},{5},{7}}=>[3,4,1,6,5,2,7]=>000001
[3,4,1,6,5,7,2]=>{{1,3},{2,4,6,7},{5}}=>[3,4,1,6,5,7,2]=>000000
[3,4,1,6,7,2,5]=>{{1,3},{2,4,6},{5,7}}=>[3,4,1,6,7,2,5]=>000000
[3,4,1,6,7,5,2]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,4,1,7,2,5,6]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,4,1,7,2,6,5]=>{{1,3},{2,4,5,7},{6}}=>[3,4,1,5,7,6,2]=>000000
[3,4,1,7,5,2,6]=>{{1,3},{2,4,6,7},{5}}=>[3,4,1,6,5,7,2]=>000000
[3,4,1,7,5,6,2]=>{{1,3},{2,4,7},{5},{6}}=>[3,4,1,7,5,6,2]=>000000
[3,4,1,7,6,2,5]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,4,1,7,6,5,2]=>{{1,3},{2,4,7},{5,6}}=>[3,4,1,7,6,5,2]=>000000
[3,4,2,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>000111
[3,4,2,1,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>000110
[3,4,2,1,6,5,7]=>{{1,2,3,4},{5,6},{7}}=>[2,3,4,1,6,5,7]=>000101
[3,4,2,1,6,7,5]=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100
[3,4,2,1,7,5,6]=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100
[3,4,2,1,7,6,5]=>{{1,2,3,4},{5,7},{6}}=>[2,3,4,1,7,6,5]=>000100
[3,4,2,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[3,4,2,5,1,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[3,4,2,5,6,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,4,2,5,6,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,2,5,7,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,2,5,7,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,4,2,6,1,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,4,2,6,1,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,2,6,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[3,4,2,6,5,7,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,4,2,6,7,1,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[3,4,2,6,7,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,2,7,1,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,2,7,1,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,4,2,7,5,1,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,4,2,7,5,6,1]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[3,4,2,7,6,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,2,7,6,5,1]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[3,4,5,1,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[3,4,5,1,2,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[3,4,5,1,6,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,4,5,1,6,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,5,1,7,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,5,1,7,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,4,5,2,1,6,7]=>{{1,3,5},{2,4},{6},{7}}=>[3,4,5,2,1,6,7]=>000011
[3,4,5,2,1,7,6]=>{{1,3,5},{2,4},{6,7}}=>[3,4,5,2,1,7,6]=>000010
[3,4,5,2,6,1,7]=>{{1,3,5,6},{2,4},{7}}=>[3,4,5,2,6,1,7]=>000001
[3,4,5,2,6,7,1]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[3,4,5,2,7,1,6]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[3,4,5,2,7,6,1]=>{{1,3,5,7},{2,4},{6}}=>[3,4,5,2,7,6,1]=>000000
[3,4,5,6,1,2,7]=>{{1,3,5},{2,4,6},{7}}=>[3,4,5,6,1,2,7]=>000001
[3,4,5,6,1,7,2]=>{{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000
[3,4,5,6,2,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,4,5,6,2,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,5,6,7,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,5,6,7,2,1]=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000
[3,4,5,7,1,2,6]=>{{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000
[3,4,5,7,1,6,2]=>{{1,3,5},{2,4,7},{6}}=>[3,4,5,7,1,6,2]=>000000
[3,4,5,7,2,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,5,7,2,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,4,5,7,6,1,2]=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000
[3,4,5,7,6,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,6,1,2,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,4,6,1,2,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,6,1,5,2,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[3,4,6,1,5,7,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,4,6,1,7,2,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[3,4,6,1,7,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,6,2,1,5,7]=>{{1,3,5,6},{2,4},{7}}=>[3,4,5,2,6,1,7]=>000001
[3,4,6,2,1,7,5]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[3,4,6,2,5,1,7]=>{{1,3,6},{2,4},{5},{7}}=>[3,4,6,2,5,1,7]=>000001
[3,4,6,2,5,7,1]=>{{1,3,6,7},{2,4},{5}}=>[3,4,6,2,5,7,1]=>000000
[3,4,6,2,7,1,5]=>{{1,3,6},{2,4},{5,7}}=>[3,4,6,2,7,1,5]=>000000
[3,4,6,2,7,5,1]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[3,4,6,5,1,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,4,6,5,1,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,6,5,2,1,7]=>{{1,3,6},{2,4,5},{7}}=>[3,4,6,5,2,1,7]=>000001
[3,4,6,5,2,7,1]=>{{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000
[3,4,6,5,7,1,2]=>{{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000
[3,4,6,5,7,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,6,7,1,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,6,7,1,5,2]=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000
[3,4,6,7,2,1,5]=>{{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000
[3,4,6,7,2,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,6,7,5,1,2]=>{{1,3,6},{2,4,7},{5}}=>[3,4,6,7,5,1,2]=>000000
[3,4,6,7,5,2,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,4,7,1,2,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,7,1,2,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,4,7,1,5,2,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,4,7,1,5,6,2]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[3,4,7,1,6,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,7,1,6,5,2]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[3,4,7,2,1,5,6]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[3,4,7,2,1,6,5]=>{{1,3,5,7},{2,4},{6}}=>[3,4,5,2,7,6,1]=>000000
[3,4,7,2,5,1,6]=>{{1,3,6,7},{2,4},{5}}=>[3,4,6,2,5,7,1]=>000000
[3,4,7,2,5,6,1]=>{{1,3,7},{2,4},{5},{6}}=>[3,4,7,2,5,6,1]=>000000
[3,4,7,2,6,1,5]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[3,4,7,2,6,5,1]=>{{1,3,7},{2,4},{5,6}}=>[3,4,7,2,6,5,1]=>000000
[3,4,7,5,1,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,7,5,1,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,4,7,5,2,1,6]=>{{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000
[3,4,7,5,2,6,1]=>{{1,3,7},{2,4,5},{6}}=>[3,4,7,5,2,6,1]=>000000
[3,4,7,5,6,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,7,5,6,2,1]=>{{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000
[3,4,7,6,1,2,5]=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000
[3,4,7,6,1,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,7,6,2,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,4,7,6,2,5,1]=>{{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000
[3,4,7,6,5,1,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,4,7,6,5,2,1]=>{{1,3,7},{2,4,6},{5}}=>[3,4,7,6,5,2,1]=>000000
[3,5,1,2,4,6,7]=>{{1,3},{2,4,5},{6},{7}}=>[3,4,1,5,2,6,7]=>000011
[3,5,1,2,4,7,6]=>{{1,3},{2,4,5},{6,7}}=>[3,4,1,5,2,7,6]=>000010
[3,5,1,2,6,4,7]=>{{1,3},{2,4,5,6},{7}}=>[3,4,1,5,6,2,7]=>000001
[3,5,1,2,6,7,4]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,5,1,2,7,4,6]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,5,1,2,7,6,4]=>{{1,3},{2,4,5,7},{6}}=>[3,4,1,5,7,6,2]=>000000
[3,5,1,4,2,6,7]=>{{1,3},{2,5},{4},{6},{7}}=>[3,5,1,4,2,6,7]=>000011
[3,5,1,4,2,7,6]=>{{1,3},{2,5},{4},{6,7}}=>[3,5,1,4,2,7,6]=>000010
[3,5,1,4,6,2,7]=>{{1,3},{2,5,6},{4},{7}}=>[3,5,1,4,6,2,7]=>000001
[3,5,1,4,6,7,2]=>{{1,3},{2,5,6,7},{4}}=>[3,5,1,4,6,7,2]=>000000
[3,5,1,4,7,2,6]=>{{1,3},{2,5,6,7},{4}}=>[3,5,1,4,6,7,2]=>000000
[3,5,1,4,7,6,2]=>{{1,3},{2,5,7},{4},{6}}=>[3,5,1,4,7,6,2]=>000000
[3,5,1,6,2,4,7]=>{{1,3},{2,5},{4,6},{7}}=>[3,5,1,6,2,4,7]=>000001
[3,5,1,6,2,7,4]=>{{1,3},{2,5},{4,6,7}}=>[3,5,1,6,2,7,4]=>000000
[3,5,1,6,4,2,7]=>{{1,3},{2,4,5,6},{7}}=>[3,4,1,5,6,2,7]=>000001
[3,5,1,6,4,7,2]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,5,1,6,7,2,4]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,5,1,6,7,4,2]=>{{1,3},{2,5,7},{4,6}}=>[3,5,1,6,7,4,2]=>000000
[3,5,1,7,2,4,6]=>{{1,3},{2,5},{4,6,7}}=>[3,5,1,6,2,7,4]=>000000
[3,5,1,7,2,6,4]=>{{1,3},{2,5},{4,7},{6}}=>[3,5,1,7,2,6,4]=>000000
[3,5,1,7,4,2,6]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,5,1,7,4,6,2]=>{{1,3},{2,4,5,7},{6}}=>[3,4,1,5,7,6,2]=>000000
[3,5,1,7,6,2,4]=>{{1,3},{2,5,6},{4,7}}=>[3,5,1,7,6,2,4]=>000000
[3,5,1,7,6,4,2]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,5,2,1,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[3,5,2,1,4,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[3,5,2,1,6,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,5,2,1,6,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,2,1,7,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,2,1,7,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,5,2,4,1,6,7]=>{{1,2,3,5},{4},{6},{7}}=>[2,3,5,4,1,6,7]=>000011
[3,5,2,4,1,7,6]=>{{1,2,3,5},{4},{6,7}}=>[2,3,5,4,1,7,6]=>000010
[3,5,2,4,6,1,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[3,5,2,4,6,7,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,5,2,4,7,1,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,5,2,4,7,6,1]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[3,5,2,6,1,4,7]=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>000001
[3,5,2,6,1,7,4]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000
[3,5,2,6,4,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,5,2,6,4,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,2,6,7,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,2,6,7,4,1]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[3,5,2,7,1,4,6]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000
[3,5,2,7,1,6,4]=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>000000
[3,5,2,7,4,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,2,7,4,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,5,2,7,6,1,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[3,5,2,7,6,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,4,1,2,6,7]=>{{1,3,4},{2,5},{6},{7}}=>[3,5,4,1,2,6,7]=>000011
[3,5,4,1,2,7,6]=>{{1,3,4},{2,5},{6,7}}=>[3,5,4,1,2,7,6]=>000010
[3,5,4,1,6,2,7]=>{{1,3,4},{2,5,6},{7}}=>[3,5,4,1,6,2,7]=>000001
[3,5,4,1,6,7,2]=>{{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000
[3,5,4,1,7,2,6]=>{{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000
[3,5,4,1,7,6,2]=>{{1,3,4},{2,5,7},{6}}=>[3,5,4,1,7,6,2]=>000000
[3,5,4,2,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[3,5,4,2,1,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[3,5,4,2,6,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,5,4,2,6,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,4,2,7,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,4,2,7,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,5,4,6,1,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,5,4,6,1,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,4,6,2,1,7]=>{{1,3,4,6},{2,5},{7}}=>[3,5,4,6,2,1,7]=>000001
[3,5,4,6,2,7,1]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[3,5,4,6,7,1,2]=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000
[3,5,4,6,7,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,4,7,1,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,4,7,1,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,5,4,7,2,1,6]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[3,5,4,7,2,6,1]=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>000000
[3,5,4,7,6,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,4,7,6,2,1]=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000
[3,5,6,1,2,4,7]=>{{1,3,4,6},{2,5},{7}}=>[3,5,4,6,2,1,7]=>000001
[3,5,6,1,2,7,4]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[3,5,6,1,4,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,5,6,1,4,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,6,1,7,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,6,1,7,4,2]=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000
[3,5,6,2,1,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,5,6,2,1,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,6,2,4,1,7]=>{{1,3,6},{2,4,5},{7}}=>[3,4,6,5,2,1,7]=>000001
[3,5,6,2,4,7,1]=>{{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000
[3,5,6,2,7,1,4]=>{{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000
[3,5,6,2,7,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,6,4,1,2,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[3,5,6,4,1,7,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,5,6,4,2,1,7]=>{{1,3,6},{2,5},{4},{7}}=>[3,5,6,4,2,1,7]=>000001
[3,5,6,4,2,7,1]=>{{1,3,6,7},{2,5},{4}}=>[3,5,6,4,2,7,1]=>000000
[3,5,6,4,7,1,2]=>{{1,3,6},{2,5,7},{4}}=>[3,5,6,4,7,1,2]=>000000
[3,5,6,4,7,2,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,5,6,7,1,2,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[3,5,6,7,1,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,6,7,2,1,4]=>{{1,3,6},{2,5},{4,7}}=>[3,5,6,7,2,1,4]=>000000
[3,5,6,7,2,4,1]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[3,5,6,7,4,1,2]=>{{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000
[3,5,6,7,4,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,7,1,2,4,6]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[3,5,7,1,2,6,4]=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>000000
[3,5,7,1,4,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,7,1,4,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,5,7,1,6,2,4]=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000
[3,5,7,1,6,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,7,2,1,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,7,2,1,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,5,7,2,4,1,6]=>{{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000
[3,5,7,2,4,6,1]=>{{1,3,7},{2,4,5},{6}}=>[3,4,7,5,2,6,1]=>000000
[3,5,7,2,6,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,7,2,6,4,1]=>{{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000
[3,5,7,4,1,2,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,5,7,4,1,6,2]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[3,5,7,4,2,1,6]=>{{1,3,6,7},{2,5},{4}}=>[3,5,6,4,2,7,1]=>000000
[3,5,7,4,2,6,1]=>{{1,3,7},{2,5},{4},{6}}=>[3,5,7,4,2,6,1]=>000000
[3,5,7,4,6,1,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,5,7,4,6,2,1]=>{{1,3,7},{2,5,6},{4}}=>[3,5,7,4,6,2,1]=>000000
[3,5,7,6,1,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,7,6,1,4,2]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[3,5,7,6,2,1,4]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[3,5,7,6,2,4,1]=>{{1,3,7},{2,5},{4,6}}=>[3,5,7,6,2,4,1]=>000000
[3,5,7,6,4,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,5,7,6,4,2,1]=>{{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000
[3,6,1,2,4,5,7]=>{{1,3},{2,4,5,6},{7}}=>[3,4,1,5,6,2,7]=>000001
[3,6,1,2,4,7,5]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,6,1,2,5,4,7]=>{{1,3},{2,4,6},{5},{7}}=>[3,4,1,6,5,2,7]=>000001
[3,6,1,2,5,7,4]=>{{1,3},{2,4,6,7},{5}}=>[3,4,1,6,5,7,2]=>000000
[3,6,1,2,7,4,5]=>{{1,3},{2,4,6},{5,7}}=>[3,4,1,6,7,2,5]=>000000
[3,6,1,2,7,5,4]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,6,1,4,2,5,7]=>{{1,3},{2,5,6},{4},{7}}=>[3,5,1,4,6,2,7]=>000001
[3,6,1,4,2,7,5]=>{{1,3},{2,5,6,7},{4}}=>[3,5,1,4,6,7,2]=>000000
[3,6,1,4,5,2,7]=>{{1,3},{2,6},{4},{5},{7}}=>[3,6,1,4,5,2,7]=>000001
[3,6,1,4,5,7,2]=>{{1,3},{2,6,7},{4},{5}}=>[3,6,1,4,5,7,2]=>000000
[3,6,1,4,7,2,5]=>{{1,3},{2,6},{4},{5,7}}=>[3,6,1,4,7,2,5]=>000000
[3,6,1,4,7,5,2]=>{{1,3},{2,5,6,7},{4}}=>[3,5,1,4,6,7,2]=>000000
[3,6,1,5,2,4,7]=>{{1,3},{2,4,5,6},{7}}=>[3,4,1,5,6,2,7]=>000001
[3,6,1,5,2,7,4]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,6,1,5,4,2,7]=>{{1,3},{2,6},{4,5},{7}}=>[3,6,1,5,4,2,7]=>000001
[3,6,1,5,4,7,2]=>{{1,3},{2,6,7},{4,5}}=>[3,6,1,5,4,7,2]=>000000
[3,6,1,5,7,2,4]=>{{1,3},{2,6},{4,5,7}}=>[3,6,1,5,7,2,4]=>000000
[3,6,1,5,7,4,2]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,6,1,7,2,4,5]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,6,1,7,2,5,4]=>{{1,3},{2,5,6},{4,7}}=>[3,5,1,7,6,2,4]=>000000
[3,6,1,7,4,2,5]=>{{1,3},{2,6},{4,5,7}}=>[3,6,1,5,7,2,4]=>000000
[3,6,1,7,4,5,2]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,6,1,7,5,2,4]=>{{1,3},{2,6},{4,7},{5}}=>[3,6,1,7,5,2,4]=>000000
[3,6,1,7,5,4,2]=>{{1,3},{2,4,6,7},{5}}=>[3,4,1,6,5,7,2]=>000000
[3,6,2,1,4,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,6,2,1,4,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,2,1,5,4,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[3,6,2,1,5,7,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,6,2,1,7,4,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[3,6,2,1,7,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,2,4,1,5,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[3,6,2,4,1,7,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,6,2,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>000001
[3,6,2,4,5,7,1]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[3,6,2,4,7,1,5]=>{{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>000000
[3,6,2,4,7,5,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,6,2,5,1,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,6,2,5,1,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,2,5,4,1,7]=>{{1,2,3,6},{4,5},{7}}=>[2,3,6,5,4,1,7]=>000001
[3,6,2,5,4,7,1]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[3,6,2,5,7,1,4]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000
[3,6,2,5,7,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,2,7,1,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,2,7,1,5,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[3,6,2,7,4,1,5]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000
[3,6,2,7,4,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,2,7,5,1,4]=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>000000
[3,6,2,7,5,4,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,6,4,1,2,5,7]=>{{1,3,4},{2,5,6},{7}}=>[3,5,4,1,6,2,7]=>000001
[3,6,4,1,2,7,5]=>{{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000
[3,6,4,1,5,2,7]=>{{1,3,4},{2,6},{5},{7}}=>[3,6,4,1,5,2,7]=>000001
[3,6,4,1,5,7,2]=>{{1,3,4},{2,6,7},{5}}=>[3,6,4,1,5,7,2]=>000000
[3,6,4,1,7,2,5]=>{{1,3,4},{2,6},{5,7}}=>[3,6,4,1,7,2,5]=>000000
[3,6,4,1,7,5,2]=>{{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000
[3,6,4,2,1,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,6,4,2,1,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,4,2,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[3,6,4,2,5,7,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,6,4,2,7,1,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[3,6,4,2,7,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,4,5,1,2,7]=>{{1,3,4,5},{2,6},{7}}=>[3,6,4,5,1,2,7]=>000001
[3,6,4,5,1,7,2]=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000
[3,6,4,5,2,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,6,4,5,2,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,4,5,7,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,4,5,7,2,1]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[3,6,4,7,1,2,5]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[3,6,4,7,1,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,4,7,2,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,4,7,2,5,1]=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000
[3,6,4,7,5,1,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,6,4,7,5,2,1]=>{{1,3,4,7},{2,6},{5}}=>[3,6,4,7,5,2,1]=>000000
[3,6,5,1,2,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,6,5,1,2,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,5,1,4,2,7]=>{{1,3,4,5},{2,6},{7}}=>[3,6,4,5,1,2,7]=>000001
[3,6,5,1,4,7,2]=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000
[3,6,5,1,7,2,4]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[3,6,5,1,7,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,5,2,1,4,7]=>{{1,3,5},{2,4,6},{7}}=>[3,4,5,6,1,2,7]=>000001
[3,6,5,2,1,7,4]=>{{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000
[3,6,5,2,4,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[3,6,5,2,4,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,5,2,7,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,5,2,7,4,1]=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000
[3,6,5,4,1,2,7]=>{{1,3,5},{2,6},{4},{7}}=>[3,6,5,4,1,2,7]=>000001
[3,6,5,4,1,7,2]=>{{1,3,5},{2,6,7},{4}}=>[3,6,5,4,1,7,2]=>000000
[3,6,5,4,2,1,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[3,6,5,4,2,7,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,6,5,4,7,1,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,6,5,4,7,2,1]=>{{1,3,5,7},{2,6},{4}}=>[3,6,5,4,7,2,1]=>000000
[3,6,5,7,1,2,4]=>{{1,3,5},{2,6},{4,7}}=>[3,6,5,7,1,2,4]=>000000
[3,6,5,7,1,4,2]=>{{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000
[3,6,5,7,2,1,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[3,6,5,7,2,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,5,7,4,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,5,7,4,2,1]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[3,6,7,1,2,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,7,1,2,5,4]=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000
[3,6,7,1,4,2,5]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[3,6,7,1,4,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,7,1,5,2,4]=>{{1,3,4,7},{2,6},{5}}=>[3,6,4,7,5,2,1]=>000000
[3,6,7,1,5,4,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,6,7,2,1,4,5]=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000
[3,6,7,2,1,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,7,2,4,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,7,2,4,5,1]=>{{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000
[3,6,7,2,5,1,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,6,7,2,5,4,1]=>{{1,3,7},{2,4,6},{5}}=>[3,4,7,6,5,2,1]=>000000
[3,6,7,4,1,2,5]=>{{1,3,5,7},{2,6},{4}}=>[3,6,5,4,7,2,1]=>000000
[3,6,7,4,1,5,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,6,7,4,2,1,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,6,7,4,2,5,1]=>{{1,3,7},{2,5,6},{4}}=>[3,5,7,4,6,2,1]=>000000
[3,6,7,4,5,1,2]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[3,6,7,4,5,2,1]=>{{1,3,7},{2,6},{4},{5}}=>[3,6,7,4,5,2,1]=>000000
[3,6,7,5,1,2,4]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[3,6,7,5,1,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,7,5,2,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,6,7,5,2,4,1]=>{{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000
[3,6,7,5,4,1,2]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[3,6,7,5,4,2,1]=>{{1,3,7},{2,6},{4,5}}=>[3,6,7,5,4,2,1]=>000000
[3,7,1,2,4,5,6]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,7,1,2,4,6,5]=>{{1,3},{2,4,5,7},{6}}=>[3,4,1,5,7,6,2]=>000000
[3,7,1,2,5,4,6]=>{{1,3},{2,4,6,7},{5}}=>[3,4,1,6,5,7,2]=>000000
[3,7,1,2,5,6,4]=>{{1,3},{2,4,7},{5},{6}}=>[3,4,1,7,5,6,2]=>000000
[3,7,1,2,6,4,5]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,7,1,2,6,5,4]=>{{1,3},{2,4,7},{5,6}}=>[3,4,1,7,6,5,2]=>000000
[3,7,1,4,2,5,6]=>{{1,3},{2,5,6,7},{4}}=>[3,5,1,4,6,7,2]=>000000
[3,7,1,4,2,6,5]=>{{1,3},{2,5,7},{4},{6}}=>[3,5,1,4,7,6,2]=>000000
[3,7,1,4,5,2,6]=>{{1,3},{2,6,7},{4},{5}}=>[3,6,1,4,5,7,2]=>000000
[3,7,1,4,5,6,2]=>{{1,3},{2,7},{4},{5},{6}}=>[3,7,1,4,5,6,2]=>000000
[3,7,1,4,6,2,5]=>{{1,3},{2,5,6,7},{4}}=>[3,5,1,4,6,7,2]=>000000
[3,7,1,4,6,5,2]=>{{1,3},{2,7},{4},{5,6}}=>[3,7,1,4,6,5,2]=>000000
[3,7,1,5,2,4,6]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,7,1,5,2,6,4]=>{{1,3},{2,4,5,7},{6}}=>[3,4,1,5,7,6,2]=>000000
[3,7,1,5,4,2,6]=>{{1,3},{2,6,7},{4,5}}=>[3,6,1,5,4,7,2]=>000000
[3,7,1,5,4,6,2]=>{{1,3},{2,7},{4,5},{6}}=>[3,7,1,5,4,6,2]=>000000
[3,7,1,5,6,2,4]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,7,1,5,6,4,2]=>{{1,3},{2,7},{4,5,6}}=>[3,7,1,5,6,4,2]=>000000
[3,7,1,6,2,4,5]=>{{1,3},{2,5,7},{4,6}}=>[3,5,1,6,7,4,2]=>000000
[3,7,1,6,2,5,4]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,7,1,6,4,2,5]=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
[3,7,1,6,4,5,2]=>{{1,3},{2,7},{4,5,6}}=>[3,7,1,5,6,4,2]=>000000
[3,7,1,6,5,2,4]=>{{1,3},{2,4,6,7},{5}}=>[3,4,1,6,5,7,2]=>000000
[3,7,1,6,5,4,2]=>{{1,3},{2,7},{4,6},{5}}=>[3,7,1,6,5,4,2]=>000000
[3,7,2,1,4,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,2,1,4,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,7,2,1,5,4,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,7,2,1,5,6,4]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[3,7,2,1,6,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,2,1,6,5,4]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[3,7,2,4,1,5,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,7,2,4,1,6,5]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[3,7,2,4,5,1,6]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[3,7,2,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}}=>[2,3,7,4,5,6,1]=>000000
[3,7,2,4,6,1,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,7,2,4,6,5,1]=>{{1,2,3,7},{4},{5,6}}=>[2,3,7,4,6,5,1]=>000000
[3,7,2,5,1,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,2,5,1,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,7,2,5,4,1,6]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[3,7,2,5,4,6,1]=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>000000
[3,7,2,5,6,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,2,5,6,4,1]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000
[3,7,2,6,1,4,5]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[3,7,2,6,1,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,2,6,4,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,2,6,4,5,1]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000
[3,7,2,6,5,1,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,7,2,6,5,4,1]=>{{1,2,3,7},{4,6},{5}}=>[2,3,7,6,5,4,1]=>000000
[3,7,4,1,2,5,6]=>{{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000
[3,7,4,1,2,6,5]=>{{1,3,4},{2,5,7},{6}}=>[3,5,4,1,7,6,2]=>000000
[3,7,4,1,5,2,6]=>{{1,3,4},{2,6,7},{5}}=>[3,6,4,1,5,7,2]=>000000
[3,7,4,1,5,6,2]=>{{1,3,4},{2,7},{5},{6}}=>[3,7,4,1,5,6,2]=>000000
[3,7,4,1,6,2,5]=>{{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000
[3,7,4,1,6,5,2]=>{{1,3,4},{2,7},{5,6}}=>[3,7,4,1,6,5,2]=>000000
[3,7,4,2,1,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,4,2,1,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,7,4,2,5,1,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,7,4,2,5,6,1]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[3,7,4,2,6,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,4,2,6,5,1]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[3,7,4,5,1,2,6]=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000
[3,7,4,5,1,6,2]=>{{1,3,4,5},{2,7},{6}}=>[3,7,4,5,1,6,2]=>000000
[3,7,4,5,2,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,4,5,2,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,7,4,5,6,1,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[3,7,4,5,6,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,4,6,1,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,4,6,1,5,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[3,7,4,6,2,1,5]=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000
[3,7,4,6,2,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,4,6,5,1,2]=>{{1,3,4,6},{2,7},{5}}=>[3,7,4,6,5,1,2]=>000000
[3,7,4,6,5,2,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,7,5,1,2,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,5,1,2,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,7,5,1,4,2,6]=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000
[3,7,5,1,4,6,2]=>{{1,3,4,5},{2,7},{6}}=>[3,7,4,5,1,6,2]=>000000
[3,7,5,1,6,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,5,1,6,4,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[3,7,5,2,1,4,6]=>{{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000
[3,7,5,2,1,6,4]=>{{1,3,5},{2,4,7},{6}}=>[3,4,5,7,1,6,2]=>000000
[3,7,5,2,4,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,5,2,4,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[3,7,5,2,6,1,4]=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000
[3,7,5,2,6,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,5,4,1,2,6]=>{{1,3,5},{2,6,7},{4}}=>[3,6,5,4,1,7,2]=>000000
[3,7,5,4,1,6,2]=>{{1,3,5},{2,7},{4},{6}}=>[3,7,5,4,1,6,2]=>000000
[3,7,5,4,2,1,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,7,5,4,2,6,1]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[3,7,5,4,6,1,2]=>{{1,3,5,6},{2,7},{4}}=>[3,7,5,4,6,1,2]=>000000
[3,7,5,4,6,2,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,7,5,6,1,2,4]=>{{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000
[3,7,5,6,1,4,2]=>{{1,3,5},{2,7},{4,6}}=>[3,7,5,6,1,4,2]=>000000
[3,7,5,6,2,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,5,6,2,4,1]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[3,7,5,6,4,1,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[3,7,5,6,4,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,6,1,2,4,5]=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000
[3,7,6,1,2,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,6,1,4,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,6,1,4,5,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[3,7,6,1,5,2,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,7,6,1,5,4,2]=>{{1,3,4,6},{2,7},{5}}=>[3,7,4,6,5,1,2]=>000000
[3,7,6,2,1,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,6,2,1,5,4]=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000
[3,7,6,2,4,1,5]=>{{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000
[3,7,6,2,4,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,6,2,5,1,4]=>{{1,3,6},{2,4,7},{5}}=>[3,4,6,7,5,1,2]=>000000
[3,7,6,2,5,4,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[3,7,6,4,1,2,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,7,6,4,1,5,2]=>{{1,3,5,6},{2,7},{4}}=>[3,7,5,4,6,1,2]=>000000
[3,7,6,4,2,1,5]=>{{1,3,6},{2,5,7},{4}}=>[3,5,6,4,7,1,2]=>000000
[3,7,6,4,2,5,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[3,7,6,4,5,1,2]=>{{1,3,6},{2,7},{4},{5}}=>[3,7,6,4,5,1,2]=>000000
[3,7,6,4,5,2,1]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[3,7,6,5,1,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,6,5,1,4,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[3,7,6,5,2,1,4]=>{{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000
[3,7,6,5,2,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[3,7,6,5,4,1,2]=>{{1,3,6},{2,7},{4,5}}=>[3,7,6,5,4,1,2]=>000000
[3,7,6,5,4,2,1]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[4,1,2,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>000111
[4,1,2,3,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>000110
[4,1,2,3,6,5,7]=>{{1,2,3,4},{5,6},{7}}=>[2,3,4,1,6,5,7]=>000101
[4,1,2,3,6,7,5]=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100
[4,1,2,3,7,5,6]=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100
[4,1,2,3,7,6,5]=>{{1,2,3,4},{5,7},{6}}=>[2,3,4,1,7,6,5]=>000100
[4,1,2,5,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[4,1,2,5,3,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[4,1,2,5,6,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,1,2,5,6,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,2,5,7,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,2,5,7,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,1,2,6,3,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,1,2,6,3,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,2,6,5,3,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[4,1,2,6,5,7,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,1,2,6,7,3,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[4,1,2,6,7,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,2,7,3,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,2,7,3,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,1,2,7,5,3,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,1,2,7,5,6,3]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[4,1,2,7,6,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,2,7,6,5,3]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[4,1,3,2,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}=>[2,4,3,1,5,6,7]=>000111
[4,1,3,2,5,7,6]=>{{1,2,4},{3},{5},{6,7}}=>[2,4,3,1,5,7,6]=>000110
[4,1,3,2,6,5,7]=>{{1,2,4},{3},{5,6},{7}}=>[2,4,3,1,6,5,7]=>000101
[4,1,3,2,6,7,5]=>{{1,2,4},{3},{5,6,7}}=>[2,4,3,1,6,7,5]=>000100
[4,1,3,2,7,5,6]=>{{1,2,4},{3},{5,6,7}}=>[2,4,3,1,6,7,5]=>000100
[4,1,3,2,7,6,5]=>{{1,2,4},{3},{5,7},{6}}=>[2,4,3,1,7,6,5]=>000100
[4,1,3,5,2,6,7]=>{{1,2,4,5},{3},{6},{7}}=>[2,4,3,5,1,6,7]=>000011
[4,1,3,5,2,7,6]=>{{1,2,4,5},{3},{6,7}}=>[2,4,3,5,1,7,6]=>000010
[4,1,3,5,6,2,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[4,1,3,5,6,7,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,1,3,5,7,2,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,1,3,5,7,6,2]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[4,1,3,6,2,5,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[4,1,3,6,2,7,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,1,3,6,5,2,7]=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>000001
[4,1,3,6,5,7,2]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[4,1,3,6,7,2,5]=>{{1,2,4,6},{3},{5,7}}=>[2,4,3,6,7,1,5]=>000000
[4,1,3,6,7,5,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,1,3,7,2,5,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,1,3,7,2,6,5]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[4,1,3,7,5,2,6]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[4,1,3,7,5,6,2]=>{{1,2,4,7},{3},{5},{6}}=>[2,4,3,7,5,6,1]=>000000
[4,1,3,7,6,2,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,1,3,7,6,5,2]=>{{1,2,4,7},{3},{5,6}}=>[2,4,3,7,6,5,1]=>000000
[4,1,5,2,3,6,7]=>{{1,2,4},{3,5},{6},{7}}=>[2,4,5,1,3,6,7]=>000011
[4,1,5,2,3,7,6]=>{{1,2,4},{3,5},{6,7}}=>[2,4,5,1,3,7,6]=>000010
[4,1,5,2,6,3,7]=>{{1,2,4},{3,5,6},{7}}=>[2,4,5,1,6,3,7]=>000001
[4,1,5,2,6,7,3]=>{{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000
[4,1,5,2,7,3,6]=>{{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000
[4,1,5,2,7,6,3]=>{{1,2,4},{3,5,7},{6}}=>[2,4,5,1,7,6,3]=>000000
[4,1,5,3,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[4,1,5,3,2,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[4,1,5,3,6,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,1,5,3,6,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,5,3,7,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,5,3,7,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,1,5,6,2,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,1,5,6,2,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,5,6,3,2,7]=>{{1,2,4,6},{3,5},{7}}=>[2,4,5,6,3,1,7]=>000001
[4,1,5,6,3,7,2]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[4,1,5,6,7,2,3]=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000
[4,1,5,6,7,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,5,7,2,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,5,7,2,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,1,5,7,3,2,6]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[4,1,5,7,3,6,2]=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>000000
[4,1,5,7,6,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,5,7,6,3,2]=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000
[4,1,6,2,3,5,7]=>{{1,2,4},{3,5,6},{7}}=>[2,4,5,1,6,3,7]=>000001
[4,1,6,2,3,7,5]=>{{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000
[4,1,6,2,5,3,7]=>{{1,2,4},{3,6},{5},{7}}=>[2,4,6,1,5,3,7]=>000001
[4,1,6,2,5,7,3]=>{{1,2,4},{3,6,7},{5}}=>[2,4,6,1,5,7,3]=>000000
[4,1,6,2,7,3,5]=>{{1,2,4},{3,6},{5,7}}=>[2,4,6,1,7,3,5]=>000000
[4,1,6,2,7,5,3]=>{{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000
[4,1,6,3,2,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,1,6,3,2,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,6,3,5,2,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[4,1,6,3,5,7,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,1,6,3,7,2,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[4,1,6,3,7,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,6,5,2,3,7]=>{{1,2,4,5},{3,6},{7}}=>[2,4,6,5,1,3,7]=>000001
[4,1,6,5,2,7,3]=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000
[4,1,6,5,3,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,1,6,5,3,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,6,5,7,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,6,5,7,3,2]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[4,1,6,7,2,3,5]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[4,1,6,7,2,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,6,7,3,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,6,7,3,5,2]=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000
[4,1,6,7,5,2,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,1,6,7,5,3,2]=>{{1,2,4,7},{3,6},{5}}=>[2,4,6,7,5,3,1]=>000000
[4,1,7,2,3,5,6]=>{{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000
[4,1,7,2,3,6,5]=>{{1,2,4},{3,5,7},{6}}=>[2,4,5,1,7,6,3]=>000000
[4,1,7,2,5,3,6]=>{{1,2,4},{3,6,7},{5}}=>[2,4,6,1,5,7,3]=>000000
[4,1,7,2,5,6,3]=>{{1,2,4},{3,7},{5},{6}}=>[2,4,7,1,5,6,3]=>000000
[4,1,7,2,6,3,5]=>{{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000
[4,1,7,2,6,5,3]=>{{1,2,4},{3,7},{5,6}}=>[2,4,7,1,6,5,3]=>000000
[4,1,7,3,2,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,7,3,2,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,1,7,3,5,2,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,1,7,3,5,6,2]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[4,1,7,3,6,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,7,3,6,5,2]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[4,1,7,5,2,3,6]=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000
[4,1,7,5,2,6,3]=>{{1,2,4,5},{3,7},{6}}=>[2,4,7,5,1,6,3]=>000000
[4,1,7,5,3,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,7,5,3,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,1,7,5,6,2,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[4,1,7,5,6,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,7,6,2,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,7,6,2,5,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[4,1,7,6,3,2,5]=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000
[4,1,7,6,3,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,1,7,6,5,2,3]=>{{1,2,4,6},{3,7},{5}}=>[2,4,7,6,5,1,3]=>000000
[4,1,7,6,5,3,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,2,1,3,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}=>[3,2,4,1,5,6,7]=>000111
[4,2,1,3,5,7,6]=>{{1,3,4},{2},{5},{6,7}}=>[3,2,4,1,5,7,6]=>000110
[4,2,1,3,6,5,7]=>{{1,3,4},{2},{5,6},{7}}=>[3,2,4,1,6,5,7]=>000101
[4,2,1,3,6,7,5]=>{{1,3,4},{2},{5,6,7}}=>[3,2,4,1,6,7,5]=>000100
[4,2,1,3,7,5,6]=>{{1,3,4},{2},{5,6,7}}=>[3,2,4,1,6,7,5]=>000100
[4,2,1,3,7,6,5]=>{{1,3,4},{2},{5,7},{6}}=>[3,2,4,1,7,6,5]=>000100
[4,2,1,5,3,6,7]=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>000011
[4,2,1,5,3,7,6]=>{{1,3,4,5},{2},{6,7}}=>[3,2,4,5,1,7,6]=>000010
[4,2,1,5,6,3,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[4,2,1,5,6,7,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,1,5,7,3,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,1,5,7,6,3]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[4,2,1,6,3,5,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[4,2,1,6,3,7,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,1,6,5,3,7]=>{{1,3,4,6},{2},{5},{7}}=>[3,2,4,6,5,1,7]=>000001
[4,2,1,6,5,7,3]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[4,2,1,6,7,3,5]=>{{1,3,4,6},{2},{5,7}}=>[3,2,4,6,7,1,5]=>000000
[4,2,1,6,7,5,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,1,7,3,5,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,1,7,3,6,5]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[4,2,1,7,5,3,6]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[4,2,1,7,5,6,3]=>{{1,3,4,7},{2},{5},{6}}=>[3,2,4,7,5,6,1]=>000000
[4,2,1,7,6,3,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,1,7,6,5,3]=>{{1,3,4,7},{2},{5,6}}=>[3,2,4,7,6,5,1]=>000000
[4,2,3,1,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}}=>[4,2,3,1,5,6,7]=>000111
[4,2,3,1,5,7,6]=>{{1,4},{2},{3},{5},{6,7}}=>[4,2,3,1,5,7,6]=>000110
[4,2,3,1,6,5,7]=>{{1,4},{2},{3},{5,6},{7}}=>[4,2,3,1,6,5,7]=>000101
[4,2,3,1,6,7,5]=>{{1,4},{2},{3},{5,6,7}}=>[4,2,3,1,6,7,5]=>000100
[4,2,3,1,7,5,6]=>{{1,4},{2},{3},{5,6,7}}=>[4,2,3,1,6,7,5]=>000100
[4,2,3,1,7,6,5]=>{{1,4},{2},{3},{5,7},{6}}=>[4,2,3,1,7,6,5]=>000100
[4,2,3,5,1,6,7]=>{{1,4,5},{2},{3},{6},{7}}=>[4,2,3,5,1,6,7]=>000011
[4,2,3,5,1,7,6]=>{{1,4,5},{2},{3},{6,7}}=>[4,2,3,5,1,7,6]=>000010
[4,2,3,5,6,1,7]=>{{1,4,5,6},{2},{3},{7}}=>[4,2,3,5,6,1,7]=>000001
[4,2,3,5,6,7,1]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[4,2,3,5,7,1,6]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[4,2,3,5,7,6,1]=>{{1,4,5,7},{2},{3},{6}}=>[4,2,3,5,7,6,1]=>000000
[4,2,3,6,1,5,7]=>{{1,4,5,6},{2},{3},{7}}=>[4,2,3,5,6,1,7]=>000001
[4,2,3,6,1,7,5]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[4,2,3,6,5,1,7]=>{{1,4,6},{2},{3},{5},{7}}=>[4,2,3,6,5,1,7]=>000001
[4,2,3,6,5,7,1]=>{{1,4,6,7},{2},{3},{5}}=>[4,2,3,6,5,7,1]=>000000
[4,2,3,6,7,1,5]=>{{1,4,6},{2},{3},{5,7}}=>[4,2,3,6,7,1,5]=>000000
[4,2,3,6,7,5,1]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[4,2,3,7,1,5,6]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[4,2,3,7,1,6,5]=>{{1,4,5,7},{2},{3},{6}}=>[4,2,3,5,7,6,1]=>000000
[4,2,3,7,5,1,6]=>{{1,4,6,7},{2},{3},{5}}=>[4,2,3,6,5,7,1]=>000000
[4,2,3,7,5,6,1]=>{{1,4,7},{2},{3},{5},{6}}=>[4,2,3,7,5,6,1]=>000000
[4,2,3,7,6,1,5]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[4,2,3,7,6,5,1]=>{{1,4,7},{2},{3},{5,6}}=>[4,2,3,7,6,5,1]=>000000
[4,2,5,1,3,6,7]=>{{1,4},{2},{3,5},{6},{7}}=>[4,2,5,1,3,6,7]=>000011
[4,2,5,1,3,7,6]=>{{1,4},{2},{3,5},{6,7}}=>[4,2,5,1,3,7,6]=>000010
[4,2,5,1,6,3,7]=>{{1,4},{2},{3,5,6},{7}}=>[4,2,5,1,6,3,7]=>000001
[4,2,5,1,6,7,3]=>{{1,4},{2},{3,5,6,7}}=>[4,2,5,1,6,7,3]=>000000
[4,2,5,1,7,3,6]=>{{1,4},{2},{3,5,6,7}}=>[4,2,5,1,6,7,3]=>000000
[4,2,5,1,7,6,3]=>{{1,4},{2},{3,5,7},{6}}=>[4,2,5,1,7,6,3]=>000000
[4,2,5,3,1,6,7]=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>000011
[4,2,5,3,1,7,6]=>{{1,3,4,5},{2},{6,7}}=>[3,2,4,5,1,7,6]=>000010
[4,2,5,3,6,1,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[4,2,5,3,6,7,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,5,3,7,1,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,5,3,7,6,1]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[4,2,5,6,1,3,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[4,2,5,6,1,7,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,5,6,3,1,7]=>{{1,4,6},{2},{3,5},{7}}=>[4,2,5,6,3,1,7]=>000001
[4,2,5,6,3,7,1]=>{{1,4,6,7},{2},{3,5}}=>[4,2,5,6,3,7,1]=>000000
[4,2,5,6,7,1,3]=>{{1,4,6},{2},{3,5,7}}=>[4,2,5,6,7,1,3]=>000000
[4,2,5,6,7,3,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,5,7,1,3,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,5,7,1,6,3]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[4,2,5,7,3,1,6]=>{{1,4,6,7},{2},{3,5}}=>[4,2,5,6,3,7,1]=>000000
[4,2,5,7,3,6,1]=>{{1,4,7},{2},{3,5},{6}}=>[4,2,5,7,3,6,1]=>000000
[4,2,5,7,6,1,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,5,7,6,3,1]=>{{1,4,7},{2},{3,5,6}}=>[4,2,5,7,6,3,1]=>000000
[4,2,6,1,3,5,7]=>{{1,4},{2},{3,5,6},{7}}=>[4,2,5,1,6,3,7]=>000001
[4,2,6,1,3,7,5]=>{{1,4},{2},{3,5,6,7}}=>[4,2,5,1,6,7,3]=>000000
[4,2,6,1,5,3,7]=>{{1,4},{2},{3,6},{5},{7}}=>[4,2,6,1,5,3,7]=>000001
[4,2,6,1,5,7,3]=>{{1,4},{2},{3,6,7},{5}}=>[4,2,6,1,5,7,3]=>000000
[4,2,6,1,7,3,5]=>{{1,4},{2},{3,6},{5,7}}=>[4,2,6,1,7,3,5]=>000000
[4,2,6,1,7,5,3]=>{{1,4},{2},{3,5,6,7}}=>[4,2,5,1,6,7,3]=>000000
[4,2,6,3,1,5,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[4,2,6,3,1,7,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,6,3,5,1,7]=>{{1,3,4,6},{2},{5},{7}}=>[3,2,4,6,5,1,7]=>000001
[4,2,6,3,5,7,1]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[4,2,6,3,7,1,5]=>{{1,3,4,6},{2},{5,7}}=>[3,2,4,6,7,1,5]=>000000
[4,2,6,3,7,5,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,6,5,1,3,7]=>{{1,4,5},{2},{3,6},{7}}=>[4,2,6,5,1,3,7]=>000001
[4,2,6,5,1,7,3]=>{{1,4,5},{2},{3,6,7}}=>[4,2,6,5,1,7,3]=>000000
[4,2,6,5,3,1,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[4,2,6,5,3,7,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,6,5,7,1,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,6,5,7,3,1]=>{{1,4,5,7},{2},{3,6}}=>[4,2,6,5,7,3,1]=>000000
[4,2,6,7,1,3,5]=>{{1,4,5,7},{2},{3,6}}=>[4,2,6,5,7,3,1]=>000000
[4,2,6,7,1,5,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,6,7,3,1,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,6,7,3,5,1]=>{{1,4,7},{2},{3,5,6}}=>[4,2,5,7,6,3,1]=>000000
[4,2,6,7,5,1,3]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[4,2,6,7,5,3,1]=>{{1,4,7},{2},{3,6},{5}}=>[4,2,6,7,5,3,1]=>000000
[4,2,7,1,3,5,6]=>{{1,4},{2},{3,5,6,7}}=>[4,2,5,1,6,7,3]=>000000
[4,2,7,1,3,6,5]=>{{1,4},{2},{3,5,7},{6}}=>[4,2,5,1,7,6,3]=>000000
[4,2,7,1,5,3,6]=>{{1,4},{2},{3,6,7},{5}}=>[4,2,6,1,5,7,3]=>000000
[4,2,7,1,5,6,3]=>{{1,4},{2},{3,7},{5},{6}}=>[4,2,7,1,5,6,3]=>000000
[4,2,7,1,6,3,5]=>{{1,4},{2},{3,5,6,7}}=>[4,2,5,1,6,7,3]=>000000
[4,2,7,1,6,5,3]=>{{1,4},{2},{3,7},{5,6}}=>[4,2,7,1,6,5,3]=>000000
[4,2,7,3,1,5,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,7,3,1,6,5]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[4,2,7,3,5,1,6]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[4,2,7,3,5,6,1]=>{{1,3,4,7},{2},{5},{6}}=>[3,2,4,7,5,6,1]=>000000
[4,2,7,3,6,1,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,7,3,6,5,1]=>{{1,3,4,7},{2},{5,6}}=>[3,2,4,7,6,5,1]=>000000
[4,2,7,5,1,3,6]=>{{1,4,5},{2},{3,6,7}}=>[4,2,6,5,1,7,3]=>000000
[4,2,7,5,1,6,3]=>{{1,4,5},{2},{3,7},{6}}=>[4,2,7,5,1,6,3]=>000000
[4,2,7,5,3,1,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,7,5,3,6,1]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[4,2,7,5,6,1,3]=>{{1,4,5,6},{2},{3,7}}=>[4,2,7,5,6,1,3]=>000000
[4,2,7,5,6,3,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,7,6,1,3,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,7,6,1,5,3]=>{{1,4,5,6},{2},{3,7}}=>[4,2,7,5,6,1,3]=>000000
[4,2,7,6,3,1,5]=>{{1,4,6},{2},{3,5,7}}=>[4,2,5,6,7,1,3]=>000000
[4,2,7,6,3,5,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[4,2,7,6,5,1,3]=>{{1,4,6},{2},{3,7},{5}}=>[4,2,7,6,5,1,3]=>000000
[4,2,7,6,5,3,1]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[4,3,1,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>000111
[4,3,1,2,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>000110
[4,3,1,2,6,5,7]=>{{1,2,3,4},{5,6},{7}}=>[2,3,4,1,6,5,7]=>000101
[4,3,1,2,6,7,5]=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100
[4,3,1,2,7,5,6]=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100
[4,3,1,2,7,6,5]=>{{1,2,3,4},{5,7},{6}}=>[2,3,4,1,7,6,5]=>000100
[4,3,1,5,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[4,3,1,5,2,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[4,3,1,5,6,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,3,1,5,6,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,1,5,7,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,1,5,7,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,3,1,6,2,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,3,1,6,2,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,1,6,5,2,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[4,3,1,6,5,7,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,3,1,6,7,2,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[4,3,1,6,7,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,1,7,2,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,1,7,2,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,3,1,7,5,2,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,3,1,7,5,6,2]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,1,7,6,5,2]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[4,3,2,1,5,6,7]=>{{1,4},{2,3},{5},{6},{7}}=>[4,3,2,1,5,6,7]=>000111
[4,3,2,1,5,7,6]=>{{1,4},{2,3},{5},{6,7}}=>[4,3,2,1,5,7,6]=>000110
[4,3,2,1,6,5,7]=>{{1,4},{2,3},{5,6},{7}}=>[4,3,2,1,6,5,7]=>000101
[4,3,2,1,6,7,5]=>{{1,4},{2,3},{5,6,7}}=>[4,3,2,1,6,7,5]=>000100
[4,3,2,1,7,5,6]=>{{1,4},{2,3},{5,6,7}}=>[4,3,2,1,6,7,5]=>000100
[4,3,2,1,7,6,5]=>{{1,4},{2,3},{5,7},{6}}=>[4,3,2,1,7,6,5]=>000100
[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}}=>[4,3,2,5,1,6,7]=>000011
[4,3,2,5,1,7,6]=>{{1,4,5},{2,3},{6,7}}=>[4,3,2,5,1,7,6]=>000010
[4,3,2,5,6,1,7]=>{{1,4,5,6},{2,3},{7}}=>[4,3,2,5,6,1,7]=>000001
[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[4,3,2,5,7,1,6]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[4,3,2,5,7,6,1]=>{{1,4,5,7},{2,3},{6}}=>[4,3,2,5,7,6,1]=>000000
[4,3,2,6,1,5,7]=>{{1,4,5,6},{2,3},{7}}=>[4,3,2,5,6,1,7]=>000001
[4,3,2,6,1,7,5]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[4,3,2,6,5,1,7]=>{{1,4,6},{2,3},{5},{7}}=>[4,3,2,6,5,1,7]=>000001
[4,3,2,6,5,7,1]=>{{1,4,6,7},{2,3},{5}}=>[4,3,2,6,5,7,1]=>000000
[4,3,2,6,7,1,5]=>{{1,4,6},{2,3},{5,7}}=>[4,3,2,6,7,1,5]=>000000
[4,3,2,6,7,5,1]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[4,3,2,7,1,5,6]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[4,3,2,7,1,6,5]=>{{1,4,5,7},{2,3},{6}}=>[4,3,2,5,7,6,1]=>000000
[4,3,2,7,5,1,6]=>{{1,4,6,7},{2,3},{5}}=>[4,3,2,6,5,7,1]=>000000
[4,3,2,7,5,6,1]=>{{1,4,7},{2,3},{5},{6}}=>[4,3,2,7,5,6,1]=>000000
[4,3,2,7,6,1,5]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[4,3,2,7,6,5,1]=>{{1,4,7},{2,3},{5,6}}=>[4,3,2,7,6,5,1]=>000000
[4,3,5,1,2,6,7]=>{{1,4},{2,3,5},{6},{7}}=>[4,3,5,1,2,6,7]=>000011
[4,3,5,1,2,7,6]=>{{1,4},{2,3,5},{6,7}}=>[4,3,5,1,2,7,6]=>000010
[4,3,5,1,6,2,7]=>{{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>000001
[4,3,5,1,6,7,2]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,3,5,1,7,2,6]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,3,5,1,7,6,2]=>{{1,4},{2,3,5,7},{6}}=>[4,3,5,1,7,6,2]=>000000
[4,3,5,2,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[4,3,5,2,1,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[4,3,5,2,6,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,3,5,2,6,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,5,2,7,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,5,2,7,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,3,5,6,1,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,3,5,6,1,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,5,6,2,1,7]=>{{1,4,6},{2,3,5},{7}}=>[4,3,5,6,2,1,7]=>000001
[4,3,5,6,2,7,1]=>{{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000
[4,3,5,6,7,1,2]=>{{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000
[4,3,5,6,7,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,5,7,1,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,5,7,1,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,3,5,7,2,1,6]=>{{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000
[4,3,5,7,2,6,1]=>{{1,4,7},{2,3,5},{6}}=>[4,3,5,7,2,6,1]=>000000
[4,3,5,7,6,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,5,7,6,2,1]=>{{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000
[4,3,6,1,2,5,7]=>{{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>000001
[4,3,6,1,2,7,5]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,3,6,1,5,2,7]=>{{1,4},{2,3,6},{5},{7}}=>[4,3,6,1,5,2,7]=>000001
[4,3,6,1,5,7,2]=>{{1,4},{2,3,6,7},{5}}=>[4,3,6,1,5,7,2]=>000000
[4,3,6,1,7,2,5]=>{{1,4},{2,3,6},{5,7}}=>[4,3,6,1,7,2,5]=>000000
[4,3,6,1,7,5,2]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,3,6,2,1,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,3,6,2,1,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,6,2,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[4,3,6,2,5,7,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,3,6,2,7,1,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[4,3,6,2,7,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,6,5,1,2,7]=>{{1,4,5},{2,3,6},{7}}=>[4,3,6,5,1,2,7]=>000001
[4,3,6,5,1,7,2]=>{{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000
[4,3,6,5,2,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,3,6,5,2,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,6,5,7,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,6,5,7,2,1]=>{{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000
[4,3,6,7,1,2,5]=>{{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000
[4,3,6,7,1,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,6,7,2,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,6,7,2,5,1]=>{{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000
[4,3,6,7,5,1,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,3,6,7,5,2,1]=>{{1,4,7},{2,3,6},{5}}=>[4,3,6,7,5,2,1]=>000000
[4,3,7,1,2,5,6]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,3,7,1,2,6,5]=>{{1,4},{2,3,5,7},{6}}=>[4,3,5,1,7,6,2]=>000000
[4,3,7,1,5,2,6]=>{{1,4},{2,3,6,7},{5}}=>[4,3,6,1,5,7,2]=>000000
[4,3,7,1,5,6,2]=>{{1,4},{2,3,7},{5},{6}}=>[4,3,7,1,5,6,2]=>000000
[4,3,7,1,6,2,5]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,3,7,1,6,5,2]=>{{1,4},{2,3,7},{5,6}}=>[4,3,7,1,6,5,2]=>000000
[4,3,7,2,1,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,7,2,1,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,3,7,2,5,1,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,3,7,2,5,6,1]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[4,3,7,2,6,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,7,2,6,5,1]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[4,3,7,5,1,2,6]=>{{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000
[4,3,7,5,1,6,2]=>{{1,4,5},{2,3,7},{6}}=>[4,3,7,5,1,6,2]=>000000
[4,3,7,5,2,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,7,5,2,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,3,7,5,6,1,2]=>{{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000
[4,3,7,5,6,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,7,6,1,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,7,6,1,5,2]=>{{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000
[4,3,7,6,2,1,5]=>{{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000
[4,3,7,6,2,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,3,7,6,5,1,2]=>{{1,4,6},{2,3,7},{5}}=>[4,3,7,6,5,1,2]=>000000
[4,3,7,6,5,2,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,5,1,2,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[4,5,1,2,3,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[4,5,1,2,6,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,5,1,2,6,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,1,2,7,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,1,2,7,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,5,1,3,2,6,7]=>{{1,3,4},{2,5},{6},{7}}=>[3,5,4,1,2,6,7]=>000011
[4,5,1,3,2,7,6]=>{{1,3,4},{2,5},{6,7}}=>[3,5,4,1,2,7,6]=>000010
[4,5,1,3,6,2,7]=>{{1,3,4},{2,5,6},{7}}=>[3,5,4,1,6,2,7]=>000001
[4,5,1,3,6,7,2]=>{{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000
[4,5,1,3,7,2,6]=>{{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000
[4,5,1,3,7,6,2]=>{{1,3,4},{2,5,7},{6}}=>[3,5,4,1,7,6,2]=>000000
[4,5,1,6,2,3,7]=>{{1,3,4,6},{2,5},{7}}=>[3,5,4,6,2,1,7]=>000001
[4,5,1,6,2,7,3]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[4,5,1,6,3,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,5,1,6,3,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,1,6,7,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,1,6,7,3,2]=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000
[4,5,1,7,2,3,6]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[4,5,1,7,2,6,3]=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>000000
[4,5,1,7,3,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,1,7,3,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,5,1,7,6,2,3]=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000
[4,5,1,7,6,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,2,1,3,6,7]=>{{1,4},{2,3,5},{6},{7}}=>[4,3,5,1,2,6,7]=>000011
[4,5,2,1,3,7,6]=>{{1,4},{2,3,5},{6,7}}=>[4,3,5,1,2,7,6]=>000010
[4,5,2,1,6,3,7]=>{{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>000001
[4,5,2,1,6,7,3]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,5,2,1,7,3,6]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,5,2,1,7,6,3]=>{{1,4},{2,3,5,7},{6}}=>[4,3,5,1,7,6,2]=>000000
[4,5,2,3,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[4,5,2,3,1,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[4,5,2,3,6,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,5,2,3,6,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,2,3,7,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,2,3,7,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,5,2,6,1,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,5,2,6,1,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,2,6,3,1,7]=>{{1,4,6},{2,3,5},{7}}=>[4,3,5,6,2,1,7]=>000001
[4,5,2,6,3,7,1]=>{{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000
[4,5,2,6,7,1,3]=>{{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000
[4,5,2,6,7,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,2,7,1,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,2,7,1,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,5,2,7,3,1,6]=>{{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000
[4,5,2,7,3,6,1]=>{{1,4,7},{2,3,5},{6}}=>[4,3,5,7,2,6,1]=>000000
[4,5,2,7,6,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,2,7,6,3,1]=>{{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000
[4,5,3,1,2,6,7]=>{{1,4},{2,5},{3},{6},{7}}=>[4,5,3,1,2,6,7]=>000011
[4,5,3,1,2,7,6]=>{{1,4},{2,5},{3},{6,7}}=>[4,5,3,1,2,7,6]=>000010
[4,5,3,1,6,2,7]=>{{1,4},{2,5,6},{3},{7}}=>[4,5,3,1,6,2,7]=>000001
[4,5,3,1,6,7,2]=>{{1,4},{2,5,6,7},{3}}=>[4,5,3,1,6,7,2]=>000000
[4,5,3,1,7,2,6]=>{{1,4},{2,5,6,7},{3}}=>[4,5,3,1,6,7,2]=>000000
[4,5,3,1,7,6,2]=>{{1,4},{2,5,7},{3},{6}}=>[4,5,3,1,7,6,2]=>000000
[4,5,3,2,1,6,7]=>{{1,2,4,5},{3},{6},{7}}=>[2,4,3,5,1,6,7]=>000011
[4,5,3,2,1,7,6]=>{{1,2,4,5},{3},{6,7}}=>[2,4,3,5,1,7,6]=>000010
[4,5,3,2,6,1,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[4,5,3,2,6,7,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,5,3,2,7,1,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,5,3,2,7,6,1]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[4,5,3,6,1,2,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[4,5,3,6,1,7,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,5,3,6,2,1,7]=>{{1,4,6},{2,5},{3},{7}}=>[4,5,3,6,2,1,7]=>000001
[4,5,3,6,2,7,1]=>{{1,4,6,7},{2,5},{3}}=>[4,5,3,6,2,7,1]=>000000
[4,5,3,6,7,1,2]=>{{1,4,6},{2,5,7},{3}}=>[4,5,3,6,7,1,2]=>000000
[4,5,3,6,7,2,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,5,3,7,1,2,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,5,3,7,1,6,2]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[4,5,3,7,2,1,6]=>{{1,4,6,7},{2,5},{3}}=>[4,5,3,6,2,7,1]=>000000
[4,5,3,7,2,6,1]=>{{1,4,7},{2,5},{3},{6}}=>[4,5,3,7,2,6,1]=>000000
[4,5,3,7,6,1,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,5,3,7,6,2,1]=>{{1,4,7},{2,5,6},{3}}=>[4,5,3,7,6,2,1]=>000000
[4,5,6,1,2,3,7]=>{{1,4},{2,5},{3,6},{7}}=>[4,5,6,1,2,3,7]=>000001
[4,5,6,1,2,7,3]=>{{1,4},{2,5},{3,6,7}}=>[4,5,6,1,2,7,3]=>000000
[4,5,6,1,3,2,7]=>{{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>000001
[4,5,6,1,3,7,2]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,5,6,1,7,2,3]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,5,6,1,7,3,2]=>{{1,4},{2,5,7},{3,6}}=>[4,5,6,1,7,3,2]=>000000
[4,5,6,2,1,3,7]=>{{1,2,4,5},{3,6},{7}}=>[2,4,6,5,1,3,7]=>000001
[4,5,6,2,1,7,3]=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000
[4,5,6,2,3,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,5,6,2,3,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,6,2,7,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,6,2,7,3,1]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[4,5,6,3,1,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,5,6,3,1,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,6,3,2,1,7]=>{{1,3,4,6},{2,5},{7}}=>[3,5,4,6,2,1,7]=>000001
[4,5,6,3,2,7,1]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[4,5,6,3,7,1,2]=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000
[4,5,6,3,7,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,6,7,1,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,6,7,1,3,2]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[4,5,6,7,2,1,3]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[4,5,6,7,2,3,1]=>{{1,4,7},{2,5},{3,6}}=>[4,5,6,7,2,3,1]=>000000
[4,5,6,7,3,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,6,7,3,2,1]=>{{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000
[4,5,7,1,2,3,6]=>{{1,4},{2,5},{3,6,7}}=>[4,5,6,1,2,7,3]=>000000
[4,5,7,1,2,6,3]=>{{1,4},{2,5},{3,7},{6}}=>[4,5,7,1,2,6,3]=>000000
[4,5,7,1,3,2,6]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,5,7,1,3,6,2]=>{{1,4},{2,3,5,7},{6}}=>[4,3,5,1,7,6,2]=>000000
[4,5,7,1,6,2,3]=>{{1,4},{2,5,6},{3,7}}=>[4,5,7,1,6,2,3]=>000000
[4,5,7,1,6,3,2]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,5,7,2,1,3,6]=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000
[4,5,7,2,1,6,3]=>{{1,2,4,5},{3,7},{6}}=>[2,4,7,5,1,6,3]=>000000
[4,5,7,2,3,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,7,2,3,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,5,7,2,6,1,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[4,5,7,2,6,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,7,3,1,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,7,3,1,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,5,7,3,2,1,6]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[4,5,7,3,2,6,1]=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>000000
[4,5,7,3,6,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,7,3,6,2,1]=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000
[4,5,7,6,1,2,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[4,5,7,6,1,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,5,7,6,2,1,3]=>{{1,4,6},{2,5},{3,7}}=>[4,5,7,6,2,1,3]=>000000
[4,5,7,6,2,3,1]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[4,5,7,6,3,1,2]=>{{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000
[4,5,7,6,3,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,1,2,3,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,6,1,2,3,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,1,2,5,3,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[4,6,1,2,5,7,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,6,1,2,7,3,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[4,6,1,2,7,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,1,3,2,5,7]=>{{1,3,4},{2,5,6},{7}}=>[3,5,4,1,6,2,7]=>000001
[4,6,1,3,2,7,5]=>{{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000
[4,6,1,3,5,2,7]=>{{1,3,4},{2,6},{5},{7}}=>[3,6,4,1,5,2,7]=>000001
[4,6,1,3,5,7,2]=>{{1,3,4},{2,6,7},{5}}=>[3,6,4,1,5,7,2]=>000000
[4,6,1,3,7,2,5]=>{{1,3,4},{2,6},{5,7}}=>[3,6,4,1,7,2,5]=>000000
[4,6,1,3,7,5,2]=>{{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000
[4,6,1,5,2,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,6,1,5,2,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,1,5,3,2,7]=>{{1,3,4,5},{2,6},{7}}=>[3,6,4,5,1,2,7]=>000001
[4,6,1,5,3,7,2]=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000
[4,6,1,5,7,2,3]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[4,6,1,5,7,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,1,7,2,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,1,7,2,5,3]=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000
[4,6,1,7,3,2,5]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[4,6,1,7,3,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,1,7,5,2,3]=>{{1,3,4,7},{2,6},{5}}=>[3,6,4,7,5,2,1]=>000000
[4,6,1,7,5,3,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,6,2,1,3,5,7]=>{{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>000001
[4,6,2,1,3,7,5]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,6,2,1,5,3,7]=>{{1,4},{2,3,6},{5},{7}}=>[4,3,6,1,5,2,7]=>000001
[4,6,2,1,5,7,3]=>{{1,4},{2,3,6,7},{5}}=>[4,3,6,1,5,7,2]=>000000
[4,6,2,1,7,3,5]=>{{1,4},{2,3,6},{5,7}}=>[4,3,6,1,7,2,5]=>000000
[4,6,2,1,7,5,3]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,6,2,3,1,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,6,2,3,1,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,2,3,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[4,6,2,3,5,7,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,6,2,3,7,1,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[4,6,2,3,7,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,2,5,1,3,7]=>{{1,4,5},{2,3,6},{7}}=>[4,3,6,5,1,2,7]=>000001
[4,6,2,5,1,7,3]=>{{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000
[4,6,2,5,3,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,6,2,5,3,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,2,5,7,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,2,5,7,3,1]=>{{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000
[4,6,2,7,1,3,5]=>{{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000
[4,6,2,7,1,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,2,7,3,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,2,7,3,5,1]=>{{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000
[4,6,2,7,5,1,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,6,2,7,5,3,1]=>{{1,4,7},{2,3,6},{5}}=>[4,3,6,7,5,2,1]=>000000
[4,6,3,1,2,5,7]=>{{1,4},{2,5,6},{3},{7}}=>[4,5,3,1,6,2,7]=>000001
[4,6,3,1,2,7,5]=>{{1,4},{2,5,6,7},{3}}=>[4,5,3,1,6,7,2]=>000000
[4,6,3,1,5,2,7]=>{{1,4},{2,6},{3},{5},{7}}=>[4,6,3,1,5,2,7]=>000001
[4,6,3,1,5,7,2]=>{{1,4},{2,6,7},{3},{5}}=>[4,6,3,1,5,7,2]=>000000
[4,6,3,1,7,2,5]=>{{1,4},{2,6},{3},{5,7}}=>[4,6,3,1,7,2,5]=>000000
[4,6,3,1,7,5,2]=>{{1,4},{2,5,6,7},{3}}=>[4,5,3,1,6,7,2]=>000000
[4,6,3,2,1,5,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[4,6,3,2,1,7,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,6,3,2,5,1,7]=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>000001
[4,6,3,2,5,7,1]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[4,6,3,2,7,1,5]=>{{1,2,4,6},{3},{5,7}}=>[2,4,3,6,7,1,5]=>000000
[4,6,3,2,7,5,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,6,3,5,1,2,7]=>{{1,4,5},{2,6},{3},{7}}=>[4,6,3,5,1,2,7]=>000001
[4,6,3,5,1,7,2]=>{{1,4,5},{2,6,7},{3}}=>[4,6,3,5,1,7,2]=>000000
[4,6,3,5,2,1,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[4,6,3,5,2,7,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,6,3,5,7,1,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,6,3,5,7,2,1]=>{{1,4,5,7},{2,6},{3}}=>[4,6,3,5,7,2,1]=>000000
[4,6,3,7,1,2,5]=>{{1,4,5,7},{2,6},{3}}=>[4,6,3,5,7,2,1]=>000000
[4,6,3,7,1,5,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,6,3,7,2,1,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,6,3,7,2,5,1]=>{{1,4,7},{2,5,6},{3}}=>[4,5,3,7,6,2,1]=>000000
[4,6,3,7,5,1,2]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[4,6,3,7,5,2,1]=>{{1,4,7},{2,6},{3},{5}}=>[4,6,3,7,5,2,1]=>000000
[4,6,5,1,2,3,7]=>{{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>000001
[4,6,5,1,2,7,3]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,6,5,1,3,2,7]=>{{1,4},{2,6},{3,5},{7}}=>[4,6,5,1,3,2,7]=>000001
[4,6,5,1,3,7,2]=>{{1,4},{2,6,7},{3,5}}=>[4,6,5,1,3,7,2]=>000000
[4,6,5,1,7,2,3]=>{{1,4},{2,6},{3,5,7}}=>[4,6,5,1,7,2,3]=>000000
[4,6,5,1,7,3,2]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,6,5,2,1,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,6,5,2,1,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,5,2,3,1,7]=>{{1,2,4,6},{3,5},{7}}=>[2,4,5,6,3,1,7]=>000001
[4,6,5,2,3,7,1]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[4,6,5,2,7,1,3]=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000
[4,6,5,2,7,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,5,3,1,2,7]=>{{1,3,4,5},{2,6},{7}}=>[3,6,4,5,1,2,7]=>000001
[4,6,5,3,1,7,2]=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000
[4,6,5,3,2,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[4,6,5,3,2,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,5,3,7,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,5,3,7,2,1]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[4,6,5,7,1,2,3]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[4,6,5,7,1,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,5,7,2,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,5,7,2,3,1]=>{{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000
[4,6,5,7,3,1,2]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[4,6,5,7,3,2,1]=>{{1,4,7},{2,6},{3,5}}=>[4,6,5,7,3,2,1]=>000000
[4,6,7,1,2,3,5]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,6,7,1,2,5,3]=>{{1,4},{2,5,6},{3,7}}=>[4,5,7,1,6,2,3]=>000000
[4,6,7,1,3,2,5]=>{{1,4},{2,6},{3,5,7}}=>[4,6,5,1,7,2,3]=>000000
[4,6,7,1,3,5,2]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,6,7,1,5,2,3]=>{{1,4},{2,6},{3,7},{5}}=>[4,6,7,1,5,2,3]=>000000
[4,6,7,1,5,3,2]=>{{1,4},{2,3,6,7},{5}}=>[4,3,6,1,5,7,2]=>000000
[4,6,7,2,1,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,7,2,1,5,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[4,6,7,2,3,1,5]=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000
[4,6,7,2,3,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,7,2,5,1,3]=>{{1,2,4,6},{3,7},{5}}=>[2,4,7,6,5,1,3]=>000000
[4,6,7,2,5,3,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,6,7,3,1,2,5]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[4,6,7,3,1,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,7,3,2,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,7,3,2,5,1]=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000
[4,6,7,3,5,1,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,6,7,3,5,2,1]=>{{1,3,4,7},{2,6},{5}}=>[3,6,4,7,5,2,1]=>000000
[4,6,7,5,1,2,3]=>{{1,4,5},{2,6},{3,7}}=>[4,6,7,5,1,2,3]=>000000
[4,6,7,5,1,3,2]=>{{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000
[4,6,7,5,2,1,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[4,6,7,5,2,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,7,5,3,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,6,7,5,3,2,1]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[4,7,1,2,3,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,1,2,3,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,7,1,2,5,3,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,7,1,2,5,6,3]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[4,7,1,2,6,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,1,2,6,5,3]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[4,7,1,3,2,5,6]=>{{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000
[4,7,1,3,2,6,5]=>{{1,3,4},{2,5,7},{6}}=>[3,5,4,1,7,6,2]=>000000
[4,7,1,3,5,2,6]=>{{1,3,4},{2,6,7},{5}}=>[3,6,4,1,5,7,2]=>000000
[4,7,1,3,5,6,2]=>{{1,3,4},{2,7},{5},{6}}=>[3,7,4,1,5,6,2]=>000000
[4,7,1,3,6,2,5]=>{{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000
[4,7,1,3,6,5,2]=>{{1,3,4},{2,7},{5,6}}=>[3,7,4,1,6,5,2]=>000000
[4,7,1,5,2,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,1,5,2,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,7,1,5,3,2,6]=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000
[4,7,1,5,3,6,2]=>{{1,3,4,5},{2,7},{6}}=>[3,7,4,5,1,6,2]=>000000
[4,7,1,5,6,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,1,5,6,3,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[4,7,1,6,2,3,5]=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000
[4,7,1,6,2,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,1,6,3,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,1,6,3,5,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[4,7,1,6,5,2,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,7,1,6,5,3,2]=>{{1,3,4,6},{2,7},{5}}=>[3,7,4,6,5,1,2]=>000000
[4,7,2,1,3,5,6]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,7,2,1,3,6,5]=>{{1,4},{2,3,5,7},{6}}=>[4,3,5,1,7,6,2]=>000000
[4,7,2,1,5,3,6]=>{{1,4},{2,3,6,7},{5}}=>[4,3,6,1,5,7,2]=>000000
[4,7,2,1,5,6,3]=>{{1,4},{2,3,7},{5},{6}}=>[4,3,7,1,5,6,2]=>000000
[4,7,2,1,6,3,5]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,7,2,1,6,5,3]=>{{1,4},{2,3,7},{5,6}}=>[4,3,7,1,6,5,2]=>000000
[4,7,2,3,1,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,2,3,1,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,7,2,3,5,1,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,7,2,3,5,6,1]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[4,7,2,3,6,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,2,3,6,5,1]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[4,7,2,5,1,3,6]=>{{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000
[4,7,2,5,1,6,3]=>{{1,4,5},{2,3,7},{6}}=>[4,3,7,5,1,6,2]=>000000
[4,7,2,5,3,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,2,5,3,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,7,2,5,6,1,3]=>{{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000
[4,7,2,5,6,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,2,6,1,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,2,6,1,5,3]=>{{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000
[4,7,2,6,3,1,5]=>{{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000
[4,7,2,6,3,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,2,6,5,1,3]=>{{1,4,6},{2,3,7},{5}}=>[4,3,7,6,5,1,2]=>000000
[4,7,2,6,5,3,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,7,3,1,2,5,6]=>{{1,4},{2,5,6,7},{3}}=>[4,5,3,1,6,7,2]=>000000
[4,7,3,1,2,6,5]=>{{1,4},{2,5,7},{3},{6}}=>[4,5,3,1,7,6,2]=>000000
[4,7,3,1,5,2,6]=>{{1,4},{2,6,7},{3},{5}}=>[4,6,3,1,5,7,2]=>000000
[4,7,3,1,5,6,2]=>{{1,4},{2,7},{3},{5},{6}}=>[4,7,3,1,5,6,2]=>000000
[4,7,3,1,6,2,5]=>{{1,4},{2,5,6,7},{3}}=>[4,5,3,1,6,7,2]=>000000
[4,7,3,1,6,5,2]=>{{1,4},{2,7},{3},{5,6}}=>[4,7,3,1,6,5,2]=>000000
[4,7,3,2,1,5,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,7,3,2,1,6,5]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[4,7,3,2,5,1,6]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[4,7,3,2,5,6,1]=>{{1,2,4,7},{3},{5},{6}}=>[2,4,3,7,5,6,1]=>000000
[4,7,3,2,6,1,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,7,3,2,6,5,1]=>{{1,2,4,7},{3},{5,6}}=>[2,4,3,7,6,5,1]=>000000
[4,7,3,5,1,2,6]=>{{1,4,5},{2,6,7},{3}}=>[4,6,3,5,1,7,2]=>000000
[4,7,3,5,1,6,2]=>{{1,4,5},{2,7},{3},{6}}=>[4,7,3,5,1,6,2]=>000000
[4,7,3,5,2,1,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,7,3,5,2,6,1]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[4,7,3,5,6,1,2]=>{{1,4,5,6},{2,7},{3}}=>[4,7,3,5,6,1,2]=>000000
[4,7,3,5,6,2,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,7,3,6,1,2,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,7,3,6,1,5,2]=>{{1,4,5,6},{2,7},{3}}=>[4,7,3,5,6,1,2]=>000000
[4,7,3,6,2,1,5]=>{{1,4,6},{2,5,7},{3}}=>[4,5,3,6,7,1,2]=>000000
[4,7,3,6,2,5,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[4,7,3,6,5,1,2]=>{{1,4,6},{2,7},{3},{5}}=>[4,7,3,6,5,1,2]=>000000
[4,7,3,6,5,2,1]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[4,7,5,1,2,3,6]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,7,5,1,2,6,3]=>{{1,4},{2,3,5,7},{6}}=>[4,3,5,1,7,6,2]=>000000
[4,7,5,1,3,2,6]=>{{1,4},{2,6,7},{3,5}}=>[4,6,5,1,3,7,2]=>000000
[4,7,5,1,3,6,2]=>{{1,4},{2,7},{3,5},{6}}=>[4,7,5,1,3,6,2]=>000000
[4,7,5,1,6,2,3]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,7,5,1,6,3,2]=>{{1,4},{2,7},{3,5,6}}=>[4,7,5,1,6,3,2]=>000000
[4,7,5,2,1,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,5,2,1,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,7,5,2,3,1,6]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[4,7,5,2,3,6,1]=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>000000
[4,7,5,2,6,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,5,2,6,3,1]=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000
[4,7,5,3,1,2,6]=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000
[4,7,5,3,1,6,2]=>{{1,3,4,5},{2,7},{6}}=>[3,7,4,5,1,6,2]=>000000
[4,7,5,3,2,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,5,3,2,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[4,7,5,3,6,1,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[4,7,5,3,6,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,5,6,1,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,5,6,1,3,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[4,7,5,6,2,1,3]=>{{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000
[4,7,5,6,2,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,5,6,3,1,2]=>{{1,4,6},{2,7},{3,5}}=>[4,7,5,6,3,1,2]=>000000
[4,7,5,6,3,2,1]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[4,7,6,1,2,3,5]=>{{1,4},{2,5,7},{3,6}}=>[4,5,6,1,7,3,2]=>000000
[4,7,6,1,2,5,3]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,7,6,1,3,2,5]=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
[4,7,6,1,3,5,2]=>{{1,4},{2,7},{3,5,6}}=>[4,7,5,1,6,3,2]=>000000
[4,7,6,1,5,2,3]=>{{1,4},{2,3,6,7},{5}}=>[4,3,6,1,5,7,2]=>000000
[4,7,6,1,5,3,2]=>{{1,4},{2,7},{3,6},{5}}=>[4,7,6,1,5,3,2]=>000000
[4,7,6,2,1,3,5]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[4,7,6,2,1,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,6,2,3,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,6,2,3,5,1]=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000
[4,7,6,2,5,1,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,7,6,2,5,3,1]=>{{1,2,4,7},{3,6},{5}}=>[2,4,6,7,5,3,1]=>000000
[4,7,6,3,1,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,6,3,1,5,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[4,7,6,3,2,1,5]=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000
[4,7,6,3,2,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,6,3,5,1,2]=>{{1,3,4,6},{2,7},{5}}=>[3,7,4,6,5,1,2]=>000000
[4,7,6,3,5,2,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[4,7,6,5,1,2,3]=>{{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000
[4,7,6,5,1,3,2]=>{{1,4,5},{2,7},{3,6}}=>[4,7,6,5,1,3,2]=>000000
[4,7,6,5,2,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[4,7,6,5,2,3,1]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[4,7,6,5,3,1,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[4,7,6,5,3,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,2,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[5,1,2,3,4,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[5,1,2,3,6,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,1,2,3,6,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,2,3,7,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,2,3,7,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,1,2,4,3,6,7]=>{{1,2,3,5},{4},{6},{7}}=>[2,3,5,4,1,6,7]=>000011
[5,1,2,4,3,7,6]=>{{1,2,3,5},{4},{6,7}}=>[2,3,5,4,1,7,6]=>000010
[5,1,2,4,6,3,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[5,1,2,4,6,7,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,1,2,4,7,3,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,1,2,4,7,6,3]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[5,1,2,6,3,4,7]=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>000001
[5,1,2,6,3,7,4]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000
[5,1,2,6,4,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,1,2,6,4,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,2,6,7,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,2,6,7,4,3]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[5,1,2,7,3,4,6]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000
[5,1,2,7,3,6,4]=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>000000
[5,1,2,7,4,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,2,7,4,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,1,2,7,6,3,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[5,1,2,7,6,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,3,2,4,6,7]=>{{1,2,4,5},{3},{6},{7}}=>[2,4,3,5,1,6,7]=>000011
[5,1,3,2,4,7,6]=>{{1,2,4,5},{3},{6,7}}=>[2,4,3,5,1,7,6]=>000010
[5,1,3,2,6,4,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[5,1,3,2,6,7,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,1,3,2,7,4,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,1,3,2,7,6,4]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[5,1,3,4,2,6,7]=>{{1,2,5},{3},{4},{6},{7}}=>[2,5,3,4,1,6,7]=>000011
[5,1,3,4,2,7,6]=>{{1,2,5},{3},{4},{6,7}}=>[2,5,3,4,1,7,6]=>000010
[5,1,3,4,6,2,7]=>{{1,2,5,6},{3},{4},{7}}=>[2,5,3,4,6,1,7]=>000001
[5,1,3,4,6,7,2]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[5,1,3,4,7,2,6]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[5,1,3,4,7,6,2]=>{{1,2,5,7},{3},{4},{6}}=>[2,5,3,4,7,6,1]=>000000
[5,1,3,6,2,4,7]=>{{1,2,5},{3},{4,6},{7}}=>[2,5,3,6,1,4,7]=>000001
[5,1,3,6,2,7,4]=>{{1,2,5},{3},{4,6,7}}=>[2,5,3,6,1,7,4]=>000000
[5,1,3,6,4,2,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[5,1,3,6,4,7,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,1,3,6,7,2,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,1,3,6,7,4,2]=>{{1,2,5,7},{3},{4,6}}=>[2,5,3,6,7,4,1]=>000000
[5,1,3,7,2,4,6]=>{{1,2,5},{3},{4,6,7}}=>[2,5,3,6,1,7,4]=>000000
[5,1,3,7,2,6,4]=>{{1,2,5},{3},{4,7},{6}}=>[2,5,3,7,1,6,4]=>000000
[5,1,3,7,4,2,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,1,3,7,4,6,2]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[5,1,3,7,6,2,4]=>{{1,2,5,6},{3},{4,7}}=>[2,5,3,7,6,1,4]=>000000
[5,1,3,7,6,4,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,1,4,2,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[5,1,4,2,3,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[5,1,4,2,6,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,1,4,2,6,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,4,2,7,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,4,2,7,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,1,4,3,2,6,7]=>{{1,2,5},{3,4},{6},{7}}=>[2,5,4,3,1,6,7]=>000011
[5,1,4,3,2,7,6]=>{{1,2,5},{3,4},{6,7}}=>[2,5,4,3,1,7,6]=>000010
[5,1,4,3,6,2,7]=>{{1,2,5,6},{3,4},{7}}=>[2,5,4,3,6,1,7]=>000001
[5,1,4,3,6,7,2]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[5,1,4,3,7,2,6]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[5,1,4,3,7,6,2]=>{{1,2,5,7},{3,4},{6}}=>[2,5,4,3,7,6,1]=>000000
[5,1,4,6,2,3,7]=>{{1,2,5},{3,4,6},{7}}=>[2,5,4,6,1,3,7]=>000001
[5,1,4,6,2,7,3]=>{{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000
[5,1,4,6,3,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,1,4,6,3,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,4,6,7,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,4,6,7,3,2]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000
[5,1,4,7,2,3,6]=>{{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000
[5,1,4,7,2,6,3]=>{{1,2,5},{3,4,7},{6}}=>[2,5,4,7,1,6,3]=>000000
[5,1,4,7,3,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,4,7,3,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,1,4,7,6,2,3]=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000
[5,1,4,7,6,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,6,2,3,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,1,6,2,3,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,6,2,4,3,7]=>{{1,2,4,5},{3,6},{7}}=>[2,4,6,5,1,3,7]=>000001
[5,1,6,2,4,7,3]=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000
[5,1,6,2,7,3,4]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[5,1,6,2,7,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,6,3,2,4,7]=>{{1,2,5},{3,4,6},{7}}=>[2,5,4,6,1,3,7]=>000001
[5,1,6,3,2,7,4]=>{{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000
[5,1,6,3,4,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,1,6,3,4,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,6,3,7,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,6,3,7,4,2]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000
[5,1,6,4,2,3,7]=>{{1,2,5},{3,6},{4},{7}}=>[2,5,6,4,1,3,7]=>000001
[5,1,6,4,2,7,3]=>{{1,2,5},{3,6,7},{4}}=>[2,5,6,4,1,7,3]=>000000
[5,1,6,4,3,2,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[5,1,6,4,3,7,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,1,6,4,7,2,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,1,6,4,7,3,2]=>{{1,2,5,7},{3,6},{4}}=>[2,5,6,4,7,3,1]=>000000
[5,1,6,7,2,3,4]=>{{1,2,5},{3,6},{4,7}}=>[2,5,6,7,1,3,4]=>000000
[5,1,6,7,2,4,3]=>{{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000
[5,1,6,7,3,2,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[5,1,6,7,3,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,6,7,4,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,6,7,4,3,2]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[5,1,7,2,3,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,7,2,3,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,1,7,2,4,3,6]=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000
[5,1,7,2,4,6,3]=>{{1,2,4,5},{3,7},{6}}=>[2,4,7,5,1,6,3]=>000000
[5,1,7,2,6,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,7,2,6,4,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[5,1,7,3,2,4,6]=>{{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000
[5,1,7,3,2,6,4]=>{{1,2,5},{3,4,7},{6}}=>[2,5,4,7,1,6,3]=>000000
[5,1,7,3,4,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,7,3,4,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,1,7,3,6,2,4]=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000
[5,1,7,3,6,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,7,4,2,3,6]=>{{1,2,5},{3,6,7},{4}}=>[2,5,6,4,1,7,3]=>000000
[5,1,7,4,2,6,3]=>{{1,2,5},{3,7},{4},{6}}=>[2,5,7,4,1,6,3]=>000000
[5,1,7,4,3,2,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,1,7,4,3,6,2]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[5,1,7,4,6,2,3]=>{{1,2,5,6},{3,7},{4}}=>[2,5,7,4,6,1,3]=>000000
[5,1,7,4,6,3,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,1,7,6,2,3,4]=>{{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000
[5,1,7,6,2,4,3]=>{{1,2,5},{3,7},{4,6}}=>[2,5,7,6,1,4,3]=>000000
[5,1,7,6,3,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,1,7,6,3,4,2]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[5,1,7,6,4,2,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[5,1,7,6,4,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,2,1,3,4,6,7]=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>000011
[5,2,1,3,4,7,6]=>{{1,3,4,5},{2},{6,7}}=>[3,2,4,5,1,7,6]=>000010
[5,2,1,3,6,4,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[5,2,1,3,6,7,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,1,3,7,4,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,1,3,7,6,4]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[5,2,1,4,3,6,7]=>{{1,3,5},{2},{4},{6},{7}}=>[3,2,5,4,1,6,7]=>000011
[5,2,1,4,3,7,6]=>{{1,3,5},{2},{4},{6,7}}=>[3,2,5,4,1,7,6]=>000010
[5,2,1,4,6,3,7]=>{{1,3,5,6},{2},{4},{7}}=>[3,2,5,4,6,1,7]=>000001
[5,2,1,4,6,7,3]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[5,2,1,4,7,3,6]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[5,2,1,4,7,6,3]=>{{1,3,5,7},{2},{4},{6}}=>[3,2,5,4,7,6,1]=>000000
[5,2,1,6,3,4,7]=>{{1,3,5},{2},{4,6},{7}}=>[3,2,5,6,1,4,7]=>000001
[5,2,1,6,3,7,4]=>{{1,3,5},{2},{4,6,7}}=>[3,2,5,6,1,7,4]=>000000
[5,2,1,6,4,3,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[5,2,1,6,4,7,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,1,6,7,3,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,1,6,7,4,3]=>{{1,3,5,7},{2},{4,6}}=>[3,2,5,6,7,4,1]=>000000
[5,2,1,7,3,4,6]=>{{1,3,5},{2},{4,6,7}}=>[3,2,5,6,1,7,4]=>000000
[5,2,1,7,3,6,4]=>{{1,3,5},{2},{4,7},{6}}=>[3,2,5,7,1,6,4]=>000000
[5,2,1,7,4,3,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,1,7,4,6,3]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[5,2,1,7,6,3,4]=>{{1,3,5,6},{2},{4,7}}=>[3,2,5,7,6,1,4]=>000000
[5,2,1,7,6,4,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,3,1,4,6,7]=>{{1,4,5},{2},{3},{6},{7}}=>[4,2,3,5,1,6,7]=>000011
[5,2,3,1,4,7,6]=>{{1,4,5},{2},{3},{6,7}}=>[4,2,3,5,1,7,6]=>000010
[5,2,3,1,6,4,7]=>{{1,4,5,6},{2},{3},{7}}=>[4,2,3,5,6,1,7]=>000001
[5,2,3,1,6,7,4]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[5,2,3,1,7,4,6]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[5,2,3,1,7,6,4]=>{{1,4,5,7},{2},{3},{6}}=>[4,2,3,5,7,6,1]=>000000
[5,2,3,4,1,6,7]=>{{1,5},{2},{3},{4},{6},{7}}=>[5,2,3,4,1,6,7]=>000011
[5,2,3,4,1,7,6]=>{{1,5},{2},{3},{4},{6,7}}=>[5,2,3,4,1,7,6]=>000010
[5,2,3,4,6,1,7]=>{{1,5,6},{2},{3},{4},{7}}=>[5,2,3,4,6,1,7]=>000001
[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>000000
[5,2,3,4,7,1,6]=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>000000
[5,2,3,4,7,6,1]=>{{1,5,7},{2},{3},{4},{6}}=>[5,2,3,4,7,6,1]=>000000
[5,2,3,6,1,4,7]=>{{1,5},{2},{3},{4,6},{7}}=>[5,2,3,6,1,4,7]=>000001
[5,2,3,6,1,7,4]=>{{1,5},{2},{3},{4,6,7}}=>[5,2,3,6,1,7,4]=>000000
[5,2,3,6,4,1,7]=>{{1,4,5,6},{2},{3},{7}}=>[4,2,3,5,6,1,7]=>000001
[5,2,3,6,4,7,1]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[5,2,3,6,7,1,4]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[5,2,3,6,7,4,1]=>{{1,5,7},{2},{3},{4,6}}=>[5,2,3,6,7,4,1]=>000000
[5,2,3,7,1,4,6]=>{{1,5},{2},{3},{4,6,7}}=>[5,2,3,6,1,7,4]=>000000
[5,2,3,7,1,6,4]=>{{1,5},{2},{3},{4,7},{6}}=>[5,2,3,7,1,6,4]=>000000
[5,2,3,7,4,1,6]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[5,2,3,7,4,6,1]=>{{1,4,5,7},{2},{3},{6}}=>[4,2,3,5,7,6,1]=>000000
[5,2,3,7,6,1,4]=>{{1,5,6},{2},{3},{4,7}}=>[5,2,3,7,6,1,4]=>000000
[5,2,3,7,6,4,1]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[5,2,4,1,3,6,7]=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>000011
[5,2,4,1,3,7,6]=>{{1,3,4,5},{2},{6,7}}=>[3,2,4,5,1,7,6]=>000010
[5,2,4,1,6,3,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[5,2,4,1,6,7,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,4,1,7,3,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,4,1,7,6,3]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[5,2,4,3,1,6,7]=>{{1,5},{2},{3,4},{6},{7}}=>[5,2,4,3,1,6,7]=>000011
[5,2,4,3,1,7,6]=>{{1,5},{2},{3,4},{6,7}}=>[5,2,4,3,1,7,6]=>000010
[5,2,4,3,6,1,7]=>{{1,5,6},{2},{3,4},{7}}=>[5,2,4,3,6,1,7]=>000001
[5,2,4,3,6,7,1]=>{{1,5,6,7},{2},{3,4}}=>[5,2,4,3,6,7,1]=>000000
[5,2,4,3,7,1,6]=>{{1,5,6,7},{2},{3,4}}=>[5,2,4,3,6,7,1]=>000000
[5,2,4,3,7,6,1]=>{{1,5,7},{2},{3,4},{6}}=>[5,2,4,3,7,6,1]=>000000
[5,2,4,6,1,3,7]=>{{1,5},{2},{3,4,6},{7}}=>[5,2,4,6,1,3,7]=>000001
[5,2,4,6,1,7,3]=>{{1,5},{2},{3,4,6,7}}=>[5,2,4,6,1,7,3]=>000000
[5,2,4,6,3,1,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[5,2,4,6,3,7,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,4,6,7,1,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,4,6,7,3,1]=>{{1,5,7},{2},{3,4,6}}=>[5,2,4,6,7,3,1]=>000000
[5,2,4,7,1,3,6]=>{{1,5},{2},{3,4,6,7}}=>[5,2,4,6,1,7,3]=>000000
[5,2,4,7,1,6,3]=>{{1,5},{2},{3,4,7},{6}}=>[5,2,4,7,1,6,3]=>000000
[5,2,4,7,3,1,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,4,7,3,6,1]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[5,2,4,7,6,1,3]=>{{1,5,6},{2},{3,4,7}}=>[5,2,4,7,6,1,3]=>000000
[5,2,4,7,6,3,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,6,1,3,4,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[5,2,6,1,3,7,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,6,1,4,3,7]=>{{1,4,5},{2},{3,6},{7}}=>[4,2,6,5,1,3,7]=>000001
[5,2,6,1,4,7,3]=>{{1,4,5},{2},{3,6,7}}=>[4,2,6,5,1,7,3]=>000000
[5,2,6,1,7,3,4]=>{{1,4,5,7},{2},{3,6}}=>[4,2,6,5,7,3,1]=>000000
[5,2,6,1,7,4,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,6,3,1,4,7]=>{{1,5},{2},{3,4,6},{7}}=>[5,2,4,6,1,3,7]=>000001
[5,2,6,3,1,7,4]=>{{1,5},{2},{3,4,6,7}}=>[5,2,4,6,1,7,3]=>000000
[5,2,6,3,4,1,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[5,2,6,3,4,7,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,6,3,7,1,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,6,3,7,4,1]=>{{1,5,7},{2},{3,4,6}}=>[5,2,4,6,7,3,1]=>000000
[5,2,6,4,1,3,7]=>{{1,5},{2},{3,6},{4},{7}}=>[5,2,6,4,1,3,7]=>000001
[5,2,6,4,1,7,3]=>{{1,5},{2},{3,6,7},{4}}=>[5,2,6,4,1,7,3]=>000000
[5,2,6,4,3,1,7]=>{{1,3,5,6},{2},{4},{7}}=>[3,2,5,4,6,1,7]=>000001
[5,2,6,4,3,7,1]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[5,2,6,4,7,1,3]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[5,2,6,4,7,3,1]=>{{1,5,7},{2},{3,6},{4}}=>[5,2,6,4,7,3,1]=>000000
[5,2,6,7,1,3,4]=>{{1,5},{2},{3,6},{4,7}}=>[5,2,6,7,1,3,4]=>000000
[5,2,6,7,1,4,3]=>{{1,5},{2},{3,4,6,7}}=>[5,2,4,6,1,7,3]=>000000
[5,2,6,7,3,1,4]=>{{1,3,5,6},{2},{4,7}}=>[3,2,5,7,6,1,4]=>000000
[5,2,6,7,3,4,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,6,7,4,1,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,6,7,4,3,1]=>{{1,4,5,7},{2},{3,6}}=>[4,2,6,5,7,3,1]=>000000
[5,2,7,1,3,4,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,7,1,3,6,4]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[5,2,7,1,4,3,6]=>{{1,4,5},{2},{3,6,7}}=>[4,2,6,5,1,7,3]=>000000
[5,2,7,1,4,6,3]=>{{1,4,5},{2},{3,7},{6}}=>[4,2,7,5,1,6,3]=>000000
[5,2,7,1,6,3,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,7,1,6,4,3]=>{{1,4,5,6},{2},{3,7}}=>[4,2,7,5,6,1,3]=>000000
[5,2,7,3,1,4,6]=>{{1,5},{2},{3,4,6,7}}=>[5,2,4,6,1,7,3]=>000000
[5,2,7,3,1,6,4]=>{{1,5},{2},{3,4,7},{6}}=>[5,2,4,7,1,6,3]=>000000
[5,2,7,3,4,1,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,7,3,4,6,1]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[5,2,7,3,6,1,4]=>{{1,5,6},{2},{3,4,7}}=>[5,2,4,7,6,1,3]=>000000
[5,2,7,3,6,4,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,7,4,1,3,6]=>{{1,5},{2},{3,6,7},{4}}=>[5,2,6,4,1,7,3]=>000000
[5,2,7,4,1,6,3]=>{{1,5},{2},{3,7},{4},{6}}=>[5,2,7,4,1,6,3]=>000000
[5,2,7,4,3,1,6]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[5,2,7,4,3,6,1]=>{{1,3,5,7},{2},{4},{6}}=>[3,2,5,4,7,6,1]=>000000
[5,2,7,4,6,1,3]=>{{1,5,6},{2},{3,7},{4}}=>[5,2,7,4,6,1,3]=>000000
[5,2,7,4,6,3,1]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[5,2,7,6,1,3,4]=>{{1,5},{2},{3,4,6,7}}=>[5,2,4,6,1,7,3]=>000000
[5,2,7,6,1,4,3]=>{{1,5},{2},{3,7},{4,6}}=>[5,2,7,6,1,4,3]=>000000
[5,2,7,6,3,1,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,2,7,6,3,4,1]=>{{1,3,5,7},{2},{4,6}}=>[3,2,5,6,7,4,1]=>000000
[5,2,7,6,4,1,3]=>{{1,4,5,6},{2},{3,7}}=>[4,2,7,5,6,1,3]=>000000
[5,2,7,6,4,3,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[5,3,1,2,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[5,3,1,2,4,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[5,3,1,2,6,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,3,1,2,6,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,1,2,7,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,1,2,7,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,3,1,4,2,6,7]=>{{1,2,3,5},{4},{6},{7}}=>[2,3,5,4,1,6,7]=>000011
[5,3,1,4,2,7,6]=>{{1,2,3,5},{4},{6,7}}=>[2,3,5,4,1,7,6]=>000010
[5,3,1,4,6,2,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[5,3,1,4,6,7,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,3,1,4,7,2,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,3,1,4,7,6,2]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[5,3,1,6,2,4,7]=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>000001
[5,3,1,6,2,7,4]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000
[5,3,1,6,4,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,3,1,6,4,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,1,6,7,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,1,6,7,4,2]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[5,3,1,7,2,4,6]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000
[5,3,1,7,2,6,4]=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>000000
[5,3,1,7,4,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,1,7,4,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,3,1,7,6,2,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[5,3,1,7,6,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,2,1,4,6,7]=>{{1,4,5},{2,3},{6},{7}}=>[4,3,2,5,1,6,7]=>000011
[5,3,2,1,4,7,6]=>{{1,4,5},{2,3},{6,7}}=>[4,3,2,5,1,7,6]=>000010
[5,3,2,1,6,4,7]=>{{1,4,5,6},{2,3},{7}}=>[4,3,2,5,6,1,7]=>000001
[5,3,2,1,6,7,4]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[5,3,2,1,7,4,6]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[5,3,2,1,7,6,4]=>{{1,4,5,7},{2,3},{6}}=>[4,3,2,5,7,6,1]=>000000
[5,3,2,4,1,6,7]=>{{1,5},{2,3},{4},{6},{7}}=>[5,3,2,4,1,6,7]=>000011
[5,3,2,4,1,7,6]=>{{1,5},{2,3},{4},{6,7}}=>[5,3,2,4,1,7,6]=>000010
[5,3,2,4,6,1,7]=>{{1,5,6},{2,3},{4},{7}}=>[5,3,2,4,6,1,7]=>000001
[5,3,2,4,6,7,1]=>{{1,5,6,7},{2,3},{4}}=>[5,3,2,4,6,7,1]=>000000
[5,3,2,4,7,1,6]=>{{1,5,6,7},{2,3},{4}}=>[5,3,2,4,6,7,1]=>000000
[5,3,2,4,7,6,1]=>{{1,5,7},{2,3},{4},{6}}=>[5,3,2,4,7,6,1]=>000000
[5,3,2,6,1,4,7]=>{{1,5},{2,3},{4,6},{7}}=>[5,3,2,6,1,4,7]=>000001
[5,3,2,6,1,7,4]=>{{1,5},{2,3},{4,6,7}}=>[5,3,2,6,1,7,4]=>000000
[5,3,2,6,4,1,7]=>{{1,4,5,6},{2,3},{7}}=>[4,3,2,5,6,1,7]=>000001
[5,3,2,6,4,7,1]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[5,3,2,6,7,1,4]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[5,3,2,6,7,4,1]=>{{1,5,7},{2,3},{4,6}}=>[5,3,2,6,7,4,1]=>000000
[5,3,2,7,1,4,6]=>{{1,5},{2,3},{4,6,7}}=>[5,3,2,6,1,7,4]=>000000
[5,3,2,7,1,6,4]=>{{1,5},{2,3},{4,7},{6}}=>[5,3,2,7,1,6,4]=>000000
[5,3,2,7,4,1,6]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[5,3,2,7,4,6,1]=>{{1,4,5,7},{2,3},{6}}=>[4,3,2,5,7,6,1]=>000000
[5,3,2,7,6,1,4]=>{{1,5,6},{2,3},{4,7}}=>[5,3,2,7,6,1,4]=>000000
[5,3,2,7,6,4,1]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[5,3,4,1,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[5,3,4,1,2,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[5,3,4,1,6,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,3,4,1,6,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,4,1,7,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,4,1,7,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,3,4,2,1,6,7]=>{{1,5},{2,3,4},{6},{7}}=>[5,3,4,2,1,6,7]=>000011
[5,3,4,2,1,7,6]=>{{1,5},{2,3,4},{6,7}}=>[5,3,4,2,1,7,6]=>000010
[5,3,4,2,6,1,7]=>{{1,5,6},{2,3,4},{7}}=>[5,3,4,2,6,1,7]=>000001
[5,3,4,2,6,7,1]=>{{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000
[5,3,4,2,7,1,6]=>{{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000
[5,3,4,2,7,6,1]=>{{1,5,7},{2,3,4},{6}}=>[5,3,4,2,7,6,1]=>000000
[5,3,4,6,1,2,7]=>{{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>000001
[5,3,4,6,1,7,2]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,3,4,6,2,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,3,4,6,2,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,4,6,7,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,4,6,7,2,1]=>{{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000
[5,3,4,7,1,2,6]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,3,4,7,1,6,2]=>{{1,5},{2,3,4,7},{6}}=>[5,3,4,7,1,6,2]=>000000
[5,3,4,7,2,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,4,7,2,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,3,4,7,6,1,2]=>{{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000
[5,3,4,7,6,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,6,1,2,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,3,6,1,2,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,6,1,4,2,7]=>{{1,4,5},{2,3,6},{7}}=>[4,3,6,5,1,2,7]=>000001
[5,3,6,1,4,7,2]=>{{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000
[5,3,6,1,7,2,4]=>{{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000
[5,3,6,1,7,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,6,2,1,4,7]=>{{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>000001
[5,3,6,2,1,7,4]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,3,6,2,4,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,3,6,2,4,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,6,2,7,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,6,2,7,4,1]=>{{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000
[5,3,6,4,1,2,7]=>{{1,5},{2,3,6},{4},{7}}=>[5,3,6,4,1,2,7]=>000001
[5,3,6,4,1,7,2]=>{{1,5},{2,3,6,7},{4}}=>[5,3,6,4,1,7,2]=>000000
[5,3,6,4,2,1,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[5,3,6,4,2,7,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,3,6,4,7,1,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,3,6,4,7,2,1]=>{{1,5,7},{2,3,6},{4}}=>[5,3,6,4,7,2,1]=>000000
[5,3,6,7,1,2,4]=>{{1,5},{2,3,6},{4,7}}=>[5,3,6,7,1,2,4]=>000000
[5,3,6,7,1,4,2]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,3,6,7,2,1,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[5,3,6,7,2,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,6,7,4,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,6,7,4,2,1]=>{{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000
[5,3,7,1,2,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,7,1,2,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,3,7,1,4,2,6]=>{{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000
[5,3,7,1,4,6,2]=>{{1,4,5},{2,3,7},{6}}=>[4,3,7,5,1,6,2]=>000000
[5,3,7,1,6,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,7,1,6,4,2]=>{{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000
[5,3,7,2,1,4,6]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,3,7,2,1,6,4]=>{{1,5},{2,3,4,7},{6}}=>[5,3,4,7,1,6,2]=>000000
[5,3,7,2,4,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,7,2,4,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,3,7,2,6,1,4]=>{{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000
[5,3,7,2,6,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,7,4,1,2,6]=>{{1,5},{2,3,6,7},{4}}=>[5,3,6,4,1,7,2]=>000000
[5,3,7,4,1,6,2]=>{{1,5},{2,3,7},{4},{6}}=>[5,3,7,4,1,6,2]=>000000
[5,3,7,4,2,1,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,3,7,4,2,6,1]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[5,3,7,4,6,1,2]=>{{1,5,6},{2,3,7},{4}}=>[5,3,7,4,6,1,2]=>000000
[5,3,7,4,6,2,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,3,7,6,1,2,4]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,3,7,6,1,4,2]=>{{1,5},{2,3,7},{4,6}}=>[5,3,7,6,1,4,2]=>000000
[5,3,7,6,2,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,3,7,6,2,4,1]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[5,3,7,6,4,1,2]=>{{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000
[5,3,7,6,4,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,1,2,3,6,7]=>{{1,3,5},{2,4},{6},{7}}=>[3,4,5,2,1,6,7]=>000011
[5,4,1,2,3,7,6]=>{{1,3,5},{2,4},{6,7}}=>[3,4,5,2,1,7,6]=>000010
[5,4,1,2,6,3,7]=>{{1,3,5,6},{2,4},{7}}=>[3,4,5,2,6,1,7]=>000001
[5,4,1,2,6,7,3]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[5,4,1,2,7,3,6]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[5,4,1,2,7,6,3]=>{{1,3,5,7},{2,4},{6}}=>[3,4,5,2,7,6,1]=>000000
[5,4,1,3,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[5,4,1,3,2,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[5,4,1,3,6,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,4,1,3,6,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,1,3,7,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,1,3,7,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,4,1,6,2,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,4,1,6,2,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,1,6,3,2,7]=>{{1,3,5},{2,4,6},{7}}=>[3,4,5,6,1,2,7]=>000001
[5,4,1,6,3,7,2]=>{{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000
[5,4,1,6,7,2,3]=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000
[5,4,1,6,7,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,1,7,2,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,1,7,2,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,4,1,7,3,2,6]=>{{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000
[5,4,1,7,3,6,2]=>{{1,3,5},{2,4,7},{6}}=>[3,4,5,7,1,6,2]=>000000
[5,4,1,7,6,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,1,7,6,3,2]=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000
[5,4,2,1,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
[5,4,2,1,3,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
[5,4,2,1,6,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,4,2,1,6,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,2,1,7,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,2,1,7,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,4,2,3,1,6,7]=>{{1,5},{2,3,4},{6},{7}}=>[5,3,4,2,1,6,7]=>000011
[5,4,2,3,1,7,6]=>{{1,5},{2,3,4},{6,7}}=>[5,3,4,2,1,7,6]=>000010
[5,4,2,3,6,1,7]=>{{1,5,6},{2,3,4},{7}}=>[5,3,4,2,6,1,7]=>000001
[5,4,2,3,6,7,1]=>{{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000
[5,4,2,3,7,1,6]=>{{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000
[5,4,2,3,7,6,1]=>{{1,5,7},{2,3,4},{6}}=>[5,3,4,2,7,6,1]=>000000
[5,4,2,6,1,3,7]=>{{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>000001
[5,4,2,6,1,7,3]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,4,2,6,3,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,4,2,6,3,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,2,6,7,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,2,6,7,3,1]=>{{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000
[5,4,2,7,1,3,6]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,4,2,7,1,6,3]=>{{1,5},{2,3,4,7},{6}}=>[5,3,4,7,1,6,2]=>000000
[5,4,2,7,3,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,2,7,3,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,4,2,7,6,1,3]=>{{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000
[5,4,2,7,6,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,3,1,2,6,7]=>{{1,2,4,5},{3},{6},{7}}=>[2,4,3,5,1,6,7]=>000011
[5,4,3,1,2,7,6]=>{{1,2,4,5},{3},{6,7}}=>[2,4,3,5,1,7,6]=>000010
[5,4,3,1,6,2,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[5,4,3,1,6,7,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,4,3,1,7,2,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,4,3,1,7,6,2]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[5,4,3,2,1,6,7]=>{{1,5},{2,4},{3},{6},{7}}=>[5,4,3,2,1,6,7]=>000011
[5,4,3,2,1,7,6]=>{{1,5},{2,4},{3},{6,7}}=>[5,4,3,2,1,7,6]=>000010
[5,4,3,2,6,1,7]=>{{1,5,6},{2,4},{3},{7}}=>[5,4,3,2,6,1,7]=>000001
[5,4,3,2,6,7,1]=>{{1,5,6,7},{2,4},{3}}=>[5,4,3,2,6,7,1]=>000000
[5,4,3,2,7,1,6]=>{{1,5,6,7},{2,4},{3}}=>[5,4,3,2,6,7,1]=>000000
[5,4,3,2,7,6,1]=>{{1,5,7},{2,4},{3},{6}}=>[5,4,3,2,7,6,1]=>000000
[5,4,3,6,1,2,7]=>{{1,5},{2,4,6},{3},{7}}=>[5,4,3,6,1,2,7]=>000001
[5,4,3,6,1,7,2]=>{{1,5},{2,4,6,7},{3}}=>[5,4,3,6,1,7,2]=>000000
[5,4,3,6,2,1,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[5,4,3,6,2,7,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,4,3,6,7,1,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,4,3,6,7,2,1]=>{{1,5,7},{2,4,6},{3}}=>[5,4,3,6,7,2,1]=>000000
[5,4,3,7,1,2,6]=>{{1,5},{2,4,6,7},{3}}=>[5,4,3,6,1,7,2]=>000000
[5,4,3,7,1,6,2]=>{{1,5},{2,4,7},{3},{6}}=>[5,4,3,7,1,6,2]=>000000
[5,4,3,7,2,1,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,4,3,7,2,6,1]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[5,4,3,7,6,1,2]=>{{1,5,6},{2,4,7},{3}}=>[5,4,3,7,6,1,2]=>000000
[5,4,3,7,6,2,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,4,6,1,2,3,7]=>{{1,2,4,5},{3,6},{7}}=>[2,4,6,5,1,3,7]=>000001
[5,4,6,1,2,7,3]=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000
[5,4,6,1,3,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,4,6,1,3,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,6,1,7,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,6,1,7,3,2]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[5,4,6,2,1,3,7]=>{{1,5},{2,4},{3,6},{7}}=>[5,4,6,2,1,3,7]=>000001
[5,4,6,2,1,7,3]=>{{1,5},{2,4},{3,6,7}}=>[5,4,6,2,1,7,3]=>000000
[5,4,6,2,3,1,7]=>{{1,3,5,6},{2,4},{7}}=>[3,4,5,2,6,1,7]=>000001
[5,4,6,2,3,7,1]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[5,4,6,2,7,1,3]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[5,4,6,2,7,3,1]=>{{1,5,7},{2,4},{3,6}}=>[5,4,6,2,7,3,1]=>000000
[5,4,6,3,1,2,7]=>{{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>000001
[5,4,6,3,1,7,2]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,4,6,3,2,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,4,6,3,2,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,6,3,7,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,6,3,7,2,1]=>{{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000
[5,4,6,7,1,2,3]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,4,6,7,1,3,2]=>{{1,5},{2,4,7},{3,6}}=>[5,4,6,7,1,3,2]=>000000
[5,4,6,7,2,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,6,7,2,3,1]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[5,4,6,7,3,1,2]=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000
[5,4,6,7,3,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,7,1,2,3,6]=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000
[5,4,7,1,2,6,3]=>{{1,2,4,5},{3,7},{6}}=>[2,4,7,5,1,6,3]=>000000
[5,4,7,1,3,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,7,1,3,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,4,7,1,6,2,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[5,4,7,1,6,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,7,2,1,3,6]=>{{1,5},{2,4},{3,6,7}}=>[5,4,6,2,1,7,3]=>000000
[5,4,7,2,1,6,3]=>{{1,5},{2,4},{3,7},{6}}=>[5,4,7,2,1,6,3]=>000000
[5,4,7,2,3,1,6]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[5,4,7,2,3,6,1]=>{{1,3,5,7},{2,4},{6}}=>[3,4,5,2,7,6,1]=>000000
[5,4,7,2,6,1,3]=>{{1,5,6},{2,4},{3,7}}=>[5,4,7,2,6,1,3]=>000000
[5,4,7,2,6,3,1]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[5,4,7,3,1,2,6]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,4,7,3,1,6,2]=>{{1,5},{2,3,4,7},{6}}=>[5,3,4,7,1,6,2]=>000000
[5,4,7,3,2,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,7,3,2,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,4,7,3,6,1,2]=>{{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000
[5,4,7,3,6,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,7,6,1,2,3]=>{{1,5},{2,4,6},{3,7}}=>[5,4,7,6,1,2,3]=>000000
[5,4,7,6,1,3,2]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,4,7,6,2,1,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[5,4,7,6,2,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,7,6,3,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,4,7,6,3,2,1]=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000
[5,6,1,2,3,4,7]=>{{1,3,5},{2,4,6},{7}}=>[3,4,5,6,1,2,7]=>000001
[5,6,1,2,3,7,4]=>{{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000
[5,6,1,2,4,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,6,1,2,4,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,1,2,7,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,1,2,7,4,3]=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000
[5,6,1,3,2,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,6,1,3,2,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,1,3,4,2,7]=>{{1,3,4,5},{2,6},{7}}=>[3,6,4,5,1,2,7]=>000001
[5,6,1,3,4,7,2]=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000
[5,6,1,3,7,2,4]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[5,6,1,3,7,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,1,4,2,3,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[5,6,1,4,2,7,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,6,1,4,3,2,7]=>{{1,3,5},{2,6},{4},{7}}=>[3,6,5,4,1,2,7]=>000001
[5,6,1,4,3,7,2]=>{{1,3,5},{2,6,7},{4}}=>[3,6,5,4,1,7,2]=>000000
[5,6,1,4,7,2,3]=>{{1,3,5,7},{2,6},{4}}=>[3,6,5,4,7,2,1]=>000000
[5,6,1,4,7,3,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,6,1,7,2,3,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[5,6,1,7,2,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,1,7,3,2,4]=>{{1,3,5},{2,6},{4,7}}=>[3,6,5,7,1,2,4]=>000000
[5,6,1,7,3,4,2]=>{{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000
[5,6,1,7,4,2,3]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[5,6,1,7,4,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,2,1,3,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,6,2,1,3,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,2,1,4,3,7]=>{{1,4,5},{2,3,6},{7}}=>[4,3,6,5,1,2,7]=>000001
[5,6,2,1,4,7,3]=>{{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000
[5,6,2,1,7,3,4]=>{{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000
[5,6,2,1,7,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,2,3,1,4,7]=>{{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>000001
[5,6,2,3,1,7,4]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,6,2,3,4,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,6,2,3,4,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,2,3,7,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,2,3,7,4,1]=>{{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000
[5,6,2,4,1,3,7]=>{{1,5},{2,3,6},{4},{7}}=>[5,3,6,4,1,2,7]=>000001
[5,6,2,4,1,7,3]=>{{1,5},{2,3,6,7},{4}}=>[5,3,6,4,1,7,2]=>000000
[5,6,2,4,3,1,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[5,6,2,4,3,7,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,6,2,4,7,1,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,6,2,4,7,3,1]=>{{1,5,7},{2,3,6},{4}}=>[5,3,6,4,7,2,1]=>000000
[5,6,2,7,1,3,4]=>{{1,5},{2,3,6},{4,7}}=>[5,3,6,7,1,2,4]=>000000
[5,6,2,7,1,4,3]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,6,2,7,3,1,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[5,6,2,7,3,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,2,7,4,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,2,7,4,3,1]=>{{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000
[5,6,3,1,2,4,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[5,6,3,1,2,7,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,6,3,1,4,2,7]=>{{1,4,5},{2,6},{3},{7}}=>[4,6,3,5,1,2,7]=>000001
[5,6,3,1,4,7,2]=>{{1,4,5},{2,6,7},{3}}=>[4,6,3,5,1,7,2]=>000000
[5,6,3,1,7,2,4]=>{{1,4,5,7},{2,6},{3}}=>[4,6,3,5,7,2,1]=>000000
[5,6,3,1,7,4,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,6,3,2,1,4,7]=>{{1,5},{2,4,6},{3},{7}}=>[5,4,3,6,1,2,7]=>000001
[5,6,3,2,1,7,4]=>{{1,5},{2,4,6,7},{3}}=>[5,4,3,6,1,7,2]=>000000
[5,6,3,2,4,1,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[5,6,3,2,4,7,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,6,3,2,7,1,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,6,3,2,7,4,1]=>{{1,5,7},{2,4,6},{3}}=>[5,4,3,6,7,2,1]=>000000
[5,6,3,4,1,2,7]=>{{1,5},{2,6},{3},{4},{7}}=>[5,6,3,4,1,2,7]=>000001
[5,6,3,4,1,7,2]=>{{1,5},{2,6,7},{3},{4}}=>[5,6,3,4,1,7,2]=>000000
[5,6,3,4,2,1,7]=>{{1,2,5,6},{3},{4},{7}}=>[2,5,3,4,6,1,7]=>000001
[5,6,3,4,2,7,1]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[5,6,3,4,7,1,2]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[5,6,3,4,7,2,1]=>{{1,5,7},{2,6},{3},{4}}=>[5,6,3,4,7,2,1]=>000000
[5,6,3,7,1,2,4]=>{{1,5},{2,6},{3},{4,7}}=>[5,6,3,7,1,2,4]=>000000
[5,6,3,7,1,4,2]=>{{1,5},{2,4,6,7},{3}}=>[5,4,3,6,1,7,2]=>000000
[5,6,3,7,2,1,4]=>{{1,2,5,6},{3},{4,7}}=>[2,5,3,7,6,1,4]=>000000
[5,6,3,7,2,4,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,6,3,7,4,1,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,6,3,7,4,2,1]=>{{1,4,5,7},{2,6},{3}}=>[4,6,3,5,7,2,1]=>000000
[5,6,4,1,2,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,6,4,1,2,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,4,1,3,2,7]=>{{1,3,4,5},{2,6},{7}}=>[3,6,4,5,1,2,7]=>000001
[5,6,4,1,3,7,2]=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000
[5,6,4,1,7,2,3]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[5,6,4,1,7,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,4,2,1,3,7]=>{{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>000001
[5,6,4,2,1,7,3]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,6,4,2,3,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[5,6,4,2,3,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,4,2,7,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,4,2,7,3,1]=>{{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000
[5,6,4,3,1,2,7]=>{{1,5},{2,6},{3,4},{7}}=>[5,6,4,3,1,2,7]=>000001
[5,6,4,3,1,7,2]=>{{1,5},{2,6,7},{3,4}}=>[5,6,4,3,1,7,2]=>000000
[5,6,4,3,2,1,7]=>{{1,2,5,6},{3,4},{7}}=>[2,5,4,3,6,1,7]=>000001
[5,6,4,3,2,7,1]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[5,6,4,3,7,1,2]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[5,6,4,3,7,2,1]=>{{1,5,7},{2,6},{3,4}}=>[5,6,4,3,7,2,1]=>000000
[5,6,4,7,1,2,3]=>{{1,5},{2,6},{3,4,7}}=>[5,6,4,7,1,2,3]=>000000
[5,6,4,7,1,3,2]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,6,4,7,2,1,3]=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000
[5,6,4,7,2,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,4,7,3,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,4,7,3,2,1]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[5,6,7,1,2,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,7,1,2,4,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[5,6,7,1,3,2,4]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[5,6,7,1,3,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,7,1,4,2,3]=>{{1,4,5},{2,6},{3,7}}=>[4,6,7,5,1,2,3]=>000000
[5,6,7,1,4,3,2]=>{{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000
[5,6,7,2,1,3,4]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,6,7,2,1,4,3]=>{{1,5},{2,4,6},{3,7}}=>[5,4,7,6,1,2,3]=>000000
[5,6,7,2,3,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,7,2,3,4,1]=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000
[5,6,7,2,4,1,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[5,6,7,2,4,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,7,3,1,2,4]=>{{1,5},{2,6},{3,4,7}}=>[5,6,4,7,1,2,3]=>000000
[5,6,7,3,1,4,2]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,6,7,3,2,1,4]=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000
[5,6,7,3,2,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,7,3,4,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,6,7,3,4,2,1]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[5,6,7,4,1,2,3]=>{{1,5},{2,6},{3,7},{4}}=>[5,6,7,4,1,2,3]=>000000
[5,6,7,4,1,3,2]=>{{1,5},{2,3,6,7},{4}}=>[5,3,6,4,1,7,2]=>000000
[5,6,7,4,2,1,3]=>{{1,2,5,6},{3,7},{4}}=>[2,5,7,4,6,1,3]=>000000
[5,6,7,4,2,3,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,6,7,4,3,1,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,6,7,4,3,2,1]=>{{1,3,5,7},{2,6},{4}}=>[3,6,5,4,7,2,1]=>000000
[5,7,1,2,3,4,6]=>{{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000
[5,7,1,2,3,6,4]=>{{1,3,5},{2,4,7},{6}}=>[3,4,5,7,1,6,2]=>000000
[5,7,1,2,4,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,1,2,4,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,7,1,2,6,3,4]=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000
[5,7,1,2,6,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,1,3,2,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,1,3,2,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,7,1,3,4,2,6]=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000
[5,7,1,3,4,6,2]=>{{1,3,4,5},{2,7},{6}}=>[3,7,4,5,1,6,2]=>000000
[5,7,1,3,6,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,1,3,6,4,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[5,7,1,4,2,3,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,7,1,4,2,6,3]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[5,7,1,4,3,2,6]=>{{1,3,5},{2,6,7},{4}}=>[3,6,5,4,1,7,2]=>000000
[5,7,1,4,3,6,2]=>{{1,3,5},{2,7},{4},{6}}=>[3,7,5,4,1,6,2]=>000000
[5,7,1,4,6,2,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,7,1,4,6,3,2]=>{{1,3,5,6},{2,7},{4}}=>[3,7,5,4,6,1,2]=>000000
[5,7,1,6,2,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,1,6,2,4,3]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[5,7,1,6,3,2,4]=>{{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000
[5,7,1,6,3,4,2]=>{{1,3,5},{2,7},{4,6}}=>[3,7,5,6,1,4,2]=>000000
[5,7,1,6,4,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,1,6,4,3,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[5,7,2,1,3,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,2,1,3,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,7,2,1,4,3,6]=>{{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000
[5,7,2,1,4,6,3]=>{{1,4,5},{2,3,7},{6}}=>[4,3,7,5,1,6,2]=>000000
[5,7,2,1,6,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,2,1,6,4,3]=>{{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000
[5,7,2,3,1,4,6]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,7,2,3,1,6,4]=>{{1,5},{2,3,4,7},{6}}=>[5,3,4,7,1,6,2]=>000000
[5,7,2,3,4,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,2,3,4,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,7,2,3,6,1,4]=>{{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000
[5,7,2,3,6,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,2,4,1,3,6]=>{{1,5},{2,3,6,7},{4}}=>[5,3,6,4,1,7,2]=>000000
[5,7,2,4,1,6,3]=>{{1,5},{2,3,7},{4},{6}}=>[5,3,7,4,1,6,2]=>000000
[5,7,2,4,3,1,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,7,2,4,3,6,1]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[5,7,2,4,6,1,3]=>{{1,5,6},{2,3,7},{4}}=>[5,3,7,4,6,1,2]=>000000
[5,7,2,4,6,3,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,7,2,6,1,3,4]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,7,2,6,1,4,3]=>{{1,5},{2,3,7},{4,6}}=>[5,3,7,6,1,4,2]=>000000
[5,7,2,6,3,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,2,6,3,4,1]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[5,7,2,6,4,1,3]=>{{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000
[5,7,2,6,4,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,3,1,2,4,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,7,3,1,2,6,4]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[5,7,3,1,4,2,6]=>{{1,4,5},{2,6,7},{3}}=>[4,6,3,5,1,7,2]=>000000
[5,7,3,1,4,6,2]=>{{1,4,5},{2,7},{3},{6}}=>[4,7,3,5,1,6,2]=>000000
[5,7,3,1,6,2,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,7,3,1,6,4,2]=>{{1,4,5,6},{2,7},{3}}=>[4,7,3,5,6,1,2]=>000000
[5,7,3,2,1,4,6]=>{{1,5},{2,4,6,7},{3}}=>[5,4,3,6,1,7,2]=>000000
[5,7,3,2,1,6,4]=>{{1,5},{2,4,7},{3},{6}}=>[5,4,3,7,1,6,2]=>000000
[5,7,3,2,4,1,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,7,3,2,4,6,1]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[5,7,3,2,6,1,4]=>{{1,5,6},{2,4,7},{3}}=>[5,4,3,7,6,1,2]=>000000
[5,7,3,2,6,4,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,7,3,4,1,2,6]=>{{1,5},{2,6,7},{3},{4}}=>[5,6,3,4,1,7,2]=>000000
[5,7,3,4,1,6,2]=>{{1,5},{2,7},{3},{4},{6}}=>[5,7,3,4,1,6,2]=>000000
[5,7,3,4,2,1,6]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[5,7,3,4,2,6,1]=>{{1,2,5,7},{3},{4},{6}}=>[2,5,3,4,7,6,1]=>000000
[5,7,3,4,6,1,2]=>{{1,5,6},{2,7},{3},{4}}=>[5,7,3,4,6,1,2]=>000000
[5,7,3,4,6,2,1]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[5,7,3,6,1,2,4]=>{{1,5},{2,4,6,7},{3}}=>[5,4,3,6,1,7,2]=>000000
[5,7,3,6,1,4,2]=>{{1,5},{2,7},{3},{4,6}}=>[5,7,3,6,1,4,2]=>000000
[5,7,3,6,2,1,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,7,3,6,2,4,1]=>{{1,2,5,7},{3},{4,6}}=>[2,5,3,6,7,4,1]=>000000
[5,7,3,6,4,1,2]=>{{1,4,5,6},{2,7},{3}}=>[4,7,3,5,6,1,2]=>000000
[5,7,3,6,4,2,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[5,7,4,1,2,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,4,1,2,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,7,4,1,3,2,6]=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000
[5,7,4,1,3,6,2]=>{{1,3,4,5},{2,7},{6}}=>[3,7,4,5,1,6,2]=>000000
[5,7,4,1,6,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,4,1,6,3,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[5,7,4,2,1,3,6]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,7,4,2,1,6,3]=>{{1,5},{2,3,4,7},{6}}=>[5,3,4,7,1,6,2]=>000000
[5,7,4,2,3,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,4,2,3,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[5,7,4,2,6,1,3]=>{{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000
[5,7,4,2,6,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,4,3,1,2,6]=>{{1,5},{2,6,7},{3,4}}=>[5,6,4,3,1,7,2]=>000000
[5,7,4,3,1,6,2]=>{{1,5},{2,7},{3,4},{6}}=>[5,7,4,3,1,6,2]=>000000
[5,7,4,3,2,1,6]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[5,7,4,3,2,6,1]=>{{1,2,5,7},{3,4},{6}}=>[2,5,4,3,7,6,1]=>000000
[5,7,4,3,6,1,2]=>{{1,5,6},{2,7},{3,4}}=>[5,7,4,3,6,1,2]=>000000
[5,7,4,3,6,2,1]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[5,7,4,6,1,2,3]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,7,4,6,1,3,2]=>{{1,5},{2,7},{3,4,6}}=>[5,7,4,6,1,3,2]=>000000
[5,7,4,6,2,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,4,6,2,3,1]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000
[5,7,4,6,3,1,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[5,7,4,6,3,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,6,1,2,3,4]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[5,7,6,1,2,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,6,1,3,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,6,1,3,4,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[5,7,6,1,4,2,3]=>{{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000
[5,7,6,1,4,3,2]=>{{1,4,5},{2,7},{3,6}}=>[4,7,6,5,1,3,2]=>000000
[5,7,6,2,1,3,4]=>{{1,5},{2,4,7},{3,6}}=>[5,4,6,7,1,3,2]=>000000
[5,7,6,2,1,4,3]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,7,6,2,3,1,4]=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000
[5,7,6,2,3,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,6,2,4,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,6,2,4,3,1]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[5,7,6,3,1,2,4]=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
[5,7,6,3,1,4,2]=>{{1,5},{2,7},{3,4,6}}=>[5,7,4,6,1,3,2]=>000000
[5,7,6,3,2,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,6,3,2,4,1]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000
[5,7,6,3,4,1,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[5,7,6,3,4,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[5,7,6,4,1,2,3]=>{{1,5},{2,3,6,7},{4}}=>[5,3,6,4,1,7,2]=>000000
[5,7,6,4,1,3,2]=>{{1,5},{2,7},{3,6},{4}}=>[5,7,6,4,1,3,2]=>000000
[5,7,6,4,2,1,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[5,7,6,4,2,3,1]=>{{1,2,5,7},{3,6},{4}}=>[2,5,6,4,7,3,1]=>000000
[5,7,6,4,3,1,2]=>{{1,3,5,6},{2,7},{4}}=>[3,7,5,4,6,1,2]=>000000
[5,7,6,4,3,2,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,1,2,3,4,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,1,2,3,4,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,2,3,5,4,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[6,1,2,3,5,7,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,1,2,3,7,4,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[6,1,2,3,7,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,2,4,3,5,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[6,1,2,4,3,7,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,1,2,4,5,3,7]=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>000001
[6,1,2,4,5,7,3]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[6,1,2,4,7,3,5]=>{{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>000000
[6,1,2,4,7,5,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,1,2,5,3,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,1,2,5,3,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,2,5,4,3,7]=>{{1,2,3,6},{4,5},{7}}=>[2,3,6,5,4,1,7]=>000001
[6,1,2,5,4,7,3]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[6,1,2,5,7,3,4]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000
[6,1,2,5,7,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,2,7,3,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,2,7,3,5,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[6,1,2,7,4,3,5]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000
[6,1,2,7,4,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,2,7,5,3,4]=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>000000
[6,1,2,7,5,4,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,1,3,2,4,5,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[6,1,3,2,4,7,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,1,3,2,5,4,7]=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>000001
[6,1,3,2,5,7,4]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[6,1,3,2,7,4,5]=>{{1,2,4,6},{3},{5,7}}=>[2,4,3,6,7,1,5]=>000000
[6,1,3,2,7,5,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,1,3,4,2,5,7]=>{{1,2,5,6},{3},{4},{7}}=>[2,5,3,4,6,1,7]=>000001
[6,1,3,4,2,7,5]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[6,1,3,4,5,2,7]=>{{1,2,6},{3},{4},{5},{7}}=>[2,6,3,4,5,1,7]=>000001
[6,1,3,4,5,7,2]=>{{1,2,6,7},{3},{4},{5}}=>[2,6,3,4,5,7,1]=>000000
[6,1,3,4,7,2,5]=>{{1,2,6},{3},{4},{5,7}}=>[2,6,3,4,7,1,5]=>000000
[6,1,3,4,7,5,2]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[6,1,3,5,2,4,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[6,1,3,5,2,7,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,1,3,5,4,2,7]=>{{1,2,6},{3},{4,5},{7}}=>[2,6,3,5,4,1,7]=>000001
[6,1,3,5,4,7,2]=>{{1,2,6,7},{3},{4,5}}=>[2,6,3,5,4,7,1]=>000000
[6,1,3,5,7,2,4]=>{{1,2,6},{3},{4,5,7}}=>[2,6,3,5,7,1,4]=>000000
[6,1,3,5,7,4,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,1,3,7,2,4,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,1,3,7,2,5,4]=>{{1,2,5,6},{3},{4,7}}=>[2,5,3,7,6,1,4]=>000000
[6,1,3,7,4,2,5]=>{{1,2,6},{3},{4,5,7}}=>[2,6,3,5,7,1,4]=>000000
[6,1,3,7,4,5,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,1,3,7,5,2,4]=>{{1,2,6},{3},{4,7},{5}}=>[2,6,3,7,5,1,4]=>000000
[6,1,3,7,5,4,2]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[6,1,4,2,3,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,1,4,2,3,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,4,2,5,3,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[6,1,4,2,5,7,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,1,4,2,7,3,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[6,1,4,2,7,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,4,3,2,5,7]=>{{1,2,5,6},{3,4},{7}}=>[2,5,4,3,6,1,7]=>000001
[6,1,4,3,2,7,5]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[6,1,4,3,5,2,7]=>{{1,2,6},{3,4},{5},{7}}=>[2,6,4,3,5,1,7]=>000001
[6,1,4,3,5,7,2]=>{{1,2,6,7},{3,4},{5}}=>[2,6,4,3,5,7,1]=>000000
[6,1,4,3,7,2,5]=>{{1,2,6},{3,4},{5,7}}=>[2,6,4,3,7,1,5]=>000000
[6,1,4,3,7,5,2]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[6,1,4,5,2,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,1,4,5,2,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,4,5,3,2,7]=>{{1,2,6},{3,4,5},{7}}=>[2,6,4,5,3,1,7]=>000001
[6,1,4,5,3,7,2]=>{{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000
[6,1,4,5,7,2,3]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000
[6,1,4,5,7,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,4,7,2,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,4,7,2,5,3]=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000
[6,1,4,7,3,2,5]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000
[6,1,4,7,3,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,4,7,5,2,3]=>{{1,2,6},{3,4,7},{5}}=>[2,6,4,7,5,1,3]=>000000
[6,1,4,7,5,3,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,1,5,2,3,4,7]=>{{1,2,4,6},{3,5},{7}}=>[2,4,5,6,3,1,7]=>000001
[6,1,5,2,3,7,4]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[6,1,5,2,4,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,1,5,2,4,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,5,2,7,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,5,2,7,4,3]=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000
[6,1,5,3,2,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,1,5,3,2,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,5,3,4,2,7]=>{{1,2,6},{3,4,5},{7}}=>[2,6,4,5,3,1,7]=>000001
[6,1,5,3,4,7,2]=>{{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000
[6,1,5,3,7,2,4]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000
[6,1,5,3,7,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,5,4,2,3,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[6,1,5,4,2,7,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,1,5,4,3,2,7]=>{{1,2,6},{3,5},{4},{7}}=>[2,6,5,4,3,1,7]=>000001
[6,1,5,4,3,7,2]=>{{1,2,6,7},{3,5},{4}}=>[2,6,5,4,3,7,1]=>000000
[6,1,5,4,7,2,3]=>{{1,2,6},{3,5,7},{4}}=>[2,6,5,4,7,1,3]=>000000
[6,1,5,4,7,3,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,1,5,7,2,3,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[6,1,5,7,2,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,5,7,3,2,4]=>{{1,2,6},{3,5},{4,7}}=>[2,6,5,7,3,1,4]=>000000
[6,1,5,7,3,4,2]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[6,1,5,7,4,2,3]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000
[6,1,5,7,4,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,7,2,3,4,5]=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000
[6,1,7,2,3,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,7,2,4,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,7,2,4,5,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[6,1,7,2,5,3,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,1,7,2,5,4,3]=>{{1,2,4,6},{3,7},{5}}=>[2,4,7,6,5,1,3]=>000000
[6,1,7,3,2,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,7,3,2,5,4]=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000
[6,1,7,3,4,2,5]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000
[6,1,7,3,4,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,7,3,5,2,4]=>{{1,2,6},{3,4,7},{5}}=>[2,6,4,7,5,1,3]=>000000
[6,1,7,3,5,4,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,1,7,4,2,3,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,1,7,4,2,5,3]=>{{1,2,5,6},{3,7},{4}}=>[2,5,7,4,6,1,3]=>000000
[6,1,7,4,3,2,5]=>{{1,2,6},{3,5,7},{4}}=>[2,6,5,4,7,1,3]=>000000
[6,1,7,4,3,5,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,1,7,4,5,2,3]=>{{1,2,6},{3,7},{4},{5}}=>[2,6,7,4,5,1,3]=>000000
[6,1,7,4,5,3,2]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[6,1,7,5,2,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,7,5,2,4,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[6,1,7,5,3,2,4]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000
[6,1,7,5,3,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,1,7,5,4,2,3]=>{{1,2,6},{3,7},{4,5}}=>[2,6,7,5,4,1,3]=>000000
[6,1,7,5,4,3,2]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[6,2,1,3,4,5,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[6,2,1,3,4,7,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,1,3,5,4,7]=>{{1,3,4,6},{2},{5},{7}}=>[3,2,4,6,5,1,7]=>000001
[6,2,1,3,5,7,4]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[6,2,1,3,7,4,5]=>{{1,3,4,6},{2},{5,7}}=>[3,2,4,6,7,1,5]=>000000
[6,2,1,3,7,5,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,1,4,3,5,7]=>{{1,3,5,6},{2},{4},{7}}=>[3,2,5,4,6,1,7]=>000001
[6,2,1,4,3,7,5]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[6,2,1,4,5,3,7]=>{{1,3,6},{2},{4},{5},{7}}=>[3,2,6,4,5,1,7]=>000001
[6,2,1,4,5,7,3]=>{{1,3,6,7},{2},{4},{5}}=>[3,2,6,4,5,7,1]=>000000
[6,2,1,4,7,3,5]=>{{1,3,6},{2},{4},{5,7}}=>[3,2,6,4,7,1,5]=>000000
[6,2,1,4,7,5,3]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[6,2,1,5,3,4,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[6,2,1,5,3,7,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,1,5,4,3,7]=>{{1,3,6},{2},{4,5},{7}}=>[3,2,6,5,4,1,7]=>000001
[6,2,1,5,4,7,3]=>{{1,3,6,7},{2},{4,5}}=>[3,2,6,5,4,7,1]=>000000
[6,2,1,5,7,3,4]=>{{1,3,6},{2},{4,5,7}}=>[3,2,6,5,7,1,4]=>000000
[6,2,1,5,7,4,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,1,7,3,4,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,1,7,3,5,4]=>{{1,3,5,6},{2},{4,7}}=>[3,2,5,7,6,1,4]=>000000
[6,2,1,7,4,3,5]=>{{1,3,6},{2},{4,5,7}}=>[3,2,6,5,7,1,4]=>000000
[6,2,1,7,4,5,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,1,7,5,3,4]=>{{1,3,6},{2},{4,7},{5}}=>[3,2,6,7,5,1,4]=>000000
[6,2,1,7,5,4,3]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[6,2,3,1,4,5,7]=>{{1,4,5,6},{2},{3},{7}}=>[4,2,3,5,6,1,7]=>000001
[6,2,3,1,4,7,5]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[6,2,3,1,5,4,7]=>{{1,4,6},{2},{3},{5},{7}}=>[4,2,3,6,5,1,7]=>000001
[6,2,3,1,5,7,4]=>{{1,4,6,7},{2},{3},{5}}=>[4,2,3,6,5,7,1]=>000000
[6,2,3,1,7,4,5]=>{{1,4,6},{2},{3},{5,7}}=>[4,2,3,6,7,1,5]=>000000
[6,2,3,1,7,5,4]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[6,2,3,4,1,5,7]=>{{1,5,6},{2},{3},{4},{7}}=>[5,2,3,4,6,1,7]=>000001
[6,2,3,4,1,7,5]=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>000000
[6,2,3,4,5,1,7]=>{{1,6},{2},{3},{4},{5},{7}}=>[6,2,3,4,5,1,7]=>000001
[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}}=>[6,2,3,4,5,7,1]=>000000
[6,2,3,4,7,1,5]=>{{1,6},{2},{3},{4},{5,7}}=>[6,2,3,4,7,1,5]=>000000
[6,2,3,4,7,5,1]=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>000000
[6,2,3,5,1,4,7]=>{{1,4,5,6},{2},{3},{7}}=>[4,2,3,5,6,1,7]=>000001
[6,2,3,5,1,7,4]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[6,2,3,5,4,1,7]=>{{1,6},{2},{3},{4,5},{7}}=>[6,2,3,5,4,1,7]=>000001
[6,2,3,5,4,7,1]=>{{1,6,7},{2},{3},{4,5}}=>[6,2,3,5,4,7,1]=>000000
[6,2,3,5,7,1,4]=>{{1,6},{2},{3},{4,5,7}}=>[6,2,3,5,7,1,4]=>000000
[6,2,3,5,7,4,1]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[6,2,3,7,1,4,5]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[6,2,3,7,1,5,4]=>{{1,5,6},{2},{3},{4,7}}=>[5,2,3,7,6,1,4]=>000000
[6,2,3,7,4,1,5]=>{{1,6},{2},{3},{4,5,7}}=>[6,2,3,5,7,1,4]=>000000
[6,2,3,7,4,5,1]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[6,2,3,7,5,1,4]=>{{1,6},{2},{3},{4,7},{5}}=>[6,2,3,7,5,1,4]=>000000
[6,2,3,7,5,4,1]=>{{1,4,6,7},{2},{3},{5}}=>[4,2,3,6,5,7,1]=>000000
[6,2,4,1,3,5,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[6,2,4,1,3,7,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,4,1,5,3,7]=>{{1,3,4,6},{2},{5},{7}}=>[3,2,4,6,5,1,7]=>000001
[6,2,4,1,5,7,3]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[6,2,4,1,7,3,5]=>{{1,3,4,6},{2},{5,7}}=>[3,2,4,6,7,1,5]=>000000
[6,2,4,1,7,5,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,4,3,1,5,7]=>{{1,5,6},{2},{3,4},{7}}=>[5,2,4,3,6,1,7]=>000001
[6,2,4,3,1,7,5]=>{{1,5,6,7},{2},{3,4}}=>[5,2,4,3,6,7,1]=>000000
[6,2,4,3,5,1,7]=>{{1,6},{2},{3,4},{5},{7}}=>[6,2,4,3,5,1,7]=>000001
[6,2,4,3,5,7,1]=>{{1,6,7},{2},{3,4},{5}}=>[6,2,4,3,5,7,1]=>000000
[6,2,4,3,7,1,5]=>{{1,6},{2},{3,4},{5,7}}=>[6,2,4,3,7,1,5]=>000000
[6,2,4,3,7,5,1]=>{{1,5,6,7},{2},{3,4}}=>[5,2,4,3,6,7,1]=>000000
[6,2,4,5,1,3,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[6,2,4,5,1,7,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,4,5,3,1,7]=>{{1,6},{2},{3,4,5},{7}}=>[6,2,4,5,3,1,7]=>000001
[6,2,4,5,3,7,1]=>{{1,6,7},{2},{3,4,5}}=>[6,2,4,5,3,7,1]=>000000
[6,2,4,5,7,1,3]=>{{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>000000
[6,2,4,5,7,3,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,4,7,1,3,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,4,7,1,5,3]=>{{1,5,6},{2},{3,4,7}}=>[5,2,4,7,6,1,3]=>000000
[6,2,4,7,3,1,5]=>{{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>000000
[6,2,4,7,3,5,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,4,7,5,1,3]=>{{1,6},{2},{3,4,7},{5}}=>[6,2,4,7,5,1,3]=>000000
[6,2,4,7,5,3,1]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[6,2,5,1,3,4,7]=>{{1,4,6},{2},{3,5},{7}}=>[4,2,5,6,3,1,7]=>000001
[6,2,5,1,3,7,4]=>{{1,4,6,7},{2},{3,5}}=>[4,2,5,6,3,7,1]=>000000
[6,2,5,1,4,3,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[6,2,5,1,4,7,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,5,1,7,3,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,5,1,7,4,3]=>{{1,4,6},{2},{3,5,7}}=>[4,2,5,6,7,1,3]=>000000
[6,2,5,3,1,4,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
[6,2,5,3,1,7,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,5,3,4,1,7]=>{{1,6},{2},{3,4,5},{7}}=>[6,2,4,5,3,1,7]=>000001
[6,2,5,3,4,7,1]=>{{1,6,7},{2},{3,4,5}}=>[6,2,4,5,3,7,1]=>000000
[6,2,5,3,7,1,4]=>{{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>000000
[6,2,5,3,7,4,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,5,4,1,3,7]=>{{1,3,5,6},{2},{4},{7}}=>[3,2,5,4,6,1,7]=>000001
[6,2,5,4,1,7,3]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[6,2,5,4,3,1,7]=>{{1,6},{2},{3,5},{4},{7}}=>[6,2,5,4,3,1,7]=>000001
[6,2,5,4,3,7,1]=>{{1,6,7},{2},{3,5},{4}}=>[6,2,5,4,3,7,1]=>000000
[6,2,5,4,7,1,3]=>{{1,6},{2},{3,5,7},{4}}=>[6,2,5,4,7,1,3]=>000000
[6,2,5,4,7,3,1]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[6,2,5,7,1,3,4]=>{{1,3,5,6},{2},{4,7}}=>[3,2,5,7,6,1,4]=>000000
[6,2,5,7,1,4,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,5,7,3,1,4]=>{{1,6},{2},{3,5},{4,7}}=>[6,2,5,7,3,1,4]=>000000
[6,2,5,7,3,4,1]=>{{1,4,6,7},{2},{3,5}}=>[4,2,5,6,3,7,1]=>000000
[6,2,5,7,4,1,3]=>{{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>000000
[6,2,5,7,4,3,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,7,1,3,4,5]=>{{1,4,6},{2},{3,5,7}}=>[4,2,5,6,7,1,3]=>000000
[6,2,7,1,3,5,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,7,1,4,3,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,7,1,4,5,3]=>{{1,4,5,6},{2},{3,7}}=>[4,2,7,5,6,1,3]=>000000
[6,2,7,1,5,3,4]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[6,2,7,1,5,4,3]=>{{1,4,6},{2},{3,7},{5}}=>[4,2,7,6,5,1,3]=>000000
[6,2,7,3,1,4,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,7,3,1,5,4]=>{{1,5,6},{2},{3,4,7}}=>[5,2,4,7,6,1,3]=>000000
[6,2,7,3,4,1,5]=>{{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>000000
[6,2,7,3,4,5,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,7,3,5,1,4]=>{{1,6},{2},{3,4,7},{5}}=>[6,2,4,7,5,1,3]=>000000
[6,2,7,3,5,4,1]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[6,2,7,4,1,3,5]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[6,2,7,4,1,5,3]=>{{1,5,6},{2},{3,7},{4}}=>[5,2,7,4,6,1,3]=>000000
[6,2,7,4,3,1,5]=>{{1,6},{2},{3,5,7},{4}}=>[6,2,5,4,7,1,3]=>000000
[6,2,7,4,3,5,1]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[6,2,7,4,5,1,3]=>{{1,6},{2},{3,7},{4},{5}}=>[6,2,7,4,5,1,3]=>000000
[6,2,7,4,5,3,1]=>{{1,3,6,7},{2},{4},{5}}=>[3,2,6,4,5,7,1]=>000000
[6,2,7,5,1,3,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,7,5,1,4,3]=>{{1,4,5,6},{2},{3,7}}=>[4,2,7,5,6,1,3]=>000000
[6,2,7,5,3,1,4]=>{{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>000000
[6,2,7,5,3,4,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[6,2,7,5,4,1,3]=>{{1,6},{2},{3,7},{4,5}}=>[6,2,7,5,4,1,3]=>000000
[6,2,7,5,4,3,1]=>{{1,3,6,7},{2},{4,5}}=>[3,2,6,5,4,7,1]=>000000
[6,3,1,2,4,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,3,1,2,4,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,1,2,5,4,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[6,3,1,2,5,7,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,3,1,2,7,4,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[6,3,1,2,7,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,1,4,2,5,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[6,3,1,4,2,7,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,3,1,4,5,2,7]=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>000001
[6,3,1,4,5,7,2]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[6,3,1,4,7,2,5]=>{{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>000000
[6,3,1,4,7,5,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,3,1,5,2,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,3,1,5,2,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,1,5,4,2,7]=>{{1,2,3,6},{4,5},{7}}=>[2,3,6,5,4,1,7]=>000001
[6,3,1,5,4,7,2]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[6,3,1,5,7,2,4]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000
[6,3,1,5,7,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,1,7,2,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,1,7,2,5,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[6,3,1,7,4,2,5]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000
[6,3,1,7,4,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,1,7,5,2,4]=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>000000
[6,3,1,7,5,4,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,3,2,1,4,5,7]=>{{1,4,5,6},{2,3},{7}}=>[4,3,2,5,6,1,7]=>000001
[6,3,2,1,4,7,5]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[6,3,2,1,5,4,7]=>{{1,4,6},{2,3},{5},{7}}=>[4,3,2,6,5,1,7]=>000001
[6,3,2,1,5,7,4]=>{{1,4,6,7},{2,3},{5}}=>[4,3,2,6,5,7,1]=>000000
[6,3,2,1,7,4,5]=>{{1,4,6},{2,3},{5,7}}=>[4,3,2,6,7,1,5]=>000000
[6,3,2,1,7,5,4]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[6,3,2,4,1,5,7]=>{{1,5,6},{2,3},{4},{7}}=>[5,3,2,4,6,1,7]=>000001
[6,3,2,4,1,7,5]=>{{1,5,6,7},{2,3},{4}}=>[5,3,2,4,6,7,1]=>000000
[6,3,2,4,5,1,7]=>{{1,6},{2,3},{4},{5},{7}}=>[6,3,2,4,5,1,7]=>000001
[6,3,2,4,5,7,1]=>{{1,6,7},{2,3},{4},{5}}=>[6,3,2,4,5,7,1]=>000000
[6,3,2,4,7,1,5]=>{{1,6},{2,3},{4},{5,7}}=>[6,3,2,4,7,1,5]=>000000
[6,3,2,4,7,5,1]=>{{1,5,6,7},{2,3},{4}}=>[5,3,2,4,6,7,1]=>000000
[6,3,2,5,1,4,7]=>{{1,4,5,6},{2,3},{7}}=>[4,3,2,5,6,1,7]=>000001
[6,3,2,5,1,7,4]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[6,3,2,5,4,1,7]=>{{1,6},{2,3},{4,5},{7}}=>[6,3,2,5,4,1,7]=>000001
[6,3,2,5,4,7,1]=>{{1,6,7},{2,3},{4,5}}=>[6,3,2,5,4,7,1]=>000000
[6,3,2,5,7,1,4]=>{{1,6},{2,3},{4,5,7}}=>[6,3,2,5,7,1,4]=>000000
[6,3,2,5,7,4,1]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[6,3,2,7,1,4,5]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[6,3,2,7,1,5,4]=>{{1,5,6},{2,3},{4,7}}=>[5,3,2,7,6,1,4]=>000000
[6,3,2,7,4,1,5]=>{{1,6},{2,3},{4,5,7}}=>[6,3,2,5,7,1,4]=>000000
[6,3,2,7,4,5,1]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[6,3,2,7,5,1,4]=>{{1,6},{2,3},{4,7},{5}}=>[6,3,2,7,5,1,4]=>000000
[6,3,2,7,5,4,1]=>{{1,4,6,7},{2,3},{5}}=>[4,3,2,6,5,7,1]=>000000
[6,3,4,1,2,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,3,4,1,2,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,4,1,5,2,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[6,3,4,1,5,7,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,3,4,1,7,2,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[6,3,4,1,7,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,4,2,1,5,7]=>{{1,5,6},{2,3,4},{7}}=>[5,3,4,2,6,1,7]=>000001
[6,3,4,2,1,7,5]=>{{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000
[6,3,4,2,5,1,7]=>{{1,6},{2,3,4},{5},{7}}=>[6,3,4,2,5,1,7]=>000001
[6,3,4,2,5,7,1]=>{{1,6,7},{2,3,4},{5}}=>[6,3,4,2,5,7,1]=>000000
[6,3,4,2,7,1,5]=>{{1,6},{2,3,4},{5,7}}=>[6,3,4,2,7,1,5]=>000000
[6,3,4,2,7,5,1]=>{{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000
[6,3,4,5,1,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,3,4,5,1,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,4,5,2,1,7]=>{{1,6},{2,3,4,5},{7}}=>[6,3,4,5,2,1,7]=>000001
[6,3,4,5,2,7,1]=>{{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000
[6,3,4,5,7,1,2]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,3,4,5,7,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,4,7,1,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,4,7,1,5,2]=>{{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000
[6,3,4,7,2,1,5]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,3,4,7,2,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,4,7,5,1,2]=>{{1,6},{2,3,4,7},{5}}=>[6,3,4,7,5,1,2]=>000000
[6,3,4,7,5,2,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,3,5,1,2,4,7]=>{{1,4,6},{2,3,5},{7}}=>[4,3,5,6,2,1,7]=>000001
[6,3,5,1,2,7,4]=>{{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000
[6,3,5,1,4,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,3,5,1,4,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,5,1,7,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,5,1,7,4,2]=>{{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000
[6,3,5,2,1,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,3,5,2,1,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,5,2,4,1,7]=>{{1,6},{2,3,4,5},{7}}=>[6,3,4,5,2,1,7]=>000001
[6,3,5,2,4,7,1]=>{{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000
[6,3,5,2,7,1,4]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,3,5,2,7,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,5,4,1,2,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[6,3,5,4,1,7,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,3,5,4,2,1,7]=>{{1,6},{2,3,5},{4},{7}}=>[6,3,5,4,2,1,7]=>000001
[6,3,5,4,2,7,1]=>{{1,6,7},{2,3,5},{4}}=>[6,3,5,4,2,7,1]=>000000
[6,3,5,4,7,1,2]=>{{1,6},{2,3,5,7},{4}}=>[6,3,5,4,7,1,2]=>000000
[6,3,5,4,7,2,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,3,5,7,1,2,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[6,3,5,7,1,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,5,7,2,1,4]=>{{1,6},{2,3,5},{4,7}}=>[6,3,5,7,2,1,4]=>000000
[6,3,5,7,2,4,1]=>{{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000
[6,3,5,7,4,1,2]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,3,5,7,4,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,7,1,2,4,5]=>{{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000
[6,3,7,1,2,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,7,1,4,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,7,1,4,5,2]=>{{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000
[6,3,7,1,5,2,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,3,7,1,5,4,2]=>{{1,4,6},{2,3,7},{5}}=>[4,3,7,6,5,1,2]=>000000
[6,3,7,2,1,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,7,2,1,5,4]=>{{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000
[6,3,7,2,4,1,5]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,3,7,2,4,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,7,2,5,1,4]=>{{1,6},{2,3,4,7},{5}}=>[6,3,4,7,5,1,2]=>000000
[6,3,7,2,5,4,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,3,7,4,1,2,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,3,7,4,1,5,2]=>{{1,5,6},{2,3,7},{4}}=>[5,3,7,4,6,1,2]=>000000
[6,3,7,4,2,1,5]=>{{1,6},{2,3,5,7},{4}}=>[6,3,5,4,7,1,2]=>000000
[6,3,7,4,2,5,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,3,7,4,5,1,2]=>{{1,6},{2,3,7},{4},{5}}=>[6,3,7,4,5,1,2]=>000000
[6,3,7,4,5,2,1]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[6,3,7,5,1,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,7,5,1,4,2]=>{{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000
[6,3,7,5,2,1,4]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,3,7,5,2,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,3,7,5,4,1,2]=>{{1,6},{2,3,7},{4,5}}=>[6,3,7,5,4,1,2]=>000000
[6,3,7,5,4,2,1]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[6,4,1,2,3,5,7]=>{{1,3,5,6},{2,4},{7}}=>[3,4,5,2,6,1,7]=>000001
[6,4,1,2,3,7,5]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[6,4,1,2,5,3,7]=>{{1,3,6},{2,4},{5},{7}}=>[3,4,6,2,5,1,7]=>000001
[6,4,1,2,5,7,3]=>{{1,3,6,7},{2,4},{5}}=>[3,4,6,2,5,7,1]=>000000
[6,4,1,2,7,3,5]=>{{1,3,6},{2,4},{5,7}}=>[3,4,6,2,7,1,5]=>000000
[6,4,1,2,7,5,3]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[6,4,1,3,2,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,4,1,3,2,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,1,3,5,2,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[6,4,1,3,5,7,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,4,1,3,7,2,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[6,4,1,3,7,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,1,5,2,3,7]=>{{1,3,6},{2,4,5},{7}}=>[3,4,6,5,2,1,7]=>000001
[6,4,1,5,2,7,3]=>{{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000
[6,4,1,5,3,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,4,1,5,3,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,1,5,7,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,1,5,7,3,2]=>{{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000
[6,4,1,7,2,3,5]=>{{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000
[6,4,1,7,2,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,1,7,3,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,1,7,3,5,2]=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000
[6,4,1,7,5,2,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,4,1,7,5,3,2]=>{{1,3,6},{2,4,7},{5}}=>[3,4,6,7,5,1,2]=>000000
[6,4,2,1,3,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,4,2,1,3,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,2,1,5,3,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
[6,4,2,1,5,7,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,4,2,1,7,3,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
[6,4,2,1,7,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,2,3,1,5,7]=>{{1,5,6},{2,3,4},{7}}=>[5,3,4,2,6,1,7]=>000001
[6,4,2,3,1,7,5]=>{{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000
[6,4,2,3,5,1,7]=>{{1,6},{2,3,4},{5},{7}}=>[6,3,4,2,5,1,7]=>000001
[6,4,2,3,5,7,1]=>{{1,6,7},{2,3,4},{5}}=>[6,3,4,2,5,7,1]=>000000
[6,4,2,3,7,1,5]=>{{1,6},{2,3,4},{5,7}}=>[6,3,4,2,7,1,5]=>000000
[6,4,2,3,7,5,1]=>{{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000
[6,4,2,5,1,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,4,2,5,1,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,2,5,3,1,7]=>{{1,6},{2,3,4,5},{7}}=>[6,3,4,5,2,1,7]=>000001
[6,4,2,5,3,7,1]=>{{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000
[6,4,2,5,7,1,3]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,4,2,5,7,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,2,7,1,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,2,7,1,5,3]=>{{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000
[6,4,2,7,3,1,5]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,4,2,7,3,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,2,7,5,1,3]=>{{1,6},{2,3,4,7},{5}}=>[6,3,4,7,5,1,2]=>000000
[6,4,2,7,5,3,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,4,3,1,2,5,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[6,4,3,1,2,7,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,4,3,1,5,2,7]=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>000001
[6,4,3,1,5,7,2]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[6,4,3,1,7,2,5]=>{{1,2,4,6},{3},{5,7}}=>[2,4,3,6,7,1,5]=>000000
[6,4,3,1,7,5,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,4,3,2,1,5,7]=>{{1,5,6},{2,4},{3},{7}}=>[5,4,3,2,6,1,7]=>000001
[6,4,3,2,1,7,5]=>{{1,5,6,7},{2,4},{3}}=>[5,4,3,2,6,7,1]=>000000
[6,4,3,2,5,1,7]=>{{1,6},{2,4},{3},{5},{7}}=>[6,4,3,2,5,1,7]=>000001
[6,4,3,2,5,7,1]=>{{1,6,7},{2,4},{3},{5}}=>[6,4,3,2,5,7,1]=>000000
[6,4,3,2,7,1,5]=>{{1,6},{2,4},{3},{5,7}}=>[6,4,3,2,7,1,5]=>000000
[6,4,3,2,7,5,1]=>{{1,5,6,7},{2,4},{3}}=>[5,4,3,2,6,7,1]=>000000
[6,4,3,5,1,2,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[6,4,3,5,1,7,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,4,3,5,2,1,7]=>{{1,6},{2,4,5},{3},{7}}=>[6,4,3,5,2,1,7]=>000001
[6,4,3,5,2,7,1]=>{{1,6,7},{2,4,5},{3}}=>[6,4,3,5,2,7,1]=>000000
[6,4,3,5,7,1,2]=>{{1,6},{2,4,5,7},{3}}=>[6,4,3,5,7,1,2]=>000000
[6,4,3,5,7,2,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,4,3,7,1,2,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,4,3,7,1,5,2]=>{{1,5,6},{2,4,7},{3}}=>[5,4,3,7,6,1,2]=>000000
[6,4,3,7,2,1,5]=>{{1,6},{2,4,5,7},{3}}=>[6,4,3,5,7,1,2]=>000000
[6,4,3,7,2,5,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,4,3,7,5,1,2]=>{{1,6},{2,4,7},{3},{5}}=>[6,4,3,7,5,1,2]=>000000
[6,4,3,7,5,2,1]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[6,4,5,1,2,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,4,5,1,2,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,5,1,3,2,7]=>{{1,2,4,6},{3,5},{7}}=>[2,4,5,6,3,1,7]=>000001
[6,4,5,1,3,7,2]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[6,4,5,1,7,2,3]=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000
[6,4,5,1,7,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,5,2,1,3,7]=>{{1,3,5,6},{2,4},{7}}=>[3,4,5,2,6,1,7]=>000001
[6,4,5,2,1,7,3]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[6,4,5,2,3,1,7]=>{{1,6},{2,4},{3,5},{7}}=>[6,4,5,2,3,1,7]=>000001
[6,4,5,2,3,7,1]=>{{1,6,7},{2,4},{3,5}}=>[6,4,5,2,3,7,1]=>000000
[6,4,5,2,7,1,3]=>{{1,6},{2,4},{3,5,7}}=>[6,4,5,2,7,1,3]=>000000
[6,4,5,2,7,3,1]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[6,4,5,3,1,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,4,5,3,1,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,5,3,2,1,7]=>{{1,6},{2,3,4,5},{7}}=>[6,3,4,5,2,1,7]=>000001
[6,4,5,3,2,7,1]=>{{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000
[6,4,5,3,7,1,2]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,4,5,3,7,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,5,7,1,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,5,7,1,3,2]=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000
[6,4,5,7,2,1,3]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,4,5,7,2,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,5,7,3,1,2]=>{{1,6},{2,4,7},{3,5}}=>[6,4,5,7,3,1,2]=>000000
[6,4,5,7,3,2,1]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[6,4,7,1,2,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,7,1,2,5,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[6,4,7,1,3,2,5]=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000
[6,4,7,1,3,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,7,1,5,2,3]=>{{1,2,4,6},{3,7},{5}}=>[2,4,7,6,5,1,3]=>000000
[6,4,7,1,5,3,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,4,7,2,1,3,5]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[6,4,7,2,1,5,3]=>{{1,5,6},{2,4},{3,7}}=>[5,4,7,2,6,1,3]=>000000
[6,4,7,2,3,1,5]=>{{1,6},{2,4},{3,5,7}}=>[6,4,5,2,7,1,3]=>000000
[6,4,7,2,3,5,1]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[6,4,7,2,5,1,3]=>{{1,6},{2,4},{3,7},{5}}=>[6,4,7,2,5,1,3]=>000000
[6,4,7,2,5,3,1]=>{{1,3,6,7},{2,4},{5}}=>[3,4,6,2,5,7,1]=>000000
[6,4,7,3,1,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,7,3,1,5,2]=>{{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000
[6,4,7,3,2,1,5]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,4,7,3,2,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,7,3,5,1,2]=>{{1,6},{2,3,4,7},{5}}=>[6,3,4,7,5,1,2]=>000000
[6,4,7,3,5,2,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,4,7,5,1,2,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[6,4,7,5,1,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,4,7,5,2,1,3]=>{{1,6},{2,4,5},{3,7}}=>[6,4,7,5,2,1,3]=>000000
[6,4,7,5,2,3,1]=>{{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000
[6,4,7,5,3,1,2]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,4,7,5,3,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,1,2,3,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,5,1,2,3,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,1,2,4,3,7]=>{{1,3,6},{2,4,5},{7}}=>[3,4,6,5,2,1,7]=>000001
[6,5,1,2,4,7,3]=>{{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000
[6,5,1,2,7,3,4]=>{{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000
[6,5,1,2,7,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,1,3,2,4,7]=>{{1,3,4,6},{2,5},{7}}=>[3,5,4,6,2,1,7]=>000001
[6,5,1,3,2,7,4]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[6,5,1,3,4,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,5,1,3,4,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,1,3,7,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,1,3,7,4,2]=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000
[6,5,1,4,2,3,7]=>{{1,3,6},{2,5},{4},{7}}=>[3,5,6,4,2,1,7]=>000001
[6,5,1,4,2,7,3]=>{{1,3,6,7},{2,5},{4}}=>[3,5,6,4,2,7,1]=>000000
[6,5,1,4,3,2,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[6,5,1,4,3,7,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,5,1,4,7,2,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,5,1,4,7,3,2]=>{{1,3,6},{2,5,7},{4}}=>[3,5,6,4,7,1,2]=>000000
[6,5,1,7,2,3,4]=>{{1,3,6},{2,5},{4,7}}=>[3,5,6,7,2,1,4]=>000000
[6,5,1,7,2,4,3]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[6,5,1,7,3,2,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[6,5,1,7,3,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,1,7,4,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,1,7,4,3,2]=>{{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000
[6,5,2,1,3,4,7]=>{{1,4,6},{2,3,5},{7}}=>[4,3,5,6,2,1,7]=>000001
[6,5,2,1,3,7,4]=>{{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000
[6,5,2,1,4,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,5,2,1,4,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,2,1,7,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,2,1,7,4,3]=>{{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000
[6,5,2,3,1,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,5,2,3,1,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,2,3,4,1,7]=>{{1,6},{2,3,4,5},{7}}=>[6,3,4,5,2,1,7]=>000001
[6,5,2,3,4,7,1]=>{{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000
[6,5,2,3,7,1,4]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,5,2,3,7,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,2,4,1,3,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
[6,5,2,4,1,7,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,5,2,4,3,1,7]=>{{1,6},{2,3,5},{4},{7}}=>[6,3,5,4,2,1,7]=>000001
[6,5,2,4,3,7,1]=>{{1,6,7},{2,3,5},{4}}=>[6,3,5,4,2,7,1]=>000000
[6,5,2,4,7,1,3]=>{{1,6},{2,3,5,7},{4}}=>[6,3,5,4,7,1,2]=>000000
[6,5,2,4,7,3,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,5,2,7,1,3,4]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
[6,5,2,7,1,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,2,7,3,1,4]=>{{1,6},{2,3,5},{4,7}}=>[6,3,5,7,2,1,4]=>000000
[6,5,2,7,3,4,1]=>{{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000
[6,5,2,7,4,1,3]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,5,2,7,4,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,3,1,2,4,7]=>{{1,4,6},{2,5},{3},{7}}=>[4,5,3,6,2,1,7]=>000001
[6,5,3,1,2,7,4]=>{{1,4,6,7},{2,5},{3}}=>[4,5,3,6,2,7,1]=>000000
[6,5,3,1,4,2,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[6,5,3,1,4,7,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,5,3,1,7,2,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,5,3,1,7,4,2]=>{{1,4,6},{2,5,7},{3}}=>[4,5,3,6,7,1,2]=>000000
[6,5,3,2,1,4,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
[6,5,3,2,1,7,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,5,3,2,4,1,7]=>{{1,6},{2,4,5},{3},{7}}=>[6,4,3,5,2,1,7]=>000001
[6,5,3,2,4,7,1]=>{{1,6,7},{2,4,5},{3}}=>[6,4,3,5,2,7,1]=>000000
[6,5,3,2,7,1,4]=>{{1,6},{2,4,5,7},{3}}=>[6,4,3,5,7,1,2]=>000000
[6,5,3,2,7,4,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,5,3,4,1,2,7]=>{{1,2,5,6},{3},{4},{7}}=>[2,5,3,4,6,1,7]=>000001
[6,5,3,4,1,7,2]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[6,5,3,4,2,1,7]=>{{1,6},{2,5},{3},{4},{7}}=>[6,5,3,4,2,1,7]=>000001
[6,5,3,4,2,7,1]=>{{1,6,7},{2,5},{3},{4}}=>[6,5,3,4,2,7,1]=>000000
[6,5,3,4,7,1,2]=>{{1,6},{2,5,7},{3},{4}}=>[6,5,3,4,7,1,2]=>000000
[6,5,3,4,7,2,1]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[6,5,3,7,1,2,4]=>{{1,2,5,6},{3},{4,7}}=>[2,5,3,7,6,1,4]=>000000
[6,5,3,7,1,4,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,5,3,7,2,1,4]=>{{1,6},{2,5},{3},{4,7}}=>[6,5,3,7,2,1,4]=>000000
[6,5,3,7,2,4,1]=>{{1,4,6,7},{2,5},{3}}=>[4,5,3,6,2,7,1]=>000000
[6,5,3,7,4,1,2]=>{{1,6},{2,4,5,7},{3}}=>[6,4,3,5,7,1,2]=>000000
[6,5,3,7,4,2,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,5,4,1,2,3,7]=>{{1,3,4,6},{2,5},{7}}=>[3,5,4,6,2,1,7]=>000001
[6,5,4,1,2,7,3]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[6,5,4,1,3,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,5,4,1,3,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,4,1,7,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,4,1,7,3,2]=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000
[6,5,4,2,1,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
[6,5,4,2,1,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,4,2,3,1,7]=>{{1,6},{2,3,4,5},{7}}=>[6,3,4,5,2,1,7]=>000001
[6,5,4,2,3,7,1]=>{{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000
[6,5,4,2,7,1,3]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,5,4,2,7,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,4,3,1,2,7]=>{{1,2,5,6},{3,4},{7}}=>[2,5,4,3,6,1,7]=>000001
[6,5,4,3,1,7,2]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[6,5,4,3,2,1,7]=>{{1,6},{2,5},{3,4},{7}}=>[6,5,4,3,2,1,7]=>000001
[6,5,4,3,2,7,1]=>{{1,6,7},{2,5},{3,4}}=>[6,5,4,3,2,7,1]=>000000
[6,5,4,3,7,1,2]=>{{1,6},{2,5,7},{3,4}}=>[6,5,4,3,7,1,2]=>000000
[6,5,4,3,7,2,1]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[6,5,4,7,1,2,3]=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000
[6,5,4,7,1,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,4,7,2,1,3]=>{{1,6},{2,5},{3,4,7}}=>[6,5,4,7,2,1,3]=>000000
[6,5,4,7,2,3,1]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[6,5,4,7,3,1,2]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,5,4,7,3,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,7,1,2,3,4]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[6,5,7,1,2,4,3]=>{{1,4,6},{2,5},{3,7}}=>[4,5,7,6,2,1,3]=>000000
[6,5,7,1,3,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,7,1,3,4,2]=>{{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000
[6,5,7,1,4,2,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[6,5,7,1,4,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,7,2,1,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,7,2,1,4,3]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
[6,5,7,2,3,1,4]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,5,7,2,3,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,7,2,4,1,3]=>{{1,6},{2,4,5},{3,7}}=>[6,4,7,5,2,1,3]=>000000
[6,5,7,2,4,3,1]=>{{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000
[6,5,7,3,1,2,4]=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000
[6,5,7,3,1,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,7,3,2,1,4]=>{{1,6},{2,5},{3,4,7}}=>[6,5,4,7,2,1,3]=>000000
[6,5,7,3,2,4,1]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[6,5,7,3,4,1,2]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,5,7,3,4,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,5,7,4,1,2,3]=>{{1,2,5,6},{3,7},{4}}=>[2,5,7,4,6,1,3]=>000000
[6,5,7,4,1,3,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,5,7,4,2,1,3]=>{{1,6},{2,5},{3,7},{4}}=>[6,5,7,4,2,1,3]=>000000
[6,5,7,4,2,3,1]=>{{1,3,6,7},{2,5},{4}}=>[3,5,6,4,2,7,1]=>000000
[6,5,7,4,3,1,2]=>{{1,6},{2,3,5,7},{4}}=>[6,3,5,4,7,1,2]=>000000
[6,5,7,4,3,2,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,7,1,2,3,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,1,2,3,5,4]=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000
[6,7,1,2,4,3,5]=>{{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000
[6,7,1,2,4,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,1,2,5,3,4]=>{{1,3,6},{2,4,7},{5}}=>[3,4,6,7,5,1,2]=>000000
[6,7,1,2,5,4,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,7,1,3,2,4,5]=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000
[6,7,1,3,2,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,1,3,4,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,1,3,4,5,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[6,7,1,3,5,2,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,7,1,3,5,4,2]=>{{1,3,4,6},{2,7},{5}}=>[3,7,4,6,5,1,2]=>000000
[6,7,1,4,2,3,5]=>{{1,3,6},{2,5,7},{4}}=>[3,5,6,4,7,1,2]=>000000
[6,7,1,4,2,5,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,7,1,4,3,2,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,7,1,4,3,5,2]=>{{1,3,5,6},{2,7},{4}}=>[3,7,5,4,6,1,2]=>000000
[6,7,1,4,5,2,3]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[6,7,1,4,5,3,2]=>{{1,3,6},{2,7},{4},{5}}=>[3,7,6,4,5,1,2]=>000000
[6,7,1,5,2,3,4]=>{{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000
[6,7,1,5,2,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,1,5,3,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,1,5,3,4,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[6,7,1,5,4,2,3]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[6,7,1,5,4,3,2]=>{{1,3,6},{2,7},{4,5}}=>[3,7,6,5,4,1,2]=>000000
[6,7,2,1,3,4,5]=>{{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000
[6,7,2,1,3,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,2,1,4,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,2,1,4,5,3]=>{{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000
[6,7,2,1,5,3,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,7,2,1,5,4,3]=>{{1,4,6},{2,3,7},{5}}=>[4,3,7,6,5,1,2]=>000000
[6,7,2,3,1,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,2,3,1,5,4]=>{{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000
[6,7,2,3,4,1,5]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,7,2,3,4,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,2,3,5,1,4]=>{{1,6},{2,3,4,7},{5}}=>[6,3,4,7,5,1,2]=>000000
[6,7,2,3,5,4,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,7,2,4,1,3,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,7,2,4,1,5,3]=>{{1,5,6},{2,3,7},{4}}=>[5,3,7,4,6,1,2]=>000000
[6,7,2,4,3,1,5]=>{{1,6},{2,3,5,7},{4}}=>[6,3,5,4,7,1,2]=>000000
[6,7,2,4,3,5,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,7,2,4,5,1,3]=>{{1,6},{2,3,7},{4},{5}}=>[6,3,7,4,5,1,2]=>000000
[6,7,2,4,5,3,1]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[6,7,2,5,1,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,2,5,1,4,3]=>{{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000
[6,7,2,5,3,1,4]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,7,2,5,3,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,2,5,4,1,3]=>{{1,6},{2,3,7},{4,5}}=>[6,3,7,5,4,1,2]=>000000
[6,7,2,5,4,3,1]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[6,7,3,1,2,4,5]=>{{1,4,6},{2,5,7},{3}}=>[4,5,3,6,7,1,2]=>000000
[6,7,3,1,2,5,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,7,3,1,4,2,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,7,3,1,4,5,2]=>{{1,4,5,6},{2,7},{3}}=>[4,7,3,5,6,1,2]=>000000
[6,7,3,1,5,2,4]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[6,7,3,1,5,4,2]=>{{1,4,6},{2,7},{3},{5}}=>[4,7,3,6,5,1,2]=>000000
[6,7,3,2,1,4,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,7,3,2,1,5,4]=>{{1,5,6},{2,4,7},{3}}=>[5,4,3,7,6,1,2]=>000000
[6,7,3,2,4,1,5]=>{{1,6},{2,4,5,7},{3}}=>[6,4,3,5,7,1,2]=>000000
[6,7,3,2,4,5,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,7,3,2,5,1,4]=>{{1,6},{2,4,7},{3},{5}}=>[6,4,3,7,5,1,2]=>000000
[6,7,3,2,5,4,1]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[6,7,3,4,1,2,5]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[6,7,3,4,1,5,2]=>{{1,5,6},{2,7},{3},{4}}=>[5,7,3,4,6,1,2]=>000000
[6,7,3,4,2,1,5]=>{{1,6},{2,5,7},{3},{4}}=>[6,5,3,4,7,1,2]=>000000
[6,7,3,4,2,5,1]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[6,7,3,4,5,1,2]=>{{1,6},{2,7},{3},{4},{5}}=>[6,7,3,4,5,1,2]=>000000
[6,7,3,4,5,2,1]=>{{1,2,6,7},{3},{4},{5}}=>[2,6,3,4,5,7,1]=>000000
[6,7,3,5,1,2,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,7,3,5,1,4,2]=>{{1,4,5,6},{2,7},{3}}=>[4,7,3,5,6,1,2]=>000000
[6,7,3,5,2,1,4]=>{{1,6},{2,4,5,7},{3}}=>[6,4,3,5,7,1,2]=>000000
[6,7,3,5,2,4,1]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[6,7,3,5,4,1,2]=>{{1,6},{2,7},{3},{4,5}}=>[6,7,3,5,4,1,2]=>000000
[6,7,3,5,4,2,1]=>{{1,2,6,7},{3},{4,5}}=>[2,6,3,5,4,7,1]=>000000
[6,7,4,1,2,3,5]=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000
[6,7,4,1,2,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,4,1,3,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,4,1,3,5,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[6,7,4,1,5,2,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,7,4,1,5,3,2]=>{{1,3,4,6},{2,7},{5}}=>[3,7,4,6,5,1,2]=>000000
[6,7,4,2,1,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,4,2,1,5,3]=>{{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000
[6,7,4,2,3,1,5]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,7,4,2,3,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,4,2,5,1,3]=>{{1,6},{2,3,4,7},{5}}=>[6,3,4,7,5,1,2]=>000000
[6,7,4,2,5,3,1]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[6,7,4,3,1,2,5]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[6,7,4,3,1,5,2]=>{{1,5,6},{2,7},{3,4}}=>[5,7,4,3,6,1,2]=>000000
[6,7,4,3,2,1,5]=>{{1,6},{2,5,7},{3,4}}=>[6,5,4,3,7,1,2]=>000000
[6,7,4,3,2,5,1]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[6,7,4,3,5,1,2]=>{{1,6},{2,7},{3,4},{5}}=>[6,7,4,3,5,1,2]=>000000
[6,7,4,3,5,2,1]=>{{1,2,6,7},{3,4},{5}}=>[2,6,4,3,5,7,1]=>000000
[6,7,4,5,1,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,4,5,1,3,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[6,7,4,5,2,1,3]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,7,4,5,2,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,4,5,3,1,2]=>{{1,6},{2,7},{3,4,5}}=>[6,7,4,5,3,1,2]=>000000
[6,7,4,5,3,2,1]=>{{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000
[6,7,5,1,2,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,5,1,2,4,3]=>{{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000
[6,7,5,1,3,2,4]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[6,7,5,1,3,4,2]=>{{1,4,6},{2,7},{3,5}}=>[4,7,5,6,3,1,2]=>000000
[6,7,5,1,4,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,5,1,4,3,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[6,7,5,2,1,3,4]=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000
[6,7,5,2,1,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,5,2,3,1,4]=>{{1,6},{2,4,7},{3,5}}=>[6,4,5,7,3,1,2]=>000000
[6,7,5,2,3,4,1]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[6,7,5,2,4,1,3]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,7,5,2,4,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,5,3,1,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,5,3,1,4,2]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
[6,7,5,3,2,1,4]=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
[6,7,5,3,2,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[6,7,5,3,4,1,2]=>{{1,6},{2,7},{3,4,5}}=>[6,7,4,5,3,1,2]=>000000
[6,7,5,3,4,2,1]=>{{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000
[6,7,5,4,1,2,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,7,5,4,1,3,2]=>{{1,3,5,6},{2,7},{4}}=>[3,7,5,4,6,1,2]=>000000
[6,7,5,4,2,1,3]=>{{1,6},{2,3,5,7},{4}}=>[6,3,5,4,7,1,2]=>000000
[6,7,5,4,2,3,1]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[6,7,5,4,3,1,2]=>{{1,6},{2,7},{3,5},{4}}=>[6,7,5,4,3,1,2]=>000000
[6,7,5,4,3,2,1]=>{{1,2,6,7},{3,5},{4}}=>[2,6,5,4,3,7,1]=>000000
[7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,2,3,4,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,1,2,3,5,4,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,1,2,3,5,6,4]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[7,1,2,3,6,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,2,3,6,5,4]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[7,1,2,4,3,5,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,1,2,4,3,6,5]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[7,1,2,4,5,3,6]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[7,1,2,4,5,6,3]=>{{1,2,3,7},{4},{5},{6}}=>[2,3,7,4,5,6,1]=>000000
[7,1,2,4,6,3,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,1,2,4,6,5,3]=>{{1,2,3,7},{4},{5,6}}=>[2,3,7,4,6,5,1]=>000000
[7,1,2,5,3,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,2,5,3,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,1,2,5,4,3,6]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[7,1,2,5,4,6,3]=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>000000
[7,1,2,5,6,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,2,5,6,4,3]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000
[7,1,2,6,3,4,5]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[7,1,2,6,3,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,2,6,4,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,2,6,4,5,3]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000
[7,1,2,6,5,3,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,1,2,6,5,4,3]=>{{1,2,3,7},{4,6},{5}}=>[2,3,7,6,5,4,1]=>000000
[7,1,3,2,4,5,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,1,3,2,4,6,5]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[7,1,3,2,5,4,6]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[7,1,3,2,5,6,4]=>{{1,2,4,7},{3},{5},{6}}=>[2,4,3,7,5,6,1]=>000000
[7,1,3,2,6,4,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,1,3,2,6,5,4]=>{{1,2,4,7},{3},{5,6}}=>[2,4,3,7,6,5,1]=>000000
[7,1,3,4,2,5,6]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[7,1,3,4,2,6,5]=>{{1,2,5,7},{3},{4},{6}}=>[2,5,3,4,7,6,1]=>000000
[7,1,3,4,5,2,6]=>{{1,2,6,7},{3},{4},{5}}=>[2,6,3,4,5,7,1]=>000000
[7,1,3,4,5,6,2]=>{{1,2,7},{3},{4},{5},{6}}=>[2,7,3,4,5,6,1]=>000000
[7,1,3,4,6,2,5]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[7,1,3,4,6,5,2]=>{{1,2,7},{3},{4},{5,6}}=>[2,7,3,4,6,5,1]=>000000
[7,1,3,5,2,4,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,1,3,5,2,6,4]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[7,1,3,5,4,2,6]=>{{1,2,6,7},{3},{4,5}}=>[2,6,3,5,4,7,1]=>000000
[7,1,3,5,4,6,2]=>{{1,2,7},{3},{4,5},{6}}=>[2,7,3,5,4,6,1]=>000000
[7,1,3,5,6,2,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,1,3,5,6,4,2]=>{{1,2,7},{3},{4,5,6}}=>[2,7,3,5,6,4,1]=>000000
[7,1,3,6,2,4,5]=>{{1,2,5,7},{3},{4,6}}=>[2,5,3,6,7,4,1]=>000000
[7,1,3,6,2,5,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,1,3,6,4,2,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,1,3,6,4,5,2]=>{{1,2,7},{3},{4,5,6}}=>[2,7,3,5,6,4,1]=>000000
[7,1,3,6,5,2,4]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[7,1,3,6,5,4,2]=>{{1,2,7},{3},{4,6},{5}}=>[2,7,3,6,5,4,1]=>000000
[7,1,4,2,3,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,4,2,3,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,1,4,2,5,3,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,1,4,2,5,6,3]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[7,1,4,2,6,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,4,2,6,5,3]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[7,1,4,3,2,5,6]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[7,1,4,3,2,6,5]=>{{1,2,5,7},{3,4},{6}}=>[2,5,4,3,7,6,1]=>000000
[7,1,4,3,5,2,6]=>{{1,2,6,7},{3,4},{5}}=>[2,6,4,3,5,7,1]=>000000
[7,1,4,3,5,6,2]=>{{1,2,7},{3,4},{5},{6}}=>[2,7,4,3,5,6,1]=>000000
[7,1,4,3,6,2,5]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[7,1,4,3,6,5,2]=>{{1,2,7},{3,4},{5,6}}=>[2,7,4,3,6,5,1]=>000000
[7,1,4,5,2,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,4,5,2,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,1,4,5,3,2,6]=>{{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000
[7,1,4,5,3,6,2]=>{{1,2,7},{3,4,5},{6}}=>[2,7,4,5,3,6,1]=>000000
[7,1,4,5,6,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,4,5,6,3,2]=>{{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000
[7,1,4,6,2,3,5]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000
[7,1,4,6,2,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,4,6,3,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,4,6,3,5,2]=>{{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000
[7,1,4,6,5,2,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,1,4,6,5,3,2]=>{{1,2,7},{3,4,6},{5}}=>[2,7,4,6,5,3,1]=>000000
[7,1,5,2,3,4,6]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[7,1,5,2,3,6,4]=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>000000
[7,1,5,2,4,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,5,2,4,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,1,5,2,6,3,4]=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000
[7,1,5,2,6,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,5,3,2,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,5,3,2,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,1,5,3,4,2,6]=>{{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000
[7,1,5,3,4,6,2]=>{{1,2,7},{3,4,5},{6}}=>[2,7,4,5,3,6,1]=>000000
[7,1,5,3,6,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,5,3,6,4,2]=>{{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000
[7,1,5,4,2,3,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,1,5,4,2,6,3]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[7,1,5,4,3,2,6]=>{{1,2,6,7},{3,5},{4}}=>[2,6,5,4,3,7,1]=>000000
[7,1,5,4,3,6,2]=>{{1,2,7},{3,5},{4},{6}}=>[2,7,5,4,3,6,1]=>000000
[7,1,5,4,6,2,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,1,5,4,6,3,2]=>{{1,2,7},{3,5,6},{4}}=>[2,7,5,4,6,3,1]=>000000
[7,1,5,6,2,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,5,6,2,4,3]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[7,1,5,6,3,2,4]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[7,1,5,6,3,4,2]=>{{1,2,7},{3,5},{4,6}}=>[2,7,5,6,3,4,1]=>000000
[7,1,5,6,4,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,5,6,4,3,2]=>{{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000
[7,1,6,2,3,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,6,2,3,5,4]=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000
[7,1,6,2,4,3,5]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[7,1,6,2,4,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,6,2,5,3,4]=>{{1,2,4,7},{3,6},{5}}=>[2,4,6,7,5,3,1]=>000000
[7,1,6,2,5,4,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,1,6,3,2,4,5]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000
[7,1,6,3,2,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,6,3,4,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,6,3,4,5,2]=>{{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000
[7,1,6,3,5,2,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,1,6,3,5,4,2]=>{{1,2,7},{3,4,6},{5}}=>[2,7,4,6,5,3,1]=>000000
[7,1,6,4,2,3,5]=>{{1,2,5,7},{3,6},{4}}=>[2,5,6,4,7,3,1]=>000000
[7,1,6,4,2,5,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,1,6,4,3,2,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,1,6,4,3,5,2]=>{{1,2,7},{3,5,6},{4}}=>[2,7,5,4,6,3,1]=>000000
[7,1,6,4,5,2,3]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[7,1,6,4,5,3,2]=>{{1,2,7},{3,6},{4},{5}}=>[2,7,6,4,5,3,1]=>000000
[7,1,6,5,2,3,4]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[7,1,6,5,2,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,6,5,3,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,1,6,5,3,4,2]=>{{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000
[7,1,6,5,4,2,3]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[7,1,6,5,4,3,2]=>{{1,2,7},{3,6},{4,5}}=>[2,7,6,5,4,3,1]=>000000
[7,2,1,3,4,5,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,1,3,4,6,5]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[7,2,1,3,5,4,6]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[7,2,1,3,5,6,4]=>{{1,3,4,7},{2},{5},{6}}=>[3,2,4,7,5,6,1]=>000000
[7,2,1,3,6,4,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,1,3,6,5,4]=>{{1,3,4,7},{2},{5,6}}=>[3,2,4,7,6,5,1]=>000000
[7,2,1,4,3,5,6]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[7,2,1,4,3,6,5]=>{{1,3,5,7},{2},{4},{6}}=>[3,2,5,4,7,6,1]=>000000
[7,2,1,4,5,3,6]=>{{1,3,6,7},{2},{4},{5}}=>[3,2,6,4,5,7,1]=>000000
[7,2,1,4,5,6,3]=>{{1,3,7},{2},{4},{5},{6}}=>[3,2,7,4,5,6,1]=>000000
[7,2,1,4,6,3,5]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[7,2,1,4,6,5,3]=>{{1,3,7},{2},{4},{5,6}}=>[3,2,7,4,6,5,1]=>000000
[7,2,1,5,3,4,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,1,5,3,6,4]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[7,2,1,5,4,3,6]=>{{1,3,6,7},{2},{4,5}}=>[3,2,6,5,4,7,1]=>000000
[7,2,1,5,4,6,3]=>{{1,3,7},{2},{4,5},{6}}=>[3,2,7,5,4,6,1]=>000000
[7,2,1,5,6,3,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,1,5,6,4,3]=>{{1,3,7},{2},{4,5,6}}=>[3,2,7,5,6,4,1]=>000000
[7,2,1,6,3,4,5]=>{{1,3,5,7},{2},{4,6}}=>[3,2,5,6,7,4,1]=>000000
[7,2,1,6,3,5,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,1,6,4,3,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,1,6,4,5,3]=>{{1,3,7},{2},{4,5,6}}=>[3,2,7,5,6,4,1]=>000000
[7,2,1,6,5,3,4]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[7,2,1,6,5,4,3]=>{{1,3,7},{2},{4,6},{5}}=>[3,2,7,6,5,4,1]=>000000
[7,2,3,1,4,5,6]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[7,2,3,1,4,6,5]=>{{1,4,5,7},{2},{3},{6}}=>[4,2,3,5,7,6,1]=>000000
[7,2,3,1,5,4,6]=>{{1,4,6,7},{2},{3},{5}}=>[4,2,3,6,5,7,1]=>000000
[7,2,3,1,5,6,4]=>{{1,4,7},{2},{3},{5},{6}}=>[4,2,3,7,5,6,1]=>000000
[7,2,3,1,6,4,5]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[7,2,3,1,6,5,4]=>{{1,4,7},{2},{3},{5,6}}=>[4,2,3,7,6,5,1]=>000000
[7,2,3,4,1,5,6]=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>000000
[7,2,3,4,1,6,5]=>{{1,5,7},{2},{3},{4},{6}}=>[5,2,3,4,7,6,1]=>000000
[7,2,3,4,5,1,6]=>{{1,6,7},{2},{3},{4},{5}}=>[6,2,3,4,5,7,1]=>000000
[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}}=>[7,2,3,4,5,6,1]=>000000
[7,2,3,4,6,1,5]=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>000000
[7,2,3,4,6,5,1]=>{{1,7},{2},{3},{4},{5,6}}=>[7,2,3,4,6,5,1]=>000000
[7,2,3,5,1,4,6]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[7,2,3,5,1,6,4]=>{{1,4,5,7},{2},{3},{6}}=>[4,2,3,5,7,6,1]=>000000
[7,2,3,5,4,1,6]=>{{1,6,7},{2},{3},{4,5}}=>[6,2,3,5,4,7,1]=>000000
[7,2,3,5,4,6,1]=>{{1,7},{2},{3},{4,5},{6}}=>[7,2,3,5,4,6,1]=>000000
[7,2,3,5,6,1,4]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[7,2,3,5,6,4,1]=>{{1,7},{2},{3},{4,5,6}}=>[7,2,3,5,6,4,1]=>000000
[7,2,3,6,1,4,5]=>{{1,5,7},{2},{3},{4,6}}=>[5,2,3,6,7,4,1]=>000000
[7,2,3,6,1,5,4]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[7,2,3,6,4,1,5]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
[7,2,3,6,4,5,1]=>{{1,7},{2},{3},{4,5,6}}=>[7,2,3,5,6,4,1]=>000000
[7,2,3,6,5,1,4]=>{{1,4,6,7},{2},{3},{5}}=>[4,2,3,6,5,7,1]=>000000
[7,2,3,6,5,4,1]=>{{1,7},{2},{3},{4,6},{5}}=>[7,2,3,6,5,4,1]=>000000
[7,2,4,1,3,5,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,4,1,3,6,5]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[7,2,4,1,5,3,6]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[7,2,4,1,5,6,3]=>{{1,3,4,7},{2},{5},{6}}=>[3,2,4,7,5,6,1]=>000000
[7,2,4,1,6,3,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,4,1,6,5,3]=>{{1,3,4,7},{2},{5,6}}=>[3,2,4,7,6,5,1]=>000000
[7,2,4,3,1,5,6]=>{{1,5,6,7},{2},{3,4}}=>[5,2,4,3,6,7,1]=>000000
[7,2,4,3,1,6,5]=>{{1,5,7},{2},{3,4},{6}}=>[5,2,4,3,7,6,1]=>000000
[7,2,4,3,5,1,6]=>{{1,6,7},{2},{3,4},{5}}=>[6,2,4,3,5,7,1]=>000000
[7,2,4,3,5,6,1]=>{{1,7},{2},{3,4},{5},{6}}=>[7,2,4,3,5,6,1]=>000000
[7,2,4,3,6,1,5]=>{{1,5,6,7},{2},{3,4}}=>[5,2,4,3,6,7,1]=>000000
[7,2,4,3,6,5,1]=>{{1,7},{2},{3,4},{5,6}}=>[7,2,4,3,6,5,1]=>000000
[7,2,4,5,1,3,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,4,5,1,6,3]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[7,2,4,5,3,1,6]=>{{1,6,7},{2},{3,4,5}}=>[6,2,4,5,3,7,1]=>000000
[7,2,4,5,3,6,1]=>{{1,7},{2},{3,4,5},{6}}=>[7,2,4,5,3,6,1]=>000000
[7,2,4,5,6,1,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,4,5,6,3,1]=>{{1,7},{2},{3,4,5,6}}=>[7,2,4,5,6,3,1]=>000000
[7,2,4,6,1,3,5]=>{{1,5,7},{2},{3,4,6}}=>[5,2,4,6,7,3,1]=>000000
[7,2,4,6,1,5,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,4,6,3,1,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,4,6,3,5,1]=>{{1,7},{2},{3,4,5,6}}=>[7,2,4,5,6,3,1]=>000000
[7,2,4,6,5,1,3]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[7,2,4,6,5,3,1]=>{{1,7},{2},{3,4,6},{5}}=>[7,2,4,6,5,3,1]=>000000
[7,2,5,1,3,4,6]=>{{1,4,6,7},{2},{3,5}}=>[4,2,5,6,3,7,1]=>000000
[7,2,5,1,3,6,4]=>{{1,4,7},{2},{3,5},{6}}=>[4,2,5,7,3,6,1]=>000000
[7,2,5,1,4,3,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,5,1,4,6,3]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[7,2,5,1,6,3,4]=>{{1,4,7},{2},{3,5,6}}=>[4,2,5,7,6,3,1]=>000000
[7,2,5,1,6,4,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,5,3,1,4,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,5,3,1,6,4]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
[7,2,5,3,4,1,6]=>{{1,6,7},{2},{3,4,5}}=>[6,2,4,5,3,7,1]=>000000
[7,2,5,3,4,6,1]=>{{1,7},{2},{3,4,5},{6}}=>[7,2,4,5,3,6,1]=>000000
[7,2,5,3,6,1,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,5,3,6,4,1]=>{{1,7},{2},{3,4,5,6}}=>[7,2,4,5,6,3,1]=>000000
[7,2,5,4,1,3,6]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[7,2,5,4,1,6,3]=>{{1,3,5,7},{2},{4},{6}}=>[3,2,5,4,7,6,1]=>000000
[7,2,5,4,3,1,6]=>{{1,6,7},{2},{3,5},{4}}=>[6,2,5,4,3,7,1]=>000000
[7,2,5,4,3,6,1]=>{{1,7},{2},{3,5},{4},{6}}=>[7,2,5,4,3,6,1]=>000000
[7,2,5,4,6,1,3]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[7,2,5,4,6,3,1]=>{{1,7},{2},{3,5,6},{4}}=>[7,2,5,4,6,3,1]=>000000
[7,2,5,6,1,3,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,5,6,1,4,3]=>{{1,3,5,7},{2},{4,6}}=>[3,2,5,6,7,4,1]=>000000
[7,2,5,6,3,1,4]=>{{1,4,6,7},{2},{3,5}}=>[4,2,5,6,3,7,1]=>000000
[7,2,5,6,3,4,1]=>{{1,7},{2},{3,5},{4,6}}=>[7,2,5,6,3,4,1]=>000000
[7,2,5,6,4,1,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,5,6,4,3,1]=>{{1,7},{2},{3,4,5,6}}=>[7,2,4,5,6,3,1]=>000000
[7,2,6,1,3,4,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,6,1,3,5,4]=>{{1,4,7},{2},{3,5,6}}=>[4,2,5,7,6,3,1]=>000000
[7,2,6,1,4,3,5]=>{{1,4,5,7},{2},{3,6}}=>[4,2,6,5,7,3,1]=>000000
[7,2,6,1,4,5,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,6,1,5,3,4]=>{{1,4,7},{2},{3,6},{5}}=>[4,2,6,7,5,3,1]=>000000
[7,2,6,1,5,4,3]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[7,2,6,3,1,4,5]=>{{1,5,7},{2},{3,4,6}}=>[5,2,4,6,7,3,1]=>000000
[7,2,6,3,1,5,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,6,3,4,1,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,6,3,4,5,1]=>{{1,7},{2},{3,4,5,6}}=>[7,2,4,5,6,3,1]=>000000
[7,2,6,3,5,1,4]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
[7,2,6,3,5,4,1]=>{{1,7},{2},{3,4,6},{5}}=>[7,2,4,6,5,3,1]=>000000
[7,2,6,4,1,3,5]=>{{1,5,7},{2},{3,6},{4}}=>[5,2,6,4,7,3,1]=>000000
[7,2,6,4,1,5,3]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[7,2,6,4,3,1,5]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
[7,2,6,4,3,5,1]=>{{1,7},{2},{3,5,6},{4}}=>[7,2,5,4,6,3,1]=>000000
[7,2,6,4,5,1,3]=>{{1,3,6,7},{2},{4},{5}}=>[3,2,6,4,5,7,1]=>000000
[7,2,6,4,5,3,1]=>{{1,7},{2},{3,6},{4},{5}}=>[7,2,6,4,5,3,1]=>000000
[7,2,6,5,1,3,4]=>{{1,4,5,7},{2},{3,6}}=>[4,2,6,5,7,3,1]=>000000
[7,2,6,5,1,4,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,6,5,3,1,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
[7,2,6,5,3,4,1]=>{{1,7},{2},{3,4,5,6}}=>[7,2,4,5,6,3,1]=>000000
[7,2,6,5,4,1,3]=>{{1,3,6,7},{2},{4,5}}=>[3,2,6,5,4,7,1]=>000000
[7,2,6,5,4,3,1]=>{{1,7},{2},{3,6},{4,5}}=>[7,2,6,5,4,3,1]=>000000
[7,3,1,2,4,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,1,2,4,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,3,1,2,5,4,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,3,1,2,5,6,4]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[7,3,1,2,6,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,1,2,6,5,4]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[7,3,1,4,2,5,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,3,1,4,2,6,5]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[7,3,1,4,5,2,6]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[7,3,1,4,5,6,2]=>{{1,2,3,7},{4},{5},{6}}=>[2,3,7,4,5,6,1]=>000000
[7,3,1,4,6,2,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,3,1,4,6,5,2]=>{{1,2,3,7},{4},{5,6}}=>[2,3,7,4,6,5,1]=>000000
[7,3,1,5,2,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,1,5,2,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,3,1,5,4,2,6]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[7,3,1,5,4,6,2]=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>000000
[7,3,1,5,6,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,1,5,6,4,2]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000
[7,3,1,6,2,4,5]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[7,3,1,6,2,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,1,6,4,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,1,6,4,5,2]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000
[7,3,1,6,5,2,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,3,1,6,5,4,2]=>{{1,2,3,7},{4,6},{5}}=>[2,3,7,6,5,4,1]=>000000
[7,3,2,1,4,5,6]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[7,3,2,1,4,6,5]=>{{1,4,5,7},{2,3},{6}}=>[4,3,2,5,7,6,1]=>000000
[7,3,2,1,5,4,6]=>{{1,4,6,7},{2,3},{5}}=>[4,3,2,6,5,7,1]=>000000
[7,3,2,1,5,6,4]=>{{1,4,7},{2,3},{5},{6}}=>[4,3,2,7,5,6,1]=>000000
[7,3,2,1,6,4,5]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[7,3,2,1,6,5,4]=>{{1,4,7},{2,3},{5,6}}=>[4,3,2,7,6,5,1]=>000000
[7,3,2,4,1,5,6]=>{{1,5,6,7},{2,3},{4}}=>[5,3,2,4,6,7,1]=>000000
[7,3,2,4,1,6,5]=>{{1,5,7},{2,3},{4},{6}}=>[5,3,2,4,7,6,1]=>000000
[7,3,2,4,5,1,6]=>{{1,6,7},{2,3},{4},{5}}=>[6,3,2,4,5,7,1]=>000000
[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}}=>[7,3,2,4,5,6,1]=>000000
[7,3,2,4,6,1,5]=>{{1,5,6,7},{2,3},{4}}=>[5,3,2,4,6,7,1]=>000000
[7,3,2,4,6,5,1]=>{{1,7},{2,3},{4},{5,6}}=>[7,3,2,4,6,5,1]=>000000
[7,3,2,5,1,4,6]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[7,3,2,5,1,6,4]=>{{1,4,5,7},{2,3},{6}}=>[4,3,2,5,7,6,1]=>000000
[7,3,2,5,4,1,6]=>{{1,6,7},{2,3},{4,5}}=>[6,3,2,5,4,7,1]=>000000
[7,3,2,5,4,6,1]=>{{1,7},{2,3},{4,5},{6}}=>[7,3,2,5,4,6,1]=>000000
[7,3,2,5,6,1,4]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[7,3,2,5,6,4,1]=>{{1,7},{2,3},{4,5,6}}=>[7,3,2,5,6,4,1]=>000000
[7,3,2,6,1,4,5]=>{{1,5,7},{2,3},{4,6}}=>[5,3,2,6,7,4,1]=>000000
[7,3,2,6,1,5,4]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[7,3,2,6,4,1,5]=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
[7,3,2,6,4,5,1]=>{{1,7},{2,3},{4,5,6}}=>[7,3,2,5,6,4,1]=>000000
[7,3,2,6,5,1,4]=>{{1,4,6,7},{2,3},{5}}=>[4,3,2,6,5,7,1]=>000000
[7,3,2,6,5,4,1]=>{{1,7},{2,3},{4,6},{5}}=>[7,3,2,6,5,4,1]=>000000
[7,3,4,1,2,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,4,1,2,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,3,4,1,5,2,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,3,4,1,5,6,2]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[7,3,4,1,6,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,4,1,6,5,2]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[7,3,4,2,1,5,6]=>{{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000
[7,3,4,2,1,6,5]=>{{1,5,7},{2,3,4},{6}}=>[5,3,4,2,7,6,1]=>000000
[7,3,4,2,5,1,6]=>{{1,6,7},{2,3,4},{5}}=>[6,3,4,2,5,7,1]=>000000
[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}}=>[7,3,4,2,5,6,1]=>000000
[7,3,4,2,6,1,5]=>{{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000
[7,3,4,2,6,5,1]=>{{1,7},{2,3,4},{5,6}}=>[7,3,4,2,6,5,1]=>000000
[7,3,4,5,1,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,4,5,1,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,3,4,5,2,1,6]=>{{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000
[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>000000
[7,3,4,5,6,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,3,4,6,1,2,5]=>{{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000
[7,3,4,6,1,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,4,6,2,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,4,6,2,5,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,3,4,6,5,1,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,3,4,6,5,2,1]=>{{1,7},{2,3,4,6},{5}}=>[7,3,4,6,5,2,1]=>000000
[7,3,5,1,2,4,6]=>{{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000
[7,3,5,1,2,6,4]=>{{1,4,7},{2,3,5},{6}}=>[4,3,5,7,2,6,1]=>000000
[7,3,5,1,4,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,5,1,4,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,3,5,1,6,2,4]=>{{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000
[7,3,5,1,6,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,5,2,1,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,5,2,1,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,3,5,2,4,1,6]=>{{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000
[7,3,5,2,4,6,1]=>{{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>000000
[7,3,5,2,6,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,5,2,6,4,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,3,5,4,1,2,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,3,5,4,1,6,2]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[7,3,5,4,2,1,6]=>{{1,6,7},{2,3,5},{4}}=>[6,3,5,4,2,7,1]=>000000
[7,3,5,4,2,6,1]=>{{1,7},{2,3,5},{4},{6}}=>[7,3,5,4,2,6,1]=>000000
[7,3,5,4,6,1,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,3,5,4,6,2,1]=>{{1,7},{2,3,5,6},{4}}=>[7,3,5,4,6,2,1]=>000000
[7,3,5,6,1,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,5,6,1,4,2]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[7,3,5,6,2,1,4]=>{{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000
[7,3,5,6,2,4,1]=>{{1,7},{2,3,5},{4,6}}=>[7,3,5,6,2,4,1]=>000000
[7,3,5,6,4,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,5,6,4,2,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,3,6,1,2,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,6,1,2,5,4]=>{{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000
[7,3,6,1,4,2,5]=>{{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000
[7,3,6,1,4,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,6,1,5,2,4]=>{{1,4,7},{2,3,6},{5}}=>[4,3,6,7,5,2,1]=>000000
[7,3,6,1,5,4,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,3,6,2,1,4,5]=>{{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000
[7,3,6,2,1,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,6,2,4,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,6,2,4,5,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,3,6,2,5,1,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,3,6,2,5,4,1]=>{{1,7},{2,3,4,6},{5}}=>[7,3,4,6,5,2,1]=>000000
[7,3,6,4,1,2,5]=>{{1,5,7},{2,3,6},{4}}=>[5,3,6,4,7,2,1]=>000000
[7,3,6,4,1,5,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,3,6,4,2,1,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,3,6,4,2,5,1]=>{{1,7},{2,3,5,6},{4}}=>[7,3,5,4,6,2,1]=>000000
[7,3,6,4,5,1,2]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[7,3,6,4,5,2,1]=>{{1,7},{2,3,6},{4},{5}}=>[7,3,6,4,5,2,1]=>000000
[7,3,6,5,1,2,4]=>{{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000
[7,3,6,5,1,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,6,5,2,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,3,6,5,2,4,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,3,6,5,4,1,2]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[7,3,6,5,4,2,1]=>{{1,7},{2,3,6},{4,5}}=>[7,3,6,5,4,2,1]=>000000
[7,4,1,2,3,5,6]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[7,4,1,2,3,6,5]=>{{1,3,5,7},{2,4},{6}}=>[3,4,5,2,7,6,1]=>000000
[7,4,1,2,5,3,6]=>{{1,3,6,7},{2,4},{5}}=>[3,4,6,2,5,7,1]=>000000
[7,4,1,2,5,6,3]=>{{1,3,7},{2,4},{5},{6}}=>[3,4,7,2,5,6,1]=>000000
[7,4,1,2,6,3,5]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[7,4,1,2,6,5,3]=>{{1,3,7},{2,4},{5,6}}=>[3,4,7,2,6,5,1]=>000000
[7,4,1,3,2,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,1,3,2,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,4,1,3,5,2,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,4,1,3,5,6,2]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[7,4,1,3,6,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,1,3,6,5,2]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[7,4,1,5,2,3,6]=>{{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000
[7,4,1,5,2,6,3]=>{{1,3,7},{2,4,5},{6}}=>[3,4,7,5,2,6,1]=>000000
[7,4,1,5,3,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,1,5,3,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,4,1,5,6,2,3]=>{{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000
[7,4,1,5,6,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,1,6,2,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,1,6,2,5,3]=>{{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000
[7,4,1,6,3,2,5]=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000
[7,4,1,6,3,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,1,6,5,2,3]=>{{1,3,7},{2,4,6},{5}}=>[3,4,7,6,5,2,1]=>000000
[7,4,1,6,5,3,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,4,2,1,3,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,2,1,3,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,4,2,1,5,3,6]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,4,2,1,5,6,3]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
[7,4,2,1,6,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,2,1,6,5,3]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
[7,4,2,3,1,5,6]=>{{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000
[7,4,2,3,1,6,5]=>{{1,5,7},{2,3,4},{6}}=>[5,3,4,2,7,6,1]=>000000
[7,4,2,3,5,1,6]=>{{1,6,7},{2,3,4},{5}}=>[6,3,4,2,5,7,1]=>000000
[7,4,2,3,5,6,1]=>{{1,7},{2,3,4},{5},{6}}=>[7,3,4,2,5,6,1]=>000000
[7,4,2,3,6,1,5]=>{{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000
[7,4,2,3,6,5,1]=>{{1,7},{2,3,4},{5,6}}=>[7,3,4,2,6,5,1]=>000000
[7,4,2,5,1,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,2,5,1,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,4,2,5,3,1,6]=>{{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000
[7,4,2,5,3,6,1]=>{{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>000000
[7,4,2,5,6,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,2,5,6,3,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,4,2,6,1,3,5]=>{{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000
[7,4,2,6,1,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,2,6,3,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,2,6,3,5,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,4,2,6,5,1,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,4,2,6,5,3,1]=>{{1,7},{2,3,4,6},{5}}=>[7,3,4,6,5,2,1]=>000000
[7,4,3,1,2,5,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,4,3,1,2,6,5]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[7,4,3,1,5,2,6]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[7,4,3,1,5,6,2]=>{{1,2,4,7},{3},{5},{6}}=>[2,4,3,7,5,6,1]=>000000
[7,4,3,1,6,2,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,4,3,1,6,5,2]=>{{1,2,4,7},{3},{5,6}}=>[2,4,3,7,6,5,1]=>000000
[7,4,3,2,1,5,6]=>{{1,5,6,7},{2,4},{3}}=>[5,4,3,2,6,7,1]=>000000
[7,4,3,2,1,6,5]=>{{1,5,7},{2,4},{3},{6}}=>[5,4,3,2,7,6,1]=>000000
[7,4,3,2,5,1,6]=>{{1,6,7},{2,4},{3},{5}}=>[6,4,3,2,5,7,1]=>000000
[7,4,3,2,5,6,1]=>{{1,7},{2,4},{3},{5},{6}}=>[7,4,3,2,5,6,1]=>000000
[7,4,3,2,6,1,5]=>{{1,5,6,7},{2,4},{3}}=>[5,4,3,2,6,7,1]=>000000
[7,4,3,2,6,5,1]=>{{1,7},{2,4},{3},{5,6}}=>[7,4,3,2,6,5,1]=>000000
[7,4,3,5,1,2,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,4,3,5,1,6,2]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[7,4,3,5,2,1,6]=>{{1,6,7},{2,4,5},{3}}=>[6,4,3,5,2,7,1]=>000000
[7,4,3,5,2,6,1]=>{{1,7},{2,4,5},{3},{6}}=>[7,4,3,5,2,6,1]=>000000
[7,4,3,5,6,1,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,4,3,5,6,2,1]=>{{1,7},{2,4,5,6},{3}}=>[7,4,3,5,6,2,1]=>000000
[7,4,3,6,1,2,5]=>{{1,5,7},{2,4,6},{3}}=>[5,4,3,6,7,2,1]=>000000
[7,4,3,6,1,5,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,4,3,6,2,1,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,4,3,6,2,5,1]=>{{1,7},{2,4,5,6},{3}}=>[7,4,3,5,6,2,1]=>000000
[7,4,3,6,5,1,2]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[7,4,3,6,5,2,1]=>{{1,7},{2,4,6},{3},{5}}=>[7,4,3,6,5,2,1]=>000000
[7,4,5,1,2,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,5,1,2,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,4,5,1,3,2,6]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[7,4,5,1,3,6,2]=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>000000
[7,4,5,1,6,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,5,1,6,3,2]=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000
[7,4,5,2,1,3,6]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[7,4,5,2,1,6,3]=>{{1,3,5,7},{2,4},{6}}=>[3,4,5,2,7,6,1]=>000000
[7,4,5,2,3,1,6]=>{{1,6,7},{2,4},{3,5}}=>[6,4,5,2,3,7,1]=>000000
[7,4,5,2,3,6,1]=>{{1,7},{2,4},{3,5},{6}}=>[7,4,5,2,3,6,1]=>000000
[7,4,5,2,6,1,3]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[7,4,5,2,6,3,1]=>{{1,7},{2,4},{3,5,6}}=>[7,4,5,2,6,3,1]=>000000
[7,4,5,3,1,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,5,3,1,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,4,5,3,2,1,6]=>{{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000
[7,4,5,3,2,6,1]=>{{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>000000
[7,4,5,3,6,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,5,3,6,2,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,4,5,6,1,2,3]=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000
[7,4,5,6,1,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,5,6,2,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,5,6,2,3,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,4,5,6,3,1,2]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[7,4,5,6,3,2,1]=>{{1,7},{2,4,6},{3,5}}=>[7,4,5,6,3,2,1]=>000000
[7,4,6,1,2,3,5]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[7,4,6,1,2,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,6,1,3,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,6,1,3,5,2]=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000
[7,4,6,1,5,2,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,4,6,1,5,3,2]=>{{1,2,4,7},{3,6},{5}}=>[2,4,6,7,5,3,1]=>000000
[7,4,6,2,1,3,5]=>{{1,5,7},{2,4},{3,6}}=>[5,4,6,2,7,3,1]=>000000
[7,4,6,2,1,5,3]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[7,4,6,2,3,1,5]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
[7,4,6,2,3,5,1]=>{{1,7},{2,4},{3,5,6}}=>[7,4,5,2,6,3,1]=>000000
[7,4,6,2,5,1,3]=>{{1,3,6,7},{2,4},{5}}=>[3,4,6,2,5,7,1]=>000000
[7,4,6,2,5,3,1]=>{{1,7},{2,4},{3,6},{5}}=>[7,4,6,2,5,3,1]=>000000
[7,4,6,3,1,2,5]=>{{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000
[7,4,6,3,1,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,6,3,2,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,6,3,2,5,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,4,6,3,5,1,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,4,6,3,5,2,1]=>{{1,7},{2,3,4,6},{5}}=>[7,3,4,6,5,2,1]=>000000
[7,4,6,5,1,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,6,5,1,3,2]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[7,4,6,5,2,1,3]=>{{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000
[7,4,6,5,2,3,1]=>{{1,7},{2,4,5},{3,6}}=>[7,4,6,5,2,3,1]=>000000
[7,4,6,5,3,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,4,6,5,3,2,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,5,1,2,3,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,1,2,3,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,5,1,2,4,3,6]=>{{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000
[7,5,1,2,4,6,3]=>{{1,3,7},{2,4,5},{6}}=>[3,4,7,5,2,6,1]=>000000
[7,5,1,2,6,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,1,2,6,4,3]=>{{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000
[7,5,1,3,2,4,6]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[7,5,1,3,2,6,4]=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>000000
[7,5,1,3,4,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,1,3,4,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,5,1,3,6,2,4]=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000
[7,5,1,3,6,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,1,4,2,3,6]=>{{1,3,6,7},{2,5},{4}}=>[3,5,6,4,2,7,1]=>000000
[7,5,1,4,2,6,3]=>{{1,3,7},{2,5},{4},{6}}=>[3,5,7,4,2,6,1]=>000000
[7,5,1,4,3,2,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,5,1,4,3,6,2]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[7,5,1,4,6,2,3]=>{{1,3,7},{2,5,6},{4}}=>[3,5,7,4,6,2,1]=>000000
[7,5,1,4,6,3,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,5,1,6,2,3,4]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[7,5,1,6,2,4,3]=>{{1,3,7},{2,5},{4,6}}=>[3,5,7,6,2,4,1]=>000000
[7,5,1,6,3,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,1,6,3,4,2]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[7,5,1,6,4,2,3]=>{{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000
[7,5,1,6,4,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,2,1,3,4,6]=>{{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000
[7,5,2,1,3,6,4]=>{{1,4,7},{2,3,5},{6}}=>[4,3,5,7,2,6,1]=>000000
[7,5,2,1,4,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,2,1,4,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,5,2,1,6,3,4]=>{{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000
[7,5,2,1,6,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,2,3,1,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,2,3,1,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,5,2,3,4,1,6]=>{{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000
[7,5,2,3,4,6,1]=>{{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>000000
[7,5,2,3,6,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,2,3,6,4,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,5,2,4,1,3,6]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,5,2,4,1,6,3]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
[7,5,2,4,3,1,6]=>{{1,6,7},{2,3,5},{4}}=>[6,3,5,4,2,7,1]=>000000
[7,5,2,4,3,6,1]=>{{1,7},{2,3,5},{4},{6}}=>[7,3,5,4,2,6,1]=>000000
[7,5,2,4,6,1,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,5,2,4,6,3,1]=>{{1,7},{2,3,5,6},{4}}=>[7,3,5,4,6,2,1]=>000000
[7,5,2,6,1,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,2,6,1,4,3]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
[7,5,2,6,3,1,4]=>{{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000
[7,5,2,6,3,4,1]=>{{1,7},{2,3,5},{4,6}}=>[7,3,5,6,2,4,1]=>000000
[7,5,2,6,4,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,2,6,4,3,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,5,3,1,2,4,6]=>{{1,4,6,7},{2,5},{3}}=>[4,5,3,6,2,7,1]=>000000
[7,5,3,1,2,6,4]=>{{1,4,7},{2,5},{3},{6}}=>[4,5,3,7,2,6,1]=>000000
[7,5,3,1,4,2,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,5,3,1,4,6,2]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[7,5,3,1,6,2,4]=>{{1,4,7},{2,5,6},{3}}=>[4,5,3,7,6,2,1]=>000000
[7,5,3,1,6,4,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,5,3,2,1,4,6]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,5,3,2,1,6,4]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
[7,5,3,2,4,1,6]=>{{1,6,7},{2,4,5},{3}}=>[6,4,3,5,2,7,1]=>000000
[7,5,3,2,4,6,1]=>{{1,7},{2,4,5},{3},{6}}=>[7,4,3,5,2,6,1]=>000000
[7,5,3,2,6,1,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,5,3,2,6,4,1]=>{{1,7},{2,4,5,6},{3}}=>[7,4,3,5,6,2,1]=>000000
[7,5,3,4,1,2,6]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[7,5,3,4,1,6,2]=>{{1,2,5,7},{3},{4},{6}}=>[2,5,3,4,7,6,1]=>000000
[7,5,3,4,2,1,6]=>{{1,6,7},{2,5},{3},{4}}=>[6,5,3,4,2,7,1]=>000000
[7,5,3,4,2,6,1]=>{{1,7},{2,5},{3},{4},{6}}=>[7,5,3,4,2,6,1]=>000000
[7,5,3,4,6,1,2]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[7,5,3,4,6,2,1]=>{{1,7},{2,5,6},{3},{4}}=>[7,5,3,4,6,2,1]=>000000
[7,5,3,6,1,2,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,5,3,6,1,4,2]=>{{1,2,5,7},{3},{4,6}}=>[2,5,3,6,7,4,1]=>000000
[7,5,3,6,2,1,4]=>{{1,4,6,7},{2,5},{3}}=>[4,5,3,6,2,7,1]=>000000
[7,5,3,6,2,4,1]=>{{1,7},{2,5},{3},{4,6}}=>[7,5,3,6,2,4,1]=>000000
[7,5,3,6,4,1,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,5,3,6,4,2,1]=>{{1,7},{2,4,5,6},{3}}=>[7,4,3,5,6,2,1]=>000000
[7,5,4,1,2,3,6]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[7,5,4,1,2,6,3]=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>000000
[7,5,4,1,3,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,4,1,3,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,5,4,1,6,2,3]=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000
[7,5,4,1,6,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,4,2,1,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,4,2,1,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
[7,5,4,2,3,1,6]=>{{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000
[7,5,4,2,3,6,1]=>{{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>000000
[7,5,4,2,6,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,4,2,6,3,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,5,4,3,1,2,6]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[7,5,4,3,1,6,2]=>{{1,2,5,7},{3,4},{6}}=>[2,5,4,3,7,6,1]=>000000
[7,5,4,3,2,1,6]=>{{1,6,7},{2,5},{3,4}}=>[6,5,4,3,2,7,1]=>000000
[7,5,4,3,2,6,1]=>{{1,7},{2,5},{3,4},{6}}=>[7,5,4,3,2,6,1]=>000000
[7,5,4,3,6,1,2]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[7,5,4,3,6,2,1]=>{{1,7},{2,5,6},{3,4}}=>[7,5,4,3,6,2,1]=>000000
[7,5,4,6,1,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,4,6,1,3,2]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000
[7,5,4,6,2,1,3]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[7,5,4,6,2,3,1]=>{{1,7},{2,5},{3,4,6}}=>[7,5,4,6,2,3,1]=>000000
[7,5,4,6,3,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,4,6,3,2,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,5,6,1,2,3,4]=>{{1,4,7},{2,5},{3,6}}=>[4,5,6,7,2,3,1]=>000000
[7,5,6,1,2,4,3]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[7,5,6,1,3,2,4]=>{{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000
[7,5,6,1,3,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,6,1,4,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,6,1,4,3,2]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[7,5,6,2,1,3,4]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
[7,5,6,2,1,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,6,2,3,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,6,2,3,4,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,5,6,2,4,1,3]=>{{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000
[7,5,6,2,4,3,1]=>{{1,7},{2,4,5},{3,6}}=>[7,4,6,5,2,3,1]=>000000
[7,5,6,3,1,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,6,3,1,4,2]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000
[7,5,6,3,2,1,4]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
[7,5,6,3,2,4,1]=>{{1,7},{2,5},{3,4,6}}=>[7,5,4,6,2,3,1]=>000000
[7,5,6,3,4,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,5,6,3,4,2,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,5,6,4,1,2,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,5,6,4,1,3,2]=>{{1,2,5,7},{3,6},{4}}=>[2,5,6,4,7,3,1]=>000000
[7,5,6,4,2,1,3]=>{{1,3,6,7},{2,5},{4}}=>[3,5,6,4,2,7,1]=>000000
[7,5,6,4,2,3,1]=>{{1,7},{2,5},{3,6},{4}}=>[7,5,6,4,2,3,1]=>000000
[7,5,6,4,3,1,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,5,6,4,3,2,1]=>{{1,7},{2,3,5,6},{4}}=>[7,3,5,4,6,2,1]=>000000
[7,6,1,2,3,4,5]=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000
[7,6,1,2,3,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,1,2,4,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,1,2,4,5,3]=>{{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000
[7,6,1,2,5,3,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,6,1,2,5,4,3]=>{{1,3,7},{2,4,6},{5}}=>[3,4,7,6,5,2,1]=>000000
[7,6,1,3,2,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,1,3,2,5,4]=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000
[7,6,1,3,4,2,5]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[7,6,1,3,4,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,1,3,5,2,4]=>{{1,3,4,7},{2,6},{5}}=>[3,6,4,7,5,2,1]=>000000
[7,6,1,3,5,4,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,6,1,4,2,3,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,6,1,4,2,5,3]=>{{1,3,7},{2,5,6},{4}}=>[3,5,7,4,6,2,1]=>000000
[7,6,1,4,3,2,5]=>{{1,3,5,7},{2,6},{4}}=>[3,6,5,4,7,2,1]=>000000
[7,6,1,4,3,5,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,6,1,4,5,2,3]=>{{1,3,7},{2,6},{4},{5}}=>[3,6,7,4,5,2,1]=>000000
[7,6,1,4,5,3,2]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[7,6,1,5,2,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,1,5,2,4,3]=>{{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000
[7,6,1,5,3,2,4]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[7,6,1,5,3,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,1,5,4,2,3]=>{{1,3,7},{2,6},{4,5}}=>[3,6,7,5,4,2,1]=>000000
[7,6,1,5,4,3,2]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[7,6,2,1,3,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,2,1,3,5,4]=>{{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000
[7,6,2,1,4,3,5]=>{{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000
[7,6,2,1,4,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,2,1,5,3,4]=>{{1,4,7},{2,3,6},{5}}=>[4,3,6,7,5,2,1]=>000000
[7,6,2,1,5,4,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,6,2,3,1,4,5]=>{{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000
[7,6,2,3,1,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,2,3,4,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,2,3,4,5,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,6,2,3,5,1,4]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,6,2,3,5,4,1]=>{{1,7},{2,3,4,6},{5}}=>[7,3,4,6,5,2,1]=>000000
[7,6,2,4,1,3,5]=>{{1,5,7},{2,3,6},{4}}=>[5,3,6,4,7,2,1]=>000000
[7,6,2,4,1,5,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,6,2,4,3,1,5]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,6,2,4,3,5,1]=>{{1,7},{2,3,5,6},{4}}=>[7,3,5,4,6,2,1]=>000000
[7,6,2,4,5,1,3]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
[7,6,2,4,5,3,1]=>{{1,7},{2,3,6},{4},{5}}=>[7,3,6,4,5,2,1]=>000000
[7,6,2,5,1,3,4]=>{{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000
[7,6,2,5,1,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,2,5,3,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,2,5,3,4,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,6,2,5,4,1,3]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
[7,6,2,5,4,3,1]=>{{1,7},{2,3,6},{4,5}}=>[7,3,6,5,4,2,1]=>000000
[7,6,3,1,2,4,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,6,3,1,2,5,4]=>{{1,4,7},{2,5,6},{3}}=>[4,5,3,7,6,2,1]=>000000
[7,6,3,1,4,2,5]=>{{1,4,5,7},{2,6},{3}}=>[4,6,3,5,7,2,1]=>000000
[7,6,3,1,4,5,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,6,3,1,5,2,4]=>{{1,4,7},{2,6},{3},{5}}=>[4,6,3,7,5,2,1]=>000000
[7,6,3,1,5,4,2]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[7,6,3,2,1,4,5]=>{{1,5,7},{2,4,6},{3}}=>[5,4,3,6,7,2,1]=>000000
[7,6,3,2,1,5,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,6,3,2,4,1,5]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,6,3,2,4,5,1]=>{{1,7},{2,4,5,6},{3}}=>[7,4,3,5,6,2,1]=>000000
[7,6,3,2,5,1,4]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
[7,6,3,2,5,4,1]=>{{1,7},{2,4,6},{3},{5}}=>[7,4,3,6,5,2,1]=>000000
[7,6,3,4,1,2,5]=>{{1,5,7},{2,6},{3},{4}}=>[5,6,3,4,7,2,1]=>000000
[7,6,3,4,1,5,2]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[7,6,3,4,2,1,5]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
[7,6,3,4,2,5,1]=>{{1,7},{2,5,6},{3},{4}}=>[7,5,3,4,6,2,1]=>000000
[7,6,3,4,5,1,2]=>{{1,2,6,7},{3},{4},{5}}=>[2,6,3,4,5,7,1]=>000000
[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}}=>[7,6,3,4,5,2,1]=>000000
[7,6,3,5,1,2,4]=>{{1,4,5,7},{2,6},{3}}=>[4,6,3,5,7,2,1]=>000000
[7,6,3,5,1,4,2]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,6,3,5,2,1,4]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
[7,6,3,5,2,4,1]=>{{1,7},{2,4,5,6},{3}}=>[7,4,3,5,6,2,1]=>000000
[7,6,3,5,4,1,2]=>{{1,2,6,7},{3},{4,5}}=>[2,6,3,5,4,7,1]=>000000
[7,6,3,5,4,2,1]=>{{1,7},{2,6},{3},{4,5}}=>[7,6,3,5,4,2,1]=>000000
[7,6,4,1,2,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,4,1,2,5,3]=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000
[7,6,4,1,3,2,5]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[7,6,4,1,3,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,4,1,5,2,3]=>{{1,3,4,7},{2,6},{5}}=>[3,6,4,7,5,2,1]=>000000
[7,6,4,1,5,3,2]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,6,4,2,1,3,5]=>{{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000
[7,6,4,2,1,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,4,2,3,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,4,2,3,5,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,6,4,2,5,1,3]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
[7,6,4,2,5,3,1]=>{{1,7},{2,3,4,6},{5}}=>[7,3,4,6,5,2,1]=>000000
[7,6,4,3,1,2,5]=>{{1,5,7},{2,6},{3,4}}=>[5,6,4,3,7,2,1]=>000000
[7,6,4,3,1,5,2]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[7,6,4,3,2,1,5]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
[7,6,4,3,2,5,1]=>{{1,7},{2,5,6},{3,4}}=>[7,5,4,3,6,2,1]=>000000
[7,6,4,3,5,1,2]=>{{1,2,6,7},{3,4},{5}}=>[2,6,4,3,5,7,1]=>000000
[7,6,4,3,5,2,1]=>{{1,7},{2,6},{3,4},{5}}=>[7,6,4,3,5,2,1]=>000000
[7,6,4,5,1,2,3]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[7,6,4,5,1,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,4,5,2,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,4,5,2,3,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,6,4,5,3,1,2]=>{{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000
[7,6,4,5,3,2,1]=>{{1,7},{2,6},{3,4,5}}=>[7,6,4,5,3,2,1]=>000000
[7,6,5,1,2,3,4]=>{{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000
[7,6,5,1,2,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,5,1,3,2,4]=>{{1,4,7},{2,6},{3,5}}=>[4,6,5,7,3,2,1]=>000000
[7,6,5,1,3,4,2]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[7,6,5,1,4,2,3]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[7,6,5,1,4,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,5,2,1,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,5,2,1,4,3]=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000
[7,6,5,2,3,1,4]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
[7,6,5,2,3,4,1]=>{{1,7},{2,4,6},{3,5}}=>[7,4,5,6,3,2,1]=>000000
[7,6,5,2,4,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,5,2,4,3,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,6,5,3,1,2,4]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
[7,6,5,3,1,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,5,3,2,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
[7,6,5,3,2,4,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
[7,6,5,3,4,1,2]=>{{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000
[7,6,5,3,4,2,1]=>{{1,7},{2,6},{3,4,5}}=>[7,6,4,5,3,2,1]=>000000
[7,6,5,4,1,2,3]=>{{1,3,5,7},{2,6},{4}}=>[3,6,5,4,7,2,1]=>000000
[7,6,5,4,1,3,2]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,6,5,4,2,1,3]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
[7,6,5,4,2,3,1]=>{{1,7},{2,3,5,6},{4}}=>[7,3,5,4,6,2,1]=>000000
[7,6,5,4,3,1,2]=>{{1,2,6,7},{3,5},{4}}=>[2,6,5,4,3,7,1]=>000000
[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}}=>[7,6,5,4,3,2,1]=>000000
[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}}=>[8,7,6,5,4,3,2,1]=>0000000
[7,6,8,5,4,3,2,1]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[7,6,5,8,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,6,8,4,3,2,1]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[6,5,7,8,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,8,4,3,2,1]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[7,6,8,4,5,3,2,1]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[7,6,4,5,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,5,6,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,4,7,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,6,7,8,3,2,1]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[7,6,8,5,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,5,6,3,4,2,1]=>{{1,8},{2,7},{3,5},{4,6}}=>[8,7,5,6,3,4,2,1]=>0000000
[5,6,7,8,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,8,3,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,6,7,3,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,4,3,6,8,2,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[6,5,4,3,7,8,2,1]=>{{1,6,8},{2,5,7},{3,4}}=>[6,5,4,3,7,8,2,1]=>0000000
[8,6,7,5,4,2,3,1]=>{{1,8},{2,6},{3,7},{4,5}}=>[8,6,7,5,4,2,3,1]=>0000000
[7,6,5,8,4,2,3,1]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[6,7,5,8,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,6,8,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,4,5,2,3,1]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[4,5,6,7,8,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,6,5,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,8,5,3,2,4,1]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[6,7,8,5,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,5,7,3,2,4,1]=>{{1,8},{2,6},{3,5},{4,7}}=>[8,6,5,7,3,2,4,1]=>0000000
[7,6,5,8,3,2,4,1]=>{{1,4,7,8},{2,6},{3,5}}=>[4,6,5,7,3,2,8,1]=>0000000
[5,6,7,8,3,2,4,1]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[7,6,8,5,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,5,2,3,4,1]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[7,8,5,6,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,6,7,2,3,4,1]=>{{1,8},{2,5},{3,6},{4,7}}=>[8,5,6,7,2,3,4,1]=>0000000
[6,7,5,8,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,8,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,8,3,4,2,5,1]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[7,8,6,2,3,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,2,3,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,5,3,4,2,6,1]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[7,8,4,3,2,5,6,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[7,8,3,2,4,5,6,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,5,7,3,4,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,4,3,7,2,8,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[6,4,5,3,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,6,3,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,5,2,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,4,7,2,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,6,7,2,3,8,1]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[6,7,5,3,2,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,3,2,5,8,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[6,7,3,2,4,5,8,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,7,2,3,4,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,4,3,2,7,8,1]=>{{1,6,7,8},{2,5},{3,4}}=>[6,5,4,3,2,7,8,1]=>0000000
[5,4,6,3,2,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,3,6,2,7,8,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,4,5,6,2,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,4,2,3,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,5,2,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,2,3,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,2,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,4,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,6,5,4,3,1,2]=>{{1,7},{2,8},{3,6},{4,5}}=>[7,8,6,5,4,3,1,2]=>0000000
[6,7,5,8,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,8,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,7,4,5,3,1,2]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[6,7,4,5,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,4,7,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,6,7,8,3,1,2]=>{{1,4,7},{2,5,8},{3,6}}=>[4,5,6,7,8,3,1,2]=>0000000
[6,7,8,5,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,5,6,3,4,1,2]=>{{1,7},{2,8},{3,5},{4,6}}=>[7,8,5,6,3,4,1,2]=>0000000
[8,5,6,7,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,7,8,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,8,3,4,1,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[7,8,4,3,5,6,1,2]=>{{1,7},{2,8},{3,4},{5},{6}}=>[7,8,4,3,5,6,1,2]=>0000000
[8,5,4,6,3,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,4,3,6,7,1,2]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[8,4,3,5,6,7,1,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,7,4,5,3,8,1,2]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[6,5,4,7,3,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,6,7,3,8,1,2]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[6,5,4,3,7,8,1,2]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[5,4,6,3,7,8,1,2]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[4,5,6,3,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,3,5,7,8,1,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,3,4,5,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,3,6,7,8,1,2]=>{{1,5,7},{2,4,6,8},{3}}=>[5,4,3,6,7,8,1,2]=>0000000
[4,5,3,6,7,8,1,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,3,4,6,7,8,1,2]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[4,3,5,6,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,5,6,7,8,1,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[8,7,6,5,4,2,1,3]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[7,6,8,5,4,2,1,3]=>{{1,7},{2,6},{3,8},{4,5}}=>[7,6,8,5,4,2,1,3]=>0000000
[8,7,5,6,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,5,8,4,2,1,3]=>{{1,7},{2,6},{3,4,5,8}}=>[7,6,4,5,8,2,1,3]=>0000000
[6,5,7,8,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,8,4,2,1,3]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[7,6,4,5,8,2,1,3]=>{{1,7},{2,6},{3,4,5,8}}=>[7,6,4,5,8,2,1,3]=>0000000
[4,5,6,7,8,2,1,3]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[6,7,8,5,4,1,2,3]=>{{1,6},{2,7},{3,8},{4,5}}=>[6,7,8,5,4,1,2,3]=>0000000
[7,8,5,6,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,6,7,4,1,2,3]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[7,5,6,8,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,8,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,7,4,5,1,2,3]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[8,6,4,5,7,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,6,7,8,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,6,5,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,7,5,3,2,1,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[7,6,8,5,3,2,1,4]=>{{1,7},{2,6},{3,4,5,8}}=>[7,6,4,5,8,2,1,3]=>0000000
[8,6,5,7,3,2,1,4]=>{{1,4,7,8},{2,6},{3,5}}=>[4,6,5,7,3,2,8,1]=>0000000
[7,6,5,8,3,2,1,4]=>{{1,7},{2,6},{3,5},{4,8}}=>[7,6,5,8,3,2,1,4]=>0000000
[7,5,6,8,3,2,1,4]=>{{1,7},{2,3,5,6},{4,8}}=>[7,3,5,8,6,2,1,4]=>0000000
[6,5,7,8,3,2,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[5,6,7,8,3,2,1,4]=>{{1,3,5,7},{2,6},{4,8}}=>[3,6,5,8,7,2,1,4]=>0000000
[8,7,6,5,2,3,1,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,6,7,5,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,5,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,5,6,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,5,8,2,3,1,4]=>{{1,7},{2,3,5,6},{4,8}}=>[7,3,5,8,6,2,1,4]=>0000000
[6,7,5,8,2,3,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[7,5,6,8,2,3,1,4]=>{{1,7},{2,5},{3,6},{4,8}}=>[7,5,6,8,2,3,1,4]=>0000000
[5,6,7,8,2,3,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[7,8,6,5,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,5,8,3,1,2,4]=>{{1,6},{2,7},{3,5},{4,8}}=>[6,7,5,8,3,1,2,4]=>0000000
[7,5,6,8,3,1,2,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[5,6,7,8,3,1,2,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[8,7,6,5,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,8,5,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,5,6,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,5,7,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,5,8,2,1,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[6,5,7,8,2,1,3,4]=>{{1,6},{2,5},{3,7},{4,8}}=>[6,5,7,8,2,1,3,4]=>0000000
[8,7,6,5,1,2,3,4]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[7,8,6,5,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,8,5,1,2,3,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[6,7,8,5,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,5,6,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,5,6,1,2,3,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[8,6,5,7,1,2,3,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[8,5,6,7,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,5,8,1,2,3,4]=>{{1,3,5,7},{2,6},{4,8}}=>[3,6,5,8,7,2,1,4]=>0000000
[6,7,5,8,1,2,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[7,5,6,8,1,2,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[5,6,7,8,1,2,3,4]=>{{1,5},{2,6},{3,7},{4,8}}=>[5,6,7,8,1,2,3,4]=>0000000
[8,7,6,3,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,7,3,2,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,3,2,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,6,2,3,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,6,3,2,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,8,3,2,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,6,3,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,3,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,6,2,1,3,4,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,7,6,1,2,3,4,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[7,8,6,1,2,3,4,5]=>{{1,4,7},{2,5,8},{3,6}}=>[4,5,6,7,8,3,1,2]=>0000000
[8,6,7,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,8,1,2,3,4,5]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[6,7,8,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,5,3,4,2,1,6]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[8,7,4,5,2,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,5,3,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,4,3,2,5,1,6]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[8,7,4,5,1,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,5,3,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,5,3,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,5,2,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,5,1,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,5,1,2,3,4,6]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[8,7,4,3,2,1,5,6]=>{{1,6,8},{2,5,7},{3,4}}=>[6,5,4,3,7,8,2,1]=>0000000
[7,8,4,3,2,1,5,6]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[7,8,4,2,3,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,3,2,4,1,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,2,3,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,4,2,1,3,5,6]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[7,8,4,1,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,3,2,1,4,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,3,2,1,4,5,6]=>{{1,5,7},{2,4,6,8},{3}}=>[5,4,3,6,7,8,1,2]=>0000000
[7,8,2,3,1,4,5,6]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[7,8,3,1,2,4,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,2,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,1,2,3,4,5,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[8,6,4,5,3,1,2,7]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[8,5,6,3,4,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,5,3,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,3,5,6,1,2,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,3,4,5,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,5,3,2,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,6,2,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,6,3,1,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,5,2,1,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,6,2,1,3,4,7]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,6,4,3,2,1,5,7]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[8,6,4,2,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,3,2,4,1,5,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,6,4,1,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,4,2,1,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,3,2,1,4,6,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,3,4,1,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,2,1,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,6,7,3,2,1,8]=>{{1,4,7},{2,3,5,6},{8}}=>[4,3,5,7,6,2,1,8]=>0000001
[7,5,6,3,4,2,1,8]=>{{1,7},{2,3,4,5,6},{8}}=>[7,3,4,5,6,2,1,8]=>0000001
[7,3,4,5,6,2,1,8]=>{{1,7},{2,3,4,5,6},{8}}=>[7,3,4,5,6,2,1,8]=>0000001
[7,6,4,5,2,3,1,8]=>{{1,7},{2,3,4,5,6},{8}}=>[7,3,4,5,6,2,1,8]=>0000001
[6,5,4,7,2,3,1,8]=>{{1,3,4,6,7},{2,5},{8}}=>[3,5,4,6,2,7,1,8]=>0000001
[7,5,6,2,3,4,1,8]=>{{1,7},{2,3,4,5,6},{8}}=>[7,3,4,5,6,2,1,8]=>0000001
[7,6,4,2,3,5,1,8]=>{{1,7},{2,3,4,5,6},{8}}=>[7,3,4,5,6,2,1,8]=>0000001
[7,6,2,3,4,5,1,8]=>{{1,7},{2,3,4,5,6},{8}}=>[7,3,4,5,6,2,1,8]=>0000001
[4,5,6,7,2,1,3,8]=>{{1,3,4,6,7},{2,5},{8}}=>[3,5,4,6,2,7,1,8]=>0000001
[5,6,7,4,1,2,3,8]=>{{1,5},{2,6},{3,7},{4},{8}}=>[5,6,7,4,1,2,3,8]=>0000001
[7,6,5,1,2,3,4,8]=>{{1,4,7},{2,3,5,6},{8}}=>[4,3,5,7,6,2,1,8]=>0000001
[6,5,7,1,2,3,4,8]=>{{1,3,4,6,7},{2,5},{8}}=>[3,5,4,6,2,7,1,8]=>0000001
[5,6,3,4,1,2,7,8]=>{{1,5},{2,6},{3},{4},{7},{8}}=>[5,6,3,4,1,2,7,8]=>0000011
[4,3,5,2,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[3,4,5,2,1,6,7,8]=>{{1,3,5},{2,4},{6},{7},{8}}=>[3,4,5,2,1,6,7,8]=>0000111
[4,5,2,3,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[5,2,3,4,1,6,7,8]=>{{1,5},{2},{3},{4},{6},{7},{8}}=>[5,2,3,4,1,6,7,8]=>0000111
[3,4,2,5,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[2,3,4,5,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[5,3,4,1,2,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[5,4,2,1,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[5,4,1,2,3,6,7,8]=>{{1,3,5},{2,4},{6},{7},{8}}=>[3,4,5,2,1,6,7,8]=>0000111
[4,5,1,2,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[5,3,1,2,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[5,1,2,3,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[4,3,2,1,5,6,7,8]=>{{1,4},{2,3},{5},{6},{7},{8}}=>[4,3,2,1,5,6,7,8]=>0001111
[3,4,2,1,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}=>[2,3,4,1,5,6,7,8]=>0001111
[2,3,4,1,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}=>[2,3,4,1,5,6,7,8]=>0001111
[4,3,1,2,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}=>[2,3,4,1,5,6,7,8]=>0001111
[3,4,1,2,5,6,7,8]=>{{1,3},{2,4},{5},{6},{7},{8}}=>[3,4,1,2,5,6,7,8]=>0001111
[4,1,2,3,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}=>[2,3,4,1,5,6,7,8]=>0001111
[3,2,1,4,5,6,7,8]=>{{1,3},{2},{4},{5},{6},{7},{8}}=>[3,2,1,4,5,6,7,8]=>0011111
[2,3,1,4,5,6,7,8]=>{{1,2,3},{4},{5},{6},{7},{8}}=>[2,3,1,4,5,6,7,8]=>0011111
[3,1,2,4,5,6,7,8]=>{{1,2,3},{4},{5},{6},{7},{8}}=>[2,3,1,4,5,6,7,8]=>0011111
[2,1,3,4,5,6,7,8]=>{{1,2},{3},{4},{5},{6},{7},{8}}=>[2,1,3,4,5,6,7,8]=>0111111
[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}=>[1,2,3,4,5,6,7,8]=>1111111
[6,8,7,5,4,3,2,1]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[5,8,7,6,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,8,7,4,3,2,1]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[5,6,8,7,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,7,6,5,3,2,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,6,8,7,5,3,2,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,6,7,8,5,3,2,1]=>{{1,4,8},{2,3,6,7},{5}}=>[4,3,6,8,5,7,2,1]=>0000000
[4,5,8,7,6,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,7,5,8,3,2,1]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[4,5,7,6,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,5,7,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,7,8,6,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,7,8,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,7,8,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,3,7,8,6,2,1]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[4,5,6,3,8,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,5,8,7,2,1]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[4,5,3,6,8,7,2,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,3,5,6,8,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,7,6,5,8,2,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,5,3,7,6,8,2,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,3,5,7,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,6,5,7,8,2,1]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[2,8,7,6,5,4,3,1]=>{{1,2,8},{3,7},{4,6},{5}}=>[2,8,7,6,5,4,3,1]=>0000000
[2,7,6,8,5,4,3,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,5,6,4,8,7,3,1]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>0000000
[2,7,6,5,4,8,3,1]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[2,4,7,6,5,8,3,1]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[2,6,5,4,7,8,3,1]=>{{1,2,6,8},{3,5,7},{4}}=>[2,6,5,4,7,8,3,1]=>0000000
[2,3,8,7,6,5,4,1]=>{{1,2,3,8},{4,7},{5,6}}=>[2,3,8,7,6,5,4,1]=>0000000
[2,3,7,6,5,8,4,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,3,5,6,7,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,2,8,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[2,3,4,8,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[2,5,4,3,7,8,6,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[4,3,2,5,8,7,6,1]=>{{1,4,5,8},{2,3},{6,7}}=>[4,3,2,5,8,7,6,1]=>0000000
[6,5,4,3,2,8,7,1]=>{{1,6,8},{2,5},{3,4},{7}}=>[6,5,4,3,2,8,7,1]=>0000000
[4,6,5,3,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,6,3,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,3,6,5,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,3,6,2,8,7,1]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[2,4,6,5,3,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,3,2,6,5,8,7,1]=>{{1,4,6,8},{2,3},{5},{7}}=>[4,3,2,6,5,8,7,1]=>0000000
[3,4,2,6,5,8,7,1]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,4,3,6,5,8,7,1]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>0000000
[2,3,4,6,5,8,7,1]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[4,3,2,5,6,8,7,1]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[3,4,2,5,6,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,4,3,5,6,8,7,1]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[2,3,4,5,6,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,7,6,5,3,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,5,7,3,2,8,1]=>{{1,4,7,8},{2,6},{3,5}}=>[4,6,5,7,3,2,8,1]=>0000000
[3,5,6,7,4,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,7,6,5,2,8,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,3,6,7,5,2,8,1]=>{{1,4,7,8},{2,3,6},{5}}=>[4,3,6,7,5,2,8,1]=>0000000
[5,4,3,7,6,2,8,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,5,3,7,2,8,1]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[3,5,4,6,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,4,7,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,6,5,7,3,8,1]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[2,4,5,6,7,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,3,5,7,6,8,1]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[2,3,6,5,4,7,8,1]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[2,3,5,6,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,2,6,5,7,8,1]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[3,4,2,6,5,7,8,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,4,3,6,5,7,8,1]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[2,3,4,6,5,7,8,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,5,4,2,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,4,3,6,7,8,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[2,4,5,3,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,3,5,6,7,8,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[1,3,4,6,7,8,5,2]=>{{1},{2,3,4,6,8},{5,7}}=>[1,3,4,6,7,8,5,2]=>1000000
[1,4,3,6,5,8,7,2]=>{{1},{2,4,6,8},{3},{5},{7}}=>[1,4,3,6,5,8,7,2]=>1000000
[2,1,8,7,6,5,4,3]=>{{1,2},{3,8},{4,7},{5,6}}=>[2,1,8,7,6,5,4,3]=>0100000
[2,1,4,6,7,8,5,3]=>{{1,2},{3,4,6,8},{5,7}}=>[2,1,4,6,7,8,5,3]=>0100000
[2,1,4,6,5,8,7,3]=>{{1,2},{3,4,6,8},{5},{7}}=>[2,1,4,6,5,8,7,3]=>0100000
[2,1,4,5,6,8,7,3]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[2,1,5,6,7,4,8,3]=>{{1,2},{3,5,7,8},{4,6}}=>[2,1,5,6,7,4,8,3]=>0100000
[3,2,1,6,8,7,5,4]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[3,2,1,7,6,8,5,4]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[3,2,1,6,7,8,5,4]=>{{1,3},{2},{4,6,8},{5,7}}=>[3,2,1,6,7,8,5,4]=>0010000
[3,2,1,5,7,8,6,4]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[3,2,1,6,7,5,8,4]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[3,2,1,5,6,7,8,4]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[2,3,1,6,8,7,5,4]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[2,3,1,7,6,8,5,4]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[2,3,1,6,5,8,7,4]=>{{1,2,3},{4,6,8},{5},{7}}=>[2,3,1,6,5,8,7,4]=>0010000
[2,3,1,5,6,7,8,4]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[1,2,3,6,8,7,5,4]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[4,3,2,1,8,7,6,5]=>{{1,4},{2,3},{5,8},{6,7}}=>[4,3,2,1,8,7,6,5]=>0001000
[4,3,2,1,7,8,6,5]=>{{1,4},{2,3},{5,6,7,8}}=>[4,3,2,1,6,7,8,5]=>0001000
[4,3,2,1,6,8,7,5]=>{{1,4},{2,3},{5,6,8},{7}}=>[4,3,2,1,6,8,7,5]=>0001000
[4,3,2,1,7,6,8,5]=>{{1,4},{2,3},{5,7,8},{6}}=>[4,3,2,1,7,6,8,5]=>0001000
[4,3,2,1,6,7,8,5]=>{{1,4},{2,3},{5,6,7,8}}=>[4,3,2,1,6,7,8,5]=>0001000
[3,4,2,1,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}=>[2,3,4,1,8,7,6,5]=>0001000
[3,4,2,1,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[3,4,2,1,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[2,4,3,1,8,7,6,5]=>{{1,2,4},{3},{5,8},{6,7}}=>[2,4,3,1,8,7,6,5]=>0001000
[3,2,4,1,8,7,6,5]=>{{1,3,4},{2},{5,8},{6,7}}=>[3,2,4,1,8,7,6,5]=>0001000
[2,3,4,1,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}=>[2,3,4,1,8,7,6,5]=>0001000
[2,3,4,1,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[2,3,4,1,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[1,4,3,2,8,7,6,5]=>{{1},{2,4},{3},{5,8},{6,7}}=>[1,4,3,2,8,7,6,5]=>1001000
[1,3,4,2,8,7,6,5]=>{{1},{2,3,4},{5,8},{6,7}}=>[1,3,4,2,8,7,6,5]=>1001000
[2,1,4,3,8,7,6,5]=>{{1,2},{3,4},{5,8},{6,7}}=>[2,1,4,3,8,7,6,5]=>0101000
[2,1,4,3,6,8,7,5]=>{{1,2},{3,4},{5,6,8},{7}}=>[2,1,4,3,6,8,7,5]=>0101000
[1,2,4,3,8,7,6,5]=>{{1},{2},{3,4},{5,8},{6,7}}=>[1,2,4,3,8,7,6,5]=>1101000
[3,2,1,4,8,7,6,5]=>{{1,3},{2},{4},{5,8},{6,7}}=>[3,2,1,4,8,7,6,5]=>0011000
[2,3,1,4,8,7,6,5]=>{{1,2,3},{4},{5,8},{6,7}}=>[2,3,1,4,8,7,6,5]=>0011000
[1,3,2,4,8,7,6,5]=>{{1},{2,3},{4},{5,8},{6,7}}=>[1,3,2,4,8,7,6,5]=>1011000
[2,1,3,4,8,7,6,5]=>{{1,2},{3},{4},{5,8},{6,7}}=>[2,1,3,4,8,7,6,5]=>0111000
[1,2,3,4,8,7,6,5]=>{{1},{2},{3},{4},{5,8},{6,7}}=>[1,2,3,4,8,7,6,5]=>1111000
[3,5,4,2,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[4,3,5,2,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[3,4,5,2,1,8,7,6]=>{{1,3,5},{2,4},{6,8},{7}}=>[3,4,5,2,1,8,7,6]=>0000100
[2,4,5,3,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[3,2,5,4,1,7,8,6]=>{{1,3,5},{2},{4},{6,7,8}}=>[3,2,5,4,1,7,8,6]=>0000100
[3,4,2,5,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[2,3,4,5,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[4,3,2,1,5,8,7,6]=>{{1,4},{2,3},{5},{6,8},{7}}=>[4,3,2,1,5,8,7,6]=>0001100
[4,3,2,1,5,7,8,6]=>{{1,4},{2,3},{5},{6,7,8}}=>[4,3,2,1,5,7,8,6]=>0001100
[6,5,4,3,2,1,8,7]=>{{1,6},{2,5},{3,4},{7,8}}=>[6,5,4,3,2,1,8,7]=>0000010
[2,1,6,5,4,3,8,7]=>{{1,2},{3,6},{4,5},{7,8}}=>[2,1,6,5,4,3,8,7]=>0100010
[2,1,5,6,4,3,8,7]=>{{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>0100010
[2,1,4,5,6,3,8,7]=>{{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>0100010
[4,3,2,1,6,5,8,7]=>{{1,4},{2,3},{5,6},{7,8}}=>[4,3,2,1,6,5,8,7]=>0001010
[3,2,4,1,6,5,8,7]=>{{1,3,4},{2},{5,6},{7,8}}=>[3,2,4,1,6,5,8,7]=>0001010
[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}}=>[2,1,4,3,6,5,8,7]=>0101010
[4,3,2,1,5,6,8,7]=>{{1,4},{2,3},{5},{6},{7,8}}=>[4,3,2,1,5,6,8,7]=>0001110
[4,3,5,7,6,2,1,8]=>{{1,4,7},{2,3,5,6},{8}}=>[4,3,5,7,6,2,1,8]=>0000001
[2,3,5,6,7,4,1,8]=>{{1,2,3,5,7},{4,6},{8}}=>[2,3,5,6,7,4,1,8]=>0000001
[3,2,5,4,7,6,1,8]=>{{1,3,5,7},{2},{4},{6},{8}}=>[3,2,5,4,7,6,1,8]=>0000001
[3,5,4,6,2,7,1,8]=>{{1,3,4,6,7},{2,5},{8}}=>[3,5,4,6,2,7,1,8]=>0000001
[4,3,2,1,7,6,5,8]=>{{1,4},{2,3},{5,7},{6},{8}}=>[4,3,2,1,7,6,5,8]=>0001001
[4,3,2,1,6,7,5,8]=>{{1,4},{2,3},{5,6,7},{8}}=>[4,3,2,1,6,7,5,8]=>0001001
[2,3,1,5,4,7,6,8]=>{{1,2,3},{4,5},{6,7},{8}}=>[2,3,1,5,4,7,6,8]=>0010101
[4,3,2,1,5,7,6,8]=>{{1,4},{2,3},{5},{6,7},{8}}=>[4,3,2,1,5,7,6,8]=>0001101
[4,3,2,1,6,5,7,8]=>{{1,4},{2,3},{5,6},{7},{8}}=>[4,3,2,1,6,5,7,8]=>0001011
[2,1,4,3,6,5,7,8]=>{{1,2},{3,4},{5,6},{7},{8}}=>[2,1,4,3,6,5,7,8]=>0101011
[3,5,4,2,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[2,4,5,3,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[3,2,5,4,1,6,7,8]=>{{1,3,5},{2},{4},{6},{7},{8}}=>[3,2,5,4,1,6,7,8]=>0000111
[2,1,4,3,5,6,7,8]=>{{1,2},{3,4},{5},{6},{7},{8}}=>[2,1,4,3,5,6,7,8]=>0101111
[1,4,3,8,6,7,5,2]=>{{1},{2,4,8},{3},{5,6,7}}=>[1,4,3,8,6,7,5,2]=>1000000
[1,6,4,5,3,8,7,2]=>{{1},{2,6,8},{3,4,5},{7}}=>[1,6,4,5,3,8,7,2]=>1000000
[1,8,4,5,6,7,3,2]=>{{1},{2,8},{3,4,5,6,7}}=>[1,8,4,5,6,7,3,2]=>1000000
[2,1,8,5,4,7,6,3]=>{{1,2},{3,8},{4,5},{6,7}}=>[2,1,8,5,4,7,6,3]=>0100000
[2,3,1,8,6,7,5,4]=>{{1,2,3},{4,8},{5,6,7}}=>[2,3,1,8,6,7,5,4]=>0010000
[2,3,6,4,5,7,8,1]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[2,3,7,4,5,6,8,1]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>0000000
[2,3,7,5,6,4,8,1]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[2,6,4,5,3,7,8,1]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[2,8,7,5,6,4,3,1]=>{{1,2,8},{3,7},{4,5,6}}=>[2,8,7,5,6,4,3,1]=>0000000
[3,2,7,5,6,4,1,8]=>{{1,3,7},{2},{4,5,6},{8}}=>[3,2,7,5,6,4,1,8]=>0000001
[4,2,3,1,8,7,6,5]=>{{1,4},{2},{3},{5,8},{6,7}}=>[4,2,3,1,8,7,6,5]=>0001000
[4,3,2,1,8,6,7,5]=>{{1,4},{2,3},{5,8},{6},{7}}=>[4,3,2,1,8,6,7,5]=>0001000
[4,3,2,8,6,7,5,1]=>{{1,4,8},{2,3},{5,6,7}}=>[4,3,2,8,6,7,5,1]=>0000000
[6,3,2,5,4,1,8,7]=>{{1,6},{2,3},{4,5},{7,8}}=>[6,3,2,5,4,1,8,7]=>0000010
[8,3,2,5,4,7,6,1]=>{{1,8},{2,3},{4,5},{6,7}}=>[8,3,2,5,4,7,6,1]=>0000000
[8,3,2,7,6,5,4,1]=>{{1,8},{2,3},{4,7},{5,6}}=>[8,3,2,7,6,5,4,1]=>0000000
[5,3,4,2,1,7,8,6]=>{{1,5},{2,3,4},{6,7,8}}=>[5,3,4,2,1,7,8,6]=>0000100
[5,3,4,2,7,6,1,8]=>{{1,5,7},{2,3,4},{6},{8}}=>[5,3,4,2,7,6,1,8]=>0000001
[8,5,4,3,2,7,6,1]=>{{1,8},{2,5},{3,4},{6,7}}=>[8,5,4,3,2,7,6,1]=>0000000
[8,7,4,3,6,5,2,1]=>{{1,8},{2,7},{3,4},{5,6}}=>[8,7,4,3,6,5,2,1]=>0000000
[2,1,4,6,3,5,8,7]=>{{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>0100010
[2,4,1,3,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,6,1,8,3,5,7]=>{{1,2,4},{3,6},{5,7,8}}=>[2,4,6,1,7,3,8,5]=>0000000
[2,4,6,8,1,3,5,7]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[2,4,1,3,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,6,1,7,3,8,5]=>{{1,2,4},{3,6},{5,7,8}}=>[2,4,6,1,7,3,8,5]=>0000000
[2,4,6,7,1,3,8,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[2,4,1,6,7,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,6,7,8,1,3,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[2,4,1,3,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[2,4,1,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,1,4,3,7,8,5,6]=>{{1,2},{3,4},{5,7},{6,8}}=>[2,1,4,3,7,8,5,6]=>0101000
[2,4,1,7,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,1,3,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[2,4,1,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,5,6,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,1,3,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}=>[2,3,4,1,5,6,7,8]=>0001111
[2,4,1,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,5,6,7,1,8,3]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[2,1,5,3,6,4,8,7]=>{{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>0100010
[2,1,5,6,3,4,8,7]=>{{1,2},{3,5},{4,6},{7,8}}=>[2,1,5,6,3,4,8,7]=>0100010
[2,5,1,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,1,6,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,1,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,1,5,6,3,7,8,4]=>{{1,2},{3,5},{4,6,7,8}}=>[2,1,5,6,3,7,8,4]=>0100000
[2,5,1,6,3,7,8,4]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[2,5,6,1,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,1,6,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,1,5,6,7,8,3,4]=>{{1,2},{3,5,7},{4,6,8}}=>[2,1,5,6,7,8,3,4]=>0100000
[2,5,1,6,7,8,3,4]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[2,5,6,1,7,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,1,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,1,5,7,3,4,8,6]=>{{1,2},{3,5},{4,6,7,8}}=>[2,1,5,6,3,7,8,4]=>0100000
[2,5,1,7,3,4,8,6]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[2,5,7,1,3,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,1,5,7,3,8,4,6]=>{{1,2},{3,5},{4,7},{6,8}}=>[2,1,5,7,3,8,4,6]=>0100000
[2,3,5,7,1,4,8,6]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[2,3,5,6,1,8,4,7]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[2,3,5,6,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,1,3,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,5,6,1,7,8,4]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[2,3,5,6,7,8,1,4]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[2,6,7,1,3,4,8,5]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[2,1,6,7,8,3,4,5]=>{{1,2},{3,6},{4,7},{5,8}}=>[2,1,6,7,8,3,4,5]=>0100000
[2,6,1,7,8,3,4,5]=>{{1,2,3,6},{4,7},{5,8}}=>[2,3,6,7,8,1,4,5]=>0000000
[2,6,7,8,1,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,6,1,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,1,6,7,8,4,5]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[2,3,6,7,8,1,4,5]=>{{1,2,3,6},{4,7},{5,8}}=>[2,3,6,7,8,1,4,5]=>0000000
[2,6,1,8,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,1,6,4,8,5,7]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[2,1,6,3,4,5,8,7]=>{{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>0100010
[2,3,4,1,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,4,6,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,1,3,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,1,7,8,3,4,5,6]=>{{1,2},{3,5,7},{4,6,8}}=>[2,1,5,6,7,8,3,4]=>0100000
[2,7,1,8,3,4,5,6]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[2,7,8,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,1,7,8,4,5,6]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[2,3,1,7,4,5,8,6]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[2,3,7,1,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,4,1,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[2,3,4,7,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,1,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,1,8,4,5,6,7]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[2,3,8,1,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,4,1,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[2,3,4,8,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,4,5,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,1,2,6,5,8,7]=>{{1,3},{2,4},{5,6},{7,8}}=>[3,4,1,2,6,5,8,7]=>0001010
[3,1,4,2,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[3,4,1,2,6,8,5,7]=>{{1,3},{2,4},{5,6,7,8}}=>[3,4,1,2,6,7,8,5]=>0001000
[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,4,2,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[3,4,1,2,6,7,8,5]=>{{1,3},{2,4},{5,6,7,8}}=>[3,4,1,2,6,7,8,5]=>0001000
[3,4,6,1,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,4,6,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,6,1,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,4,2,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[3,4,1,2,7,5,8,6]=>{{1,3},{2,4},{5,6,7,8}}=>[3,4,1,2,6,7,8,5]=>0001000
[3,4,7,1,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,1,2,7,8,5,6]=>{{1,3},{2,4},{5,7},{6,8}}=>[3,4,1,2,7,8,5,6]=>0001000
[3,4,7,1,8,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,1,5,7,8,2,6]=>{{1,3},{2,4,5,7},{6,8}}=>[3,4,1,5,7,8,2,6]=>0000000
[3,1,4,2,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[3,4,1,2,8,5,6,7]=>{{1,3},{2,4},{5,6,7,8}}=>[3,4,1,2,6,7,8,5]=>0001000
[3,1,4,8,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,8,1,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,5,6,1,8,2,7]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[3,4,5,6,8,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,4,2,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}=>[2,3,4,1,5,6,7,8]=>0001111
[3,1,4,5,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,5,1,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,5,6,1,7,8,2]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[3,5,1,6,2,4,8,7]=>{{1,3},{2,5},{4,6},{7,8}}=>[3,5,1,6,2,4,8,7]=>0000010
[3,1,5,6,2,8,4,7]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[3,1,5,6,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,1,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,1,6,2,4,7,8]=>{{1,3},{2,5},{4,6},{7},{8}}=>[3,5,1,6,2,4,7,8]=>0000011
[3,5,6,1,2,7,4,8]=>{{1,3,4,6,7},{2,5},{8}}=>[3,5,4,6,2,7,1,8]=>0000001
[3,1,5,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,5,6,2,7,8,4]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[3,5,1,6,2,7,8,4]=>{{1,3},{2,5},{4,6,7,8}}=>[3,5,1,6,2,7,8,4]=>0000000
[3,1,5,6,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,1,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,5,6,7,8,2,4]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,5,7,2,4,8,6]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[3,5,1,7,2,4,8,6]=>{{1,3},{2,5},{4,6,7,8}}=>[3,5,1,6,2,7,8,4]=>0000000
[3,5,1,2,7,8,4,6]=>{{1,3},{2,4,5,7},{6,8}}=>[3,4,1,5,7,8,2,6]=>0000000
[3,5,1,7,2,8,4,6]=>{{1,3},{2,5},{4,7},{6,8}}=>[3,5,1,7,2,8,4,6]=>0000000
[3,5,7,8,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,7,1,2,4,6,8]=>{{1,3,4,6,7},{2,5},{8}}=>[3,5,4,6,2,7,1,8]=>0000001
[3,1,2,5,4,7,6,8]=>{{1,2,3},{4,5},{6,7},{8}}=>[2,3,1,5,4,7,6,8]=>0010101
[3,1,2,5,7,4,8,6]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[3,1,5,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,5,8,2,4,6,7]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[3,5,1,8,2,4,6,7]=>{{1,3},{2,5},{4,6,7,8}}=>[3,5,1,6,2,7,8,4]=>0000000
[3,1,2,5,8,4,6,7]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[3,1,2,5,6,8,4,7]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[3,1,2,5,6,7,8,4]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}=>[1,3,5,6,7,8,2,4]=>1000000
[3,6,7,1,2,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,7,1,2,8,4,5]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[3,6,1,7,8,2,4,5]=>{{1,3},{2,6},{4,7},{5,8}}=>[3,6,1,7,8,2,4,5]=>0000000
[3,6,7,8,1,2,4,5]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[3,1,6,2,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,2,6,4,7,8,5]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[3,1,6,8,2,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,6,2,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,7,8,2,4,5,6]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[3,7,1,2,4,8,5,6]=>{{1,3},{2,4,5,7},{6,8}}=>[3,4,1,5,7,8,2,6]=>0000000
[3,1,2,7,8,4,5,6]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[3,1,8,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,2,8,4,5,6,7]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[4,5,6,1,2,3,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>[4,5,6,1,2,3,8,7]=>0000010
[4,5,1,2,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,5,6,2,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,5,6,8,2,3,7]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[4,5,6,8,1,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,1,6,2,7,3,8]=>{{1,3,4,6,7},{2,5},{8}}=>[3,5,4,6,2,7,1,8]=>0000001
[4,5,1,2,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,5,6,7,2,8,3]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[4,5,1,6,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,6,7,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,5,6,7,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,1,2,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,7,1,2,8,3,6]=>{{1,4},{2,5},{3,7},{6,8}}=>[4,5,7,1,2,8,3,6]=>0000000
[4,5,1,7,8,2,3,6]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[4,1,2,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,1,2,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,2,7,3,8,5]=>{{1,2,4},{3,6},{5,7,8}}=>[2,4,6,1,7,3,8,5]=>0000000
[4,1,6,7,2,3,8,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,6,7,1,8,2,3,5]=>{{1,4},{2,6},{3,7},{5,8}}=>[4,6,7,1,8,2,3,5]=>0000000
[4,1,2,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,2,8,3,5,7]=>{{1,2,4},{3,6},{5,7,8}}=>[2,4,6,1,7,3,8,5]=>0000000
[4,1,6,8,2,3,5,7]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,6,1,8,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,1,2,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,3,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[4,1,2,3,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[4,7,1,2,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,7,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,3,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[4,8,1,2,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,3,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[5,1,6,2,7,3,8,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[5,6,1,2,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,6,7,2,8,3,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[5,1,6,7,8,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,1,7,8,2,3,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[5,1,6,2,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,1,2,3,7,8,4]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[5,1,2,6,3,7,8,4]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[5,1,2,6,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,2,6,7,8,3,4]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[5,1,6,2,8,3,4,7]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[5,6,1,2,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,8,1,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,6,2,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,1,2,3,8,4,7]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[5,1,2,6,3,8,4,7]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[5,1,2,6,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,2,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,2,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,2,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,2,3,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,2,7,3,4,8,6]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[5,1,2,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,2,3,5,7,4,8,6]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[5,1,2,8,3,4,6,7]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[1,2,3,5,8,4,6,7]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[1,2,3,5,6,8,4,7]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[6,1,7,2,8,3,4,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[6,1,7,8,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,7,2,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,7,2,3,4,8,5]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[6,7,1,2,3,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,2,7,3,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,2,3,7,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,2,3,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,2,3,6,4,7,8,5]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[1,2,3,6,7,8,4,5]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[6,1,8,2,3,4,5,7]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[6,1,2,8,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,2,3,6,4,8,5,7]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[7,1,2,8,3,4,5,6]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[1,7,2,8,3,4,5,6]=>{{1},{2,3,5,7},{4,6,8}}=>[1,3,5,6,7,8,2,4]=>1000000
[7,1,2,3,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,2,3,7,8,4,5,6]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[1,2,3,7,4,5,8,6]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[1,2,3,8,4,5,6,7]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[5,3,2,6,1,4,8,7]=>{{1,5},{2,3},{4,6},{7,8}}=>[5,3,2,6,1,4,8,7]=>0000010
[7,3,2,5,4,8,1,6]=>{{1,7},{2,3},{4,5},{6,8}}=>[7,3,2,5,4,8,1,6]=>0000000
[8,4,5,2,3,7,6,1]=>{{1,8},{2,4},{3,5},{6,7}}=>[8,4,5,2,3,7,6,1]=>0000000
[7,4,5,2,3,8,1,6]=>{{1,7},{2,4},{3,5},{6,8}}=>[7,4,5,2,3,8,1,6]=>0000000
[6,4,5,2,3,1,8,7]=>{{1,6},{2,4},{3,5},{7,8}}=>[6,4,5,2,3,1,8,7]=>0000010
[5,4,6,2,1,3,8,7]=>{{1,5},{2,4},{3,6},{7,8}}=>[5,4,6,2,1,3,8,7]=>0000010
[3,6,1,5,4,2,8,7]=>{{1,3},{2,6},{4,5},{7,8}}=>[3,6,1,5,4,2,8,7]=>0000010
[4,6,5,1,3,2,8,7]=>{{1,4},{2,6},{3,5},{7,8}}=>[4,6,5,1,3,2,8,7]=>0000010
[5,6,4,3,1,2,8,7]=>{{1,5},{2,6},{3,4},{7,8}}=>[5,6,4,3,1,2,8,7]=>0000010
[7,5,4,3,2,8,1,6]=>{{1,7},{2,5},{3,4},{6,8}}=>[7,5,4,3,2,8,1,6]=>0000000
[8,6,4,3,7,2,5,1]=>{{1,8},{2,6},{3,4},{5,7}}=>[8,6,4,3,7,2,5,1]=>0000000
[7,6,4,3,8,2,1,5]=>{{1,7},{2,6},{3,4},{5,8}}=>[7,6,4,3,8,2,1,5]=>0000000
[6,7,4,3,8,1,2,5]=>{{1,6},{2,7},{3,4},{5,8}}=>[6,7,4,3,8,1,2,5]=>0000000
[5,7,4,3,1,8,2,6]=>{{1,5},{2,7},{3,4},{6,8}}=>[5,7,4,3,1,8,2,6]=>0000000
[4,7,5,1,3,8,2,6]=>{{1,4},{2,7},{3,5},{6,8}}=>[4,7,5,1,3,8,2,6]=>0000000
[3,7,1,5,4,8,2,6]=>{{1,3},{2,7},{4,5},{6,8}}=>[3,7,1,5,4,8,2,6]=>0000000
[2,1,7,5,4,8,3,6]=>{{1,2},{3,7},{4,5},{6,8}}=>[2,1,7,5,4,8,3,6]=>0100000
[3,8,1,5,4,7,6,2]=>{{1,3},{2,8},{4,5},{6,7}}=>[3,8,1,5,4,7,6,2]=>0000000
[4,8,5,1,3,7,6,2]=>{{1,4},{2,8},{3,5},{6,7}}=>[4,8,5,1,3,7,6,2]=>0000000
[5,8,4,3,1,7,6,2]=>{{1,5},{2,8},{3,4},{6,7}}=>[5,8,4,3,1,7,6,2]=>0000000
[6,8,4,3,7,1,5,2]=>{{1,6},{2,8},{3,4},{5,7}}=>[6,8,4,3,7,1,5,2]=>0000000
[7,8,4,3,6,5,1,2]=>{{1,7},{2,8},{3,4},{5,6}}=>[7,8,4,3,6,5,1,2]=>0000000
[6,8,5,7,3,1,4,2]=>{{1,6},{2,8},{3,5},{4,7}}=>[6,8,5,7,3,1,4,2]=>0000000
[5,8,6,7,1,3,4,2]=>{{1,5},{2,8},{3,6},{4,7}}=>[5,8,6,7,1,3,4,2]=>0000000
[4,8,6,1,7,3,5,2]=>{{1,4},{2,8},{3,6},{5,7}}=>[4,8,6,1,7,3,5,2]=>0000000
[3,8,1,6,7,4,5,2]=>{{1,3},{2,8},{4,6},{5,7}}=>[3,8,1,6,7,4,5,2]=>0000000
[2,1,8,6,7,4,5,3]=>{{1,2},{3,8},{4,6},{5,7}}=>[2,1,8,6,7,4,5,3]=>0100000
[2,1,7,6,8,4,3,5]=>{{1,2},{3,7},{4,6},{5,8}}=>[2,1,7,6,8,4,3,5]=>0100000
[3,7,1,6,8,4,2,5]=>{{1,3},{2,7},{4,6},{5,8}}=>[3,7,1,6,8,4,2,5]=>0000000
[4,7,6,1,8,3,2,5]=>{{1,4},{2,7},{3,6},{5,8}}=>[4,7,6,1,8,3,2,5]=>0000000
[5,7,6,8,1,3,2,4]=>{{1,5},{2,7},{3,6},{4,8}}=>[5,7,6,8,1,3,2,4]=>0000000
[5,4,7,2,1,8,3,6]=>{{1,5},{2,4},{3,7},{6,8}}=>[5,4,7,2,1,8,3,6]=>0000000
[6,4,7,2,8,1,3,5]=>{{1,6},{2,4},{3,7},{5,8}}=>[6,4,7,2,8,1,3,5]=>0000000
[7,4,6,2,8,3,1,5]=>{{1,7},{2,4},{3,6},{5,8}}=>[7,4,6,2,8,3,1,5]=>0000000
[8,4,6,2,7,3,5,1]=>{{1,8},{2,4},{3,6},{5,7}}=>[8,4,6,2,7,3,5,1]=>0000000
[8,3,2,6,7,4,5,1]=>{{1,8},{2,3},{4,6},{5,7}}=>[8,3,2,6,7,4,5,1]=>0000000
[7,3,2,6,8,4,1,5]=>{{1,7},{2,3},{4,6},{5,8}}=>[7,3,2,6,8,4,1,5]=>0000000
[6,3,2,7,8,1,4,5]=>{{1,6},{2,3},{4,7},{5,8}}=>[6,3,2,7,8,1,4,5]=>0000000
[5,3,2,7,1,8,4,6]=>{{1,5},{2,3},{4,7},{6,8}}=>[5,3,2,7,1,8,4,6]=>0000000
[4,3,2,1,7,8,5,6]=>{{1,4},{2,3},{5,7},{6,8}}=>[4,3,2,1,7,8,5,6]=>0001000
[3,4,1,2,8,7,6,5]=>{{1,3},{2,4},{5,8},{6,7}}=>[3,4,1,2,8,7,6,5]=>0001000
[5,3,2,8,1,7,6,4]=>{{1,5},{2,3},{4,8},{6,7}}=>[5,3,2,8,1,7,6,4]=>0000000
[6,3,2,8,7,1,5,4]=>{{1,6},{2,3},{4,8},{5,7}}=>[6,3,2,8,7,1,5,4]=>0000000
[7,3,2,8,6,5,1,4]=>{{1,7},{2,3},{4,8},{5,6}}=>[7,3,2,8,6,5,1,4]=>0000000
[8,4,7,2,6,5,3,1]=>{{1,8},{2,4},{3,7},{5,6}}=>[8,4,7,2,6,5,3,1]=>0000000
[7,4,8,2,6,5,1,3]=>{{1,7},{2,4},{3,8},{5,6}}=>[7,4,8,2,6,5,1,3]=>0000000
[6,4,8,2,7,1,5,3]=>{{1,6},{2,4},{3,8},{5,7}}=>[6,4,8,2,7,1,5,3]=>0000000
[5,4,8,2,1,7,6,3]=>{{1,5},{2,4},{3,8},{6,7}}=>[5,4,8,2,1,7,6,3]=>0000000
[4,5,8,1,2,7,6,3]=>{{1,4},{2,5},{3,8},{6,7}}=>[4,5,8,1,2,7,6,3]=>0000000
[3,5,1,8,2,7,6,4]=>{{1,3},{2,5},{4,8},{6,7}}=>[3,5,1,8,2,7,6,4]=>0000000
[2,1,5,8,3,7,6,4]=>{{1,2},{3,5},{4,8},{6,7}}=>[2,1,5,8,3,7,6,4]=>0100000
[2,1,6,8,7,3,5,4]=>{{1,2},{3,6},{4,8},{5,7}}=>[2,1,6,8,7,3,5,4]=>0100000
[3,6,1,8,7,2,5,4]=>{{1,3},{2,6},{4,8},{5,7}}=>[3,6,1,8,7,2,5,4]=>0000000
[4,6,8,1,7,2,5,3]=>{{1,4},{2,6},{3,8},{5,7}}=>[4,6,8,1,7,2,5,3]=>0000000
[5,6,8,7,1,2,4,3]=>{{1,5},{2,6},{3,8},{4,7}}=>[5,6,8,7,1,2,4,3]=>0000000
[6,5,8,7,2,1,4,3]=>{{1,6},{2,5},{3,8},{4,7}}=>[6,5,8,7,2,1,4,3]=>0000000
[7,5,8,6,2,4,1,3]=>{{1,7},{2,5},{3,8},{4,6}}=>[7,5,8,6,2,4,1,3]=>0000000
[8,5,7,6,2,4,3,1]=>{{1,8},{2,5},{3,7},{4,6}}=>[8,5,7,6,2,4,3,1]=>0000000
[5,7,8,6,1,4,2,3]=>{{1,5},{2,7},{3,8},{4,6}}=>[5,7,8,6,1,4,2,3]=>0000000
[4,7,8,1,6,5,2,3]=>{{1,4},{2,7},{3,8},{5,6}}=>[4,7,8,1,6,5,2,3]=>0000000
[3,7,1,8,6,5,2,4]=>{{1,3},{2,7},{4,8},{5,6}}=>[3,7,1,8,6,5,2,4]=>0000000
[2,1,7,8,6,5,3,4]=>{{1,2},{3,7},{4,8},{5,6}}=>[2,1,7,8,6,5,3,4]=>0100000
[3,8,1,7,6,5,4,2]=>{{1,3},{2,8},{4,7},{5,6}}=>[3,8,1,7,6,5,4,2]=>0000000
[4,8,7,1,6,5,3,2]=>{{1,4},{2,8},{3,7},{5,6}}=>[4,8,7,1,6,5,3,2]=>0000000
[5,8,7,6,1,4,3,2]=>{{1,5},{2,8},{3,7},{4,6}}=>[5,8,7,6,1,4,3,2]=>0000000
[6,8,7,5,4,1,3,2]=>{{1,6},{2,8},{3,7},{4,5}}=>[6,8,7,5,4,1,3,2]=>0000000
[6,2,7,1,3,4,5,8]=>{{1,4,6},{2},{3,5,7},{8}}=>[4,2,5,6,7,1,3,8]=>0000001
[8,3,6,1,2,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,1,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,5,8,1,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,7,8,1,4,5,6]=>{{1,3,5,7},{2},{4,6,8}}=>[3,2,5,6,7,8,1,4]=>0000000
[4,3,7,8,1,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,7,8,1,2,3,6]=>{{1,5},{2,4,6,8},{3,7}}=>[5,4,7,6,1,8,3,2]=>0000000
[6,3,7,8,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,7,8,1,2,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[7,3,5,8,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,5,8,1,2,3,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[3,7,2,6,1,4,5,8]=>{{1,2,3,5,7},{4,6},{8}}=>[2,3,5,6,7,4,1,8]=>0000001
[4,8,2,5,1,3,6,7]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[6,8,3,5,1,2,4,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,8,2,7,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,2,7,1,3,5,6]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[6,8,5,7,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,2,4,1,3,5,6]=>{{1,5,7},{2,3,6,8},{4}}=>[5,3,6,4,7,8,1,2]=>0000000
[7,8,2,5,1,3,4,6]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[7,8,4,6,1,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,2,6,1,4,7,8]=>{{1,5},{2,3},{4,6},{7},{8}}=>[5,3,2,6,1,4,7,8]=>0000011
[5,3,2,7,1,4,6,8]=>{{1,5},{2,3},{4,6,7},{8}}=>[5,3,2,6,1,7,4,8]=>0000001
[5,3,2,8,1,4,6,7]=>{{1,5},{2,3},{4,6,7,8}}=>[5,3,2,6,1,7,8,4]=>0000000
[6,4,3,8,1,2,5,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,4,2,8,1,3,5,6]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[7,5,3,8,1,2,4,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,4,2,5,1,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,3,6,1,2,4,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,4,2,7,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,3,7,1,2,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,2,5,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,3,5,1,2,4,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,8,3,5,7,1,2,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,8,2,6,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,2,5,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,3,5,6,1,2,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,4,2,6,8,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,3,6,8,1,2,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,4,2,5,8,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,3,6,8,1,2,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,6,2,5,7,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,3,5,7,1,2,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,7,2,5,1,3,8]=>{{1,6},{2,4},{3,7},{5},{8}}=>[6,4,7,2,5,1,3,8]=>0000001
[4,3,8,2,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,8,2,6,1,4,7]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[5,4,8,2,6,1,3,7]=>{{1,5,6},{2,4},{3,7,8}}=>[5,4,7,2,6,1,8,3]=>0000000
[6,4,8,2,5,1,3,7]=>{{1,6},{2,4},{3,7,8},{5}}=>[6,4,7,2,5,1,8,3]=>0000000
[5,3,8,2,7,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,8,2,5,1,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,4,8,3,5,1,2,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,5,8,2,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,6,2,5,1,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,5,7,2,6,1,3,4]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[8,6,7,2,4,1,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[8,6,7,2,5,1,3,4]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[8,6,7,3,5,1,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,5,4,3,8,1,2,7]=>{{1,6},{2,5,7,8},{3,4}}=>[6,5,4,3,7,1,8,2]=>0000000
[7,5,3,2,8,1,4,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,5,3,2,6,1,4,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,5,4,2,6,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,5,2,4,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,3,2,7,1,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,5,2,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,6,2,4,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,6,2,5,1,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,8,3,7,2,6,1,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,8,3,7,2,5,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,8,4,7,2,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,5,7,2,4,1,3]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[6,4,3,8,2,7,1,5]=>{{1,6,7},{2,4,5,8},{3}}=>[6,4,3,5,8,7,1,2]=>0000000
[7,5,3,8,2,6,1,4]=>{{1,7},{2,5},{3},{4,8},{6}}=>[7,5,3,8,2,6,1,4]=>0000000
[8,4,3,7,2,6,1,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[8,6,4,7,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,5,7,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,3,6,2,5,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,5,4,3,2,8,1,7]=>{{1,6,7,8},{2,5},{3,4}}=>[6,5,4,3,2,7,8,1]=>0000000
[8,5,4,3,2,7,1,6]=>{{1,6,7,8},{2,5},{3,4}}=>[6,5,4,3,2,7,8,1]=>0000000
[8,7,6,3,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,6,5,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,2,5,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,2,5,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,7,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,2,5,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,2,5,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,5,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,2,5,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,7,2,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,8,2,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,4,2,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,4,2,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,4,2,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,4,2,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,4,2,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,4,2,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,4,2,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,5,2,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,4,2,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,4,2,6,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,4,2,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,6,5,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,8,5,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,4,5,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,8,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,6,5,2,3,8,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[3,1,4,8,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,7,5,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,8,5,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,4,5,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,1,3,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,1,8,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,1,5,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,1,5,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,1,8,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,1,5,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,1,2,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,2,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,2,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,1,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,2,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,1,2,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,1,2,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,1,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,1,2,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,1,2,6,7,3,4]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[4,3,1,8,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,7,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,5,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,5,2,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,1,6,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,8,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,6,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,1,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,1,6,2,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,7,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,5,6,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,1,5,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,5,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,5,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,7,1,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,5,1,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,4,1,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,1,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,1,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,4,1,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,5,1,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,4,1,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,4,1,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,1,2,7,4,5]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[6,8,5,1,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,5,1,2,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,4,1,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,8,1,6,2,4,5]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[7,8,4,1,6,2,3,5]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[7,8,5,1,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,4,1,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,4,8,1,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,6,5,1,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,6,5,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,6,5,1,3,4,7]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[2,7,6,5,1,3,8,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[2,6,4,5,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,8,5,1,2,4,6]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[2,3,4,8,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,4,7,6,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,7,5,6,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,7,5,6,1,3,4]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[2,3,4,5,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,4,8,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,4,5,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,8,7,3,4,1,2]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[4,6,7,3,8,5,1,2]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[3,6,7,4,5,8,1,2]=>{{1,3,7},{2,6,8},{4},{5}}=>[3,6,7,4,5,8,1,2]=>0000000
[1,6,7,4,5,2,3,8]=>{{1},{2,6},{3,7},{4},{5},{8}}=>[1,6,7,4,5,2,3,8]=>1000001
[2,5,4,7,6,1,8,3]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[3,5,4,7,6,8,1,2]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[5,4,3,8,7,6,1,2]=>{{1,5,7},{2,4,8},{3},{6}}=>[5,4,3,8,7,6,1,2]=>0000000
[6,4,8,3,7,5,1,2]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[6,3,8,4,5,7,1,2]=>{{1,6,7},{2,3,8},{4},{5}}=>[6,3,8,4,5,7,1,2]=>0000000
[5,3,4,8,6,7,1,2]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[4,3,5,6,8,7,1,2]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[7,8,2,4,5,1,6,3]=>{{1,6,7},{2,3,8},{4},{5}}=>[6,3,8,4,5,7,1,2]=>0000000
[7,8,1,4,5,2,3,6]=>{{1,3,7},{2,6,8},{4},{5}}=>[3,6,7,4,5,8,1,2]=>0000000
[5,1,4,8,6,2,3,7]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[6,1,8,3,2,5,4,7]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[7,8,1,3,2,5,4,6]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[7,8,2,3,1,5,6,4]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[5,2,3,8,1,6,7,4]=>{{1,5},{2},{3},{4,8},{6},{7}}=>[5,2,3,8,1,6,7,4]=>0000000
[6,3,8,2,1,7,5,4]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[7,8,3,2,1,6,5,4]=>{{1,5,7},{2,4,8},{3},{6}}=>[5,4,3,8,7,6,1,2]=>0000000
[7,8,4,2,6,1,5,3]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[5,4,2,8,7,1,6,3]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[4,5,2,7,8,1,6,3]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[3,5,2,7,1,8,6,4]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[2,6,7,3,1,5,8,4]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[3,6,7,2,1,8,5,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[4,6,7,2,8,1,5,3]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[5,6,7,8,2,1,4,3]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[7,8,5,6,2,1,4,3]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[6,5,8,7,1,2,3,4]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[5,4,1,8,7,2,3,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[6,4,8,1,7,2,3,5]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[5,3,1,8,2,7,4,6]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[4,3,1,2,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[7,8,2,1,3,4,6,5]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[8,4,3,6,5,1,2,7]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[4,6,2,7,3,5,1,8]=>{{1,4,7},{2,3,5,6},{8}}=>[4,3,5,7,6,2,1,8]=>0000001
[5,8,6,2,4,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,6,5,8,7,3]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[1,8,6,7,4,5,3,2]=>{{1},{2,8},{3,4,5,6,7}}=>[1,8,4,5,6,7,3,2]=>1000000
[8,1,6,7,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,7,8,2,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,2,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,7,8,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,1,7,8,5,6,4]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[4,8,2,7,1,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,2,1,4,3,6]=>{{1,5},{2,4,6,8},{3,7}}=>[5,4,7,6,1,8,3,2]=>0000000
[7,8,6,1,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,7,1,3,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,2,8,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,2,8,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,8,2,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,8,3,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,7,3,1,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,2,3,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,2,3,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[6,4,3,1,2,8,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[8,4,3,1,7,6,2,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[7,5,1,3,8,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,1,2,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,1,8,3,2,5,4]=>{{1,3,5,7},{2,6},{4,8}}=>[3,6,5,8,7,2,1,4]=>0000000
[6,8,1,7,2,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,1,2,7,6,3,4]=>{{1,3,5,7},{2,4,8},{6}}=>[3,4,5,8,7,6,1,2]=>0000000
[4,1,2,8,7,6,5,3]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[4,3,5,2,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,5,3,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,5,7,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,3,7,5,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,6,2,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,6,2,7,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,6,5,7,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,5,7,3,8,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,6,1,3,4,2,5,7]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[8,1,2,4,5,6,3,7]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>0000000
[8,2,5,1,3,6,4,7]=>{{1,4,7,8},{2},{3,5},{6}}=>[4,2,5,7,3,6,8,1]=>0000000
[8,6,1,4,5,3,2,7]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[3,6,4,1,8,7,5,2]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[2,7,6,8,1,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,6,5,8,2,1,4]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[5,2,7,1,3,8,4,6]=>{{1,3,4,5,7},{2},{6,8}}=>[3,2,4,5,7,8,1,6]=>0000000
[3,7,2,6,4,8,1,5]=>{{1,2,3,7},{4,5,6,8}}=>[2,3,7,5,6,8,1,4]=>0000000
[4,7,3,2,1,5,8,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,5,3,7,1,6,2,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[8,7,6,3,5,1,4,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,4,7,6,5,1,3,2]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[8,7,1,5,6,4,3,2]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[3,6,2,5,4,8,1,7]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[5,3,1,6,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,2,8,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,2,1,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,2,1,8,3,4,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[5,7,3,1,8,2,4,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,4,8,6,3,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,6,2,4,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,6,2,4,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,2,5,7,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,3,6,2,1,5,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,6,2,7,5,1,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,1,6,8,2,7,4,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[6,5,2,8,1,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,2,7,6,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,7,2,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,4,6,1,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,7,1,6,4,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[6,3,7,5,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,2,7,1,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,4,6,2,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,3,5,1,7,4,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,4,8,6,5,7,1,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,1,4,6,8,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,5,4,6,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,6,3,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,3,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,1,8,2,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[4,3,7,2,6,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,3,2,4,1,7,5]=>{{1,6},{2,4,5,8},{3},{7}}=>[6,4,3,5,8,1,7,2]=>0000000
[5,7,3,8,1,4,2,6]=>{{1,5},{2,7},{3},{4,6,8}}=>[5,7,3,6,1,8,2,4]=>0000000
[5,3,8,7,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,1,4,3,8,5,7,6]=>{{1,2},{3,4},{5,6,8},{7}}=>[2,1,4,3,6,8,7,5]=>0101000
[5,3,6,1,8,7,2,4]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[5,6,2,8,7,4,1,3]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[8,1,6,4,5,7,2,3]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[6,3,4,1,5,7,8,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,1,4,5,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,5,2,7,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,7,5,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,2,3,4,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,3,7,4,2,6,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,8,6,3,1,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,6,3,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,4,1,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,8,3,5,2,7,4,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,5,3,2,8,7,1,4]=>{{1,6,7},{2,4,5,8},{3}}=>[6,4,3,5,8,7,1,2]=>0000000
[2,4,1,8,7,6,5,3]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[8,4,2,1,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,3,5,8,1,7,2]=>{{1,6},{2,4,5,8},{3},{7}}=>[6,4,3,5,8,1,7,2]=>0000000
[5,7,3,6,1,8,2,4]=>{{1,5},{2,7},{3},{4,6,8}}=>[5,7,3,6,1,8,2,4]=>0000000
[8,6,2,5,1,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,2,1,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,1,3,7,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,2,5,1,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,1,4,8,3,5,7,6]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[4,8,2,3,5,1,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,8,4,2,1,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,1,7,2,5,6]=>{{1,4},{2,3,6,8},{5,7}}=>[4,3,6,1,7,8,5,2]=>0000000
[7,8,2,6,4,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,2,5,8,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,3,7,5,8,1,2]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[3,7,2,8,6,4,1,5]=>{{1,2,3,7},{4,5,6,8}}=>[2,3,7,5,6,8,1,4]=>0000000
[5,6,7,3,8,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,7,6,1,8,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[6,3,4,5,8,7,1,2]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[6,1,4,2,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,5,8,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,6,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,7,5,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,6,5,2,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,7,8,2,1,6,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[3,6,7,8,5,1,4,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,7,8,5,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,8,6,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,6,7,5,1,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,3,7,8,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,1,2,5,4,6,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,5,2,1,8,7,4,3]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[4,7,2,8,1,3,6,5]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[7,3,8,6,1,2,5,4]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[3,4,7,1,8,2,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[1,2,3,8,4,7,5,6]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[2,8,5,3,4,1,6,7]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[2,8,6,5,7,3,1,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[6,4,8,5,1,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,5,2,6,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,3,2,1,8,6,5,7]=>{{1,4},{2,3},{5,7,8},{6}}=>[4,3,2,1,7,6,8,5]=>0001000
[4,2,1,3,8,7,6,5]=>{{1,3,4},{2},{5,8},{6,7}}=>[3,2,4,1,8,7,6,5]=>0001000
[7,1,6,8,4,3,5,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[6,1,2,8,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,6,8,2,3,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,1,8,3,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,3,4,8,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,3,6,1,4,8,2,7]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[6,3,5,1,8,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,7,1,6,3,8,4,2]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[2,5,4,6,1,7,8,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[6,7,3,2,5,4,8,1]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[6,4,7,5,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,8,5,6,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,1,8,6,7,4,5]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[5,3,7,1,6,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,7,6,1,8,3,2]=>{{1,5},{2,4,6,8},{3,7}}=>[5,4,7,6,1,8,3,2]=>0000000
[4,6,7,5,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,6,1,7,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,2,1,6,7,8,3,4]=>{{1,3,5,7},{2},{4,6,8}}=>[3,2,5,6,7,8,1,4]=>0000000
[6,3,5,1,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,4,7,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,3,2,8,1,7,6]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[4,7,3,2,8,6,5,1]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[3,6,4,8,2,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,5,8,7,2,1,4]=>{{1,3,5,7},{2,6},{4,8}}=>[3,6,5,8,7,2,1,4]=>0000000
[3,5,7,8,6,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,8,1,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[8,1,6,7,3,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,5,3,7,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,3,5,6,2,7,4]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[3,7,8,5,6,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,8,2,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,2,8,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,6,7,4,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,4,2,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,5,1,7,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,2,3,1,8,6,7]=>{{1,5},{2,3,4},{6,7,8}}=>[5,3,4,2,1,7,8,6]=>0000100
[6,5,3,1,8,2,7,4]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[6,5,4,1,8,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,3,2,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,2,1,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,8,3,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,5,8,7,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,2,1,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,1,2,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,1,8,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,1,8,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,1,3,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,8,2,3,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,8,3,2,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,3,8,2,1,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[3,5,6,7,8,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,6,1,8,3,5,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[7,3,5,1,8,4,6,2]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[7,3,4,1,8,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,7,3,1,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,3,1,8,6,5,2]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[7,5,6,1,8,3,4,2]=>{{1,4,7},{2,5,8},{3,6}}=>[4,5,6,7,8,3,1,2]=>0000000
[7,6,5,1,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,2,1,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,5,1,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,7,1,3,8,2,6]=>{{1,4},{2,3,5,7},{6,8}}=>[4,3,5,1,7,8,2,6]=>0000000
[2,6,1,5,7,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,1,5,8,3,2,4]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[3,6,7,1,5,8,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,1,6,5,8,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,6,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,5,2,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,7,1,4,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,3,2,8,4,7,6]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[7,1,3,5,8,2,4,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,1,3,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,4,2,5,1,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,8,2,1,6,3,4,5]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[2,4,8,5,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,2,1,4,7,8,3]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[6,4,7,3,5,8,1,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,5,6,7,8,1,4,2]=>{{1,3,6},{2,5,8},{4,7}}=>[3,5,6,7,8,1,4,2]=>0000000
[3,6,5,7,8,2,1,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[2,7,1,8,5,3,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,7,6,8,5,4,1,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,4,2,8,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,1,8,3,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,8,6,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,5,8,1,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,5,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,6,5,3,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,1,5,2,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,5,2,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,1,2,3,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,5,1,7,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,7,8,1,4,6,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[5,8,4,7,6,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,8,3,1,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,7,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,5,2,4,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,8,5,3,1,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,5,1,2,6,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,5,2,7,8,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,6,8,5,2,7,1]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[4,1,2,7,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,4,2,5,3,8,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,1,2,6,8,5,4,7]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[3,6,4,8,5,1,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,6,3,7,5,8,1,4]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[4,6,8,3,1,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,1,8,2,7,4,6]=>{{1,3},{2,5},{4,6,7,8}}=>[3,5,1,6,2,7,8,4]=>0000000
[5,6,2,1,7,8,4,3]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[4,7,2,5,8,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,3,8,2,6,1,4]=>{{1,2,5,7},{3},{4,8},{6}}=>[2,5,3,8,7,6,1,4]=>0000000
[3,4,7,8,2,6,1,5]=>{{1,3,7},{2,4,5,8},{6}}=>[3,4,7,5,8,6,1,2]=>0000000
[8,4,3,6,5,1,7,2]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>0000000
[7,1,8,2,6,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,8,3,2,7,4,6]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[3,2,1,8,4,7,5,6]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[8,7,6,1,5,4,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,6,7,1,4,5,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[7,6,8,1,4,3,5,2]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[4,7,2,8,1,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,2,8,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,5,8,3,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,3,7,1,6,5,2]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,4,3,8,2,1,7,5]=>{{1,6},{2,4,5,8},{3},{7}}=>[6,4,3,5,8,1,7,2]=>0000000
[4,5,2,3,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,6,1,2,5,3,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[7,8,1,2,3,5,6,4]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[5,8,7,3,4,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,5,1,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,7,6,2,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,7,6,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,3,7,5,1,2,6]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[4,5,6,7,1,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,2,7,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,1,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,3,2,5,4,6,7]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[4,3,1,7,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,2,1,7,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,2,6,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,7,2,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,3,1,5,8,4,2]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[6,7,2,1,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,2,1,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,6,2,1,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,1,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,1,2,8,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,1,3,4,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,3,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,1,7,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,8,2,7,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,2,8,7,5,6,4]=>{{1,2,3},{4,8},{5,6,7}}=>[2,3,1,8,6,7,5,4]=>0010000
[4,1,3,7,5,8,6,2]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[6,3,8,5,2,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,4,5,8,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,8,5,7,1,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,1,4,8,6,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,4,2,8,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,5,2,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,2,7,4,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,5,7,2,8,1]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[6,4,1,5,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,2,5,7,3,6,8,1]=>{{1,4,7,8},{2},{3,5},{6}}=>[4,2,5,7,3,6,8,1]=>0000000
[7,8,1,6,3,2,5,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[2,8,1,7,3,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,1,3,7,2,6,5]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[7,6,1,8,4,3,2,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[7,1,2,8,3,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,3,1,6,8,2,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,7,3,8,2,6,4,1]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,8,7,2,5,4,3,1]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[6,7,4,8,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,5,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,4,6,3,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,4,8,3,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,3,7,2,8,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,8,4,6,2,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,4,5,2,7,1,3]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[6,8,4,5,2,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,4,8,2,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,3,8,2,4,1,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,3,5,2,8,1,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,8,3,6,2,5,1,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,8,3,5,2,4,1,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,8,3,5,2,7,1,4]=>{{1,6,7},{2,4,5,8},{3}}=>[6,4,3,5,8,7,1,2]=>0000000
[5,8,3,6,2,7,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,3,8,2,7,1,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,7,3,6,2,8,1,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,7,3,8,2,6,1,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,7,3,5,2,8,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,7,5,8,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,5,7,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,8,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,3,8,2,4,1,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,8,4,7,2,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,3,7,2,4,1,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,7,3,8,2,5,1,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,7,3,5,2,8,1,6]=>{{1,2,4,5,7},{3},{6,8}}=>[2,4,3,5,7,8,1,6]=>0000000
[4,5,3,7,2,6,1,8]=>{{1,4,7},{2,5},{3},{6},{8}}=>[4,5,3,7,2,6,1,8]=>0000001
[4,8,3,5,2,7,1,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,8,3,4,2,7,1,5]=>{{1,6,7},{2,5,8},{3},{4}}=>[6,5,3,4,8,7,1,2]=>0000000
[4,8,3,5,2,6,1,7]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,4,7,1,8,2,5,3]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[5,8,7,6,3,2,1,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[4,7,6,2,8,1,3,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[6,8,4,2,7,5,1,3]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[8,6,4,3,7,5,1,2]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[7,6,5,8,1,4,3,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[5,1,8,4,7,6,2,3]=>{{1,2,5,7},{3,8},{4},{6}}=>[2,5,8,4,7,6,1,3]=>0000000
[6,1,4,5,3,7,8,2]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[5,1,7,8,6,2,4,3]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[6,1,8,3,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,5,2,1,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,6,2,1,4,8,3,7]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[2,3,8,5,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,6,4,1,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,1,2,3,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,8,1,6,3,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,1,8,6,4,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,6,7,4,3,2,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,6,1,3,7,2,4,5]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[4,7,2,8,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,2,1,4,3,5,6]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[5,8,4,7,2,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,7,3,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,8,1,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,6,1,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,2,7,8,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,3,4,2,1,6,5]=>{{1,6,7},{2,5,8},{3},{4}}=>[6,5,3,4,8,7,1,2]=>0000000
[8,6,3,2,4,1,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[8,5,3,2,6,7,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,4,6,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,1,6,4,5,2,3]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[6,8,1,7,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,1,6,3,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,3,6,1,5,2,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,2,6,1,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,2,7,1,5,3,4]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[6,8,2,7,3,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,6,7,4,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,6,7,1,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,3,7,1,6,2,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,8,4,7,1,5,2,3]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[6,8,5,7,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,7,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,6,7,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,6,7,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,6,7,2,5,1,3]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[3,8,1,7,2,6,4,5]=>{{1,3},{2,5,8},{4,7},{6}}=>[3,5,1,7,8,6,4,2]=>0000000
[2,8,3,7,4,6,1,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[7,4,2,8,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,1,7,2,3,4,5]=>{{1,3,6},{2,5,8},{4,7}}=>[3,5,6,7,8,1,4,2]=>0000000
[2,5,3,7,8,1,6,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,8,1,3,6,7,2,5]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[5,3,8,2,4,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,3,1,2,8,5,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,2,8,1,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,3,8,1,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,5,8,2,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,2,6,8,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,3,6,8,4,7,2,1]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[3,7,2,5,4,8,6,1]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[4,1,6,5,8,3,2,7]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[5,1,6,8,4,3,2,7]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,3,1,5,4,7,2,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[8,4,1,5,7,3,2,6]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[8,4,6,1,7,3,2,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,3,6,1,4,7,2,5]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[6,7,8,2,4,3,5,1]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[4,7,6,2,8,3,5,1]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[3,7,6,2,4,8,5,1]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[8,7,2,1,4,3,6,5]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[8,7,2,5,1,3,6,4]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[8,4,6,5,7,1,2,3]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[8,7,6,5,2,1,4,3]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[3,6,4,8,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,4,3,8,7,1,2]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[4,3,6,7,8,5,1,2]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[4,6,8,5,3,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,2,1,4,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,5,3,1,7,2,6]=>{{1,3,4,5},{2,6,7,8}}=>[3,6,4,5,1,7,8,2]=>0000000
[7,6,1,8,3,2,4,5]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[3,1,6,7,5,8,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,8,1,6,5,3,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,3,2,7,5,8,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,6,4,1,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,5,8,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,7,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,3,8,1,2,7,5]=>{{1,4,5,8},{2,6},{3},{7}}=>[4,6,3,5,8,2,7,1]=>0000000
[7,8,1,3,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,5,7,4,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,7,3,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,5,8,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,1,2,4,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[7,8,2,3,4,1,6,5]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[2,4,7,3,6,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,6,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,6,8,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,2,1,3,6,5,8,7]=>{{1,3,4},{2},{5,6},{7,8}}=>[3,2,4,1,6,5,8,7]=>0001010
[7,8,2,1,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,1,6,4,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,1,7,5,2,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,6,1,7,4,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,5,1,6,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,1,7,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,1,8,4,5,3,6]=>{{1,2,3,7},{4,5,6,8}}=>[2,3,7,5,6,8,1,4]=>0000000
[2,6,1,4,5,8,3,7]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[8,4,2,1,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,3,1,5,8,2,7]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[6,3,5,8,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,3,8,6,7,2,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,8,6,7,4,3,2,1]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,8,7,5,6,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,2,1,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,8,1,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,6,1,4,3,5,7]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,8,6,2,1,3,5,7]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,3,8,2,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,7,6,8,1,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[4,3,6,5,8,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,1,6,5,8,3,4,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,4,6,1,3,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,6,3,4,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,3,5,2,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,3,2,7,4,6,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,1,8,3,5,4,7,6]=>{{1,2},{3,4,6,8},{5},{7}}=>[2,1,4,6,5,8,7,3]=>0100000
[8,1,3,2,5,4,7,6]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>0000000
[8,1,5,2,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,6,8,1,3,2,5,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[6,1,8,4,7,2,5,3]=>{{1,2,6},{3,8},{4},{5,7}}=>[2,6,8,4,7,1,5,3]=>0000000
[6,5,8,1,3,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,6,3,8,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,2,1,5,8,4,6,7]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[2,8,3,1,5,4,6,7]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[8,1,5,3,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,1,3,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,4,7,8,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,4,3,8,7,5,6,2]=>{{1},{2,4,8},{3},{5,6,7}}=>[1,4,3,8,6,7,5,2]=>1000000
[6,4,8,7,1,5,2,3]=>{{1,5,6},{2,4,7},{3,8}}=>[5,4,8,7,6,1,2,3]=>0000000
[3,7,8,1,5,2,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,1,2,8,5,3,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,7,1,8,3,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,1,3,6,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,2,6,3,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,7,1,5,6,2,4]=>{{1,4,8},{2,3,7},{5},{6}}=>[4,3,7,8,5,6,2,1]=>0000000
[7,8,1,6,4,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,5,6,4,3,2]=>{{1,2,8},{3,7},{4,5,6}}=>[2,8,7,5,6,4,3,1]=>0000000
[8,5,2,7,4,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,3,7,1,4,2,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,3,4,7,5,8,1,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,8,3,7,1,2,6,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,6,3,1,2,4,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[5,3,7,8,2,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,7,6,2,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,7,2,5,6,8,3]=>{{1,2,4},{3,7,8},{5},{6}}=>[2,4,7,1,5,6,8,3]=>0000000
[4,6,1,2,5,8,7,3]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[3,4,6,1,5,7,8,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,3,1,5,4,2,8,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[3,6,2,7,1,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,3,2,7,1,6,4]=>{{1,5,6,7},{2,4,8},{3}}=>[5,4,3,8,6,7,1,2]=>0000000
[8,7,2,6,1,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,8,5,7,4,3,6,2]=>{{1},{2,8},{3,4,5,6,7}}=>[1,8,4,5,6,7,3,2]=>1000000
[3,6,5,8,1,4,2,7]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[4,3,6,7,8,1,2,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[8,1,5,2,7,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,6,4,7,8,1,2]=>{{1,5,7},{2,3,6,8},{4}}=>[5,3,6,4,7,8,1,2]=>0000000
[6,3,1,8,4,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,8,5,2,4,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,5,8,7,1,3,6,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[8,3,7,6,1,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,7,6,2,1,5]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[2,4,8,7,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,8,6,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,3,6,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,5,3,1,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,8,3,4,1,6,2]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[7,5,6,3,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,3,1,6,4,8,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,5,3,6,4,1,8,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,5,3,8,4,1,6,2]=>{{1,6,7},{2,4,5,8},{3}}=>[6,4,3,5,8,7,1,2]=>0000000
[7,5,3,8,1,4,6,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,5,3,1,8,2,6,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,5,3,1,8,6,2,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[7,5,3,8,6,1,4,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,5,8,3,6,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,3,8,4,1,2,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,5,8,6,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,8,6,3,1,4,2]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[7,5,6,8,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,6,3,8,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,6,3,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,3,6,1,8,4,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,8,3,5,7,1,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,8,1,2,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,8,2,5,7,1,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,3,6,8,4,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,7,8,2,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[5,8,7,1,4,2,6,3]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[6,4,8,7,5,3,1,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,1,2,7,6,4,8,5]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[1,6,2,3,7,8,5,4]=>{{1},{2,3,4,6,8},{5,7}}=>[1,3,4,6,7,8,5,2]=>1000000
[5,7,1,8,2,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,2,7,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,2,1,7,3,8,5,6]=>{{1,3,4,5,7},{2},{6,8}}=>[3,2,4,5,7,8,1,6]=>0000000
[3,7,2,8,6,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,6,5,2,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,1,2,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,8,2,3,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,2,6,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,1,7,5,4,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,3,1,2,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}=>[2,3,4,1,8,7,6,5]=>0001000
[8,6,5,3,2,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,7,2,4,5,3,1,6]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[8,5,1,2,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,1,3,6,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,3,1,8,7,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,4,6,8,7,2,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[8,4,1,6,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,5,2,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,2,7,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,1,3,8,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,4,5,2,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,8,2,1,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,2,5,8,3,6,4]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[7,1,4,6,5,8,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,8,7,1,5,4,2,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,8,1,6,3,7,2,4]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[4,6,3,8,5,1,7,2]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>0000000
[1,7,5,6,2,8,3,4]=>{{1},{2,3,5,7},{4,6,8}}=>[1,3,5,6,7,8,2,4]=>1000000
[7,8,1,2,4,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,2,1,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,6,5,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,5,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,3,8,4,5,1,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,5,3,8,6,7,1,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,6,3,8,4,7,1,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,6,4,5,1,8,2,7]=>{{1,3,4,5},{2,6,7,8}}=>[3,6,4,5,1,7,8,2]=>0000000
[2,6,4,8,1,5,3,7]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[2,8,3,6,1,5,4,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,7,1,8,2,5,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[5,8,6,7,2,3,1,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[2,7,5,8,1,4,3,6]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[2,3,1,8,4,7,5,6]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[2,3,1,8,6,7,4,5]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[5,6,7,8,1,4,3,2]=>{{1,5},{2,4,6,8},{3,7}}=>[5,4,7,6,1,8,3,2]=>0000000
[7,4,3,8,2,1,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,4,1,5,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,8,7,2,5,3,1,4]=>{{1,3,6,7},{2,4,8},{5}}=>[3,4,6,8,5,7,1,2]=>0000000
[6,1,2,3,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,3,5,8,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[8,6,7,1,5,4,3,2]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[2,1,6,5,8,4,7,3]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[3,1,8,2,7,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,2,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,3,5,8,1,4,2,6]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[6,8,1,3,5,7,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,7,1,2,5,3,8,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,5,4,3,6,8,1,7]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[4,3,7,8,5,1,6,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,8,1,5,2,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,6,1,2,8,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,3,2,8,1,6,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,3,8,2,1,5,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,1,7,2,5,4,3,6]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[8,1,7,2,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,6,3,2,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,5,8,2,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,3,5,2,6,4,7]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,1,4,5,8,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,4,3,8,2,1,7]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[4,7,8,3,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,8,1,4,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,3,8,2,1,4,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,4,3,7,6,2,1,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,8,4,2,7,1,6,3]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[8,6,7,5,1,4,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[5,8,4,2,6,1,3,7]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[4,8,7,2,5,1,3,6]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[4,3,7,2,5,1,8,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,8,7,6,5,1,3,4]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[6,4,7,3,1,5,8,2]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[6,5,3,7,1,4,8,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,7,1,5,8,3,2]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[6,4,3,1,5,8,7,2]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>0000000
[6,4,2,1,5,8,3,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,8,2,1,5,4,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,8,7,1,5,4,3,6]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[5,4,1,6,7,8,3,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[4,3,1,6,5,7,8,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,7,8,5,4,3,2]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[4,1,7,6,5,8,3,2]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[3,6,8,1,7,2,4,5]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[3,4,5,6,8,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,2,3,5,4,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,2,1,6,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,2,1,3,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,4,1,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,1,8,6,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,7,2,5,4,8,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,1,4,2,8,3,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[7,1,8,2,5,3,6,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,3,8,4,5,1,6,2]=>{{1,6,7},{2,3,8},{4},{5}}=>[6,3,8,4,5,7,1,2]=>0000000
[8,1,7,6,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,8,1,7,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,8,6,3,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,6,5,4,3,2]=>{{1,2,8},{3,7},{4,6},{5}}=>[2,8,7,6,5,4,3,1]=>0000000
[7,8,1,5,2,6,3,4]=>{{1,3,7},{2,4,5,8},{6}}=>[3,4,7,5,8,6,1,2]=>0000000
[5,8,3,7,6,2,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,7,1,8,3,6,2,4]=>{{1,3,5},{2,7},{4,8},{6}}=>[3,7,5,8,1,6,2,4]=>0000000
[8,7,3,6,5,1,4,2]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[3,5,2,7,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,2,7,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,2,8,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,2,1,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,2,1,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,2,8,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,2,1,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,3,8,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,7,3,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,7,3,8,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,8,3,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,7,3,2,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,2,3,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,2,7,4,8,1,3]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[5,6,2,7,8,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,8,3,4,2,1,7]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[6,1,2,3,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,7,8,4,5,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[7,1,2,3,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,2,3,8,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,2,8,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,8,3,4,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,1,2,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,5,8,6,1,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,6,8,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,3,5,6,8,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,1,7,8,6,4,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[2,5,7,8,6,3,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[8,3,1,6,5,2,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,5,3,8,7,6,1,4]=>{{1,2,5,7},{3},{4,8},{6}}=>[2,5,3,8,7,6,1,4]=>0000000
[7,3,2,6,5,1,8,4]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[4,8,6,5,7,3,2,1]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,8,5,6,7,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,3,4,5,1,7,2]=>{{1,6},{2,8},{3},{4},{5},{7}}=>[6,8,3,4,5,1,7,2]=>0000000
[8,3,2,1,5,4,7,6]=>{{1,4,6,8},{2,3},{5},{7}}=>[4,3,2,6,5,8,7,1]=>0000000
[2,5,1,8,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,3,6,2,4,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,6,5,8,2,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,4,1,5,2,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[3,4,7,8,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,8,2,4,6,1,3]=>{{1,7},{2,4,5},{3,8},{6}}=>[7,4,8,5,2,6,1,3]=>0000000
[3,2,6,4,8,1,7,5]=>{{1,3,6},{2},{4},{5,8},{7}}=>[3,2,6,4,8,1,7,5]=>0000000
[2,7,8,5,4,1,3,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[4,7,5,3,1,2,8,6]=>{{1,3,4,5},{2,6,7,8}}=>[3,6,4,5,1,7,8,2]=>0000000
[5,7,3,2,4,1,8,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,8,4,7,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,2,1,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,2,6,5,8,1,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,4,7,8,2,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,5,6,1,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,1,4,6,5,7,8,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,1,7,2,6,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,7,1,6,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,7,1,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,7,1,5,3,4,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,6,5,4,1,3,2]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[8,5,7,6,4,1,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[8,3,7,6,5,1,4,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,1,7,5,6,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,7,5,6,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,5,6,1,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[8,7,6,4,5,1,3,2]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[8,4,7,3,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,3,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,7,2,6,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,7,2,6,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,7,2,5,1,4,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,6,1,5,2,4,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,4,7,1,6,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,7,3,8,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,2,6,3,8,1,4]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[4,8,1,2,5,7,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,7,1,3,2,8,6,5]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[3,4,2,7,8,1,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[4,3,2,1,5,8,6,7]=>{{1,4},{2,3},{5},{6,7,8}}=>[4,3,2,1,5,7,8,6]=>0001100
[3,4,6,1,5,8,2,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,7,3,5,4,8,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,5,4,1,6,7,8,2]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[2,4,8,3,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,8,2,1,5,7,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,3,6,1,4,7,8,2]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[4,3,8,7,5,2,6,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,6,1,3,5,4,2,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,4,8,7,3,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,2,6,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,2,7,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,1,6,4,8,5,7]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[2,7,4,1,5,3,8,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,1,8,6,5,3,2,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,8,5,3,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,7,4,3,6,2,8,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[2,1,5,6,8,3,7,4]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[7,5,1,2,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,8,3,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,8,2,7,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,3,8,2,4,6,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,8,5,7,1,4,2,6]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[4,7,2,5,1,3,8,6]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[6,3,2,1,4,8,7,5]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[3,1,4,6,2,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,7,6,3,8,1,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[3,7,2,6,8,5,1,4]=>{{1,2,3,7},{4,5,6,8}}=>[2,3,7,5,6,8,1,4]=>0000000
[7,3,8,1,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,4,2,6,1,5]=>{{1,3,7},{2,5,8},{4},{6}}=>[3,5,7,4,8,6,1,2]=>0000000
[6,4,2,8,7,5,1,3]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[3,5,4,6,1,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,5,7,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,5,7,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,5,3,8,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,7,4,5,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,7,3,6,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,3,1,8,2,7,6]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[3,1,6,8,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,7,1,3,8,5,6,2]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[3,7,2,1,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,8,7,4,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,3,2,6,4,1,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,2,5,4,3,1,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[4,8,6,5,7,2,1,3]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[5,8,3,2,7,6,4,1]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[5,8,3,2,6,7,1,4]=>{{1,5,6,7},{2,4,8},{3}}=>[5,4,3,8,6,7,1,2]=>0000000
[6,5,3,2,8,1,7,4]=>{{1,6},{2,4,5,8},{3},{7}}=>[6,4,3,5,8,1,7,2]=>0000000
[6,3,4,1,2,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,2,1,4,3,6,7,8]=>{{1,3,5},{2},{4},{6},{7},{8}}=>[3,2,5,4,1,6,7,8]=>0000111
[3,4,5,8,6,7,1,2]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[2,1,5,3,8,4,7,6]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[3,1,8,2,5,4,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[8,1,3,2,6,4,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[3,1,8,2,6,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,1,8,3,6,4,7,5]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[8,1,4,2,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,7,2,8,4,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[7,1,3,2,5,4,8,6]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[7,1,3,2,6,4,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,1,8,2,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,5,2,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,2,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,8,2,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,8,2,6,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,4,2,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,4,2,5,3,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[3,1,5,2,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,1,4,2,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,1,8,2,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,1,3,2,7,4,8,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,1,5,2,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,8,2,5,3,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[6,1,7,2,8,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,7,2,5,3,8,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,7,2,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,5,2,4,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,6,2,4,3,8,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[7,1,6,2,8,3,5,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[7,1,8,2,6,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,3,1,2,5,6,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,2,5,7,1,8,4,6]=>{{1,3,5},{2},{4,7},{6,8}}=>[3,2,5,7,1,8,4,6]=>0000000
[3,5,2,8,1,7,4,6]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[4,3,1,2,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[2,5,4,6,8,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,3,5,7,6,8,1,2]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[3,4,2,1,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[7,6,4,3,2,1,8,5]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[7,6,5,8,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,4,3,2,1,6,5]=>{{1,6,7},{2,5,8},{3,4}}=>[6,5,4,3,8,7,1,2]=>0000000
[7,6,5,8,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,8,3,2,1,6,5]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[6,4,7,1,8,3,2,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[6,8,4,3,7,2,1,5]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[6,7,4,2,8,3,1,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[2,8,7,6,5,1,4,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,7,6,3,1,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,2,1,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,6,1,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,6,8,7,4,3,1,2]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[3,1,4,6,5,8,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[5,6,7,3,2,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,7,8,1,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,7,8,1,4,5,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[7,5,2,8,4,1,6,3]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[6,3,4,8,2,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,3,8,2,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,1,3,5,4,8,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,3,1,6,8,2,4,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[7,3,5,1,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,3,6,1,7,5,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,1,8,6,7,3,5,4]=>{{1,2},{3,4,6,8},{5,7}}=>[2,1,4,6,7,8,5,3]=>0100000
[7,1,3,8,6,4,5,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,3,5,8,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,1,6,3,4,8,7,5]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[4,6,7,2,5,8,3,1]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[7,4,6,8,5,1,2,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,6,8,2,4,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,1,3,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,1,5,4,7,3,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[2,6,1,3,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,7,1,3,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,1,6,5,3,8,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,8,1,7,6,5,4,3]=>{{1,2,3,8},{4,7},{5,6}}=>[2,3,8,7,6,5,4,1]=>0000000
[7,4,2,8,1,6,5,3]=>{{1,5,7},{2,3,4,8},{6}}=>[5,3,4,8,7,6,1,2]=>0000000
[8,7,5,3,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,8,5,1,7,3,2]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[5,1,8,7,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,6,2,8,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,2,6,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,8,5,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,6,8,5,7,1,2]=>{{1,3,6,7},{2,4,8},{5}}=>[3,4,6,8,5,7,1,2]=>0000000
[4,6,8,3,5,7,2,1]=>{{1,3,4,8},{2,6,7},{5}}=>[3,6,4,8,5,7,2,1]=>0000000
[6,3,7,2,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,4,1,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,5,7,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,2,6,3,5,1,8]=>{{1,7},{2,3,4,5,6},{8}}=>[7,3,4,5,6,2,1,8]=>0000001
[6,1,4,8,5,3,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[7,6,4,3,1,8,2,5]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[8,4,6,5,1,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,4,6,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,5,6,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,3,2,1,8,5,4]=>{{1,5,7},{2,4,6,8},{3}}=>[5,4,3,6,7,8,1,2]=>0000000
[3,5,4,2,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,3,1,4,5,7,2]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[5,2,1,4,7,6,3,8]=>{{1,3,5,7},{2},{4},{6},{8}}=>[3,2,5,4,7,6,1,8]=>0000001
[5,8,4,1,7,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,8,3,5,7,2,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,4,6,3,5,8,1,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,3,1,7,6,4,8,5]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[4,3,8,7,1,2,5,6]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[3,5,1,7,2,8,6,4]=>{{1,3},{2,5},{4,6,7,8}}=>[3,5,1,6,2,7,8,4]=>0000000
[5,3,1,6,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,7,6,5,1,2]=>{{1,4,7},{2,3,8},{5,6}}=>[4,3,8,7,6,5,1,2]=>0000000
[2,8,7,6,1,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,8,7,5,4,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,1,8,7,6,5,4,2]=>{{1,2,3,8},{4,7},{5,6}}=>[2,3,8,7,6,5,4,1]=>0000000
[3,8,2,1,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[3,8,7,2,1,6,5,4]=>{{1,3,5,7},{2,4,8},{6}}=>[3,4,5,8,7,6,1,2]=>0000000
[4,8,7,2,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,6,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,8,7,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,1,8,7,6,3,2]=>{{1,3,5,7},{2,4,8},{6}}=>[3,4,5,8,7,6,1,2]=>0000000
[6,4,8,1,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,8,7,6,5,2]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[2,8,4,3,6,1,5,7]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[2,4,8,3,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,6,2,4,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,2,1,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,7,8,5,1,2]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[3,4,6,8,7,5,1,2]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[5,4,6,3,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,8,5,3,7,1,2]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[5,2,8,6,4,1,3,7]=>{{1,4,5,6},{2},{3,7,8}}=>[4,2,7,5,6,1,8,3]=>0000000
[4,6,2,3,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,3,2,4,1,6,5]=>{{1,6,7},{2,4,5,8},{3}}=>[6,4,3,5,8,7,1,2]=>0000000
[5,8,2,7,4,3,1,6]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[4,1,3,6,5,8,7,2]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>0000000
[6,4,1,3,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,1,4,8,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,6,1,8,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,6,1,3,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,1,6,3,8,5,7,4]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[4,1,3,6,8,5,7,2]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[2,1,8,6,3,5,7,4]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[2,8,4,1,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,6,4,1,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,4,2,1,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,7,6,5,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,4,3,6,2,1,5]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[8,7,3,6,5,2,1,4]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[4,8,2,6,3,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,6,2,1,7,8,5,3]=>{{1,4},{2,3,6,8},{5,7}}=>[4,3,6,1,7,8,5,2]=>0000000
[2,3,8,7,4,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,2,8,1,7,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[2,8,3,5,1,7,4,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,8,5,6,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,2,8,3,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,3,8,5,2,1,6,4]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[7,3,4,8,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,8,3,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,4,3,8,1,6,5,7]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[3,4,8,7,1,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,8,5,1,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,6,5,8,1,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,3,1,4,7,2,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,1,4,5,3,2,6]=>{{1,3,6,8},{2,7},{4},{5}}=>[3,7,6,4,5,8,2,1]=>0000000
[6,8,4,3,7,5,2,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[6,3,7,2,8,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,1,8,3,2,5,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[7,1,6,8,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,8,4,6,7,5,3,2]=>{{1},{2,8},{3,4,5,6,7}}=>[1,8,4,5,6,7,3,2]=>1000000
[8,4,1,5,6,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,1,2,5,4,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,6,2,5,3,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,1,5,8,2,7,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[2,8,7,1,6,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,3,8,4,1,7,2]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[8,6,1,2,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,8,1,2,5,3,6,4]=>{{1,3,6,7},{2,4,8},{5}}=>[3,4,6,8,5,7,1,2]=>0000000
[7,4,3,8,2,5,6,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,5,3,7,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,5,3,8,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,3,4,8,7,1,2]=>{{1,6,7},{2,5,8},{3},{4}}=>[6,5,3,4,8,7,1,2]=>0000000
[6,3,8,1,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,5,7,8,1,2]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[2,6,1,5,4,8,3,7]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[3,1,6,2,5,8,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,5,1,3,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,7,8,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,6,5,8,7,1,4]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[6,3,2,8,5,7,4,1]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[3,8,4,7,2,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,7,1,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,6,5,8,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,1,2,6,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,1,5,6,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,8,2,3,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,5,1,8,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,2,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,6,1,2,4,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,2,5,4,1,3,7]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[6,7,5,3,8,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,4,2,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,1,8,3,4,6,2]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[8,1,3,7,6,4,2,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,8,1,2,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,5,8,7,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,4,5,2,6,3]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[4,6,3,5,8,1,7,2]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[5,1,7,6,2,8,4,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[4,6,2,5,3,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,6,4,2,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,5,7,1,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,3,1,2,6,4,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[5,6,8,1,4,3,2,7]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[7,8,4,1,5,3,2,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,3,8,5,1,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,1,3,8,7,5,2]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[3,6,2,5,8,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,1,3,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,2,1,7,3,8,4,6]=>{{1,3,5},{2},{4,7},{6,8}}=>[3,2,5,7,1,8,4,6]=>0000000
[7,1,8,3,4,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,7,6,3,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,4,3,2,8,6,1]=>{{1,6,7,8},{2,5},{3,4}}=>[6,5,4,3,2,7,8,1]=>0000000
[8,5,4,3,7,2,1,6]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[3,7,5,8,1,4,6,2]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[5,7,2,3,6,1,8,4]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[4,7,1,6,5,8,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,1,2,4,8,7,6,5]=>{{1,2,3},{4},{5,8},{6,7}}=>[2,3,1,4,8,7,6,5]=>0011000
[2,8,7,3,5,4,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,4,2,6,8,7,1,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[6,7,3,1,4,2,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,3,2,7,1,6,8,4]=>{{1,5},{2,3},{4,7,8},{6}}=>[5,3,2,7,1,6,8,4]=>0000000
[8,4,3,7,5,1,6,2]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[4,8,3,6,5,2,1,7]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[3,6,8,5,1,2,4,7]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[7,1,2,8,3,5,6,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[7,4,6,1,8,2,3,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[3,4,5,1,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,1,6,8,4,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,4,1,8,2,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,8,2,6,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,4,7,5,1,2,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,2,7,3,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,3,7,1,5,2,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,7,4,8,2,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,4,2,1,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,2,1,5,8,6,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,6,4,1,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,8,1,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,1,8,3,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,1,8,7,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,1,7,5,4,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,6,8,1,3,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,2,8,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,2,8,5,3,1,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,4,5,3,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,4,5,3,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,6,3,8,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,8,3,4,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,5,8,3,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,8,3,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,8,3,5,2,6,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,4,8,3,5,2,7,1]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[5,4,7,3,6,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,8,3,7,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,8,3,7,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,3,7,8,2,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,5,4,2,8,7,1,3]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[4,8,2,6,3,7,1,5]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[5,8,4,1,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,3,2,7,6,1,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[4,8,6,7,2,3,1,5]=>{{1,4,7},{2,5,8},{3,6}}=>[4,5,6,7,8,3,1,2]=>0000000
[4,8,7,3,6,2,1,5]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[4,3,8,2,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,8,7,3,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,5,1,2,8,3,6]=>{{1,4},{2,3,5,7},{6,8}}=>[4,3,5,1,7,8,2,6]=>0000000
[3,1,7,8,4,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,6,8,4,2,1,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[3,7,8,2,6,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,3,6,1,8,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[2,6,7,3,8,4,1,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[2,6,3,7,4,8,1,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,3,7,1,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,6,8,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,7,3,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,5,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,6,1,2,5,8,3,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,4,2,1,3,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,1,3,5,4,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[8,3,2,1,4,5,7,6]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[8,1,6,3,5,7,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,4,2,5,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,8,7,3,2,1,6]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[1,6,8,4,7,2,5,3]=>{{1},{2,6},{3,8},{4},{5,7}}=>[1,6,8,4,7,2,5,3]=>1000000
[1,5,8,3,7,2,6,4]=>{{1},{2,5,6,7},{3,4,8}}=>[1,5,4,8,6,7,2,3]=>1000000
[7,4,5,8,1,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,2,8,7,5,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[3,1,4,8,7,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,6,4,8,2,7,5,3]=>{{1},{2,5,6,7},{3,4,8}}=>[1,5,4,8,6,7,2,3]=>1000000
[2,6,1,8,3,7,5,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[4,6,5,8,3,2,1,7]=>{{1,4,7,8},{2,6},{3,5}}=>[4,6,5,7,3,2,8,1]=>0000000
[7,6,5,1,2,8,4,3]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[7,6,5,1,3,2,8,4]=>{{1,4,7,8},{2,6},{3,5}}=>[4,6,5,7,3,2,8,1]=>0000000
[4,5,1,3,6,8,2,7]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[4,3,5,1,7,8,2,6]=>{{1,4},{2,3,5,7},{6,8}}=>[4,3,5,1,7,8,2,6]=>0000000
[5,1,6,7,3,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,7,8,2,4,5]=>{{1,2,3,6},{4,7},{5,8}}=>[2,3,6,7,8,1,4,5]=>0000000
[2,4,6,7,1,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,7,1,5,6,8,3]=>{{1,2,4},{3,7,8},{5},{6}}=>[2,4,7,1,5,6,8,3]=>0000000
[6,4,3,7,2,5,8,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,3,7,2,8,1,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,3,7,5,1,8,2]=>{{1,6},{2,4,7,8},{3},{5}}=>[6,4,3,7,5,1,8,2]=>0000000
[5,6,3,7,4,1,8,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,7,4,2,1,5,8,3]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[5,6,3,7,8,1,2,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,6,3,7,2,4,8,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,6,7,2,3,8,1,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[5,6,7,2,8,1,3,4]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[6,7,3,8,1,2,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,5,3,2,6,1,8,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,5,3,2,7,8,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,7,2,5,1,8,3]=>{{1,6},{2,4},{3,7,8},{5}}=>[6,4,7,2,5,1,8,3]=>0000000
[3,7,8,5,6,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,3,8,6,4,1,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,3,7,8,6,1,4,2]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[7,1,8,5,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,8,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,3,1,8,6,4,2]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[5,7,8,6,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,8,6,1,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,8,1,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,1,8,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,8,1,6,3,4,2]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[3,5,1,7,8,6,4,2]=>{{1,3},{2,5,8},{4,7},{6}}=>[3,5,1,7,8,6,4,2]=>0000000
[7,1,3,5,8,6,4,2]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[2,1,6,5,3,4,8,7]=>{{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>0100010
[8,7,6,1,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,8,2,3,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,7,6,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,8,6,2,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,3,6,7,5,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,1,2,7,3,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,4,2,1,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,1,4,5,8,3,7,6]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[8,4,7,1,5,2,3,6]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[6,4,8,1,7,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,2,6,4,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,1,5,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,4,8,3,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,5,6,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,3,8,4,7,1,2]=>{{1,6,7},{2,4,5,8},{3}}=>[6,4,3,5,8,7,1,2]=>0000000
[8,6,4,7,5,3,1,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,3,8,5,4,6,1,2]=>{{1,7},{2,3,8},{4,5},{6}}=>[7,3,8,5,4,6,1,2]=>0000000
[3,4,8,5,6,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,8,3,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,5,6,1,4,7,8]=>{{1,3,5},{2},{4,6},{7},{8}}=>[3,2,5,6,1,4,7,8]=>0000011
[7,4,8,3,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,8,5,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,1,2,8,3,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[1,2,3,8,6,4,5,7]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[2,4,7,5,6,8,3,1]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[2,5,3,8,7,4,6,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,1,8,5,7,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,6,4,5,8,3,1]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[4,8,1,7,6,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,1,4,3,2,6]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[4,8,1,5,3,7,2,6]=>{{1,3,4,5},{2,6,7,8}}=>[3,6,4,5,1,7,8,2]=>0000000
[6,3,7,2,8,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,2,5,7,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,3,6,7,2,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,1,4,2,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,3,8,2,7,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,4,2,5,1,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,3,2,7,1,8,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,3,6,1,5,4,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,7,8,3,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,8,3,5,2,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,7,6,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,2,1,4,7,6,5]=>{{1,4,5,8},{2,3},{6,7}}=>[4,3,2,5,8,7,6,1]=>0000000
[6,4,1,7,3,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,3,2,7,5,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,4,2,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,1,7,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,2,7,6,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,1,6,2,8,3,4]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[2,5,1,8,6,7,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[2,6,5,8,1,7,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[3,4,2,6,5,8,1,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,4,3,8,1,7,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,1,2,7,4,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,8,3,4,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,3,4,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,2,1,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,1,3,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,1,8,4,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,5,1,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,8,7,2,1,4,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[6,8,2,1,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,6,7,4,3,1,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,6,5,2,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,6,4,5,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,6,5,8,7,2,1,3]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[2,6,8,4,7,1,5,3]=>{{1,2,6},{3,8},{4},{5,7}}=>[2,6,8,4,7,1,5,3]=>0000000
[6,8,2,5,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,1,5,7,3,8,6,4]=>{{1,2},{3,5},{4,6,7,8}}=>[2,1,5,6,3,7,8,4]=>0100000
[4,1,2,3,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[3,4,2,1,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[8,1,3,6,4,7,2,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,4,8,3,6,7,1,2]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[4,3,1,6,5,8,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[3,7,5,2,8,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,5,2,4,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[8,4,2,5,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,8,5,3,7,4,6,2]=>{{1},{2,8},{3,4,5,6,7}}=>[1,8,4,5,6,7,3,2]=>1000000
[3,5,4,8,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,5,8,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,4,5,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,6,8,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,6,1,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,8,3,6,5,2,7,4]=>{{1},{2,4,6,8},{3},{5},{7}}=>[1,4,3,6,5,8,7,2]=>1000000
[6,1,5,2,4,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,5,1,2,6,7]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[1,6,3,8,5,2,7,4]=>{{1},{2,6},{3},{4,8},{5},{7}}=>[1,6,3,8,5,2,7,4]=>1000000
[6,2,3,7,5,1,4,8]=>{{1,6},{2},{3},{4,7},{5},{8}}=>[6,2,3,7,5,1,4,8]=>0000001
[4,2,6,1,5,3,7,8]=>{{1,4},{2},{3,6},{5},{7},{8}}=>[4,2,6,1,5,3,7,8]=>0000011
[1,2,7,8,5,6,3,4]=>{{1},{2},{3,7},{4,8},{5},{6}}=>[1,2,7,8,5,6,3,4]=>1100000
[8,7,3,2,1,6,5,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[8,7,4,1,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,7,5,4,2,8,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[7,3,6,8,5,2,4,1]=>{{1,4,7,8},{2,3,6},{5}}=>[4,3,6,7,5,2,8,1]=>0000000
[2,5,6,8,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,8,3,6,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,6,1,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,3,2,8,1,6,4,7]=>{{1,5},{2,3},{4,7,8},{6}}=>[5,3,2,7,1,6,8,4]=>0000000
[7,4,1,8,3,2,5,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[5,7,3,1,6,8,4,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,7,2,8,3,1,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[4,8,1,2,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,5,6,7,3,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,3,2,7,6,1,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[2,5,1,3,6,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,3,8,5,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,6,8,1,2,5,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[5,8,7,6,1,2,3,4]=>{{1,5},{2,4,6,8},{3,7}}=>[5,4,7,6,1,8,3,2]=>0000000
[2,6,3,1,8,5,4,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,2,8,5,1,3,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,6,5,2,7,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,6,2,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,4,6,8,5,1,3,2]=>{{1,3,6,7},{2,4,8},{5}}=>[3,4,6,8,5,7,1,2]=>0000000
[4,1,8,5,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,3,2,4,6,1,7]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[2,8,4,1,5,3,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[4,8,7,6,5,2,3,1]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[2,1,8,6,4,3,7,5]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[3,6,7,1,8,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,2,5,6,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,1,5,7,2,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,5,1,2,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,6,2,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,7,6,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,7,5,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,1,7,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,7,1,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,2,3,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,2,3,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,8,2,7,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,6,1,3,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,5,7,2,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,2,8,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,6,8,4,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,3,8,4,2,7,6]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[3,6,5,8,4,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,1,3,7,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,3,8,2,5,7,1]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[6,8,2,3,4,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,1,8,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,1,8,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,1,2,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,8,1,5,7,2,4]=>{{1,3,4,8},{2,6,7},{5}}=>[3,6,4,8,5,7,2,1]=>0000000
[3,5,7,8,4,6,1,2]=>{{1,3,7},{2,4,5,8},{6}}=>[3,4,7,5,8,6,1,2]=>0000000
[8,4,3,1,7,5,2,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,6,2,8,5,1,4,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,7,5,8,1,6,2,4]=>{{1,3,5},{2,7},{4,8},{6}}=>[3,7,5,8,1,6,2,4]=>0000000
[5,7,2,1,8,3,6,4]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[7,8,1,2,3,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,8,3,5,4,6,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,6,2,4,3,1,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[7,6,8,1,5,4,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,4,8,7,6,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,6,3,8,5,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[3,5,7,4,8,6,1,2]=>{{1,3,7},{2,5,8},{4},{6}}=>[3,5,7,4,8,6,1,2]=>0000000
[3,4,1,2,7,8,6,5]=>{{1,3},{2,4},{5,6,7,8}}=>[3,4,1,2,6,7,8,5]=>0001000
[6,8,4,1,2,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,1,8,2,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,5,4,7,8,1,6]=>{{1,3,5,7},{2},{4},{6,8}}=>[3,2,5,4,7,8,1,6]=>0000000
[8,4,7,6,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,2,3,8,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,5,6,7,8,1,4]=>{{1,3,5,7},{2},{4,6,8}}=>[3,2,5,6,7,8,1,4]=>0000000
[5,4,2,6,8,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,5,2,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,3,1,8,2,7,4]=>{{1,4,5,8},{2,6},{3},{7}}=>[4,6,3,5,8,2,7,1]=>0000000
[5,8,6,2,3,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,1,7,2,4,3]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[3,1,2,8,6,4,5,7]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[2,4,1,6,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,6,1,8,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,8,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,8,5,7,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,3,7,6,8,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,8,7,1,4,5,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[8,7,2,3,5,4,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,4,2,8,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,3,8,5,2,1,6]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[3,8,6,2,7,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,1,4,5,2,8,6]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[6,7,5,1,4,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,5,8,4,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,5,4,1,3,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,2,1,8,5,7,6]=>{{1,4},{2,3},{5,6,8},{7}}=>[4,3,2,1,6,8,7,5]=>0001000
[2,7,5,3,8,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,6,2,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,5,8,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,8,3,2,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,1,7,8,2,4,6,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[3,6,7,8,1,2,5,4]=>{{1,3,5,7},{2,6},{4,8}}=>[3,6,5,8,7,2,1,4]=>0000000
[6,3,7,1,8,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,7,8,1,2,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[3,7,4,8,5,2,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,3,8,1,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,6,2,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,2,6,1,4,3]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[7,3,8,6,5,1,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,8,2,7,6,5,4,1]=>{{1,2,3,8},{4,7},{5,6}}=>[2,3,8,7,6,5,4,1]=>0000000
[8,3,1,7,6,5,4,2]=>{{1,2,3,8},{4,7},{5,6}}=>[2,3,8,7,6,5,4,1]=>0000000
[6,4,1,3,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,8,6,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,6,2,3,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,7,4,5,8,1,6]=>{{1,3,7},{2},{4},{5},{6,8}}=>[3,2,7,4,5,8,1,6]=>0000000
[8,1,6,2,4,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,1,6,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,6,1,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,4,2,3,6,5]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>0000000
[6,4,1,3,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,7,6,8,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,3,5,1,8,7,4]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[2,7,1,6,8,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,3,2,6,1,7,4]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[7,8,4,1,2,5,3,6]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[7,8,2,1,6,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,3,6,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,8,5,3,1,7,4]=>{{1,2,6},{3,4,5,8},{7}}=>[2,6,4,5,8,1,7,3]=>0000000
[4,8,1,2,6,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,5,6,1,7,4,2]=>{{1,3,5},{2,8},{4,6,7}}=>[3,8,5,6,1,7,4,2]=>0000000
[3,7,8,5,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,2,7,4,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,1,7,6,3,8,5,4]=>{{1,2},{3,5,7},{4,6,8}}=>[2,1,5,6,7,8,3,4]=>0100000
[2,6,5,1,8,4,3,7]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[5,8,3,2,7,6,1,4]=>{{1,5,7},{2,4,8},{3},{6}}=>[5,4,3,8,7,6,1,2]=>0000000
[2,4,8,3,1,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,8,2,7,1,4,6]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[5,8,3,1,6,2,7,4]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[5,1,7,3,6,2,8,4]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[4,3,2,1,6,8,5,7]=>{{1,4},{2,3},{5,6,7,8}}=>[4,3,2,1,6,7,8,5]=>0001000
[2,4,1,3,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}=>[2,3,4,1,8,7,6,5]=>0001000
[6,5,3,1,7,2,8,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,3,8,5,4,1,6,7]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[7,3,6,5,2,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,5,3,8,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,3,6,2,8,4,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,5,3,6,8,2,7,1]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[5,6,3,7,4,8,2,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,5,2,6,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,8,5,4,2,3,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[4,8,1,2,5,3,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,8,7,6,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,6,5,2,4,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,3,7,8,4,1,6,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[2,5,6,8,1,7,4,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[8,6,4,1,3,2,5,7]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[8,5,3,6,2,4,1,7]=>{{1,7,8},{2,5},{3},{4,6}}=>[7,5,3,6,2,4,8,1]=>0000000
[3,7,4,5,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,8,3,5,6,2]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[6,8,2,3,1,7,5,4]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[5,1,2,3,6,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,4,7,3,8,1,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[6,3,8,2,7,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,5,7,4,8,1,6]=>{{1,3,4,5,7},{2},{6,8}}=>[3,2,4,5,7,8,1,6]=>0000000
[6,4,2,1,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,5,1,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,7,5,2,6,8,3]=>{{1,2,4,5},{3,7,8},{6}}=>[2,4,7,5,1,6,8,3]=>0000000
[7,6,2,4,5,1,8,3]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[7,6,4,2,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,4,5,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,4,2,5,1,8,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,6,2,8,3,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,5,1,7,8,4,6]=>{{1,3,4,5,7},{2},{6,8}}=>[3,2,4,5,7,8,1,6]=>0000000
[5,3,8,2,4,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,4,2,5,1,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,4,3,5,8,2,1,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,3,8,5,7,2,1]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[3,4,7,6,8,1,2,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[3,5,2,7,4,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,3,8,5,2,6,1]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[3,2,6,7,8,1,4,5]=>{{1,3,6},{2},{4,7},{5,8}}=>[3,2,6,7,8,1,4,5]=>0000000
[5,1,8,6,2,7,3,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[3,4,8,1,2,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,3,1,8,2,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,1,6,4,7,8,5]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[3,6,4,2,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,8,3,2,6,7,5,4]=>{{1},{2,4,8},{3},{5,6,7}}=>[1,4,3,8,6,7,5,2]=>1000000
[4,7,5,3,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,7,8,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,5,8,7,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,2,8,5,6,3,1]=>{{1,4,8},{2,3,7},{5},{6}}=>[4,3,7,8,5,6,2,1]=>0000000
[3,8,7,5,6,4,2,1]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[8,5,7,1,3,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,7,4,5,2,8,6]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[8,7,6,5,1,3,4,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,7,6,1,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,4,6,5,1,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,4,5,6,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,8,1,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,3,6,7,1,8,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,4,7,3,6,1,8,2]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[6,8,5,3,7,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,5,7,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,2,6,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,7,5,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,6,4,2,3,1]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[2,3,6,1,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,6,1,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,1,6,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,1,7,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,5,3,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,6,3,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,7,3,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,1,6,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,1,7,4,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,6,3,4,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,6,7,8,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,4,8,2,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,5,8,2,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,8,7,5,2,3,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,8,4,2,7,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,4,7,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,2,8,7,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,4,2,1,7,5,3]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[6,8,4,7,3,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,2,3,6,1,4]=>{{1,3,5,7},{2,4,8},{6}}=>[3,4,5,8,7,6,1,2]=>0000000
[6,8,3,7,5,2,1,4]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[6,8,1,7,3,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,5,7,1,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,5,2,7,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,1,3,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[6,5,4,3,8,7,1,2]=>{{1,6,7},{2,5,8},{3,4}}=>[6,5,4,3,8,7,1,2]=>0000000
[3,1,7,2,8,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,5,7,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,4,2,7,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,5,6,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,5,8,7,6,1,2]=>{{1,3,5,7},{2,4,8},{6}}=>[3,4,5,8,7,6,1,2]=>0000000
[3,4,6,7,8,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,3,6,7,2,1,4]=>{{1,5,7},{2,4,6,8},{3}}=>[5,4,3,6,7,8,1,2]=>0000000
[5,8,7,3,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,8,2,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,7,6,2,4,1,8]=>{{1,2,3,5,7},{4,6},{8}}=>[2,3,5,6,7,4,1,8]=>0000001
[6,4,2,7,5,8,1,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,1,8,4,2,6,5,3]=>{{1,2,5,7},{3,8},{4},{6}}=>[2,5,8,4,7,6,1,3]=>0000000
[6,5,3,2,1,8,7,4]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[6,1,2,3,5,8,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[7,1,2,3,5,8,6,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,2,3,5,7,8,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,4,1,7,3,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,5,1,2,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,3,1,5,7,4,2]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[7,5,8,6,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,5,7,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,8,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,7,6,8,2,4,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[7,3,5,1,8,2,4,6]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[6,1,2,3,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,5,3,1,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,3,5,7,8,1,6]=>{{1,2,4,5,7},{3},{6,8}}=>[2,4,3,5,7,8,1,6]=>0000000
[3,4,6,1,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,1,5,6,8,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,1,7,3,5,8,6,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,6,7,8,5,1,3,2]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[4,6,8,3,5,1,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[5,6,7,8,4,1,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[5,7,3,8,4,6,1,2]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,7,3,8,5,4,1,2]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[8,4,1,3,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,1,2,3,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,1,2,5,3,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,5,8,6,1,7,3,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[5,6,8,7,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,2,1,4,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,5,1,8,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,3,1,8,4,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,8,7,6,3,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,1,7,3,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,5,6,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,5,8,6,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,6,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,1,5,8,3,7,4,6]=>{{1,2},{3,5},{4,6,7,8}}=>[2,1,5,6,3,7,8,4]=>0100000
[1,2,3,5,8,7,4,6]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[6,1,2,7,8,4,3,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[5,1,4,8,2,7,3,6]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[3,4,1,2,8,7,5,6]=>{{1,3},{2,4},{5,6,7,8}}=>[3,4,1,2,6,7,8,5]=>0001000
[2,6,8,5,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,2,3,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,4,5,1,8,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,3,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[2,3,1,8,5,4,7,6]=>{{1,2,3},{4,6,8},{5},{7}}=>[2,3,1,6,5,8,7,4]=>0010000
[5,3,1,8,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,7,2,5,8,3,4]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[4,5,1,8,7,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,6,5,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,7,5,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,2,1,5,4,3]=>{{1,5,6},{2,4,7},{3,8}}=>[5,4,8,7,6,1,2,3]=>0000000
[8,7,5,6,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,7,8,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,4,3,2,5,6,7]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[6,5,8,3,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,8,2,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,5,8,2,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,4,6,8,1,5,7,2]=>{{1,3,5,6},{2,4,8},{7}}=>[3,4,5,8,6,1,7,2]=>0000000
[3,5,2,1,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[3,5,6,8,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,7,4,2,8,1,6]=>{{1,3,7},{2,5},{4},{6,8}}=>[3,5,7,4,2,8,1,6]=>0000000
[3,6,2,7,8,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,2,7,8,1,4,5]=>{{1,2,3,6},{4,7},{5,8}}=>[2,3,6,7,8,1,4,5]=>0000000
[3,6,7,8,1,5,2,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[3,7,8,4,5,1,6,2]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[4,1,6,3,5,7,8,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,7,3,8,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,6,1,4,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,7,5,8,2,3,1]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[6,7,4,1,8,2,3,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[2,4,7,5,8,1,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[2,3,6,5,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,3,4,8,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,3,7,5,8,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,4,5,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,6,8,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,4,6,5,8,3,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,6,4,8,5,7,3,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,4,1,7,8,2,3,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[5,7,1,6,2,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,5,1,6,8,4,2]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[6,3,4,5,8,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,6,1,2,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,1,6,7,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,5,8,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,1,8,6,2,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[7,3,5,1,8,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,3,8,2,1,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[5,7,3,2,8,6,1,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,7,3,2,8,5,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[1,6,7,8,5,2,3,4]=>{{1},{2,6},{3,7},{4,8},{5}}=>[1,6,7,8,5,2,3,4]=>1000000
[6,2,3,7,8,1,4,5]=>{{1,6},{2},{3},{4,7},{5,8}}=>[6,2,3,7,8,1,4,5]=>0000000
[4,6,2,8,5,1,7,3]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[6,7,2,8,5,4,1,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,1,3,2,8,4,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,1,2,3,7,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,6,3,8,2,4,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[8,1,6,7,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,6,3,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,3,2,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,1,3,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,7,3,1,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,2,1,8,4,3,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[8,5,2,3,6,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,7,1,4,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,3,8,2,1,7,6]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[5,8,7,3,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,7,1,6,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,1,5,7,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,6,1,4,3,5,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,7,6,1,3,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,1,4,5,6,3,2]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>0000000
[3,7,2,8,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,7,6,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,7,6,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,4,5,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,1,5,3,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,6,3,4,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,3,2,1,8,6,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,4,8,5,6,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,2,1,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,8,7,4,2,1,6]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[7,4,2,1,6,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,5,8,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,7,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,2,1,7,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,4,5,2,1,7]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[7,3,6,8,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,8,4,5,6,2,1]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>0000000
[7,6,1,2,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,1,2,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,1,2,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,1,2,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,4,1,8,2,3,6]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[4,1,2,8,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,1,6,2,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,3,1,8,2,4,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[1,2,3,7,8,6,4,5]=>{{1},{2},{3},{4,7},{5,8},{6}}=>[1,2,3,7,8,6,4,5]=>1110000
[4,5,1,7,6,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,8,2,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,1,6,2,7,8,4]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[5,4,8,7,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,3,8,7,2,1,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,3,8,7,5,2,1,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,7,3,8,4,1,6,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,3,8,1,5,7,2]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[4,6,7,3,8,1,2,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[4,6,7,8,1,5,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[4,6,8,3,1,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,7,3,8,5,1,6,2]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[4,7,3,8,1,6,5,2]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[1,8,4,2,7,3,5,6]=>{{1},{2,3,4,6,8},{5,7}}=>[1,3,4,6,7,8,5,2]=>1000000
[7,4,1,2,6,8,3,5]=>{{1,3,7},{2,4},{5,6,8}}=>[3,4,7,2,6,8,1,5]=>0000000
[8,7,1,2,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,2,8,3,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,8,1,3,4,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,8,2,5,4,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,1,7,5,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,5,1,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,1,3,4,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,1,8,7,5,4,6]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[3,2,1,8,7,4,6,5]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[3,2,1,8,7,4,5,6]=>{{1,3},{2},{4,6,8},{5,7}}=>[3,2,1,6,7,8,5,4]=>0010000
[5,3,8,7,6,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,8,7,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,2,8,5,3,7,1]=>{{1,4,8},{2,3,6},{5},{7}}=>[4,3,6,8,5,2,7,1]=>0000000
[4,6,2,7,1,8,5,3]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[6,3,7,4,5,2,8,1]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[4,7,6,8,3,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,7,8,3,2,1,5]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[3,5,6,8,7,2,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[2,5,4,8,6,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,7,2,1,6,8,3]=>{{1,2,4,5},{3,7,8},{6}}=>[2,4,7,5,1,6,8,3]=>0000000
[6,3,7,8,2,5,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[6,7,4,8,2,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,7,5,6,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,4,8,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,6,3,8,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,5,8,7,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,8,3,2,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,2,8,7,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,2,8,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,2,7,5,4,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,2,8,3,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,7,6,8,3,2,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[8,1,7,3,5,4,2,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,1,6,3,4,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,3,5,2,6,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,8,5,7,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,2,3,4,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,6,7,1,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,6,1,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,6,8,2,5,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[8,6,2,3,1,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,8,7,1,2,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,4,8,7,5,1,2]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[7,3,5,6,8,1,4,2]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[4,3,1,2,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[7,4,6,5,8,3,2,1]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[2,3,4,1,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[4,2,6,5,1,8,7,3]=>{{1,4,5},{2},{3,6,8},{7}}=>[4,2,6,5,1,8,7,3]=>0000000
[8,7,4,3,6,1,5,2]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[7,8,4,2,1,5,6,3]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[7,8,2,3,6,1,5,4]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[6,8,2,7,3,4,1,5]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[5,1,4,3,7,2,8,6]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[2,6,4,3,1,8,5,7]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[7,8,2,1,5,4,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,3,4,6,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,1,6,3,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,7,5,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,7,5,8,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,4,5,6,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,8,7,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,7,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,7,5,8,6,1,2]=>{{1,3,7},{2,4,5,8},{6}}=>[3,4,7,5,8,6,1,2]=>0000000
[2,7,5,6,8,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,3,4,6,5,1,2]=>{{1,7},{2,8},{3},{4},{5,6}}=>[7,8,3,4,6,5,1,2]=>0000000
[2,1,7,6,8,4,5,3]=>{{1,2},{3,5,7,8},{4,6}}=>[2,1,5,6,7,4,8,3]=>0100000
[3,5,4,7,6,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,5,3,7,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,8,5,7,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,8,7,3,2,1,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[6,1,4,3,2,7,8,5]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[2,5,4,3,8,1,6,7]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[7,6,5,8,1,2,4,3]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[6,3,4,5,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,3,4,5,8,1,6,2]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[4,1,3,7,6,8,5,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,5,7,8,1,4,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[2,8,3,1,7,5,4,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,8,3,7,1,4,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,8,2,7,5,1,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,8,7,6,2,1,3,4]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[6,4,8,3,7,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,8,2,5,7,4,1]=>{{1,3,8},{2,4,6,7},{5}}=>[3,4,8,6,5,7,2,1]=>0000000
[4,5,6,2,7,3,8,1]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,7,5,6,2,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,5,8,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,4,1,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,6,3,4,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,2,3,5,7,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,1,2,3,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[2,8,1,6,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,2,3,5,4,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[4,8,5,2,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,8,6,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,2,8,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,1,3,2,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[3,2,7,4,1,6,5,8]=>{{1,3,5,7},{2},{4},{6},{8}}=>[3,2,5,4,7,6,1,8]=>0000001
[5,2,8,1,4,3,7,6]=>{{1,4,5},{2},{3,6,8},{7}}=>[4,2,6,5,1,8,7,3]=>0000000
[5,8,1,3,4,7,2,6]=>{{1,3,4,5},{2,6,7,8}}=>[3,6,4,5,1,7,8,2]=>0000000
[8,3,2,7,6,1,4,5]=>{{1,5,6,8},{2,3},{4,7}}=>[5,3,2,7,6,8,4,1]=>0000000
[3,8,2,7,6,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,5,2,8,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,6,5,1,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,8,5,4,7,3,1]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[2,7,4,6,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,7,8,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,7,2,6,1,8,3]=>{{1,5,6},{2,4},{3,7,8}}=>[5,4,7,2,6,1,8,3]=>0000000
[4,2,7,5,6,1,8,3]=>{{1,4,5,6},{2},{3,7,8}}=>[4,2,7,5,6,1,8,3]=>0000000
[2,6,4,3,7,5,8,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[3,6,8,5,4,7,1,2]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[2,5,4,1,7,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,5,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[1,6,3,2,5,8,7,4]=>{{1},{2,4,6,8},{3},{5},{7}}=>[1,4,3,6,5,8,7,2]=>1000000
[7,1,3,8,4,6,5,2]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[1,8,6,7,3,4,5,2]=>{{1},{2,8},{3,4,5,6,7}}=>[1,8,4,5,6,7,3,2]=>1000000
[4,5,7,2,3,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,7,3,8,2,5,1]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[3,5,1,7,4,8,2,6]=>{{1,3},{2,4,5,7},{6,8}}=>[3,4,1,5,7,8,2,6]=>0000000
[4,6,7,3,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,8,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,7,2,8,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,2,7,8,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,2,7,8,4,1,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[4,6,7,2,8,5,3,1]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[4,6,7,2,8,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,8,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,8,2,4,3,1]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[8,4,5,1,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,4,1,7,2,3,5]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[3,7,1,5,2,8,4,6]=>{{1,3},{2,4,5,7},{6,8}}=>[3,4,1,5,7,8,2,6]=>0000000
[6,8,4,1,7,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,6,1,7,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,6,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,1,6,2,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[7,4,8,1,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,7,6,1,2,3,4]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[6,8,7,5,1,2,3,4]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[6,4,7,3,8,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,2,7,6,1,8,3]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[5,4,3,7,6,8,1,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,4,3,7,8,6,1,2]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[5,4,3,8,6,7,1,2]=>{{1,5,6,7},{2,4,8},{3}}=>[5,4,3,8,6,7,1,2]=>0000000
[5,4,3,6,8,7,1,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,4,2,6,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,2,6,1,7,4,8]=>{{1,5},{2,3},{4,6,7},{8}}=>[5,3,2,6,1,7,4,8]=>0000001
[5,3,2,6,1,7,8,4]=>{{1,5},{2,3},{4,6,7,8}}=>[5,3,2,6,1,7,8,4]=>0000000
[5,3,2,6,1,8,7,4]=>{{1,5},{2,3},{4,6,8},{7}}=>[5,3,2,6,1,8,7,4]=>0000000
[5,4,2,6,8,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,4,8,2,5,1,7,3]=>{{1,6},{2,4},{3,8},{5},{7}}=>[6,4,8,2,5,1,7,3]=>0000000
[5,4,2,8,6,1,3,7]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[5,3,2,6,1,8,4,7]=>{{1,5},{2,3},{4,6,7,8}}=>[5,3,2,6,1,7,8,4]=>0000000
[6,3,8,2,1,5,4,7]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[7,8,3,2,1,5,4,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,3,2,1,5,6,4]=>{{1,5,6,7},{2,4,8},{3}}=>[5,4,3,8,6,7,1,2]=>0000000
[5,3,2,8,1,6,7,4]=>{{1,5},{2,3},{4,8},{6},{7}}=>[5,3,2,8,1,6,7,4]=>0000000
[5,4,2,7,8,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,2,7,1,8,6,4]=>{{1,5},{2,3},{4,6,7,8}}=>[5,3,2,6,1,7,8,4]=>0000000
[5,3,2,7,1,6,4,8]=>{{1,5},{2,3},{4,7},{6},{8}}=>[5,3,2,7,1,6,4,8]=>0000001
[6,3,7,2,1,5,8,4]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[6,3,7,2,1,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,2,1,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,2,7,1,4,8,6]=>{{1,5},{2,3},{4,6,7,8}}=>[5,3,2,6,1,7,8,4]=>0000000
[5,4,2,8,7,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,4,2,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,3,2,1,6,4,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,3,8,2,1,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,2,8,1,7,4,6]=>{{1,5},{2,3},{4,6,7,8}}=>[5,3,2,6,1,7,8,4]=>0000000
[4,3,2,1,8,7,5,6]=>{{1,4},{2,3},{5,6,7,8}}=>[4,3,2,1,6,7,8,5]=>0001000
[4,3,2,1,7,5,8,6]=>{{1,4},{2,3},{5,6,7,8}}=>[4,3,2,1,6,7,8,5]=>0001000
[4,3,2,1,7,5,6,8]=>{{1,4},{2,3},{5,6,7},{8}}=>[4,3,2,1,6,7,5,8]=>0001001
[5,3,2,8,1,4,7,6]=>{{1,5},{2,3},{4,6,8},{7}}=>[5,3,2,6,1,8,7,4]=>0000000
[6,3,8,2,1,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,8,3,2,1,4,6,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,3,2,1,8,5,6,7]=>{{1,4},{2,3},{5,6,7,8}}=>[4,3,2,1,6,7,8,5]=>0001000
[7,8,5,6,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,4,1,6,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,6,8,3,2,7,5,4]=>{{1},{2,5,6,7},{3,4,8}}=>[1,5,4,8,6,7,2,3]=>1000000
[7,8,3,1,2,6,5,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[7,8,2,3,1,6,5,4]=>{{1,5,7},{2,3,4,8},{6}}=>[5,3,4,8,7,6,1,2]=>0000000
[7,8,1,2,3,6,5,4]=>{{1,3,5,7},{2,4,8},{6}}=>[3,4,5,8,7,6,1,2]=>0000000
[1,5,2,8,3,7,6,4]=>{{1},{2,3,5},{4,8},{6,7}}=>[1,3,5,8,2,7,6,4]=>1000000
[5,1,2,8,3,7,6,4]=>{{1,2,3,5},{4,8},{6,7}}=>[2,3,5,8,1,7,6,4]=>0000000
[5,2,1,8,3,7,6,4]=>{{1,3,5},{2},{4,8},{6,7}}=>[3,2,5,8,1,7,6,4]=>0000000
[6,2,8,4,7,1,5,3]=>{{1,6},{2},{3,8},{4},{5,7}}=>[6,2,8,4,7,1,5,3]=>0000000
[2,5,1,8,3,7,6,4]=>{{1,2,3,5},{4,8},{6,7}}=>[2,3,5,8,1,7,6,4]=>0000000
[1,2,5,8,3,7,6,4]=>{{1},{2},{3,5},{4,8},{6,7}}=>[1,2,5,8,3,7,6,4]=>1100000
[2,5,3,8,1,7,6,4]=>{{1,2,5},{3},{4,8},{6,7}}=>[2,5,3,8,1,7,6,4]=>0000000
[5,3,4,8,7,6,1,2]=>{{1,5,7},{2,3,4,8},{6}}=>[5,3,4,8,7,6,1,2]=>0000000
[5,2,3,8,1,7,6,4]=>{{1,5},{2},{3},{4,8},{6,7}}=>[5,2,3,8,1,7,6,4]=>0000000
[4,1,2,3,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}=>[2,3,4,1,8,7,6,5]=>0001000
[1,4,2,3,8,7,6,5]=>{{1},{2,3,4},{5,8},{6,7}}=>[1,3,4,2,8,7,6,5]=>1001000
[4,1,3,2,8,7,6,5]=>{{1,2,4},{3},{5,8},{6,7}}=>[2,4,3,1,8,7,6,5]=>0001000
[6,3,8,1,2,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,1,8,2,7,6,4]=>{{1,2,3,5},{4,8},{6,7}}=>[2,3,5,8,1,7,6,4]=>0000000
[5,1,3,8,2,7,6,4]=>{{1,2,5},{3},{4,8},{6,7}}=>[2,5,3,8,1,7,6,4]=>0000000
[1,5,3,8,2,7,6,4]=>{{1},{2,5},{3},{4,8},{6,7}}=>[1,5,3,8,2,7,6,4]=>1000000
[1,5,4,8,7,2,6,3]=>{{1},{2,5,6,7},{3,4,8}}=>[1,5,4,8,6,7,2,3]=>1000000
[5,4,1,8,7,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,8,7,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,5,8,7,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,3,5,8,2,7,6,4]=>{{1},{2,3,5},{4,8},{6,7}}=>[1,3,5,8,2,7,6,4]=>1000000
[3,1,5,8,2,7,6,4]=>{{1,2,3,5},{4,8},{6,7}}=>[2,3,5,8,1,7,6,4]=>0000000
[3,6,8,2,1,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,8,3,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,3,8,7,6,1,2]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[3,5,2,8,1,7,6,4]=>{{1,2,3,5},{4,8},{6,7}}=>[2,3,5,8,1,7,6,4]=>0000000
[3,1,4,2,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}=>[2,3,4,1,8,7,6,5]=>0001000
[3,2,5,8,1,7,6,4]=>{{1,3,5},{2},{4,8},{6,7}}=>[3,2,5,8,1,7,6,4]=>0000000
[2,4,5,8,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,5,8,1,7,6,4]=>{{1,2,3,5},{4,8},{6,7}}=>[2,3,5,8,1,7,6,4]=>0000000
[8,1,4,3,7,2,6,5]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[8,2,6,1,5,3,7,4]=>{{1,4,8},{2},{3,6},{5},{7}}=>[4,2,6,8,5,3,7,1]=>0000000
[7,2,6,1,5,3,8,4]=>{{1,4,7,8},{2},{3,6},{5}}=>[4,2,6,7,5,3,8,1]=>0000000
[8,3,7,1,4,2,6,5]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[8,3,7,1,5,2,6,4]=>{{1,4,8},{2,3,6,7},{5}}=>[4,3,6,8,5,7,2,1]=>0000000
[7,3,8,1,5,2,6,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,2,8,3,7,1,5,4]=>{{1,6},{2},{3,4,8},{5,7}}=>[6,2,4,8,7,1,5,3]=>0000000
[4,1,8,3,7,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,7,3,8,2,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[5,1,7,3,8,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,8,2,6,1,5,4]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[5,3,6,2,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,2,5,8,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,1,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,1,6,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,8,3,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,5,8,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,3,8,1,5,2]=>{{1,6},{2,5,7,8},{3,4}}=>[6,5,4,3,7,1,8,2]=>0000000
[6,4,7,1,8,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,3,1,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,2,8,4,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,3,2,1,8,4]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[6,7,4,2,8,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,7,2,1,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,7,8,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,7,8,5,2,1,4]=>{{1,3,7},{2,6},{4,8},{5}}=>[3,6,7,8,5,2,1,4]=>0000000
[6,4,7,8,2,5,3,1]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[5,3,7,8,1,6,2,4]=>{{1,5},{2,3,7},{4,8},{6}}=>[5,3,7,8,1,6,2,4]=>0000000
[6,4,1,7,8,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,1,7,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,1,8,4,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[8,5,3,6,4,1,2,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,4,1,5,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,7,2,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,7,2,8,1,5]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[1,4,3,6,7,2,8,5]=>{{1},{2,4,6},{3},{5,7,8}}=>[1,4,3,6,7,2,8,5]=>1000000
[4,5,3,7,1,8,2,6]=>{{1,2,4,5,7},{3},{6,8}}=>[2,4,3,5,7,8,1,6]=>0000000
[7,4,5,8,3,6,1,2]=>{{1,7},{2,4,8},{3,5},{6}}=>[7,4,5,8,3,6,1,2]=>0000000
[4,3,6,7,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,5,6,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,1,7,8,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,7,1,4,8,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[1,5,3,6,7,8,2,4]=>{{1},{2,5,7},{3},{4,6,8}}=>[1,5,3,6,7,8,2,4]=>1000000
[4,5,2,7,8,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,2,6,7,8,3,1,5]=>{{1,4,7},{2},{3,6},{5,8}}=>[4,2,6,7,8,3,1,5]=>0000000
[3,6,2,7,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,4,2,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,4,2,1,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,2,7,1,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,3,8,2,5,4,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,7,8,5,2,3,1]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[4,6,1,7,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,2,6,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,3,8,5,1,4,2]=>{{1,6},{2,4,7,8},{3},{5}}=>[6,4,3,7,5,1,8,2]=>0000000
[6,4,7,8,5,3,1,2]=>{{1,3,6,7},{2,4,8},{5}}=>[3,4,6,8,5,7,1,2]=>0000000
[3,1,2,6,5,8,7,4]=>{{1,2,3},{4,6,8},{5},{7}}=>[2,3,1,6,5,8,7,4]=>0010000
[4,5,1,2,3,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[4,6,1,2,3,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[1,6,5,3,4,8,7,2]=>{{1},{2,6,8},{3,4,5},{7}}=>[1,6,4,5,3,8,7,2]=>1000000
[6,1,5,2,4,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,5,1,2,3,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,1,2,3,8,7,6]=>{{1,3,5},{2,4},{6,8},{7}}=>[3,4,5,2,1,8,7,6]=>0000100
[8,4,1,7,2,3,5,6]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[8,6,1,7,2,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,6,7,2,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,1,8,2,3,5,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[3,1,2,7,8,5,6,4]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[3,1,8,7,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,7,6,2,4,5,8]=>{{1,2,3,5,7},{4,6},{8}}=>[2,3,5,6,7,4,1,8]=>0000001
[5,8,1,2,7,3,6,4]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[5,8,6,1,2,3,4,7]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[7,8,1,6,2,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,8,4,5,1,2,6]=>{{1,3,6,8},{2,7},{4},{5}}=>[3,7,6,4,5,8,2,1]=>0000000
[5,6,3,8,1,7,2,4]=>{{1,5},{2,6,7},{3},{4,8}}=>[5,6,3,8,1,7,2,4]=>0000000
[7,6,1,4,5,8,3,2]=>{{1,3,7},{2,6,8},{4},{5}}=>[3,6,7,4,5,8,1,2]=>0000000
[3,7,6,4,5,8,2,1]=>{{1,3,6,8},{2,7},{4},{5}}=>[3,7,6,4,5,8,2,1]=>0000000
[2,5,8,4,7,6,1,3]=>{{1,2,5,7},{3,8},{4},{6}}=>[2,5,8,4,7,6,1,3]=>0000000
[6,5,3,8,4,1,7,2]=>{{1,6},{2,4,5,8},{3},{7}}=>[6,4,3,5,8,1,7,2]=>0000000
[5,6,3,8,4,2,7,1]=>{{1,4,5,8},{2,6},{3},{7}}=>[4,6,3,5,8,2,7,1]=>0000000
[8,6,3,1,4,2,7,5]=>{{1,4,5,8},{2,6},{3},{7}}=>[4,6,3,5,8,2,7,1]=>0000000
[8,6,3,5,1,2,7,4]=>{{1,4,5,8},{2,6},{3},{7}}=>[4,6,3,5,8,2,7,1]=>0000000
[5,8,2,4,7,6,1,3]=>{{1,5,7},{2,3,8},{4},{6}}=>[5,3,8,4,7,6,1,2]=>0000000
[6,8,3,5,2,1,7,4]=>{{1,6},{2,4,5,8},{3},{7}}=>[6,4,3,5,8,1,7,2]=>0000000
[3,8,7,4,5,2,1,6]=>{{1,3,7},{2,6,8},{4},{5}}=>[3,6,7,4,5,8,1,2]=>0000000
[4,6,3,5,8,2,7,1]=>{{1,4,5,8},{2,6},{3},{7}}=>[4,6,3,5,8,2,7,1]=>0000000
[5,4,2,3,7,6,1,8]=>{{1,5,7},{2,3,4},{6},{8}}=>[5,3,4,2,7,6,1,8]=>0000001
[3,2,7,6,4,5,1,8]=>{{1,3,7},{2},{4,5,6},{8}}=>[3,2,7,5,6,4,1,8]=>0000001
[7,1,6,8,2,3,4,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[3,2,1,7,8,4,5,6]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[8,5,7,2,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,5,4,1,8,6,7]=>{{1,3,5},{2},{4},{6,7,8}}=>[3,2,5,4,1,7,8,6]=>0000100
[7,4,2,1,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,4,2,8,7,3,5,6]=>{{1},{2,3,4,6,8},{5,7}}=>[1,3,4,6,7,8,5,2]=>1000000
[8,5,1,2,7,3,4,6]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[4,8,2,1,7,3,5,6]=>{{1,4},{2,3,6,8},{5,7}}=>[4,3,6,1,7,8,5,2]=>0000000
[3,5,7,6,1,4,2,8]=>{{1,2,3,5,7},{4,6},{8}}=>[2,3,5,6,7,4,1,8]=>0000001
[2,8,5,3,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,5,3,4,7,1,6]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[6,5,2,8,3,1,7,4]=>{{1,6},{2,3,5},{4,8},{7}}=>[6,3,5,8,2,1,7,4]=>0000000
[6,5,8,2,1,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,5,6,2,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,1,6,7,4,3,8,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[5,1,2,6,4,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,1,2,8,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,1,6,8,7,3,4,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[3,1,4,8,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,5,2,8,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,1,2,5,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,1,6,7,8,3,5,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,1,2,6,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,1,2,5,6,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,4,2,7,1,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,2,5,1,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,3,6,1,7,2,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,7,5,1,2,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,8,5,2,6,1,3]=>{{1,7},{2,4,5},{3,8},{6}}=>[7,4,8,5,2,6,1,3]=>0000000
[5,8,2,6,3,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,6,2,7,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,1,2,7,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,1,8,5,2,3,4]=>{{1,3,7},{2,6},{4,8},{5}}=>[3,6,7,8,5,2,1,4]=>0000000
[5,7,2,8,1,6,3,4]=>{{1,5},{2,3,7},{4,8},{6}}=>[5,3,7,8,1,6,2,4]=>0000000
[3,6,8,2,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,1,6,2,3,4]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[3,8,7,6,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,7,6,1,2,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[5,7,3,8,1,2,6,4]=>{{1,5},{2,6,7},{3},{4,8}}=>[5,6,3,8,1,7,2,4]=>0000000
[7,5,1,4,8,6,3,2]=>{{1,3,7},{2,5,8},{4},{6}}=>[3,5,7,4,8,6,1,2]=>0000000
[7,5,3,6,2,4,8,1]=>{{1,7,8},{2,5},{3},{4,6}}=>[7,5,3,6,2,4,8,1]=>0000000
[6,7,3,5,2,4,8,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,7,6,2,4,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,2,1,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,2,1,8,3,4,6]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[1,6,3,2,8,4,5,7]=>{{1},{2,4,6},{3},{5,7,8}}=>[1,4,3,6,7,2,8,5]=>1000000
[7,8,5,2,3,6,1,4]=>{{1,7},{2,4,8},{3,5},{6}}=>[7,4,5,8,3,6,1,2]=>0000000
[6,8,2,1,7,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,1,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,6,1,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,2,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,1,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,2,6,1,8,3,4,5]=>{{1,4,7},{2},{3,6},{5,8}}=>[4,2,6,7,8,3,1,5]=>0000000
[7,3,1,5,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,1,3,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,3,7,6,1,2,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,3,8,7,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,8,7,6,1,2,3]=>{{1,5,6},{2,4,7},{3,8}}=>[5,4,8,7,6,1,2,3]=>0000000
[6,8,3,7,5,1,2,4]=>{{1,6},{2,4,7,8},{3},{5}}=>[6,4,3,7,5,1,8,2]=>0000000
[7,8,6,2,5,1,3,4]=>{{1,3,6,7},{2,4,8},{5}}=>[3,4,6,8,5,7,1,2]=>0000000
[8,1,5,3,6,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,4,3,2,7,5,6]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[8,1,5,3,6,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,4,8,3,2,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,3,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,3,8,2,5,1,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,3,1,2,7,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,3,8,2,7,5,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,5,3,8,7,2,4,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,5,1,3,8,2,4,6]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[7,5,8,4,1,6,2,3]=>{{1,2,5,7},{3,8},{4},{6}}=>[2,5,8,4,7,6,1,3]=>0000000
[6,5,4,7,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,3,8,5,1,2,7]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[5,6,8,3,4,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,8,3,4,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,7,8,1,5,2,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,7,8,1,3,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,1,5,3,4,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,7,8,1,4,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,3,8,1,5,6,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,7,3,8,1,2,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,6,8,3,2,1,4,7]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[6,7,8,1,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,1,2,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,5,1,7,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,2,1,6,8,4,3]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[4,7,5,6,1,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,5,3,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,3,1,7,6,8,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[4,6,1,2,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,1,5,8,2,3,4]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[2,7,6,1,5,8,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,6,2,1,5,8,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,5,2,7,4,8,3]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[8,4,2,6,7,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,4,2,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,3,2,7,6,8,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[2,8,3,5,7,6,1,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[8,3,5,7,6,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,7,1,5,3,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,8,2,7,1,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,2,4,8,7,1,5,3]=>{{1,6},{2},{3,4,8},{5,7}}=>[6,2,4,8,7,1,5,3]=>0000000
[1,6,8,3,7,4,5,2]=>{{1},{2,3,4,6,8},{5,7}}=>[1,3,4,6,7,8,5,2]=>1000000
[6,8,7,2,3,5,1,4]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[8,5,7,2,3,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,8,7,5,3,4,6,2]=>{{1},{2,8},{3,4,5,6,7}}=>[1,8,4,5,6,7,3,2]=>1000000
[8,7,6,1,2,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,6,1,4,2,3,5]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[8,5,3,7,1,2,6,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,2,8,1,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,5,7,2,1,6,3]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[8,7,6,3,1,4,2,5]=>{{1,5,8},{2,7},{3,4,6}}=>[5,7,4,6,8,3,2,1]=>0000000
[8,5,3,2,7,1,6,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[1,8,7,3,4,5,6,2]=>{{1},{2,8},{3,4,5,6,7}}=>[1,8,4,5,6,7,3,2]=>1000000
[8,5,2,3,7,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,4,2,1,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,4,1,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,2,5,1,7,6,4]=>{{1,4,5,8},{2,3},{6,7}}=>[4,3,2,5,8,7,6,1]=>0000000
[8,5,4,3,1,7,2,6]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[8,5,4,1,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,4,2,6,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,7,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,7,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,6,5,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,6,5,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,4,1,5,2,8,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,1,7,3,5,2,8,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,5,7,3,4,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,3,5,1,6,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,1,7,3,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,6,2,5,1,8,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,5,6,2,3,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,3,8,5,6,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,6,2,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,1,6,2,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,4,5,1,6,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,1,8,5,6,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,1,8,5,6,3,7,4]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[5,3,8,7,6,1,2,4]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[8,3,4,6,5,1,2,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,5,8,7,6,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,4,6,2,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,3,2,7,5,4,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,8,1,2,7,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,2,3,7,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,1,7,2,5,3,6]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[3,1,4,8,7,6,5,2]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[2,8,1,3,7,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,4,3,6,8,2,5,7]=>{{1},{2,4,6},{3},{5,7,8}}=>[1,4,3,6,7,2,8,5]=>1000000
[4,1,2,6,3,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,1,3,5,2,8,4,6]=>{{1,2,4,5,7},{3},{6,8}}=>[2,4,3,5,7,8,1,6]=>0000000
[7,3,1,6,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,8,3,2,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,3,1,7,2,4,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,7,1,6,2,4,3,8]=>{{1,2,3,5,7},{4,6},{8}}=>[2,3,5,6,7,4,1,8]=>0000001
[7,1,4,5,3,8,6,2]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[6,3,5,8,2,1,7,4]=>{{1,6},{2,3,5},{4,8},{7}}=>[6,3,5,8,2,1,7,4]=>0000000
[5,4,8,6,3,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,1,8,2,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,3,8,5,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,3,8,6,1,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,6,7,1,3,5,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[2,3,8,6,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,6,1,7,3,4,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[2,3,8,1,6,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,3,8,1,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,2,6,1,4,8,7,3]=>{{1,4,5},{2},{3,6,8},{7}}=>[4,2,6,5,1,8,7,3]=>0000000
[5,6,2,1,3,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,6,1,3,2,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,6,3,1,2,8,7,4]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[5,7,3,2,8,1,6,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,1,7,8,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,2,8,1,3,5,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[6,7,2,8,3,5,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[6,1,7,8,2,5,4,3]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[6,7,8,2,4,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,7,8,5,4,2,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,6,1,8,4,7,3,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[3,7,2,6,1,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,1,6,2,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,2,6,1,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,3,6,1,8,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,7,5,1,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,6,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,2,6,4,5,3,7]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[8,1,2,5,6,4,3,7]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[4,1,5,8,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,1,7,6,3,4,8,5]=>{{1,2},{3,5,7,8},{4,6}}=>[2,1,5,6,7,4,8,3]=>0100000
[5,3,7,1,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,7,2,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,2,3,7,8,5,6,4]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[5,7,8,4,2,6,1,3]=>{{1,2,5,7},{3,8},{4},{6}}=>[2,5,8,4,7,6,1,3]=>0000000
[8,6,3,7,2,1,5,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,6,3,8,2,1,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,6,4,8,3,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,6,4,7,3,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,3,2,8,1,6,4]=>{{1,6,7},{2,4,5,8},{3}}=>[6,4,3,5,8,7,1,2]=>0000000
[6,5,4,2,7,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,4,2,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,3,7,2,1,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,6,4,7,2,8,1,5]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[3,5,4,2,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,5,3,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,7,1,3,2,5,8]=>{{1,4},{2,6},{3,5,7},{8}}=>[4,6,5,1,7,2,3,8]=>0000001
[5,2,1,4,3,7,8,6]=>{{1,3,5},{2},{4},{6,7,8}}=>[3,2,5,4,1,7,8,6]=>0000100
[4,6,5,1,7,2,3,8]=>{{1,4},{2,6},{3,5,7},{8}}=>[4,6,5,1,7,2,3,8]=>0000001
[2,4,1,5,3,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[3,4,5,1,2,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[3,5,6,2,7,8,4,1]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[2,5,8,6,7,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,1,6,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,1,6,7,4,3,8]=>{{1,2,3,5,7},{4,6},{8}}=>[2,3,5,6,7,4,1,8]=>0000001
[3,4,6,8,1,7,5,2]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[4,5,6,7,1,3,8,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[6,1,5,8,3,2,4,7]=>{{1,2,6},{3,5},{4,7,8}}=>[2,6,5,7,3,1,8,4]=>0000000
[3,6,8,2,4,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,5,7,8,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,6,1,8,3,4,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[6,1,5,8,7,3,2,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[8,7,3,2,4,6,1,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[3,7,6,5,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,1,7,8,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,1,8,4,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,2,3,8,5,1,6]=>{{1,7},{2,3,4},{5,6,8}}=>[7,3,4,2,6,8,1,5]=>0000000
[8,6,1,5,7,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,6,1,7,3,4,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[3,6,8,5,1,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,3,7,5,1,8,2]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[5,4,7,8,3,1,6,2]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[4,3,7,5,1,8,6,2]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[2,4,1,7,5,8,6,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,4,1,7,5,3,8,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,6,4,1,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,3,2,6,1,5,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,2,1,6,8,5,4,7]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[4,8,3,2,6,7,1,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,3,8,2,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,2,1,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,8,2,1,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,3,7,2,1,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,3,7,2,8,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,2,8,1,4,7,5]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[4,8,3,2,1,5,6,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,3,8,2,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,7,2,4,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,5,1,4,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,7,3,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,8,6,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,2,8,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,6,1,8,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,4,6,1,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,3,1,8,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,3,6,8,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,7,8,4,2,5,1]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[7,6,1,8,4,2,5,3]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[2,8,3,7,1,6,5,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[2,8,4,5,3,1,6,7]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[4,3,1,2,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000
[2,7,6,8,4,3,5,1]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,6,8,5,1,3,2,7]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[2,7,3,8,4,6,5,1]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[7,3,2,8,5,4,6,1]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[2,8,1,5,3,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,3,5,1,4,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,6,2,8,4,3,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[7,6,1,3,2,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,1,3,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,1,2,8,4,3,6,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[8,3,7,1,5,2,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,1,2,8,6,4,3,5]=>{{1,2,3,7},{4,5,6,8}}=>[2,3,7,5,6,8,1,4]=>0000000
[2,8,1,7,6,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,2,5,1,8,3,7]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[4,5,1,8,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,2,7,3,8,1,5]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[5,6,2,7,3,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,2,8,4,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,2,8,3,7,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[4,6,2,8,3,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,3,5,2,4,1,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,8,2,4,5,7,3,1]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[8,3,7,4,5,2,1,6]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[6,3,8,4,5,7,2,1]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[4,8,3,6,1,2,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[5,8,3,6,2,1,7,4]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[6,8,3,5,1,7,2,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,5,3,8,6,1,7,2]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[2,5,7,3,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,3,7,6,1,5,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,7,2,3,5,4,8,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,4,7,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,4,7,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,1,3,5,8,4,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,5,7,1,6,8,4,2]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[6,7,2,8,1,5,4,3]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[8,3,1,2,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[6,7,1,8,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,1,5,8,3,6,4]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[2,6,5,1,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,6,1,8,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,1,8,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,4,6,1,2,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,3,1,5,8,2,6,4]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[8,1,3,5,7,2,6,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,1,2,5,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,1,3,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,6,7,2,3,5,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,7,1,2,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,3,1,4,8,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[3,6,2,1,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,5,2,1,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,3,1,2,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,6,3,5,8,7,1]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,4,1,6,5,8,3,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,4,1,6,5,8,7,3]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,6,4,3,8,7,5,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[4,2,6,8,5,3,7,1]=>{{1,4,8},{2},{3,6},{5},{7}}=>[4,2,6,8,5,3,7,1]=>0000000
[2,4,6,8,1,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,4,1,6,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,4,6,8,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,6,3,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,4,3,6,8,5,7,1]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[2,4,3,6,8,5,1,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,2,8,5,7,1,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,6,4,1,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,6,3,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,7,3,4,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,6,3,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,1,3,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,2,1,7,3,4,6]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[5,7,2,1,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,1,3,8,2,4,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[8,5,1,3,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,4,8,7,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,2,1,5,4,8,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,8,2,1,5,4,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[8,3,2,1,5,4,6,7]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[3,8,2,1,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,8,2,1,4,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,2,1,5,7,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,8,2,5,1,7,3,6]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[4,3,6,8,7,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,8,5,4,2,6,7]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[6,3,7,5,4,8,1,2]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[7,8,3,1,4,2,6,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,1,7,8,4,3,2,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[6,1,2,5,4,7,8,3]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[4,2,8,5,1,3,7,6]=>{{1,4,5},{2},{3,6,8},{7}}=>[4,2,6,5,1,8,7,3]=>0000000
[4,3,6,8,1,7,2,5]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[4,6,7,2,5,8,1,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,6,3,2,7,1,8,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,8,4,3,2,1,5,7]=>{{1,6},{2,5,7,8},{3,4}}=>[6,5,4,3,7,1,8,2]=>0000000
[8,4,6,3,2,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,7,2,8,1,4,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[2,4,1,7,8,3,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[4,8,7,3,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,5,2,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,7,6,5,1,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,5,1,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,4,8,5,7,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,4,3,5,8,7,2,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,3,5,8,7,1,2]=>{{1,6,7},{2,4,5,8},{3}}=>[6,4,3,5,8,7,1,2]=>0000000
[2,3,4,8,7,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,5,6,8,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,1,5,8,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,5,7,8,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,4,8,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,4,8,5,1,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[7,4,3,5,8,2,6,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,3,4,8,5,1,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,4,2,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,8,6,5,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,6,5,1,2,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,8,5,2,1,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,8,2,5,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,2,5,6,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,6,1,5,7,2,3,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[5,1,3,7,8,6,2,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,1,5,3,4,7,8,2]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[8,1,6,5,7,3,2,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[5,7,6,1,4,2,8,3]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[8,1,3,5,7,6,2,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[8,3,2,6,5,7,1,4]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[3,8,2,7,6,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,7,3,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,6,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,5,2,6,4,1,8]=>{{1,7},{2,3,4,5,6},{8}}=>[7,3,4,5,6,2,1,8]=>0000001
[7,2,1,5,6,4,3,8]=>{{1,3,7},{2},{4,5,6},{8}}=>[3,2,7,5,6,4,1,8]=>0000001
[3,2,1,5,7,4,8,6]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[3,2,1,6,7,8,4,5]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[5,3,6,1,7,8,4,2]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[5,4,6,7,2,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,1,7,8,5,2]=>{{1,4},{2,3,6,8},{5,7}}=>[4,3,6,1,7,8,5,2]=>0000000
[6,8,2,4,5,7,1,3]=>{{1,6,7},{2,3,8},{4},{5}}=>[6,3,8,4,5,7,1,2]=>0000000
[7,4,1,8,2,6,3,5]=>{{1,3,7},{2,4,5,8},{6}}=>[3,4,7,5,8,6,1,2]=>0000000
[7,3,1,8,4,2,6,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[2,4,8,3,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,4,1,3,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[4,8,2,3,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,1,5,2,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,3,8,1,2,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[1,5,4,8,2,7,6,3]=>{{1},{2,5},{3,4,8},{6,7}}=>[1,5,4,8,2,7,6,3]=>1000000
[6,5,1,2,8,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,5,8,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,5,2,8,7,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,8,1,7,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,2,1,5,3,6,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,3,7,5,4,1,8,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[7,8,1,5,4,2,6,3]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[7,8,2,5,4,1,3,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[7,8,2,5,4,6,1,3]=>{{1,7},{2,3,8},{4,5},{6}}=>[7,3,8,5,4,6,1,2]=>0000000
[4,7,6,5,1,8,3,2]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[4,7,6,5,1,2,8,3]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[4,7,6,3,5,8,1,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,7,6,5,8,1,3,4]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[3,7,5,8,2,4,1,6]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[5,1,7,8,4,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,7,8,5,2,3,6]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[4,1,8,7,5,2,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,7,1,6,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,3,2,4,1,6,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,1,2,3,6,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,2,8,3,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,1,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,7,1,4,2,8,5]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[8,1,7,5,4,3,2,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[8,1,7,4,5,3,2,6]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[6,1,2,3,8,7,4,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[5,1,2,3,7,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,3,2,4,7,1,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,1,2,6,3,5,4]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[2,3,6,8,4,7,1,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[3,6,4,1,2,8,5,7]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[3,5,8,7,1,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,3,8,7,6,2,4]=>{{1,2,5,7},{3},{4,8},{6}}=>[2,5,3,8,7,6,1,4]=>0000000
[4,5,8,3,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,8,7,6,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,1,3,7,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,2,6,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,8,3,7,1,5,4]=>{{1,2,6},{3,4,8},{5,7}}=>[2,6,4,8,7,1,5,3]=>0000000
[8,3,5,7,4,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,5,7,1,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,4,7,1,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,7,3,6,1,2,4]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[1,6,8,3,7,5,2,4]=>{{1},{2,5,6,7},{3,4,8}}=>[1,5,4,8,6,7,2,3]=>1000000
[6,3,8,2,7,5,1,4]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[2,8,4,5,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,3,1,5,2,4,6]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[8,6,1,2,4,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,1,5,3,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,6,1,2,5,7,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,7,8,1,3,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,1,7,3,4,6,2]=>{{1,3,5},{2,8},{4,6,7}}=>[3,8,5,6,1,7,4,2]=>0000000
[6,1,2,8,7,5,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[3,1,7,6,4,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,2,6,8,5,3,4]=>{{1,2,3,7},{4,5,6,8}}=>[2,3,7,5,6,8,1,4]=>0000000
[7,1,5,3,2,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,5,3,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,2,8,4,7,5,6]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[7,1,2,8,6,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,2,3,6,8,5,4,7]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[5,4,7,3,2,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,6,3,7,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,2,8,4,7,6,1]=>{{1,4,5,8},{2,3},{6,7}}=>[4,3,2,5,8,7,6,1]=>0000000
[5,7,4,3,2,8,6,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[4,7,5,3,2,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,4,3,8,5,2,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[7,4,6,3,8,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,2,6,8,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,2,8,7,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,2,7,8,5,4,1]=>{{1,5,6,8},{2,3},{4,7}}=>[5,3,2,7,6,8,4,1]=>0000000
[3,7,5,6,1,4,8,2]=>{{1,3,5},{2,7,8},{4,6}}=>[3,7,5,6,1,4,8,2]=>0000000
[4,7,1,3,8,2,5,6]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[7,4,1,3,8,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,3,1,2,8,5,6]=>{{1,4},{2,5,7},{3},{6,8}}=>[4,5,3,1,7,8,2,6]=>0000000
[4,8,1,3,7,2,5,6]=>{{1,3,4},{2,6,8},{5,7}}=>[3,6,4,1,7,8,5,2]=>0000000
[3,7,4,6,8,2,1,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[5,7,6,8,3,2,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[4,1,7,3,8,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,8,3,7,2,5,4]=>{{1,2,6},{3,4,8},{5,7}}=>[2,6,4,8,7,1,5,3]=>0000000
[3,7,5,8,6,2,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[3,7,8,6,5,2,1,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,8,7,5,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,6,8,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,6,8,4,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,4,6,5,8,1,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,5,4,8,6,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,5,4,8,6,7,2,3]=>{{1},{2,5,6,7},{3,4,8}}=>[1,5,4,8,6,7,2,3]=>1000000
[7,8,5,6,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,1,4,2,6,3,5]=>{{1,3,7},{2,5,8},{4},{6}}=>[3,5,7,4,8,6,1,2]=>0000000
[5,4,6,8,2,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,7,5,1,8,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,1,2,4,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,7,6,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,8,2,5,4,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,5,3,7,4,1,8,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,6,4,7,5,1,8,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,4,7,1,2,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,1,5,8,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,7,8,3,1,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,2,7,6,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,4,1,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,8,5,3,7,1]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[4,8,2,7,3,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,8,7,2,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,3,7,1,5,6,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,3,8,6,2,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,5,2,8,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,8,1,4,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,1,2,4,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,5,8,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,6,2,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,6,1,4,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,3,7,1,8,5,6]=>{{1,2,4,5,7},{3},{6,8}}=>[2,4,3,5,7,8,1,6]=>0000000
[2,4,1,8,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,4,1,3,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,8,3,7,6,1,2]=>{{1,5,7},{2,3,4,8},{6}}=>[5,3,4,8,7,6,1,2]=>0000000
[7,5,1,6,8,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,4,1,8,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,5,4,7,1,2,8,3]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[7,4,1,5,3,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,3,8,1,4,2,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,1,7,2,5,4,6,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,5,3,8,1,4,7,2]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[7,4,1,5,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,3,1,5,7,8,2]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[8,6,7,1,4,2,5,3]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[8,6,3,7,5,1,2,4]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[8,6,1,7,3,2,5,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[7,6,1,8,3,5,2,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[7,6,1,3,8,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,2,8,3,5,1,4]=>{{1,7},{2,3,5,6},{4,8}}=>[7,3,5,8,6,2,1,4]=>0000000
[8,7,1,5,2,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,2,7,3,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,7,2,4,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,7,2,1,4,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[8,5,7,2,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,2,7,1,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,4,1,2,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,3,1,7,2,6,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,1,5,8,4,2,7,3]=>{{1,2,6},{3,4,5,8},{7}}=>[2,6,4,5,8,1,7,3]=>0000000
[8,4,7,5,1,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,5,1,2,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[8,3,2,6,5,1,4,7]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[4,8,7,3,1,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,2,7,1,5,4,6]=>{{1,5,6,8},{2,3},{4,7}}=>[5,3,2,7,6,8,4,1]=>0000000
[8,7,3,1,6,2,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,3,1,2,4,6,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,2,1,3,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,3,1,5,2,8,4]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[6,7,4,5,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,1,5,2,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[5,8,3,1,6,7,2,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,6,3,1,7,8,2,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,8,3,1,7,6,2,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[4,8,6,7,5,1,2,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,5,3,1,8,6,4,7]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[1,2,3,7,4,8,6,5]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[1,2,3,7,6,4,8,5]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[5,4,2,8,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,4,8,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,2,3,8,7,4,6,5]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[3,8,5,7,1,2,6,4]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[4,8,6,7,2,3,5,1]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[3,4,8,6,1,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,8,5,7,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,8,6,2,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,7,6,2,1,4,8]=>{{1,3,4,6,7},{2,5},{8}}=>[3,5,4,6,2,7,1,8]=>0000001
[5,8,6,7,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,7,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,6,7,2,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,7,5,2,8,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,3,2,8,5,1,7,6]=>{{1,4,6,8},{2,3},{5},{7}}=>[4,3,2,6,5,8,7,1]=>0000000
[4,8,6,7,1,3,2,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,8,6,7,1,2,5,3]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[4,8,6,7,2,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,4,7,1,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,4,7,2,5,1,6]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[4,1,3,8,5,2,6,7]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[4,2,6,7,5,3,8,1]=>{{1,4,7,8},{2},{3,6},{5}}=>[4,2,6,7,5,3,8,1]=>0000000
[4,8,6,7,3,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,6,7,3,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,7,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,7,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,7,5,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,6,7,3,2,1,5]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[5,8,6,7,4,2,1,3]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[4,6,1,8,5,7,2,3]=>{{1,3,4,8},{2,6,7},{5}}=>[3,6,4,8,5,7,2,1]=>0000000
[4,7,1,2,8,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,5,8,6,1,2,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[6,8,1,5,7,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,8,1,2,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,5,8,6,2,1,4]=>{{1,7},{2,3,5,6},{4,8}}=>[7,3,5,8,6,2,1,4]=>0000000
[7,6,8,2,1,3,5,4]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[6,7,4,1,8,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,3,1,8,5,2]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[2,7,4,1,6,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,7,6,8,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,4,2,8,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,2,6,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,7,1,8,5,4,2]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[7,6,8,2,3,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,6,8,3,1,5,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[2,7,1,6,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,3,1,8,5,4,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,7,1,8,5,4,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,8,4,2,1,6,5,3]=>{{1,5,7},{2,3,4,8},{6}}=>[5,3,4,8,7,6,1,2]=>0000000
[6,3,2,5,8,7,1,4]=>{{1,6,7},{2,3},{4,5,8}}=>[6,3,2,5,8,7,1,4]=>0000000
[6,3,2,8,4,7,1,5]=>{{1,6,7},{2,3},{4,5,8}}=>[6,3,2,5,8,7,1,4]=>0000000
[6,4,3,8,7,5,1,2]=>{{1,5,6,7},{2,4,8},{3}}=>[5,4,3,8,6,7,1,2]=>0000000
[6,4,3,7,8,5,1,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,8,5,3,2,1,7]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[4,5,8,6,3,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,4,2,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,6,5,3,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,7,8,3,2,1,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[4,7,8,5,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,1,3,4,2,6,7]=>{{1,3,4,5},{2,6,7,8}}=>[3,6,4,5,1,7,8,2]=>0000000
[4,1,3,8,2,6,5,7]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[3,4,8,1,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,7,8,4,1,2,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[7,4,1,8,5,2,6,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,7,2,8,3,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,7,8,6,1,2,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[3,1,5,6,8,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,5,1,6,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,1,2,6,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,1,7,5,2,8,3,4]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[2,6,7,5,1,8,3,4]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[6,7,2,5,3,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,8,6,3,2,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[6,7,4,1,5,2,8,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,3,1,7,5,8,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,5,3,7,8,6,1,4]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,3,2,7,5,8,1,4]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[7,5,1,6,3,8,2,4]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[2,7,6,1,3,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,1,5,8,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,4,6,2,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,2,1,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,3,2,8,4,6,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,5,6,8,1,3,2,7]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[5,1,7,3,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,7,1,4,8,6,2]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[6,7,2,1,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,7,3,1,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,3,1,2,7,8,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,6,1,3,2,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,3,2,7,8,4,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,5,6,3,7,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,6,3,1,7,8,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[6,3,7,2,8,4,1,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[6,3,2,7,1,8,4,5]=>{{1,5,6,8},{2,3},{4,7}}=>[5,3,2,7,6,8,4,1]=>0000000
[7,5,3,2,1,8,4,6]=>{{1,2,4,5,7},{3},{6,8}}=>[2,4,3,5,7,8,1,6]=>0000000
[4,6,2,7,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,1,7,3,8,6,4]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[5,3,2,1,8,4,7,6]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[2,4,6,5,8,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,3,5,6,8,7,2]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[2,4,8,6,7,1,3,5]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[3,7,4,8,2,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,5,8,6,7,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[6,3,2,1,8,5,7,4]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[8,1,3,6,5,2,4,7]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[5,4,2,1,6,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,8,4,3,2,7,1,5]=>{{1,6,7},{2,5,8},{3,4}}=>[6,5,4,3,8,7,1,2]=>0000000
[3,4,8,7,2,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,7,2,6,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,5,8,7,2,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[2,5,7,8,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,1,8,5,4,6,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,1,3,6,4,8,7,2]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[4,1,2,6,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,3,5,1,4,7,6]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[5,6,2,1,7,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,2,7,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,7,6,4,5,8,1]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[2,6,1,7,5,8,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,1,2,7,8,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,1,7,4,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,1,7,8,2,5]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[5,4,6,1,3,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[1,2,3,8,6,7,4,5]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[1,2,3,8,7,5,4,6]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000
[3,1,6,2,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,1,3,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,2,5,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,2,5,3,7,1,4]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[2,5,4,7,6,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,7,5,8,1,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,8,3,7,1,4,2,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,8,4,7,1,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,6,8,2,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,3,6,5,8,1,2]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[7,6,2,8,4,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,3,7,4,5,2,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,3,5,7,8,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,3,6,8,2,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,6,7,3,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,4,7,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,8,2,4,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,3,6,2,5,7,1]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[4,8,3,5,7,2,6,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,8,3,5,6,7,2,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,8,3,7,2,5,6,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,8,4,2,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,4,2,3,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,4,8,5,3,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,3,6,2,5,8,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,7,3,6,8,2,5,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,7,3,5,8,2,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,3,4,6,7,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,3,5,7,8,2,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,5,7,3,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,5,8,4,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,4,5,8,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,5,4,7,2,3,6]=>{{1,2,6,8},{3,5,7},{4}}=>[2,6,5,4,7,8,3,1]=>0000000
[7,1,4,8,5,2,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,1,6,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,1,7,4,2,3,5]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[7,3,8,1,2,4,6,5]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[8,3,7,1,2,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,6,1,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,3,7,5,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,6,1,2,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,1,8,4,2,3,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[6,8,1,7,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,8,4,5,2,3,6]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[7,6,3,1,2,4,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,1,2,3,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,3,1,2,8,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,3,6,8,5,7,1,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,2,5,4,8,3,7]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[3,1,5,6,4,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,3,5,1,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,1,7,5,4,8,6,2]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[4,6,2,7,5,8,3,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,3,1,2,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,3,2,8,4,5,7,1]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[7,3,1,2,8,4,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[8,1,6,2,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,2,1,8,3,4,5,6]=>{{1,3,5,7},{2},{4,6,8}}=>[3,2,5,6,7,8,1,4]=>0000000
[4,6,3,8,7,1,2,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,3,4,8,7,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,8,2,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,6,1,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,2,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,3,6,1,7,5,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,8,2,6,5,1,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[4,8,5,2,6,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,5,1,3,7,2,8,6]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[8,1,3,6,2,7,5,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,4,8,6,5,1,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[8,4,6,7,1,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,2,1,6,3,8,5,4]=>{{1,3,5,7},{2},{4,6,8}}=>[3,2,5,6,7,8,1,4]=>0000000
[5,6,7,1,2,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,1,2,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,8,1,5,2,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,5,4,3,7,1,8,2]=>{{1,6},{2,5,7,8},{3,4}}=>[6,5,4,3,7,1,8,2]=>0000000
[6,5,1,7,3,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,6,2,8,7,4,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[6,3,1,7,8,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,4,1,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,2,6,3,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,2,1,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,3,1,6,7,8,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,2,4,5,1,3,6]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[7,8,1,3,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,2,3,6,1,4,7,8]=>{{1,5},{2},{3},{4,6},{7},{8}}=>[5,2,3,6,1,4,7,8]=>0000011
[3,5,4,6,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,2,5,6,7,1,3,8]=>{{1,4,6},{2},{3,5,7},{8}}=>[4,2,5,6,7,1,3,8]=>0000001
[6,3,7,4,5,8,1,2]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[5,2,1,6,3,4,7,8]=>{{1,3,5},{2},{4,6},{7},{8}}=>[3,2,5,6,1,4,7,8]=>0000011
[3,1,4,6,5,8,2,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,7,5,2,6,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,5,2,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,4,6,1,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,4,5,8,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,4,5,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,3,1,4,8,5,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,7,3,1,4,8,5,6]=>{{1,2,4,5,7},{3},{6,8}}=>[2,4,3,5,7,8,1,6]=>0000000
[2,4,7,5,1,6,8,3]=>{{1,2,4,5},{3,7,8},{6}}=>[2,4,7,5,1,6,8,3]=>0000000
[4,3,6,8,5,1,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[3,2,1,5,6,8,4,7]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[2,4,8,5,1,6,3,7]=>{{1,2,4,5},{3,7,8},{6}}=>[2,4,7,5,1,6,8,3]=>0000000
[2,7,1,8,3,5,6,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[2,1,8,3,7,4,5,6]=>{{1,2},{3,4,6,8},{5,7}}=>[2,1,4,6,7,8,5,3]=>0100000
[3,2,1,8,4,5,6,7]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[6,1,5,8,2,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,1,2,7,8,3,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[5,3,8,4,7,6,1,2]=>{{1,5,7},{2,3,8},{4},{6}}=>[5,3,8,4,7,6,1,2]=>0000000
[8,7,1,2,5,4,6,3]=>{{1,3,8},{2,4,6,7},{5}}=>[3,4,8,6,5,7,2,1]=>0000000
[7,1,6,2,8,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,7,8,6,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,7,8,3,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,7,3,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,7,8,1,3,2,5]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[4,6,7,8,1,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,7,8,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,7,8,1,2,5,3]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[3,6,7,8,1,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,7,8,1,5,4,3]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[4,5,8,3,6,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,2,3,6,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,8,1,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,4,8,1,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,5,1,4,2,8,3]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[7,6,5,1,2,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,5,1,4,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,5,1,2,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,5,1,8,2,3,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[7,6,5,1,8,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,5,1,4,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,5,1,7,8,2]=>{{1,3,4,5},{2,6,7,8}}=>[3,6,4,5,1,7,8,2]=>0000000
[7,6,5,1,8,3,4,2]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[7,6,4,8,3,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,8,5,6,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,2,5,6,3,1,8]=>{{1,7},{2,3,4,5,6},{8}}=>[7,3,4,5,6,2,1,8]=>0000001
[6,1,8,5,3,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,6,5,3,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,4,6,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,2,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,4,2,1,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,4,7,3,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,4,1,3,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,1,3,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,1,5,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,4,1,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,8,6,2,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,7,4,5,8,2,1]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[5,4,6,1,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,4,1,8,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,3,1,4,2,5,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,3,8,1,4,2,5,6]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[7,8,1,4,5,3,2,6]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[6,8,3,1,4,2,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[7,8,3,1,4,6,2,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,5,8,7,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,1,4,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,8,1,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,8,6,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,6,1,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,5,8,4,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,5,8,4,1,6,2]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[2,3,1,8,6,4,5,7]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[2,3,4,6,5,8,1,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,3,4,7,5,1,8,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,3,4,6,1,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,3,5,8,4,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,4,8,5,3,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,8,7,5,2,6,1]=>{{1,3,8},{2,4,6,7},{5}}=>[3,4,8,6,5,7,2,1]=>0000000
[3,8,7,2,5,4,6,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,3,6,2,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,7,2,5,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,8,6,2,3,4,7]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[3,7,6,1,8,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,8,5,4,1,2,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[2,6,3,7,1,4,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,6,3,8,1,4,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[8,5,4,7,1,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,7,6,1,8,5,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[3,5,2,6,7,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,5,1,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,3,1,7,2,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,7,2,5,6,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,2,1,5,7,4,6]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[2,8,3,6,4,7,1,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,5,1,7,4,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,4,7,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,3,7,1,6,8,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,4,7,8,1,5,2,3]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[6,5,7,8,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,6,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,6,8,4,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,6,7,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,7,5,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,6,5,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,8,1,5,4,2,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,6,8,1,5,4,2,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,6,2,1,5,8,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,6,2,1,5,3,4,7]=>{{1,4,7,8},{2,3,6},{5}}=>[4,3,6,7,5,2,8,1]=>0000000
[2,3,8,1,5,7,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,7,1,2,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,6,4,5,8,3,2]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[7,1,5,8,4,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,2,8,1,4,5,3,7]=>{{1,4,5,6},{2},{3,7,8}}=>[4,2,7,5,6,1,8,3]=>0000000
[7,2,6,1,5,3,4,8]=>{{1,4,7},{2},{3,6},{5},{8}}=>[4,2,6,7,5,3,1,8]=>0000001
[7,1,2,5,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,4,5,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,5,6,4,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,6,5,4,8,3,2]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[5,3,1,2,4,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[5,3,7,2,8,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,4,5,2,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[8,7,4,5,2,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,4,8,6,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,1,5,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,2,1,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,4,2,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,2,5,6,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,4,8,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,8,5,3,6,7,4,2]=>{{1},{2,8},{3,4,5,6,7}}=>[1,8,4,5,6,7,3,2]=>1000000
[8,3,5,2,1,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,8,5,6,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,5,7,3,1,8,4]=>{{1,2,6},{3,5},{4,7,8}}=>[2,6,5,7,3,1,8,4]=>0000000
[5,8,1,7,4,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,4,2,6,8,1,5]=>{{1,7},{2,3,4},{5,6,8}}=>[7,3,4,2,6,8,1,5]=>0000000
[5,8,1,7,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,1,5,4,7,8,3]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[4,6,3,5,8,7,1,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,1,7,8,2,5,6,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[4,8,1,5,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,5,3,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[4,3,6,8,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,3,1,4,8,5,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,4,8,7,5,2,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,4,8,3,2,7,5]=>{{1,2,6},{3,4,5,8},{7}}=>[2,6,4,5,8,1,7,3]=>0000000
[3,8,2,5,6,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,2,8,6,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,7,3,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,3,7,8,2,5,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,3,1,7,8,2,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,5,3,1,7,8,2,6]=>{{1,4},{2,5,7},{3},{6,8}}=>[4,5,3,1,7,8,2,6]=>0000000
[7,5,2,8,1,4,3,6]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[4,6,3,7,8,5,2,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,7,3,2,1,4,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,5,7,2,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,8,2,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,1,2,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,2,7,4,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,7,2,4,5,3,1]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[2,6,4,5,8,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,8,7,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,8,7,2,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,8,2,7,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,8,2,1,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,2,8,4,7,1,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[5,1,4,2,3,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[4,3,6,8,2,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,3,2,5,8,1,7,6]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[3,7,4,1,2,5,8,6]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[4,7,1,6,5,2,8,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,4,6,1,8,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,7,4,5,3,1,6]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[2,8,6,5,3,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,2,6,7,5,3,1,8]=>{{1,4,7},{2},{3,6},{5},{8}}=>[4,2,6,7,5,3,1,8]=>0000001
[2,8,7,3,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,7,5,3,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,7,5,4,3,1,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[8,1,7,2,4,5,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[8,1,3,6,2,5,4,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,1,5,3,4,2,6,7]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[8,1,5,6,2,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,4,5,3,2,6,7]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[5,7,1,6,2,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,6,2,7,1,4,3]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[6,5,1,2,7,8,4,3]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[5,6,2,4,7,8,1,3]=>{{1,5,7},{2,3,6,8},{4}}=>[5,3,6,4,7,8,1,2]=>0000000
[8,7,2,1,5,6,3,4]=>{{1,4,8},{2,3,7},{5},{6}}=>[4,3,7,8,5,6,2,1]=>0000000
[8,6,5,1,4,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,1,7,6,3,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,6,5,1,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,7,5,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,5,2,8,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,7,6,5,8,1,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,5,1,8,6,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,3,8,6,7,4,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,6,3,2,8,1,4,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,1,6,3,5,2,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,7,5,8,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,3,7,5,2,6,4]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[3,4,8,7,5,1,6,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,3,8,1,4,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,8,2,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,5,8,2,6,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,8,2,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,8,7,2,1,5,6]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[5,8,4,1,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,6,2,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,1,6,3,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,3,7,4,8,2,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,6,2,3,8,1,4,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[8,6,4,1,2,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,1,8,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,1,3,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,5,8,6,2,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[7,1,4,3,2,5,8,6]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[7,1,4,6,5,2,8,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,4,2,7,5,3,8,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,4,7,1,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,7,2,6,8,1,5]=>{{1,3,7},{2,4},{5,6,8}}=>[3,4,7,2,6,8,1,5]=>0000000
[4,8,7,3,5,1,2,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,4,7,1,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,1,6,3,4,2,7]=>{{1,3,5},{2,7,8},{4,6}}=>[3,7,5,6,1,4,8,2]=>0000000
[5,3,6,2,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,5,7,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,7,5,8,6,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,3,1,6,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,1,8,6,4,5,7]=>{{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000
[6,7,2,1,8,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,3,1,8,2,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,3,8,5,2,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,2,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,2,5,7,4,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,3,8,2,4,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,4,2,6,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,4,2,3,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,3,8,2,4,7,1]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[5,3,6,8,2,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,8,6,3,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,3,8,5,4,1,7]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[2,7,8,6,3,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,5,6,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,2,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,2,4,1,8,5,3]=>{{1,5,7},{2,3,6,8},{4}}=>[5,3,6,4,7,8,1,2]=>0000000
[7,6,2,3,8,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,8,4,2,1,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[4,8,5,7,6,2,1,3]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[4,7,6,2,1,3,8,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[7,5,6,1,8,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,5,8,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,2,6,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,8,5,2,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,2,3,1,7,4]=>{{1,3,5,6},{2,4,8},{7}}=>[3,4,5,8,6,1,7,2]=>0000000
[4,1,3,7,5,2,8,6]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[7,1,6,3,2,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,8,1,3,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,2,7,1,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,2,8,1,5,6,3]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[6,7,1,2,4,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,1,5,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,1,8,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,8,6,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,6,3,8,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,8,7,4,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,2,5,4,8,6,3]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[4,1,6,3,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,4,1,6,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,3,8,7,2,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[7,5,1,8,4,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,8,3,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,8,1,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,6,3,2,7,4,8,5]=>{{1},{2,4,6},{3},{5,7,8}}=>[1,4,3,6,7,2,8,5]=>1000000
[2,5,3,7,4,8,1,6]=>{{1,2,4,5,7},{3},{6,8}}=>[2,4,3,5,7,8,1,6]=>0000000
[3,5,2,7,8,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,3,7,2,8,5,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,1,6,8,2,4,3,7]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[5,3,7,8,2,4,1,6]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[8,4,6,7,2,3,1,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,6,7,8,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,8,7,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,8,7,3,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,8,7,2,3,1,5]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[6,4,8,7,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,6,8,2,3,1,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,6,4,7,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,4,8,2,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,8,6,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,7,6,4,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,5,3,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,6,5,3,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,6,5,8,3,1,7,4]=>{{1,2,6},{3,5},{4,8},{7}}=>[2,6,5,8,3,1,7,4]=>0000000
[2,6,5,3,8,1,7,4]=>{{1,2,6},{3,4,5,8},{7}}=>[2,6,4,5,8,1,7,3]=>0000000
[4,6,1,5,8,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,6,1,8,5,7,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,6,1,8,5,3,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[4,6,3,8,5,7,1,2]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[4,3,6,8,1,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,3,1,6,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,1,3,6,8,7,5,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,3,6,8,1,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,2,8,7,3,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[4,6,3,8,1,7,5,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,1,6,3,8,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,1,8,3,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,8,7,1,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,1,8,7,5,3,2]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[6,1,4,8,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,6,4,8,7,3,5,2]=>{{1},{2,3,4,6,8},{5,7}}=>[1,3,4,6,7,8,5,2]=>1000000
[3,6,4,8,2,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,2,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,8,3,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,7,8,1,5,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[5,1,8,2,7,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,2,8,4,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[6,8,1,3,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,2,3,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,6,2,3,4,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,7,2,6,1,8,4]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[2,8,7,6,4,1,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[7,8,2,6,5,1,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,4,2,1,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,7,6,4,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,6,1,2,5,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[4,8,7,6,1,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,6,4,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,3,6,5,1,2,4]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[2,3,7,5,6,8,1,4]=>{{1,2,3,7},{4,5,6,8}}=>[2,3,7,5,6,8,1,4]=>0000000
[3,4,2,6,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,8,3,5,4,1,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,8,1,2,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,2,8,5,3,6]=>{{1,3,7},{2,4},{5,6,8}}=>[3,4,7,2,6,8,1,5]=>0000000
[6,7,4,1,5,8,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,6,1,2,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,8,2,1,5,3,7]=>{{1,5,6},{2,4},{3,7,8}}=>[5,4,7,2,6,1,8,3]=>0000000
[6,8,3,2,5,1,4,7]=>{{1,6},{2,4,7,8},{3},{5}}=>[6,4,3,7,5,1,8,2]=>0000000
[8,6,1,5,3,2,4,7]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[8,6,3,1,5,2,4,7]=>{{1,4,7,8},{2,6},{3},{5}}=>[4,6,3,7,5,2,8,1]=>0000000
[8,4,6,1,5,2,3,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,6,2,1,5,4,3,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,4,1,7,5,2,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,8,1,6,7,2,3,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[5,7,6,1,8,2,3,4]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[6,5,7,1,8,2,3,4]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[7,5,8,1,3,2,4,6]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[7,3,1,8,6,4,2,5]=>{{1,2,3,7},{4,5,6,8}}=>[2,3,7,5,6,8,1,4]=>0000000
[5,6,8,1,7,2,3,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[5,8,1,7,3,2,6,4]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[7,4,3,8,1,2,6,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,3,7,1,4,2,8,6]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[3,7,5,1,2,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,3,5,1,2,6,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,3,5,8,1,2,6,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[3,6,2,5,8,7,1,4]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[4,1,5,3,2,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[4,6,2,7,5,1,8,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,4,8,7,1,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,2,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,7,2,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,3,7,5,2,1,4]=>{{1,4,7,8},{2,6},{3},{5}}=>[4,6,3,7,5,2,8,1]=>0000000
[4,6,3,8,5,2,1,7]=>{{1,4,7,8},{2,6},{3},{5}}=>[4,6,3,7,5,2,8,1]=>0000000
[4,6,3,7,5,2,8,1]=>{{1,4,7,8},{2,6},{3},{5}}=>[4,6,3,7,5,2,8,1]=>0000000
[6,4,8,5,1,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,2,5,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,7,2,5,1,6,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,5,1,2,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,8,5,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,8,7,1,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,8,5,7,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,8,6,7,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,1,8,2,3,6,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[7,1,8,2,3,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,4,7,5,1,6,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,7,4,5,1,6,2]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[4,8,6,1,7,2,5,3]=>{{1,4},{2,3,6,8},{5,7}}=>[4,3,6,1,7,8,5,2]=>0000000
[8,3,1,6,7,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,2,1,6,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,2,6,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,3,7,2,5,6,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,3,5,6,4,2,1,8]=>{{1,7},{2,3,4,5,6},{8}}=>[7,3,4,5,6,2,1,8]=>0000001
[5,3,8,2,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,2,5,4,7,1]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[5,8,6,4,7,2,1,3]=>{{1,5,7},{2,3,6,8},{4}}=>[5,3,6,4,7,8,1,2]=>0000000
[6,3,8,7,2,4,1,5]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[5,3,8,6,7,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,7,8,6,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,4,6,7,2,1,3]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[6,4,2,8,1,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,4,3,6,8,1,2]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[5,7,3,8,6,2,4,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,8,5,7,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,8,3,7,2,4,1]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[5,4,6,8,2,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,4,5,1,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,2,3,1,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,5,7,2,3,1,8]=>{{1,4,7},{2,3,5,6},{8}}=>[4,3,5,7,6,2,1,8]=>0000001
[3,6,2,7,5,4,8,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,5,2,7,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,1,5,6,8,4,3,7]=>{{1,2},{3,5,7,8},{4,6}}=>[2,1,5,6,7,4,8,3]=>0100000
[4,6,2,7,1,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,5,2,7,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,6,8,5,7,2,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,5,6,3,1,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,5,3,7,6,1,8,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,5,1,7,3,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,5,7,6,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,1,7,5,2,4,8]=>{{1,3},{2,6},{4,7},{5},{8}}=>[3,6,1,7,5,2,4,8]=>0000001
[4,1,6,3,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,2,5,3,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,2,8,3,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,8,1,5,3,2]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[3,6,8,4,5,7,1,2]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[7,8,1,2,3,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,1,4,5,2,6,3]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[2,7,4,8,3,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,2,1,5,3,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,4,1,5,3,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,3,8,4,2,5,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,1,3,6,2,4,5]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[2,6,7,1,8,5,3,4]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[2,6,7,8,5,3,4,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,7,1,2,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,1,8,3,2,5,7]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[4,1,7,8,6,2,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[4,1,8,7,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,1,7,3,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,1,6,3,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,1,5,3,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,5,2,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,5,2,4,1,6,3]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[3,1,2,6,7,5,8,4]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[8,1,7,6,5,3,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,1,2,3,5,4,8,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,2,3,5,8,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,6,5,2,4,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,2,5,3,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,7,6,2,8,3,1]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[5,7,4,1,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,2,4,8,3,1]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[5,3,6,7,4,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,8,6,2,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,8,5,7,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,8,5,7,2,3,1]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[5,6,8,2,4,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,3,2,8,7,5,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,6,3,8,2,7,4,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,6,5,8,7,2,4,1]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[5,3,6,8,2,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,2,7,6,8,4,1]=>{{1,5,6,8},{2,3},{4,7}}=>[5,3,2,7,6,8,4,1]=>0000000
[6,7,3,8,5,2,4,1]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[6,3,2,7,5,4,8,1]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[6,2,7,5,1,4,8,3]=>{{1,4,5,6},{2},{3,7,8}}=>[4,2,7,5,6,1,8,3]=>0000000
[6,3,7,8,4,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,4,8,6,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,8,7,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,2,8,5,4,7,3]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[6,5,2,1,8,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,2,3,8,7,1,4]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[5,1,6,3,8,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,5,8,7,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,2,7,8,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,6,4,8,7,5,2,3]=>{{1},{2,5,6,7},{3,4,8}}=>[1,5,4,8,6,7,2,3]=>1000000
[6,8,3,2,4,7,1,5]=>{{1,6,7},{2,4,5,8},{3}}=>[6,4,3,5,8,7,1,2]=>0000000
[5,8,2,4,7,3,1,6]=>{{1,5,7},{2,3,6,8},{4}}=>[5,3,6,4,7,8,1,2]=>0000000
[8,6,4,5,2,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,8,6,4,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,6,5,2,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,3,6,5,2,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,2,5,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,5,2,7,1,4]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[2,5,8,7,6,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,2,5,1,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,3,6,8,1,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,3,5,2,1,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,8,1,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,1,5,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,8,1,5,7,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,7,1,5,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,6,1,2,8,4,5]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[6,8,4,5,1,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,8,7,6,2,3,4]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[3,4,8,7,1,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,8,3,7,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,7,1,2,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,1,8,7,2,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[6,8,3,1,5,2,4,7]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[5,4,1,7,2,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,3,8,4,7,2,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,4,2,7,3,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,3,7,1,2,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,3,8,1,2,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[7,5,3,8,4,2,6,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,6,4,8,2,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,1,7,8,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,7,8,4,2,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[6,1,3,5,2,8,4,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,5,2,7,1,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,6,1,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,5,6,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,7,5,6,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,6,1,3,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,2,1,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,2,5,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,3,2,7,8,4,6]=>{{1,2,4,5,7},{3},{6,8}}=>[2,4,3,5,7,8,1,6]=>0000000
[5,3,8,1,7,2,4,6]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[2,6,5,1,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,1,8,4,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,8,1,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,1,3,8,7,2,6,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,5,8,1,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,8,1,7,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,8,3,2,7,5,6,4]=>{{1},{2,4,8},{3},{5,6,7}}=>[1,4,3,8,6,7,5,2]=>1000000
[3,7,2,8,6,1,5,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[5,1,7,8,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,4,8,3,6,2]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>0000000
[4,1,8,7,5,3,6,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,7,2,6,3,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,2,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,8,2,4,1,5,6]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[2,6,4,7,8,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,4,7,8,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,7,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,7,1,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,7,2,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,4,7,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,5,1,3,2,4,7]=>{{1,4,7,8},{2,6},{3,5}}=>[4,6,5,7,3,2,8,1]=>0000000
[3,5,8,7,4,1,2,6]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[7,3,8,4,1,2,5,6]=>{{1,5,7},{2,3,6,8},{4}}=>[5,3,6,4,7,8,1,2]=>0000000
[6,8,7,1,5,2,3,4]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[5,8,2,3,7,6,1,4]=>{{1,5,7},{2,3,4,8},{6}}=>[5,3,4,8,7,6,1,2]=>0000000
[6,7,2,1,5,8,4,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,4,8,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,2,5,6,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,4,1,2,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,2,1,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,7,4,5,6,1,2]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>0000000
[2,8,3,1,4,5,6,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,3,7,2,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,8,1,3,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,2,7,4,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,1,8,3,2,4]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[3,1,7,5,8,2,6,4]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[8,6,2,7,4,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,3,2,7,1,4,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,1,3,8,2,5,6,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,1,8,3,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,4,1,6,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,3,8,1,5,6,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,8,4,2,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,2,8,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,5,2,7,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,5,2,6,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,4,3,1,5,6,7]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[5,7,4,3,8,1,6,2]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[3,8,4,1,6,7,5,2]=>{{1,3,4},{2,8},{5,6,7}}=>[3,8,4,1,6,7,5,2]=>0000000
[6,1,7,5,2,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,4,3,2,8,1,7]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[5,7,4,3,8,2,1,6]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[6,7,5,8,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,8,1,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,7,5,1,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,8,1,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,3,2,6,1,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,1,2,6,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,2,8,1,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,7,5,8,4,3,2]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[6,3,7,8,5,4,1,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,5,7,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,7,8,5,1,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,7,3,8,5,1,4,6]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[7,1,6,5,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,6,1,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,1,5,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,2,8,4,5,3,6]=>{{1,2,3,7},{4,5,6,8}}=>[2,3,7,5,6,8,1,4]=>0000000
[1,5,3,8,7,4,2,6]=>{{1},{2,5,7},{3},{4,6,8}}=>[1,5,3,6,7,8,2,4]=>1000000
[7,4,2,8,6,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,6,1,8,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,5,3,8,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,1,8,7,5,4,6]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[7,5,1,8,6,3,2,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[6,1,8,7,5,3,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,6,3,1,7,4,2,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,4,2,5,3,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,3,1,8,7,4,2,6]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[7,4,6,3,1,8,5,2]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[3,5,4,8,1,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,1,3,2,4,8,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[8,7,1,5,4,2,3,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[7,1,6,2,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,2,3,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,3,1,4,8,2,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,1,7,3,2,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,1,6,2,8,4,7]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[6,1,5,2,8,4,3,7]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[7,4,3,8,1,5,2,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,1,5,3,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,4,2,8,5,1,6]=>{{1,7},{2,3,4},{5,6,8}}=>[7,3,4,2,6,8,1,5]=>0000000
[3,8,6,1,5,2,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[7,4,1,5,8,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,2,7,3,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,8,3,1,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,2,1,7,4,8,3,6]=>{{1,3,4,5,7},{2},{6,8}}=>[3,2,4,5,7,8,1,6]=>0000000
[7,1,6,4,5,2,8,3]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[4,5,7,2,8,1,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[2,3,6,7,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,6,5,3,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,6,5,2,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,5,4,7,8,2]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[4,7,6,3,8,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,6,5,2,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,6,5,1,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,2,6,1,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,6,5,8,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,3,2,4,1,6,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,2,7,1,4,8,5,6]=>{{1,3,4,5,7},{2},{6,8}}=>[3,2,4,5,7,8,1,6]=>0000000
[5,3,4,8,7,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,8,3,7,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,3,8,6,2,5,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,6,7,8,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,8,5,6,4,7,3,2]=>{{1},{2,8},{3,4,5,6,7}}=>[1,8,4,5,6,7,3,2]=>1000000
[2,5,8,6,4,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,7,8,5,6,2,1]=>{{1,4,8},{2,3,7},{5},{6}}=>[4,3,7,8,5,6,2,1]=>0000000
[4,3,6,8,5,7,2,1]=>{{1,4,8},{2,3,6,7},{5}}=>[4,3,6,8,5,7,2,1]=>0000000
[2,7,8,4,5,6,3,1]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>0000000
[5,7,4,6,8,3,2,1]=>{{1,5,8},{2,7},{3,4,6}}=>[5,7,4,6,8,3,2,1]=>0000000
[2,6,8,4,5,7,3,1]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[7,5,1,3,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,5,2,8,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,5,6,1,2,4,7]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[3,7,5,8,1,2,4,6]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[7,6,4,8,1,3,5,2]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[5,3,8,1,6,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,8,5,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,8,2,5,1,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,8,7,1,2,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,3,8,2,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[4,8,2,3,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,7,4,1,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,6,4,5,2,1,7]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[3,8,4,6,5,2,1,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,8,2,6,4,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,8,3,4,2,7,5]=>{{1,2,6},{3,4,5,8},{7}}=>[2,6,4,5,8,1,7,3]=>0000000
[3,8,4,5,6,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,6,5,4,2,1,7]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[5,1,4,8,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,1,8,4,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,2,4,5,1,6,3]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[3,7,5,1,4,8,6,2]=>{{1,3,4,5},{2,6,7,8}}=>[3,6,4,5,1,7,8,2]=>0000000
[3,5,4,7,2,1,6,8]=>{{1,3,4,6,7},{2,5},{8}}=>[3,5,4,6,2,7,1,8]=>0000001
[3,5,4,7,1,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,2,7,1,4,8,6]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[3,5,7,2,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,7,1,4,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,5,2,1,8,6,4]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[3,7,2,5,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,2,7,5,1,8,4,6]=>{{1,3,4,5,7},{2},{6,8}}=>[3,2,4,5,7,8,1,6]=>0000000
[5,8,7,2,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,2,6,5,1,3,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,4,2,8,5,1,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,6,3,4,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,2,8,7,1,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[7,6,1,4,5,3,8,2]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[7,6,1,3,5,4,8,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,3,6,5,1,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,5,8,1,7,3]=>{{1,2,6},{3,4,5,8},{7}}=>[2,6,4,5,8,1,7,3]=>0000000
[3,5,6,1,4,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,1,3,4,5,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,3,2,4,8,5,6]=>{{1,2,4,5,7},{3},{6,8}}=>[2,4,3,5,7,8,1,6]=>0000000
[7,6,1,5,3,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,1,5,4,3,8,2]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[7,6,5,8,1,3,2,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[3,4,6,8,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,8,1,7,2,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[2,5,4,7,3,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,7,1,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,3,7,1,2,8,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,5,2,3,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,7,1,8,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,4,2,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[2,6,5,3,4,7,8,1]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[5,4,1,3,2,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[2,1,4,8,6,3,7,5]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[5,1,8,3,6,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,5,8,7,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,8,1,7,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,8,1,3,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,2,7,6,3,1,5,8]=>{{1,4,6},{2},{3,5,7},{8}}=>[4,2,5,6,7,1,3,8]=>0000001
[6,3,1,8,7,5,2,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[7,6,4,2,1,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,2,1,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,4,1,5,2,6,3]=>{{1,3,4,8},{2,6,7},{5}}=>[3,6,4,8,5,7,2,1]=>0000000
[7,5,2,8,6,3,1,4]=>{{1,7},{2,3,5,6},{4,8}}=>[7,3,5,8,6,2,1,4]=>0000000
[8,7,5,2,1,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,3,1,4,7,5,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,5,2,1,6,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,8,6,3,5,2]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[8,4,6,3,1,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,4,1,2,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,2,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,1,7,8,5,2]=>{{1,3,4},{2,6,8},{5,7}}=>[3,6,4,1,7,8,5,2]=>0000000
[7,6,1,3,8,4,2,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[2,6,4,1,7,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,8,7,1,5,3]=>{{1,2,6},{3,4,8},{5,7}}=>[2,6,4,8,7,1,5,3]=>0000000
[7,6,1,3,5,8,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,1,3,8,2,6,5,4]=>{{1,2,5,7},{3},{4,8},{6}}=>[2,5,3,8,7,6,1,4]=>0000000
[7,6,1,8,5,4,2,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,3,7,5,8,2,6,1]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[4,1,7,8,6,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,3,2,1,4,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[4,5,2,6,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,5,3,8,4,2,7,1]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[7,4,5,1,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,3,5,6,2,8,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,1,6,8,4,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,6,1,5,7,4,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,4,6,7,8,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,2,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,2,3,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,4,2,3,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,8,3,2,7,1,5]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[5,8,3,7,2,1,6,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,5,3,8,4,6,2,1]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,1,8,2,3,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,1,7,2,3,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,3,7,4,6,2,1]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,8,7,3,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,2,3,5,1,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,6,3,8,7,5,4,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,4,1,6,5,3,2,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,6,1,5,4,2,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,1,7,5,4,2,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,3,8,7,5,4,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,1,7,2,6,4,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[8,1,7,5,2,4,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[4,7,6,5,1,3,8,2]=>{{1,4,5},{2,7,8},{3,6}}=>[4,7,6,5,1,3,8,2]=>0000000
[4,1,2,8,5,3,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,7,6,2,8,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,8,5,1,2,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,7,1,5,8,4,3,6]=>{{1,2,3,7},{4,5,6,8}}=>[2,3,7,5,6,8,1,4]=>0000000
[2,7,6,1,8,4,3,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[3,8,5,6,4,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,2,1,4,7,8,3,6]=>{{1,3,5,7},{2},{4},{6,8}}=>[3,2,5,4,7,8,1,6]=>0000000
[5,6,2,7,3,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,2,5,7,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,7,2,3,1,5,8,4]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[7,3,2,5,8,1,6,4]=>{{1,6,7},{2,3},{4,5,8}}=>[6,3,2,5,8,7,1,4]=>0000000
[7,6,5,2,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,5,1,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,8,7,4,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,2,4,6,1,5]=>{{1,3,7},{2,4,5,8},{6}}=>[3,4,7,5,8,6,1,2]=>0000000
[5,7,1,3,2,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,6,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,6,8,3,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,4,1,3,5,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,8,5,2,1,4,6]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[4,8,6,5,1,2,3,7]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[3,8,7,6,5,1,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,4,6,5,1,3,8,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,6,3,8,7,5,1,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,2,4,1,6,5,3]=>{{1,5,7},{2,3,8},{4},{6}}=>[5,3,8,4,7,6,1,2]=>0000000
[2,6,1,8,7,5,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[2,3,6,8,7,5,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[8,1,4,7,6,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,6,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,8,6,2,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,6,1,5,7,2,4]=>{{1,4,8},{2,3,6,7},{5}}=>[4,3,6,8,5,7,2,1]=>0000000
[6,8,1,4,5,2,3,7]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[8,7,1,5,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,2,7,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,2,6,8,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,5,7,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,6,1,5,2,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,5,7,2,3,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,8,7,4,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,7,5,3,8,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,3,5,1,4,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,7,1,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,4,7,5,3,8,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,4,3,1,5,6,2]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[4,7,3,6,1,2,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,7,6,2,3,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,8,2,5,3,4,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,3,6,1,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,8,7,5,3,1,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,4,1,7,5,2,8,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,6,2,1,5,7,4,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,8,6,7,5,2,1,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,3,7,5,8,2,4]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[7,6,4,8,5,1,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,6,7,5,2,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,5,7,2,8,1,3]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[6,3,2,8,5,4,1,7]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[2,8,6,1,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,2,6,1,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,5,1,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,6,3,8,7,4,1,2]=>{{1,5,7},{2,4,6,8},{3}}=>[5,4,3,6,7,8,1,2]=>0000000
[4,3,7,2,8,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,7,2,6,3,8,5,4]=>{{1},{2,3,5,7},{4,6,8}}=>[1,3,5,6,7,8,2,4]=>1000000
[8,6,3,1,5,4,2,7]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[8,6,4,1,5,3,2,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,8,7,3,5,2,1,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,8,4,1,5,2,7,3]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[6,8,2,1,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,7,6,5,2,1,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,8,3,5,6,7,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,4,6,3,5,7,8,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,6,4,2,5,7,8,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,3,6,1,5,7,8,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,3,6,2,5,7,8,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,6,1,2,5,7,8,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,6,4,1,5,7,8,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,4,1,6,5,7,8,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,5,6,1,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,6,1,2,3,8,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,3,6,2,1,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,4,5,8,2,1,7]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[6,1,4,5,2,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,5,4,1,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,8,4,7,2,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[5,3,6,8,2,7,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[4,3,6,8,2,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,8,1,4,7,2,6]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[6,3,8,1,5,7,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,1,2,5,7,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,8,5,6,2,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,5,8,7,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,5,8,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,7,6,1,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,5,6,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,1,8,6,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,5,8,6,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,5,8,7,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,1,5,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,4,7,1,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,8,6,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,1,5,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,7,2,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,4,6,1,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,5,6,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,6,5,2,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,5,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,1,7,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,4,6,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,4,7,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,4,7,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,2,3,8,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,2,1,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,7,3,1,4,8,6]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[6,7,3,2,8,4,5,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,6,7,4,3,8,5,1]=>{{1,2,6,8},{3,5,7},{4}}=>[2,6,5,4,7,8,3,1]=>0000000
[1,7,5,8,2,4,3,6]=>{{1},{2,3,5,7},{4,6,8}}=>[1,3,5,6,7,8,2,4]=>1000000
[6,7,1,8,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,1,5,4,3,2,7]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[2,4,3,8,5,1,6,7]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[3,1,8,7,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,8,7,5,4,2,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,8,1,7,5,3,2,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,5,6,1,4,3,2,7]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[5,8,6,1,4,3,2,7]=>{{1,4,5},{2,7,8},{3,6}}=>[4,7,6,5,1,3,8,2]=>0000000
[8,6,5,1,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,3,8,4,5,2,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,7,4,1,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,4,1,8,3,2,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[4,2,1,5,7,8,3,6]=>{{1,3,4,5,7},{2},{6,8}}=>[3,2,4,5,7,8,1,6]=>0000000
[8,1,4,6,5,2,7,3]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[8,6,4,1,5,7,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,1,7,6,4,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,6,5,1,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,7,2,8,1,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,8,1,6,5,4,2]=>{{1,4,7},{2,3,8},{5,6}}=>[4,3,8,7,6,5,1,2]=>0000000
[2,4,1,8,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,7,8,2,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,4,8,3,2,1,7]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[4,7,5,8,2,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,3,2,8,1,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,1,2,6,3,8,5,4]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[8,1,2,6,3,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,2,7,6,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,3,1,6,2,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,8,3,2,1,7,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,7,6,2,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,2,7,3,8,6,4]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[4,6,3,2,1,8,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[6,4,3,8,5,2,1,7]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[4,5,3,2,8,6,1,7]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[8,4,3,7,5,2,1,6]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[7,3,1,5,2,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,7,2,1,8,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[4,5,8,6,1,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,6,7,2,1,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,3,5,6,7,8,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,8,3,2,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,8,3,7,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,2,5,4,7,1,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[3,7,8,5,4,1,6,2]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[4,6,8,5,3,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,7,3,1,2,4,8,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,8,4,3,1,7,2,5]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[4,8,1,3,7,5,6,2]=>{{1,3,4},{2,8},{5,6,7}}=>[3,8,4,1,6,7,5,2]=>0000000
[5,6,8,7,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,5,6,2,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,3,7,2,5,8,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,6,1,3,5,7,2,4]=>{{1,3,4,8},{2,6,7},{5}}=>[3,6,4,8,5,7,2,1]=>0000000
[6,1,5,3,4,8,2,7]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[5,8,1,3,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,3,7,2,4,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,5,4,7,8,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,8,7,1,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,8,5,7,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,4,1,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,6,5,3,1,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,1,7,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,2,8,7,4,6,5]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[2,8,3,7,4,1,6,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[1,3,4,8,7,2,5,6]=>{{1},{2,3,4,6,8},{5,7}}=>[1,3,4,6,7,8,5,2]=>1000000
[3,6,8,2,5,1,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[8,5,7,1,6,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,6,5,1,2,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,5,8,1,7,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,8,3,4,2,6]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[5,7,2,1,4,3,8,6]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[7,1,8,3,5,2,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,4,8,3,1,5,6,2]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[2,6,3,5,8,7,4,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,8,1,2,5,7,4,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,6,5,3,7,2,1,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[7,4,8,6,5,3,2,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,4,7,1,3,2,8,5]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[7,3,1,8,2,5,6,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[5,1,6,3,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,6,3,5,1,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,6,3,5,2,8,7,1]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[5,8,4,6,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,4,3,8,6,2,7,1]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[5,7,8,2,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,2,8,6,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,7,4,2,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,7,8,2,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,7,3,2,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,7,2,5,8,6,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,7,3,2,5,8,6,1]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[4,7,3,2,6,8,5,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,7,3,2,6,4,8,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,3,2,8,6,4,7,1]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[7,5,6,2,8,3,4,1]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[6,3,7,5,2,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,6,2,3,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,4,2,5,8,3,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,3,8,5,4,7,2,1]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[8,7,2,6,5,1,4,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,3,8,2,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[8,6,3,1,7,5,4,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,8,3,7,6,2,5,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,4,2,1,7,6,5,3]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[3,5,6,1,8,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,6,8,7,3,1,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,7,5,2,1,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,7,3,1,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,1,8,3,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,5,3,8,4,1,7,6]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[6,3,1,2,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,4,1,3,5,8,2,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,8,4,6,7,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,3,8,4,5,6,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,6,7,1,8,2,5,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[3,1,5,7,2,8,6,4]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[2,3,4,6,8,7,1,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[7,8,5,2,4,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,2,3,1,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,8,5,2,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,8,7,4,5,1,6,3]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[5,8,3,1,2,6,4,7]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[4,8,1,7,5,2,6,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,5,3,2,1,6,4,7]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[7,6,8,4,1,3,5,2]=>{{1,5,7},{2,3,6,8},{4}}=>[5,3,6,4,7,8,1,2]=>0000000
[8,4,2,7,5,1,6,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,8,7,5,4,1,2,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[8,7,6,1,5,2,3,4]=>{{1,4,8},{2,3,6,7},{5}}=>[4,3,6,8,5,7,2,1]=>0000000
[7,1,4,8,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,1,3,5,4,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[7,8,5,2,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,8,2,5,4,6,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,3,1,6,4,5,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,3,1,4,6,5,2]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,4,1,7,8,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,1,6,5,2,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,3,2,6,1,5,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,1,7,6,5,2,3,4]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[7,1,3,6,8,5,4,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,1,7,6,4,5,3,2]=>{{1,2,8},{3,7},{4,5,6}}=>[2,8,7,5,6,4,3,1]=>0000000
[7,1,8,6,4,5,3,2]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[6,5,7,2,8,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,5,8,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,2,7,6,1,3,4]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[5,1,7,3,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,2,4,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,2,6,5,7,1,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,2,5,6,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,1,7,3,2,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[6,7,1,2,8,4,3,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[2,5,7,1,8,4,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[3,5,7,1,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,7,6,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,7,6,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,6,7,5,2,1,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,7,5,6,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,8,6,7,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,8,7,5,4,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,1,7,6,4,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,8,6,7,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,7,5,6,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,1,5,4,8,6,3]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[8,1,4,5,6,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,4,7,6,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,2,8,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,3,5,2,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,4,5,6,2,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,4,2,5,8,6,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,3,5,1,4,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100
[2,7,1,3,6,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,1,3,8,4,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[3,8,7,1,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,1,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,4,2,1,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,7,5,1,2,6,4]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[4,5,8,7,6,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,3,5,6,1,4,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,5,2,7,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,7,2,1,5,8,3]=>{{1,5,6},{2,4},{3,7,8}}=>[5,4,7,2,6,1,8,3]=>0000000
[8,5,3,1,6,4,7,2]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[8,7,3,1,4,5,6,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,5,3,1,6,4,2,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,3,1,4,2,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,4,1,2,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,2,6,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,8,6,5,7,2,1]=>{{1,3,8},{2,4,6,7},{5}}=>[3,4,8,6,5,7,2,1]=>0000000
[2,1,5,8,6,4,7,3]=>{{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000
[8,3,2,5,6,1,7,4]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[6,7,1,8,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,2,8,1,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,6,1,4,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,1,2,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,7,5,8,1,2,4]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[6,5,8,7,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,6,2,8,3,1,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[3,8,7,2,1,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,6,2,8,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,7,3,8,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,2,7,4,1,3]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[4,6,5,8,7,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,6,1,7,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,6,1,3,8,4,2]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[5,7,6,1,3,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,8,1,5,7,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,3,6,5,1,8,2,7]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[6,5,1,8,7,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,1,7,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,5,8,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,6,7,8,2,1,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[6,7,1,3,8,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,1,8,5,2,4,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,6,1,2,7,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,6,1,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,8,7,2,5,4,1,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,7,2,1,8,4,6,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[4,7,3,8,6,1,5,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,7,3,8,6,2,1,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,1,2,6,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,8,7,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,8,3,5,2,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[3,8,2,5,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,2,1,5,8,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,3,6,1,5,8,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,6,8,1,5,3,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[6,8,2,1,5,3,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[4,1,8,6,5,3,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[5,3,2,6,4,8,7,1]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[4,8,1,6,5,2,7,3]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[6,8,1,2,5,4,7,3]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[6,4,1,8,5,2,7,3]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,6,1,8,5,4,7,3]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[4,3,2,6,8,5,7,1]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[3,1,6,8,5,4,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[6,3,2,5,8,4,7,1]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[6,1,8,3,5,4,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[7,5,2,1,4,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,2,5,1,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,1,6,8,7,3,2,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,5,3,2,1,4,7,6]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[4,1,8,6,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,6,2,5,3,4,1,8]=>{{1,7},{2,3,4,5,6},{8}}=>[7,3,4,5,6,2,1,8]=>0000001
[7,8,4,3,1,5,2,6]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[7,5,8,2,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,6,1,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,6,1,4,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,8,5,3,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[5,8,2,7,3,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,5,2,6,1,4]=>{{1,3,7},{2,4,5,8},{6}}=>[3,4,7,5,8,6,1,2]=>0000000
[5,1,8,3,6,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,7,6,4,5,1,3]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[7,3,5,2,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,5,2,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,3,2,8,6,4,1]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[2,3,7,5,4,8,6,1]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[2,4,8,7,5,1,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,5,7,6,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,8,7,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,2,5,4,1,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,7,2,5,4,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,7,2,6,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,1,3,6,4,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,1,3,7,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,5,2,8,7,4,3,6]=>{{1},{2,3,5,7},{4,6,8}}=>[1,3,5,6,7,8,2,4]=>1000000
[4,3,8,2,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,6,7,2,5,3,8,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,4,7,3,1,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,1,8,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,8,6,5,2,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,3,7,6,5,1,8,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,7,2,6,8,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,6,8,5,1,4,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,3,1,6,8,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,6,8,5,2,4,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,6,2,1,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,7,5,4,2,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,8,2,7,5,4,3,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,1,8,3,7,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,7,1,5,4,6,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,2,4,1,3,8,5,6]=>{{1,3,4,5,7},{2},{6,8}}=>[3,2,4,5,7,8,1,6]=>0000000
[5,4,7,3,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,8,3,6,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,6,2,7,5,1,4]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[6,5,8,2,7,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,1,3,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,7,8,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,8,3,2,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,3,7,8,2,1,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,1,3,5,8,7,4,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,3,8,7,5,1,6,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,8,7,2,4,1,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[4,3,5,6,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,7,4,3,8,1,5,6]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[4,3,8,6,2,7,1,5]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[3,1,6,8,2,7,5,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[5,3,8,6,7,2,1,4]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[5,4,7,8,3,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,4,7,8,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,5,8,2,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,5,3,2,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,6,1,3,2,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,8,2,4,1,6,5]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[6,3,7,8,1,5,4,2]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[4,8,2,7,1,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,8,1,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,6,7,2,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,3,6,5,2,8,4]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[6,1,8,5,2,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,1,3,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,4,7,6,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,2,5,7,8,6,4]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[7,8,6,1,2,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,1,6,7,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,2,6,4,5,8,3]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[8,1,6,2,7,3,4,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,1,7,2,5,3,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,1,6,7,5,2,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,8,2,5,3,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,1,8,2,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,8,6,3,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,6,1,5,8,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,5,7,1,4,6,8,3]=>{{1,2,4,5},{3,7,8},{6}}=>[2,4,7,5,1,6,8,3]=>0000000
[8,6,5,1,2,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,4,8,3,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,5,1,4,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,3,2,4,5,1,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,8,2,5,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,1,8,5,4,3,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,8,6,2,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,3,2,8,1,7,4]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[3,4,7,5,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,7,6,4,5,1,2]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[6,4,7,1,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,4,2,3,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,2,5,1,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,4,2,3,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,5,2,1,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,7,6,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,6,5,2,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,4,2,6,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,6,8,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,1,6,8,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,1,7,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,1,8,6,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,4,1,7,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,8,3,7,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,2,8,4,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,2,8,6,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,5,7,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,8,3,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,2,8,7,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,4,2,7,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,7,8,5,1,2,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,1,2,6,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,4,7,1,2,8,5]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[2,4,7,8,5,1,3,6]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000
[8,5,4,2,6,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,3,7,5,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,2,8,7,4,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[7,2,1,5,3,8,4,6]=>{{1,3,4,5,7},{2},{6,8}}=>[3,2,4,5,7,8,1,6]=>0000000
[4,3,6,8,1,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,6,8,5,1,3,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,4,6,8,3,1,7,2]=>{{1,3,5,6},{2,4,8},{7}}=>[3,4,5,8,6,1,7,2]=>0000000
[8,6,1,7,2,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,7,6,1,8,5,4]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[8,3,1,6,2,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,7,1,5,3,8,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,3,8,2,6,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,5,7,1,4,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,6,1,2,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,3,5,7,6,2,1]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[5,7,6,2,4,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,1,6,2,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,6,2,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,3,1,4,5,7,6]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[6,1,7,2,8,4,5,3]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[7,5,2,1,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,1,5,4,8,2,3]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[7,6,3,2,1,8,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,5,1,3,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,3,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,7,3,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,5,3,7,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,1,3,2,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,2,3,4,7,1,5]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[6,7,2,3,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,3,2,4,7,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,2,5,8,7,4,1,6]=>{{1,3,5,7},{2},{4,6,8}}=>[3,2,5,6,7,8,1,4]=>0000000
[3,4,8,5,7,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,4,8,5,7,2,1]=>{{1,3,4,8},{2,6,7},{5}}=>[3,6,4,8,5,7,2,1]=>0000000
[5,1,3,2,6,8,7,4]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[3,1,6,5,8,7,2,4]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[8,7,1,2,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,7,1,6,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,5,3,8,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,6,5,4,8,1,7]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[6,3,8,7,2,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,3,8,7,1,6,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,6,4,8,1,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,3,6,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,5,6,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,7,5,6,4,1,3]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[2,6,3,5,7,8,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,1,6,8,3,7,2,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[7,5,1,8,3,4,2,6]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[4,5,8,3,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,5,8,6,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,2,1,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,7,8,4,3,1,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[3,6,4,5,2,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,1,7,4,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,4,8,3,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,3,7,5,4,1,6,2]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[2,8,4,7,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,4,8,3,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,8,7,2,6,1,5,4]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[1,8,4,7,6,3,5,2]=>{{1},{2,8},{3,4,5,6,7}}=>[1,8,4,5,6,7,3,2]=>1000000
[8,1,2,7,6,5,4,3]=>{{1,2,3,8},{4,7},{5,6}}=>[2,3,8,7,6,5,4,1]=>0000000
[7,3,6,8,5,1,4,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,8,3,1,6,2,5,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,2,6,3,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,5,2,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,2,8,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,3,2,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,8,2,5,4,3,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,7,8,3,1,5,4,2]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[7,8,1,6,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,3,7,6,1,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,1,6,5,2,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,1,7,6,5,2,8,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,3,1,8,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,1,8,5,4,7,2,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[2,6,1,8,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,1,8,3,2,6,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[5,1,8,6,3,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,6,4,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,7,1,8,4,2,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[6,3,4,7,1,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,1,2,3,8,6,4]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[2,8,6,4,1,7,3,5]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>0000000
[2,8,1,7,5,3,6,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,1,8,7,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,2,6,3,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,5,8,2,7,4,6]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[6,1,8,4,5,3,2,7]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[3,1,6,8,5,7,4,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,6,1,8,5,7,4,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,5,8,7,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,6,8,5,4,2,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,1,8,5,2,6,3,7]=>{{1,2,4,5},{3,7,8},{6}}=>[2,4,7,5,1,6,8,3]=>0000000
[6,1,8,4,5,7,3,2]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[2,4,8,3,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[2,5,8,7,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,8,7,6,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,2,1,7,8,3,6]=>{{1,4},{2,3,5,7},{6,8}}=>[4,3,5,1,7,8,2,6]=>0000000
[2,5,8,1,3,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,5,2,3,7,6,4]=>{{1,2,4,8},{3,5},{6,7}}=>[2,4,5,8,3,7,6,1]=>0000000
[5,4,7,1,3,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,7,8,1,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,1,2,7,6,5,3]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[3,7,4,8,5,2,6,1]=>{{1,3,4,8},{2,6,7},{5}}=>[3,6,4,8,5,7,2,1]=>0000000
[8,1,2,6,5,3,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,3,8,7,1,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,4,8,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,8,7,4,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,7,8,6,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,6,8,2,1,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[3,7,6,8,2,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,7,8,6,3,1,2]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[3,6,7,8,2,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,6,8,7,3,1,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[7,5,6,2,3,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,3,8,5,4,2,1]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[3,8,5,7,6,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,6,3,8,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,2,5,3,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,2,8,4,3,1,5]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[5,7,2,8,3,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,5,8,6,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,6,2,8,4,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,7,8,4,2,6,1]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[4,7,6,8,3,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,4,7,1,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,3,8,4,5,2,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,3,8,2,7,1,6,4]=>{{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000
[3,6,2,5,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,2,7,8,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,3,8,2,5,4,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,7,1,8,3,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,7,2,5,3,1,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,6,1,5,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,4,2,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,8,1,2,3,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,5,2,1,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,5,1,7,8,2]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[4,6,5,3,1,7,8,2]=>{{1,3,4,5},{2,6,7,8}}=>[3,6,4,5,1,7,8,2]=>0000000
[4,3,1,8,5,2,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,5,8,2,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,4,8,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,6,8,3,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,7,2,8,3,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,6,8,7,2,3,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[5,6,8,1,2,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,1,3,5,7,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,8,1,4,5,7,2,3]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[5,6,8,1,3,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,5,8,6,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,1,7,6,8,4,5]=>{{1,2,3},{4,7},{5,6,8}}=>[2,3,1,7,6,8,4,5]=>0010000
[2,6,8,7,1,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,8,5,6,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,8,4,5,3,1,7]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[2,5,3,8,4,1,6,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,5,1,7,6,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,5,2,7,3,1,4]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[7,1,2,6,5,3,8,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,8,6,1,2,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,8,7,5,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,1,2,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,6,8,2,3,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,2,1,3,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,5,3,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,7,1,4,5,3,6,2]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[8,3,4,1,2,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,4,1,3,2,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,3,8,6,2,1,4,5]=>{{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000
[2,5,7,1,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,2,6,3,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,6,5,3,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,7,6,2,4,1,8]=>{{1,3,7},{2,5},{4,6},{8}}=>[3,5,7,6,2,4,1,8]=>0000001
[3,5,8,2,1,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,1,8,2,4,6,7]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[5,8,2,1,4,3,6,7]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[3,8,4,6,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,4,1,5,7,2,3]=>{{1,3,4,8},{2,6,7},{5}}=>[3,6,4,8,5,7,2,1]=>0000000
[8,1,6,4,5,2,3,7]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[3,8,6,2,1,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,6,2,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,8,6,7,2,1,4,5]=>{{1,3,6},{2,5,8},{4,7}}=>[3,5,6,7,8,1,4,2]=>0000000
[3,1,8,6,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,4,6,7,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,6,1,3,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,4,6,3,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,2,1,5,3,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,8,4,1,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,8,2,4,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,8,2,6,4,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,8,4,2,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[3,8,4,2,5,1,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[3,5,2,6,4,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,8,1,5,3,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,4,3,6,2,1,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,4,1,5,8,6,3,2]=>{{1,3,7},{2,4,5,8},{6}}=>[3,4,7,5,8,6,1,2]=>0000000
[4,5,8,7,3,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,4,7,5,1,2,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,8,5,1,7,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,4,6,3,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,2,1,5,7,3,4]=>{{1,4,8},{2,3,6,7},{5}}=>[4,3,6,8,5,7,2,1]=>0000000
[3,1,5,8,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,2,7,4,3,6,1,8]=>{{1,3,5,7},{2},{4},{6},{8}}=>[3,2,5,4,7,6,1,8]=>0000001
[3,1,5,7,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,3,7,4,5,8,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,6,5,1,7,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,6,5,4,1,2,7]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[8,4,1,7,5,2,6,3]=>{{1,3,8},{2,4,6,7},{5}}=>[3,4,8,6,5,7,2,1]=>0000000
[8,4,2,7,5,3,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,5,7,6,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,7,6,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,6,5,2,7,1]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,3,8,6,5,1,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[8,4,7,1,2,5,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[5,7,8,1,3,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,2,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,5,8,1,7,2,6]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[4,5,6,2,7,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,6,2,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,1,6,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,6,3,4,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,8,4,5,3,6,2]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[4,3,2,7,5,1,8,6]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[7,1,2,4,5,6,8,3]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>0000000
[2,8,7,1,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,1,3,4,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,2,7,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,6,2,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,2,7,6,3,1,8]=>{{1,4,7},{2,3,5,6},{8}}=>[4,3,5,7,6,2,1,8]=>0000001
[3,5,2,6,7,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,7,1,8,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,4,7,6,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,8,1,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,6,1,5,8,7,3,4]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000
[8,1,3,2,7,6,4,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[7,1,4,2,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,5,4,2,6,3]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[5,1,6,7,4,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,4,1,6,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,1,2,6,8,7,5,4]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[8,6,2,4,5,1,3,7]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[6,5,2,3,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,2,3,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,6,2,3,1,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,1,3,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,8,2,3,1,5,4,7]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[2,5,4,8,1,7,3,6]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[5,1,3,2,6,7,8,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,1,2,4,5,7,8,3]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[3,7,2,8,1,4,5,6]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[3,8,4,5,2,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,6,3,5,1,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,8,7,5,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,2,6,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,5,2,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,2,8,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,2,8,7,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,3,5,2,7,8,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,5,4,1,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111
[4,5,8,2,3,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,8,2,7,3,4,1]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[4,6,1,3,7,8,5,2]=>{{1,3,4},{2,6,8},{5,7}}=>[3,6,4,1,7,8,5,2]=>0000000
[2,8,4,6,5,1,7,3]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[3,6,5,1,4,8,2,7]=>{{1,3,4,5},{2,6,7,8}}=>[3,6,4,5,1,7,8,2]=>0000000
[3,6,4,1,2,7,8,5]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[4,8,2,7,6,5,1,3]=>{{1,4,7},{2,3,8},{5,6}}=>[4,3,8,7,6,5,1,2]=>0000000
[5,4,2,8,7,6,1,3]=>{{1,5,7},{2,3,4,8},{6}}=>[5,3,4,8,7,6,1,2]=>0000000
[8,6,5,2,7,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,4,5,8,2,7]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[3,5,2,8,6,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,7,5,4,1,6,3]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[8,1,5,7,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,5,8,1,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,1,4,3,8,5,6,2]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[8,4,1,3,7,6,5,2]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000
[2,8,3,5,6,1,4,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,4,7,8,2,1,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[4,7,5,8,1,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,8,6,2,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,7,5,8,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,4,7,6,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,5,1,7,2,8,4]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[6,4,1,7,2,8,5,3]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[7,4,1,6,2,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,3,7,5,1,6,4]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[4,7,2,8,5,1,6,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,7,3,2,4,8,6,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,7,8,3,6,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,3,5,1,4,6,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,6,3,5,2,1,4,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,5,1,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,8,3,1,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,1,6,8,5,4,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,7,1,3,2,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,7,4,3,2,5,1]=>{{1,2,6,8},{3,5,7},{4}}=>[2,6,5,4,7,8,3,1]=>0000000
[2,8,5,1,3,7,6,4]=>{{1,2,4,8},{3,5},{6,7}}=>[2,4,5,8,3,7,6,1]=>0000000
[2,4,5,8,3,7,6,1]=>{{1,2,4,8},{3,5},{6,7}}=>[2,4,5,8,3,7,6,1]=>0000000
[2,5,4,1,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,5,8,2,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,1,4,2,8,7,3,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[8,7,1,3,2,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,5,2,8,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,4,3,2,7,5,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[5,3,1,6,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,6,7,1,4,8,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[5,8,1,2,7,4,3,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000
[4,6,3,7,8,1,5,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,6,3,5,2,1,7,4]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[6,8,3,1,2,5,4,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,5,1,8,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,1,7,5,4,2,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,8,2,7,5,3,6,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,8,3,1,4,7,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,3,1,7,8,5,6,4]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[2,3,1,8,7,5,6,4]=>{{1,2,3},{4,8},{5,6,7}}=>[2,3,1,8,6,7,5,4]=>0010000
[8,5,1,2,7,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,5,7,8,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,7,8,6,1,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[2,4,7,8,3,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,5,1,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,7,5,8,1,3,6,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[7,8,1,2,4,6,3,5]=>{{1,3,7},{2,4,5,8},{6}}=>[3,4,7,5,8,6,1,2]=>0000000
[5,8,2,1,7,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,8,1,4,2,3,5]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[6,4,5,1,2,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,6,3,5,2,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,6,2,5,3,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,5,2,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,4,3,6,7,2,1]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[6,8,2,1,5,3,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,5,3,8,6,7,4,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,4,5,1,8,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,8,2,5,1,4,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,8,3,7,6,1,5,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,4,3,7,2,8,6,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,5,3,8,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,6,5,7,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,1,7,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,2,5,4,8,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,1,4,2,5,3,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,8,4,1,5,3,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,4,1,3,5,2,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,4,8,1,5,2,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,1,8,3,5,2,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,1,2,5,4,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,8,1,3,5,4,6,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,1,6,8,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,2,7,1,5,8,3]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[2,6,3,7,5,4,8,1]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[6,4,1,3,8,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,3,8,1,5,7,6]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[7,5,2,3,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,2,8,1,4,5,3]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[7,1,6,2,4,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,8,1,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,8,1,3,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,2,1,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,1,5,2,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,1,8,2,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,6,3,1,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,3,2,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,2,8,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,6,3,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,5,6,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,5,6,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,1,8,4,6,3,2]=>{{1,3,7},{2,4,5,8},{6}}=>[3,4,7,5,8,6,1,2]=>0000000
[2,8,1,7,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,5,3,8,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,6,5,3,4,8,1,7]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[2,3,6,5,8,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,1,7,4,8,6,5]=>{{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000
[2,4,6,5,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,2,1,7,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,8,1,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,3,5,8,7,4,1,6]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000
[2,3,5,8,7,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,3,7,8,1,2,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,7,5,2,8,3,1]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[4,6,7,5,1,3,8,2]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[3,6,5,1,4,7,8,2]=>{{1,3,4,5},{2,6,7,8}}=>[3,6,4,5,1,7,8,2]=>0000000
[4,6,7,3,1,5,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,5,2,4,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,8,1,4,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,3,6,1,7,2,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,4,6,8,3,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,2,1,5,4,8,6]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[1,5,6,4,2,3,7,8]=>{{1},{2,5},{3,6},{4},{7},{8}}=>[1,5,6,4,2,3,7,8]=>1000011
[5,7,8,1,2,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,8,1,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,2,8,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,8,1,2,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,5,1,2,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,3,1,2,6,5,7]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[3,8,2,7,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,4,1,8,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,3,1,7,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,3,7,1,5,6,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,3,7,1,4,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,3,6,1,2,5,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,7,2,3,6,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,7,2,6,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,2,7,3,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,6,4,5,2,3]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[5,8,2,3,7,4,1,6]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[5,4,8,6,3,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,8,5,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,8,5,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,8,5,2,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,4,5,2,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,1,8,5,7,2,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,3,6,2,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,2,4,5,7,8,1,6]=>{{1,3,4,5,7},{2},{6,8}}=>[3,2,4,5,7,8,1,6]=>0000000
[3,6,7,2,4,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,3,5,2,8,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[1,4,6,8,7,2,5,3]=>{{1},{2,3,4,6,8},{5,7}}=>[1,3,4,6,7,8,5,2]=>1000000
[4,1,3,8,7,5,2,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,6,7,2,1,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,6,1,3,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,3,8,5,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,1,4,2,7,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,1,3,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,3,2,6,8,4,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,7,8,3,2,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,6,7,8,4,2,5]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000
[3,1,6,7,8,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,4,1,7,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,5,6,1,8,4,2]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[7,6,3,1,2,8,5,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,1,8,6,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,3,7,5,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,2,6,5,3,7,1]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[2,8,6,3,5,1,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[8,3,2,6,4,1,7,5]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[2,8,6,1,5,4,7,3]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[8,3,2,6,1,5,7,4]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[3,8,6,2,5,4,7,1]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[3,8,4,6,5,2,7,1]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[8,3,2,5,1,4,7,6]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[2,8,1,6,5,3,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[8,3,2,1,6,4,7,5]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000
[7,4,6,5,8,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,7,1,8,4,5,3]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000
[3,6,5,8,2,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,6,8,5,2,1,7]=>{{1,4,7,8},{2,3,6},{5}}=>[4,3,6,7,5,2,8,1]=>0000000
[4,3,6,8,5,2,7,1]=>{{1,4,8},{2,3,6},{5},{7}}=>[4,3,6,8,5,2,7,1]=>0000000
[3,6,5,8,1,7,4,2]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[4,1,6,8,5,2,3,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,4,5,8,6,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,5,8,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,1,3,6,8,5,2,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,4,5,8,6,1,7,2]=>{{1,3,5,6},{2,4,8},{7}}=>[3,4,5,8,6,1,7,2]=>0000000
[8,6,7,1,4,3,2,5]=>{{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000
[3,7,8,2,5,4,6,1]=>{{1,3,8},{2,4,6,7},{5}}=>[3,4,8,6,5,7,2,1]=>0000000
[5,4,7,8,3,6,1,2]=>{{1,3,5,7},{2,4,8},{6}}=>[3,4,5,8,7,6,1,2]=>0000000
[6,8,1,3,2,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,4,8,3,5,7,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,6,2,7,3,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,3,2,8,7,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,8,5,3,1,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,6,7,8,3,2,4]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,6,1,7,3,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,7,2,5,8,4,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,3,6,7,4,8,1,2]=>{{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000
[5,4,3,7,8,1,6,2]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,7,8,2,1,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[4,6,7,3,2,8,1,5]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[5,6,2,8,3,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,5,7,8,6,1,4,3]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[2,4,5,3,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,3,7,2,4,1,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,8,5,3,2,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,8,1,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,5,3,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,5,3,1,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,8,7,2,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,6,3,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,8,6,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,7,5,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,2,6,7,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,6,3,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,7,4,1,8,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,4,1,7,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,4,2,1,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,6,8,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,4,2,8,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,6,3,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,6,8,2,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,4,8,5,7,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,6,5,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,1,5,3,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,6,1,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,7,2,8,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,5,1,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,8,1,4,2,6,7]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[5,8,4,1,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,8,4,2,3,6]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[3,5,8,1,4,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,5,7,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,4,1,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,8,1,2,5,3,4,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,1,4,8,2,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,7,8,6,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,1,6,8,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,7,6,4,5,1,8,3]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[2,8,4,6,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,3,1,6,7,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,8,6,1,4,3,2,5]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[4,8,7,5,2,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,8,1,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,3,2,4,1,7,6]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[6,1,4,3,7,5,8,2]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[6,4,1,8,2,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,5,3,2,1,6,4]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[3,8,6,2,1,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,1,3,8,2,6,7]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[1,4,2,6,7,8,5,3]=>{{1},{2,3,4,6,8},{5,7}}=>[1,3,4,6,7,8,5,2]=>1000000
[5,6,2,7,8,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,8,2,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,4,1,7,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,7,8,2,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,8,5,4,2,1,6]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[2,7,4,5,6,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,7,8,3,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,3,6,8,1,7,2]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[3,7,4,5,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,3,5,8,1,6,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,6,1,7,3,2,8,5]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[2,5,1,8,3,7,4,6]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000
[4,8,3,5,2,1,6,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[3,8,4,1,7,5,2,6]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[6,7,1,5,2,8,4,3]=>{{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000
[4,3,7,8,2,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,7,2,1,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,3,8,6,1,2,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,3,8,4,5,1,2,6]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000
[4,8,7,5,1,3,2,6]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[4,8,7,5,1,2,6,3]=>{{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000
[7,8,6,2,1,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,5,7,1,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,6,3,1,2,5,4]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[7,4,5,8,1,3,6,2]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[4,5,3,7,1,6,8,2]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[6,8,4,1,5,7,2,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,5,6,4,1,7,3,2]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>0000000
[5,8,2,6,3,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,4,6,2,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,8,3,6,4,1,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[6,1,3,7,2,8,5,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,8,3,2,1,7,5,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,8,7,3,6,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,4,3,7,1,2,6]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[7,8,6,1,3,2,4,5]=>{{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000
[2,8,1,5,6,4,3,7]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[5,3,8,2,7,6,1,4]=>{{1,5,7},{2,3,4,8},{6}}=>[5,3,4,8,7,6,1,2]=>0000000
[7,4,8,3,1,6,5,2]=>{{1,5,7},{2,3,4,8},{6}}=>[5,3,4,8,7,6,1,2]=>0000000
[5,8,7,2,6,4,3,1]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[5,4,8,6,7,3,1,2]=>{{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000
[4,8,5,2,7,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,3,2,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,4,3,1,8,5,2,7]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,4,3,1,5,8,6,2]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[7,8,5,2,6,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,6,3,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,2,6,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,1,3,2,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,5,3,1,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,5,7,4,8,3,6,1]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>0000000
[7,4,1,3,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,3,1,8,5,2,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,5,2,3,7,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,3,2,8,5,7,4]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[3,8,5,1,2,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,3,6,5,2,7,4]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>0000000
[5,7,6,8,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,4,7,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,7,5,1,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,1,2,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,4,7,8,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,5,1,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,4,1,7,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,1,3,6,7,8,2]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[3,6,7,1,5,4,8,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,6,4,7,5,8,2,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,5,6,2,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,1,6,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,1,6,4,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,5,2,1,6,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,3,5,2,7,1,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,6,2,1,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,5,2,1,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,3,2,8,5,1,4,6]=>{{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000
[4,3,7,8,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,6,1,8,7,2,3,4]=>{{1,3,5,7},{2,6},{4,8}}=>[3,6,5,8,7,2,1,4]=>0000000
[3,4,7,5,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,7,8,5,2,6,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[3,5,6,7,2,4,1,8]=>{{1,3,4,6,7},{2,5},{8}}=>[3,5,4,6,2,7,1,8]=>0000001
[4,6,1,7,8,5,3,2]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000
[7,4,3,8,6,1,5,2]=>{{1,5,6,7},{2,4,8},{3}}=>[5,4,3,8,6,7,1,2]=>0000000
[4,8,7,2,6,1,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[7,6,2,8,4,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,2,6,4,5,3,1]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[2,3,8,7,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,5,6,8,4,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[7,1,2,6,3,4,5,8]=>{{1,2,3,5,7},{4,6},{8}}=>[2,3,5,6,7,4,1,8]=>0000001
[7,1,3,8,2,6,4,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[2,8,3,6,5,7,1,4]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000
[7,1,2,6,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,5,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,6,2,3,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,4,7,6,3,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,5,7,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,7,6,1,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,6,7,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,2,7,5,3,1,4]=>{{1,4,7,8},{2,3,6},{5}}=>[4,3,6,7,5,2,8,1]=>0000000
[4,3,7,1,2,8,5,6]=>{{1,4},{2,3,5,7},{6,8}}=>[4,3,5,1,7,8,2,6]=>0000000
[8,5,7,1,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,7,1,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,5,8,1,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,6,7,3,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,1,6,8,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,6,1,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,6,7,5,1,3,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,7,5,6,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,1,4,7,5,8,2,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,3,4,7,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,7,1,8,5,3,6,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,1,6,3,2,7,8,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000
[2,3,7,8,5,4,6,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,7,8,2,1,5,3,4]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[4,1,7,6,2,8,3,5]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[2,7,5,3,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,5,3,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[5,7,3,2,8,4,1,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,6,8,1,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,6,8,7,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,1,3,6,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,2,3,1,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,5,7,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,2,1,6,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,1,6,4,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,5,1,8,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,3,8,5,2,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,5,3,6,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,7,4,5,1,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,2,5,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,7,3,1,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,7,3,5,1,6,4,2]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[8,6,2,3,5,1,7,4]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[4,8,3,2,6,1,7,5]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000
[2,7,3,6,8,5,4,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,1,3,8,6,2,4,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[8,1,5,2,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,7,2,6,4,5,1,3]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[7,1,4,6,8,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,1,5,6,4,8,3]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[2,8,5,1,6,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,2,8,1,5,6,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[2,7,8,1,5,4,3,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,5,2,6,7,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,8,1,4,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,6,1,5,2,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,6,1,5,2,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,8,2,7,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,3,2,7,5,1,4]=>{{1,5,6,7},{2,4,8},{3}}=>[5,4,3,8,6,7,1,2]=>0000000
[5,6,4,1,7,2,8,3]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[5,4,3,1,7,2,8,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,3,6,2,5,8,1,7]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,4,2,3,1,7,8,6]=>{{1,5},{2,3,4},{6,7,8}}=>[5,3,4,2,1,7,8,6]=>0000100
[4,6,1,3,2,8,5,7]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[4,6,5,3,8,2,1,7]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[8,1,5,3,4,7,2,6]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[6,1,8,7,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,5,8,6,4,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,6,1,8,4,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,7,5,8,2,1,3]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[6,4,7,1,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,8,5,7,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,4,7,5,3,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,5,6,1,4,3,8,2]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000
[8,3,2,6,5,1,7,4]=>{{1,4,6,8},{2,3},{5},{7}}=>[4,3,2,6,5,8,7,1]=>0000000
[8,3,5,6,1,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,8,2,5,1,6,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,3,8,2,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,7,8,1,2,5,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[8,1,7,5,6,4,2,3]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000
[7,6,1,5,2,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,8,6,7,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,7,1,6,8,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,7,6,8,2,3,4]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000
[6,1,5,7,2,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,4,2,1,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,1,7,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,4,5,1,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,3,6,1,5,2,4,7]=>{{1,4,7,8},{2,3,6},{5}}=>[4,3,6,7,5,2,8,1]=>0000000
[5,4,1,6,3,7,8,2]=>{{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000
[5,4,1,3,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,4,7,1,5,2,6,3]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[8,6,7,1,4,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,1,2,7,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,7,4,1,3,6,5]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>0000000
[6,8,2,3,1,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,7,3,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,3,1,4,5,8,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[6,8,7,2,1,5,4,3]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[4,7,1,3,2,5,8,6]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[5,7,1,3,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,2,5,7,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,8,6,3,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,6,5,1,8,2,4,7]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000
[5,8,7,3,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,3,1,5,4,8,2,7]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000
[4,7,6,3,5,2,8,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[5,3,1,6,4,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,4,8,1,5,3,7,2]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[7,3,5,6,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,3,4,7,6,1,8,2]=>{{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000
[3,5,4,1,7,8,6,2]=>{{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000
[4,8,1,6,2,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,3,8,4,5,6,1]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,8,2,3,7,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,8,2,3,5,4,6,1]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,8,3,1,4,6,5,7]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[7,4,1,3,8,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,7,3,1,8,5,6,4]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[7,1,8,6,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,3,2,4,6,8,5]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
[4,8,2,3,7,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,8,5,3,4,2,1,7]=>{{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000
[8,1,3,2,7,5,4,6]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[4,5,2,3,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[6,5,2,3,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,4,5,3,8,7,1,2]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[8,2,6,7,5,3,1,4]=>{{1,4,7,8},{2},{3,6},{5}}=>[4,2,6,7,5,3,8,1]=>0000000
[6,4,5,8,7,3,1,2]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[4,6,5,3,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,6,5,8,7,3,1,4]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000
[4,8,7,2,5,3,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,8,4,7,5,3,1,6]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,8,2,7,5,3,1,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,4,3,8,1,6,5,2]=>{{1,5,7},{2,4,8},{3},{6}}=>[5,4,3,8,7,6,1,2]=>0000000
[2,6,5,7,8,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,4,8,6,2,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[2,3,6,5,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,4,2,6,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[6,1,7,3,5,8,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,4,1,3,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,8,7,2,6,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,1,8,4,5,6,2,7]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>0000000
[4,5,8,3,6,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[3,5,4,8,6,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,3,1,2,5,4,7,6]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000
[6,5,1,2,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[8,1,5,3,7,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,2,6,5,7,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[7,1,6,8,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[5,1,4,3,7,8,6,2]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[6,4,7,8,3,5,1,2]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000
[6,4,7,8,1,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,6,4,5,1,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000
[4,7,5,3,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,5,3,7,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[2,8,1,6,5,7,3,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[4,7,5,3,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,4,5,3,8,1,6,2]=>{{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000
[6,3,5,8,1,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,5,4,7,6,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,6,1,5,8,4,2]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[2,7,3,6,4,1,8,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[2,3,7,8,1,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,1,3,8,2,4,6,5]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000
[5,4,8,7,6,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,7,5,6,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[7,6,4,2,3,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,8,7,3,2,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[3,7,4,2,6,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,4,3,6,7,2,5]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000
[8,3,6,7,5,1,2,4]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000
[6,1,4,7,2,5,8,3]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000
[6,8,1,5,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[8,1,7,6,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,6,5,7,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000
[4,1,3,7,8,6,5,2]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
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