Identifier
-
Mp00151:
Permutations
—to cycle type⟶
Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
St000214: Permutations ⟶ ℤ
Values
=>
Cc0009;cc-rep-1
[1]=>{{1}}=>[1]=>[1]=>0
[1,2]=>{{1},{2}}=>[1,2]=>[1,2]=>0
[2,1]=>{{1,2}}=>[2,1]=>[2,1]=>1
[1,2,3]=>{{1},{2},{3}}=>[1,2,3]=>[1,2,3]=>0
[1,3,2]=>{{1},{2,3}}=>[1,3,2]=>[1,3,2]=>1
[2,1,3]=>{{1,2},{3}}=>[2,1,3]=>[2,1,3]=>1
[2,3,1]=>{{1,2,3}}=>[2,3,1]=>[3,1,2]=>0
[3,1,2]=>{{1,2,3}}=>[2,3,1]=>[3,1,2]=>0
[3,2,1]=>{{1,3},{2}}=>[3,2,1]=>[2,3,1]=>0
[1,2,3,4]=>{{1},{2},{3},{4}}=>[1,2,3,4]=>[1,2,3,4]=>0
[1,2,4,3]=>{{1},{2},{3,4}}=>[1,2,4,3]=>[1,2,4,3]=>1
[1,3,2,4]=>{{1},{2,3},{4}}=>[1,3,2,4]=>[1,3,2,4]=>1
[1,3,4,2]=>{{1},{2,3,4}}=>[1,3,4,2]=>[1,4,2,3]=>0
[1,4,2,3]=>{{1},{2,3,4}}=>[1,3,4,2]=>[1,4,2,3]=>0
[1,4,3,2]=>{{1},{2,4},{3}}=>[1,4,3,2]=>[1,3,4,2]=>0
[2,1,3,4]=>{{1,2},{3},{4}}=>[2,1,3,4]=>[2,1,3,4]=>1
[2,1,4,3]=>{{1,2},{3,4}}=>[2,1,4,3]=>[2,1,4,3]=>2
[2,3,1,4]=>{{1,2,3},{4}}=>[2,3,1,4]=>[3,1,2,4]=>0
[2,3,4,1]=>{{1,2,3,4}}=>[2,3,4,1]=>[4,1,2,3]=>0
[2,4,1,3]=>{{1,2,3,4}}=>[2,3,4,1]=>[4,1,2,3]=>0
[2,4,3,1]=>{{1,2,4},{3}}=>[2,4,3,1]=>[3,4,1,2]=>0
[3,1,2,4]=>{{1,2,3},{4}}=>[2,3,1,4]=>[3,1,2,4]=>0
[3,1,4,2]=>{{1,2,3,4}}=>[2,3,4,1]=>[4,1,2,3]=>0
[3,2,1,4]=>{{1,3},{2},{4}}=>[3,2,1,4]=>[2,3,1,4]=>0
[3,2,4,1]=>{{1,3,4},{2}}=>[3,2,4,1]=>[2,4,1,3]=>0
[3,4,1,2]=>{{1,3},{2,4}}=>[3,4,1,2]=>[3,1,4,2]=>0
[3,4,2,1]=>{{1,2,3,4}}=>[2,3,4,1]=>[4,1,2,3]=>0
[4,1,2,3]=>{{1,2,3,4}}=>[2,3,4,1]=>[4,1,2,3]=>0
[4,1,3,2]=>{{1,2,4},{3}}=>[2,4,3,1]=>[3,4,1,2]=>0
[4,2,1,3]=>{{1,3,4},{2}}=>[3,2,4,1]=>[2,4,1,3]=>0
[4,2,3,1]=>{{1,4},{2},{3}}=>[4,2,3,1]=>[2,3,4,1]=>0
[4,3,1,2]=>{{1,2,3,4}}=>[2,3,4,1]=>[4,1,2,3]=>0
[4,3,2,1]=>{{1,4},{2,3}}=>[4,3,2,1]=>[3,2,4,1]=>1
[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}=>[1,2,3,4,5]=>[1,2,3,4,5]=>0
[1,2,3,5,4]=>{{1},{2},{3},{4,5}}=>[1,2,3,5,4]=>[1,2,3,5,4]=>1
[1,2,4,3,5]=>{{1},{2},{3,4},{5}}=>[1,2,4,3,5]=>[1,2,4,3,5]=>1
[1,2,4,5,3]=>{{1},{2},{3,4,5}}=>[1,2,4,5,3]=>[1,2,5,3,4]=>0
[1,2,5,3,4]=>{{1},{2},{3,4,5}}=>[1,2,4,5,3]=>[1,2,5,3,4]=>0
[1,2,5,4,3]=>{{1},{2},{3,5},{4}}=>[1,2,5,4,3]=>[1,2,4,5,3]=>0
[1,3,2,4,5]=>{{1},{2,3},{4},{5}}=>[1,3,2,4,5]=>[1,3,2,4,5]=>1
[1,3,2,5,4]=>{{1},{2,3},{4,5}}=>[1,3,2,5,4]=>[1,3,2,5,4]=>2
[1,3,4,2,5]=>{{1},{2,3,4},{5}}=>[1,3,4,2,5]=>[1,4,2,3,5]=>0
[1,3,4,5,2]=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>[1,5,2,3,4]=>0
[1,3,5,2,4]=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>[1,5,2,3,4]=>0
[1,3,5,4,2]=>{{1},{2,3,5},{4}}=>[1,3,5,4,2]=>[1,4,5,2,3]=>0
[1,4,2,3,5]=>{{1},{2,3,4},{5}}=>[1,3,4,2,5]=>[1,4,2,3,5]=>0
[1,4,2,5,3]=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>[1,5,2,3,4]=>0
[1,4,3,2,5]=>{{1},{2,4},{3},{5}}=>[1,4,3,2,5]=>[1,3,4,2,5]=>0
[1,4,3,5,2]=>{{1},{2,4,5},{3}}=>[1,4,3,5,2]=>[1,3,5,2,4]=>0
[1,4,5,2,3]=>{{1},{2,4},{3,5}}=>[1,4,5,2,3]=>[1,4,2,5,3]=>0
[1,4,5,3,2]=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>[1,5,2,3,4]=>0
[1,5,2,3,4]=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>[1,5,2,3,4]=>0
[1,5,2,4,3]=>{{1},{2,3,5},{4}}=>[1,3,5,4,2]=>[1,4,5,2,3]=>0
[1,5,3,2,4]=>{{1},{2,4,5},{3}}=>[1,4,3,5,2]=>[1,3,5,2,4]=>0
[1,5,3,4,2]=>{{1},{2,5},{3},{4}}=>[1,5,3,4,2]=>[1,3,4,5,2]=>0
[1,5,4,2,3]=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>[1,5,2,3,4]=>0
[1,5,4,3,2]=>{{1},{2,5},{3,4}}=>[1,5,4,3,2]=>[1,4,3,5,2]=>1
[2,1,3,4,5]=>{{1,2},{3},{4},{5}}=>[2,1,3,4,5]=>[2,1,3,4,5]=>1
[2,1,3,5,4]=>{{1,2},{3},{4,5}}=>[2,1,3,5,4]=>[2,1,3,5,4]=>2
[2,1,4,3,5]=>{{1,2},{3,4},{5}}=>[2,1,4,3,5]=>[2,1,4,3,5]=>2
[2,1,4,5,3]=>{{1,2},{3,4,5}}=>[2,1,4,5,3]=>[2,1,5,3,4]=>1
[2,1,5,3,4]=>{{1,2},{3,4,5}}=>[2,1,4,5,3]=>[2,1,5,3,4]=>1
[2,1,5,4,3]=>{{1,2},{3,5},{4}}=>[2,1,5,4,3]=>[2,1,4,5,3]=>1
[2,3,1,4,5]=>{{1,2,3},{4},{5}}=>[2,3,1,4,5]=>[3,1,2,4,5]=>0
[2,3,1,5,4]=>{{1,2,3},{4,5}}=>[2,3,1,5,4]=>[3,1,2,5,4]=>1
[2,3,4,1,5]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>[4,1,2,3,5]=>0
[2,3,4,5,1]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[2,3,5,1,4]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[2,3,5,4,1]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>[4,5,1,2,3]=>0
[2,4,1,3,5]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>[4,1,2,3,5]=>0
[2,4,1,5,3]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[2,4,3,1,5]=>{{1,2,4},{3},{5}}=>[2,4,3,1,5]=>[3,4,1,2,5]=>0
[2,4,3,5,1]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>[3,5,1,2,4]=>0
[2,4,5,1,3]=>{{1,2,4},{3,5}}=>[2,4,5,1,3]=>[4,1,2,5,3]=>0
[2,4,5,3,1]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[2,5,1,3,4]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[2,5,1,4,3]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>[4,5,1,2,3]=>0
[2,5,3,1,4]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>[3,5,1,2,4]=>0
[2,5,3,4,1]=>{{1,2,5},{3},{4}}=>[2,5,3,4,1]=>[3,4,5,1,2]=>0
[2,5,4,1,3]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[2,5,4,3,1]=>{{1,2,5},{3,4}}=>[2,5,4,3,1]=>[4,3,5,1,2]=>1
[3,1,2,4,5]=>{{1,2,3},{4},{5}}=>[2,3,1,4,5]=>[3,1,2,4,5]=>0
[3,1,2,5,4]=>{{1,2,3},{4,5}}=>[2,3,1,5,4]=>[3,1,2,5,4]=>1
[3,1,4,2,5]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>[4,1,2,3,5]=>0
[3,1,4,5,2]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[3,1,5,2,4]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[3,1,5,4,2]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>[4,5,1,2,3]=>0
[3,2,1,4,5]=>{{1,3},{2},{4},{5}}=>[3,2,1,4,5]=>[2,3,1,4,5]=>0
[3,2,1,5,4]=>{{1,3},{2},{4,5}}=>[3,2,1,5,4]=>[2,3,1,5,4]=>1
[3,2,4,1,5]=>{{1,3,4},{2},{5}}=>[3,2,4,1,5]=>[2,4,1,3,5]=>0
[3,2,4,5,1]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>[2,5,1,3,4]=>0
[3,2,5,1,4]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>[2,5,1,3,4]=>0
[3,2,5,4,1]=>{{1,3,5},{2},{4}}=>[3,2,5,4,1]=>[2,4,5,1,3]=>0
[3,4,1,2,5]=>{{1,3},{2,4},{5}}=>[3,4,1,2,5]=>[3,1,4,2,5]=>0
[3,4,1,5,2]=>{{1,3},{2,4,5}}=>[3,4,1,5,2]=>[3,1,5,2,4]=>0
[3,4,2,1,5]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>[4,1,2,3,5]=>0
[3,4,2,5,1]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[3,4,5,1,2]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[3,4,5,2,1]=>{{1,3,5},{2,4}}=>[3,4,5,2,1]=>[4,2,5,1,3]=>0
[3,5,1,2,4]=>{{1,3},{2,4,5}}=>[3,4,1,5,2]=>[3,1,5,2,4]=>0
[3,5,1,4,2]=>{{1,3},{2,5},{4}}=>[3,5,1,4,2]=>[3,1,4,5,2]=>0
[3,5,2,1,4]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[3,5,2,4,1]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>[4,5,1,2,3]=>0
[3,5,4,1,2]=>{{1,3,4},{2,5}}=>[3,5,4,1,2]=>[4,1,3,5,2]=>0
[3,5,4,2,1]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[4,1,2,3,5]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>[4,1,2,3,5]=>0
[4,1,2,5,3]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[4,1,3,2,5]=>{{1,2,4},{3},{5}}=>[2,4,3,1,5]=>[3,4,1,2,5]=>0
[4,1,3,5,2]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>[3,5,1,2,4]=>0
[4,1,5,2,3]=>{{1,2,4},{3,5}}=>[2,4,5,1,3]=>[4,1,2,5,3]=>0
[4,1,5,3,2]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[4,2,1,3,5]=>{{1,3,4},{2},{5}}=>[3,2,4,1,5]=>[2,4,1,3,5]=>0
[4,2,1,5,3]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>[2,5,1,3,4]=>0
[4,2,3,1,5]=>{{1,4},{2},{3},{5}}=>[4,2,3,1,5]=>[2,3,4,1,5]=>0
[4,2,3,5,1]=>{{1,4,5},{2},{3}}=>[4,2,3,5,1]=>[2,3,5,1,4]=>0
[4,2,5,1,3]=>{{1,4},{2},{3,5}}=>[4,2,5,1,3]=>[2,4,1,5,3]=>0
[4,2,5,3,1]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>[2,5,1,3,4]=>0
[4,3,1,2,5]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>[4,1,2,3,5]=>0
[4,3,1,5,2]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[4,3,2,1,5]=>{{1,4},{2,3},{5}}=>[4,3,2,1,5]=>[3,2,4,1,5]=>1
[4,3,2,5,1]=>{{1,4,5},{2,3}}=>[4,3,2,5,1]=>[3,2,5,1,4]=>1
[4,3,5,1,2]=>{{1,4},{2,3,5}}=>[4,3,5,1,2]=>[4,1,5,2,3]=>0
[4,3,5,2,1]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[4,5,1,2,3]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[4,5,1,3,2]=>{{1,3,4},{2,5}}=>[3,5,4,1,2]=>[4,1,3,5,2]=>0
[4,5,2,1,3]=>{{1,4},{2,3,5}}=>[4,3,5,1,2]=>[4,1,5,2,3]=>0
[4,5,2,3,1]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[4,5,3,1,2]=>{{1,4},{2,5},{3}}=>[4,5,3,1,2]=>[3,4,1,5,2]=>0
[4,5,3,2,1]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>[3,5,1,2,4]=>0
[5,1,2,3,4]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[5,1,2,4,3]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>[4,5,1,2,3]=>0
[5,1,3,2,4]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>[3,5,1,2,4]=>0
[5,1,3,4,2]=>{{1,2,5},{3},{4}}=>[2,5,3,4,1]=>[3,4,5,1,2]=>0
[5,1,4,2,3]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[5,1,4,3,2]=>{{1,2,5},{3,4}}=>[2,5,4,3,1]=>[4,3,5,1,2]=>1
[5,2,1,3,4]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>[2,5,1,3,4]=>0
[5,2,1,4,3]=>{{1,3,5},{2},{4}}=>[3,2,5,4,1]=>[2,4,5,1,3]=>0
[5,2,3,1,4]=>{{1,4,5},{2},{3}}=>[4,2,3,5,1]=>[2,3,5,1,4]=>0
[5,2,3,4,1]=>{{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>[2,3,4,5,1]=>0
[5,2,4,1,3]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>[2,5,1,3,4]=>0
[5,2,4,3,1]=>{{1,5},{2},{3,4}}=>[5,2,4,3,1]=>[2,4,3,5,1]=>1
[5,3,1,2,4]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[5,3,1,4,2]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>[4,5,1,2,3]=>0
[5,3,2,1,4]=>{{1,4,5},{2,3}}=>[4,3,2,5,1]=>[3,2,5,1,4]=>1
[5,3,2,4,1]=>{{1,5},{2,3},{4}}=>[5,3,2,4,1]=>[3,2,4,5,1]=>1
[5,3,4,1,2]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[5,3,4,2,1]=>{{1,5},{2,3,4}}=>[5,3,4,2,1]=>[4,2,3,5,1]=>0
[5,4,1,2,3]=>{{1,3,5},{2,4}}=>[3,4,5,2,1]=>[4,2,5,1,3]=>0
[5,4,1,3,2]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[5,4,2,1,3]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>[5,1,2,3,4]=>0
[5,4,2,3,1]=>{{1,5},{2,3,4}}=>[5,3,4,2,1]=>[4,2,3,5,1]=>0
[5,4,3,1,2]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>[3,5,1,2,4]=>0
[5,4,3,2,1]=>{{1,5},{2,4},{3}}=>[5,4,3,2,1]=>[3,4,2,5,1]=>0
[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>1
[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>1
[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}=>[1,2,3,5,6,4]=>[1,2,3,6,4,5]=>0
[1,2,3,6,4,5]=>{{1},{2},{3},{4,5,6}}=>[1,2,3,5,6,4]=>[1,2,3,6,4,5]=>0
[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>0
[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>1
[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>2
[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}=>[1,2,4,5,3,6]=>[1,2,5,3,4,6]=>0
[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>0
[1,2,4,6,3,5]=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>0
[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}=>[1,2,4,6,5,3]=>[1,2,5,6,3,4]=>0
[1,2,5,3,4,6]=>{{1},{2},{3,4,5},{6}}=>[1,2,4,5,3,6]=>[1,2,5,3,4,6]=>0
[1,2,5,3,6,4]=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>0
[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>0
[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}=>[1,2,5,4,6,3]=>[1,2,4,6,3,5]=>0
[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}=>[1,2,5,6,3,4]=>[1,2,5,3,6,4]=>0
[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>0
[1,2,6,3,4,5]=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>0
[1,2,6,3,5,4]=>{{1},{2},{3,4,6},{5}}=>[1,2,4,6,5,3]=>[1,2,5,6,3,4]=>0
[1,2,6,4,3,5]=>{{1},{2},{3,5,6},{4}}=>[1,2,5,4,6,3]=>[1,2,4,6,3,5]=>0
[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}}=>[1,2,6,4,5,3]=>[1,2,4,5,6,3]=>0
[1,2,6,5,3,4]=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>0
[1,2,6,5,4,3]=>{{1},{2},{3,6},{4,5}}=>[1,2,6,5,4,3]=>[1,2,5,4,6,3]=>1
[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>2
[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}=>[1,3,2,5,6,4]=>[1,3,2,6,4,5]=>1
[1,3,2,6,4,5]=>{{1},{2,3},{4,5,6}}=>[1,3,2,5,6,4]=>[1,3,2,6,4,5]=>1
[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}}=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>1
[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}=>[1,3,4,2,5,6]=>[1,4,2,3,5,6]=>0
[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}=>[1,3,4,2,6,5]=>[1,4,2,3,6,5]=>1
[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>0
[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,3,4,6,2,5]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>[1,5,6,2,3,4]=>0
[1,3,5,2,4,6]=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>0
[1,3,5,2,6,4]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}=>[1,3,5,4,2,6]=>[1,4,5,2,3,6]=>0
[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>[1,4,6,2,3,5]=>0
[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}=>[1,3,5,6,2,4]=>[1,5,2,3,6,4]=>0
[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,3,6,2,4,5]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,3,6,2,5,4]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>[1,5,6,2,3,4]=>0
[1,3,6,4,2,5]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>[1,4,6,2,3,5]=>0
[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}=>[1,3,6,4,5,2]=>[1,4,5,6,2,3]=>0
[1,3,6,5,2,4]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,3,6,5,4,2]=>{{1},{2,3,6},{4,5}}=>[1,3,6,5,4,2]=>[1,5,4,6,2,3]=>1
[1,4,2,3,5,6]=>{{1},{2,3,4},{5},{6}}=>[1,3,4,2,5,6]=>[1,4,2,3,5,6]=>0
[1,4,2,3,6,5]=>{{1},{2,3,4},{5,6}}=>[1,3,4,2,6,5]=>[1,4,2,3,6,5]=>1
[1,4,2,5,3,6]=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>0
[1,4,2,5,6,3]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,4,2,6,3,5]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,4,2,6,5,3]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>[1,5,6,2,3,4]=>0
[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>0
[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}}=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>1
[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}=>[1,4,3,5,2,6]=>[1,3,5,2,4,6]=>0
[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>[1,3,6,2,4,5]=>0
[1,4,3,6,2,5]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>[1,3,6,2,4,5]=>0
[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}=>[1,4,3,6,5,2]=>[1,3,5,6,2,4]=>0
[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}=>[1,4,5,2,3,6]=>[1,4,2,5,3,6]=>0
[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}=>[1,4,5,2,6,3]=>[1,4,2,6,3,5]=>0
[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>0
[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,4,5,6,2,3]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,4,5,6,3,2]=>{{1},{2,4,6},{3,5}}=>[1,4,5,6,3,2]=>[1,5,3,6,2,4]=>0
[1,4,6,2,3,5]=>{{1},{2,4},{3,5,6}}=>[1,4,5,2,6,3]=>[1,4,2,6,3,5]=>0
[1,4,6,2,5,3]=>{{1},{2,4},{3,6},{5}}=>[1,4,6,2,5,3]=>[1,4,2,5,6,3]=>0
[1,4,6,3,2,5]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,4,6,3,5,2]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>[1,5,6,2,3,4]=>0
[1,4,6,5,2,3]=>{{1},{2,4,5},{3,6}}=>[1,4,6,5,2,3]=>[1,5,2,4,6,3]=>0
[1,4,6,5,3,2]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,5,2,3,4,6]=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>0
[1,5,2,3,6,4]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,5,2,4,3,6]=>{{1},{2,3,5},{4},{6}}=>[1,3,5,4,2,6]=>[1,4,5,2,3,6]=>0
[1,5,2,4,6,3]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>[1,4,6,2,3,5]=>0
[1,5,2,6,3,4]=>{{1},{2,3,5},{4,6}}=>[1,3,5,6,2,4]=>[1,5,2,3,6,4]=>0
[1,5,2,6,4,3]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,5,3,2,4,6]=>{{1},{2,4,5},{3},{6}}=>[1,4,3,5,2,6]=>[1,3,5,2,4,6]=>0
[1,5,3,2,6,4]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>[1,3,6,2,4,5]=>0
[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}}=>[1,5,3,4,2,6]=>[1,3,4,5,2,6]=>0
[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}=>[1,5,3,4,6,2]=>[1,3,4,6,2,5]=>0
[1,5,3,6,2,4]=>{{1},{2,5},{3},{4,6}}=>[1,5,3,6,2,4]=>[1,3,5,2,6,4]=>0
[1,5,3,6,4,2]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>[1,3,6,2,4,5]=>0
[1,5,4,2,3,6]=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>0
[1,5,4,2,6,3]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,5,4,3,2,6]=>{{1},{2,5},{3,4},{6}}=>[1,5,4,3,2,6]=>[1,4,3,5,2,6]=>1
[1,5,4,3,6,2]=>{{1},{2,5,6},{3,4}}=>[1,5,4,3,6,2]=>[1,4,3,6,2,5]=>1
[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}=>[1,5,4,6,2,3]=>[1,5,2,6,3,4]=>0
[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,5,6,2,3,4]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,5,6,2,4,3]=>{{1},{2,4,5},{3,6}}=>[1,4,6,5,2,3]=>[1,5,2,4,6,3]=>0
[1,5,6,3,2,4]=>{{1},{2,5},{3,4,6}}=>[1,5,4,6,2,3]=>[1,5,2,6,3,4]=>0
[1,5,6,3,4,2]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,5,6,4,2,3]=>{{1},{2,5},{3,6},{4}}=>[1,5,6,4,2,3]=>[1,4,5,2,6,3]=>0
[1,5,6,4,3,2]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>[1,4,6,2,3,5]=>0
[1,6,2,3,4,5]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,6,2,3,5,4]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>[1,5,6,2,3,4]=>0
[1,6,2,4,3,5]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>[1,4,6,2,3,5]=>0
[1,6,2,4,5,3]=>{{1},{2,3,6},{4},{5}}=>[1,3,6,4,5,2]=>[1,4,5,6,2,3]=>0
[1,6,2,5,3,4]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,6,2,5,4,3]=>{{1},{2,3,6},{4,5}}=>[1,3,6,5,4,2]=>[1,5,4,6,2,3]=>1
[1,6,3,2,4,5]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>[1,3,6,2,4,5]=>0
[1,6,3,2,5,4]=>{{1},{2,4,6},{3},{5}}=>[1,4,3,6,5,2]=>[1,3,5,6,2,4]=>0
[1,6,3,4,2,5]=>{{1},{2,5,6},{3},{4}}=>[1,5,3,4,6,2]=>[1,3,4,6,2,5]=>0
[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}}=>[1,6,3,4,5,2]=>[1,3,4,5,6,2]=>0
[1,6,3,5,2,4]=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>[1,3,6,2,4,5]=>0
[1,6,3,5,4,2]=>{{1},{2,6},{3},{4,5}}=>[1,6,3,5,4,2]=>[1,3,5,4,6,2]=>1
[1,6,4,2,3,5]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,6,4,2,5,3]=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>[1,5,6,2,3,4]=>0
[1,6,4,3,2,5]=>{{1},{2,5,6},{3,4}}=>[1,5,4,3,6,2]=>[1,4,3,6,2,5]=>1
[1,6,4,3,5,2]=>{{1},{2,6},{3,4},{5}}=>[1,6,4,3,5,2]=>[1,4,3,5,6,2]=>1
[1,6,4,5,2,3]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,6,4,5,3,2]=>{{1},{2,6},{3,4,5}}=>[1,6,4,5,3,2]=>[1,5,3,4,6,2]=>0
[1,6,5,2,3,4]=>{{1},{2,4,6},{3,5}}=>[1,4,5,6,3,2]=>[1,5,3,6,2,4]=>0
[1,6,5,2,4,3]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,6,5,3,2,4]=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>0
[1,6,5,3,4,2]=>{{1},{2,6},{3,4,5}}=>[1,6,4,5,3,2]=>[1,5,3,4,6,2]=>0
[1,6,5,4,2,3]=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>[1,4,6,2,3,5]=>0
[1,6,5,4,3,2]=>{{1},{2,6},{3,5},{4}}=>[1,6,5,4,3,2]=>[1,4,5,3,6,2]=>0
[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}}=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}}=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>2
[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}}=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>2
[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}}=>[2,1,3,5,6,4]=>[2,1,3,6,4,5]=>1
[2,1,3,6,4,5]=>{{1,2},{3},{4,5,6}}=>[2,1,3,5,6,4]=>[2,1,3,6,4,5]=>1
[2,1,3,6,5,4]=>{{1,2},{3},{4,6},{5}}=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>1
[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}}=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>3
[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}}=>[2,1,4,5,3,6]=>[2,1,5,3,4,6]=>1
[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>1
[2,1,4,6,3,5]=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>1
[2,1,4,6,5,3]=>{{1,2},{3,4,6},{5}}=>[2,1,4,6,5,3]=>[2,1,5,6,3,4]=>1
[2,1,5,3,4,6]=>{{1,2},{3,4,5},{6}}=>[2,1,4,5,3,6]=>[2,1,5,3,4,6]=>1
[2,1,5,3,6,4]=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>1
[2,1,5,4,3,6]=>{{1,2},{3,5},{4},{6}}=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>1
[2,1,5,4,6,3]=>{{1,2},{3,5,6},{4}}=>[2,1,5,4,6,3]=>[2,1,4,6,3,5]=>1
[2,1,5,6,3,4]=>{{1,2},{3,5},{4,6}}=>[2,1,5,6,3,4]=>[2,1,5,3,6,4]=>1
[2,1,5,6,4,3]=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>1
[2,1,6,3,4,5]=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>1
[2,1,6,3,5,4]=>{{1,2},{3,4,6},{5}}=>[2,1,4,6,5,3]=>[2,1,5,6,3,4]=>1
[2,1,6,4,3,5]=>{{1,2},{3,5,6},{4}}=>[2,1,5,4,6,3]=>[2,1,4,6,3,5]=>1
[2,1,6,4,5,3]=>{{1,2},{3,6},{4},{5}}=>[2,1,6,4,5,3]=>[2,1,4,5,6,3]=>1
[2,1,6,5,3,4]=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>1
[2,1,6,5,4,3]=>{{1,2},{3,6},{4,5}}=>[2,1,6,5,4,3]=>[2,1,5,4,6,3]=>2
[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>0
[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}}=>[2,3,1,4,6,5]=>[3,1,2,4,6,5]=>1
[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}}=>[2,3,1,5,4,6]=>[3,1,2,5,4,6]=>1
[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}}=>[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>0
[2,3,1,6,4,5]=>{{1,2,3},{4,5,6}}=>[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>0
[2,3,1,6,5,4]=>{{1,2,3},{4,6},{5}}=>[2,3,1,6,5,4]=>[3,1,2,5,6,4]=>0
[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>0
[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>1
[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,3,4,6,1,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[2,3,5,1,4,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[2,3,5,1,6,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,3,5,4,1,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>[4,5,1,2,3,6]=>0
[2,3,5,4,6,1]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[2,3,5,6,1,4]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>[5,1,2,3,6,4]=>0
[2,3,5,6,4,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,3,6,1,4,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,3,6,1,5,4]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[2,3,6,4,1,5]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[2,3,6,4,5,1]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>[4,5,6,1,2,3]=>0
[2,3,6,5,1,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>[5,4,6,1,2,3]=>1
[2,4,1,3,5,6]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>0
[2,4,1,3,6,5]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>1
[2,4,1,5,3,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[2,4,1,5,6,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,4,1,6,3,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,4,1,6,5,3]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[2,4,3,1,5,6]=>{{1,2,4},{3},{5},{6}}=>[2,4,3,1,5,6]=>[3,4,1,2,5,6]=>0
[2,4,3,1,6,5]=>{{1,2,4},{3},{5,6}}=>[2,4,3,1,6,5]=>[3,4,1,2,6,5]=>1
[2,4,3,5,1,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>[3,5,1,2,4,6]=>0
[2,4,3,5,6,1]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[2,4,3,6,1,5]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[2,4,3,6,5,1]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>[3,5,6,1,2,4]=>0
[2,4,5,1,3,6]=>{{1,2,4},{3,5},{6}}=>[2,4,5,1,3,6]=>[4,1,2,5,3,6]=>0
[2,4,5,1,6,3]=>{{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>[4,1,2,6,3,5]=>0
[2,4,5,3,1,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[2,4,5,3,6,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,4,5,6,1,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,4,5,6,3,1]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>[5,3,6,1,2,4]=>0
[2,4,6,1,3,5]=>{{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>[4,1,2,6,3,5]=>0
[2,4,6,1,5,3]=>{{1,2,4},{3,6},{5}}=>[2,4,6,1,5,3]=>[4,1,2,5,6,3]=>0
[2,4,6,3,1,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,4,6,3,5,1]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[2,4,6,5,1,3]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>[5,1,2,4,6,3]=>0
[2,4,6,5,3,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,5,1,3,4,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[2,5,1,3,6,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,5,1,4,3,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>[4,5,1,2,3,6]=>0
[2,5,1,4,6,3]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[2,5,1,6,3,4]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>[5,1,2,3,6,4]=>0
[2,5,1,6,4,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,5,3,1,4,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>[3,5,1,2,4,6]=>0
[2,5,3,1,6,4]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[2,5,3,4,1,6]=>{{1,2,5},{3},{4},{6}}=>[2,5,3,4,1,6]=>[3,4,5,1,2,6]=>0
[2,5,3,4,6,1]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>[3,4,6,1,2,5]=>0
[2,5,3,6,1,4]=>{{1,2,5},{3},{4,6}}=>[2,5,3,6,1,4]=>[3,5,1,2,6,4]=>0
[2,5,3,6,4,1]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[2,5,4,1,3,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[2,5,4,1,6,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,5,4,3,1,6]=>{{1,2,5},{3,4},{6}}=>[2,5,4,3,1,6]=>[4,3,5,1,2,6]=>1
[2,5,4,3,6,1]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>[4,3,6,1,2,5]=>1
[2,5,4,6,1,3]=>{{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>[5,1,2,6,3,4]=>0
[2,5,4,6,3,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,5,6,1,3,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,5,6,1,4,3]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>[5,1,2,4,6,3]=>0
[2,5,6,3,1,4]=>{{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>[5,1,2,6,3,4]=>0
[2,5,6,3,4,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,5,6,4,1,3]=>{{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>[4,5,1,2,6,3]=>0
[2,5,6,4,3,1]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[2,6,1,3,4,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,6,1,3,5,4]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[2,6,1,4,3,5]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[2,6,1,4,5,3]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>[4,5,6,1,2,3]=>0
[2,6,1,5,3,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,6,1,5,4,3]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>[5,4,6,1,2,3]=>1
[2,6,3,1,4,5]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[2,6,3,1,5,4]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>[3,5,6,1,2,4]=>0
[2,6,3,4,1,5]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>[3,4,6,1,2,5]=>0
[2,6,3,4,5,1]=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>[3,4,5,6,1,2]=>0
[2,6,3,5,1,4]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[2,6,3,5,4,1]=>{{1,2,6},{3},{4,5}}=>[2,6,3,5,4,1]=>[3,5,4,6,1,2]=>1
[2,6,4,1,3,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,6,4,1,5,3]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[2,6,4,3,1,5]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>[4,3,6,1,2,5]=>1
[2,6,4,3,5,1]=>{{1,2,6},{3,4},{5}}=>[2,6,4,3,5,1]=>[4,3,5,6,1,2]=>1
[2,6,4,5,1,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,6,4,5,3,1]=>{{1,2,6},{3,4,5}}=>[2,6,4,5,3,1]=>[5,3,4,6,1,2]=>0
[2,6,5,1,3,4]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>[5,3,6,1,2,4]=>0
[2,6,5,1,4,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,6,5,3,1,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[2,6,5,3,4,1]=>{{1,2,6},{3,4,5}}=>[2,6,4,5,3,1]=>[5,3,4,6,1,2]=>0
[2,6,5,4,1,3]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[2,6,5,4,3,1]=>{{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>[4,5,3,6,1,2]=>0
[3,1,2,4,5,6]=>{{1,2,3},{4},{5},{6}}=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>0
[3,1,2,4,6,5]=>{{1,2,3},{4},{5,6}}=>[2,3,1,4,6,5]=>[3,1,2,4,6,5]=>1
[3,1,2,5,4,6]=>{{1,2,3},{4,5},{6}}=>[2,3,1,5,4,6]=>[3,1,2,5,4,6]=>1
[3,1,2,5,6,4]=>{{1,2,3},{4,5,6}}=>[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>0
[3,1,2,6,4,5]=>{{1,2,3},{4,5,6}}=>[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>0
[3,1,2,6,5,4]=>{{1,2,3},{4,6},{5}}=>[2,3,1,6,5,4]=>[3,1,2,5,6,4]=>0
[3,1,4,2,5,6]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>0
[3,1,4,2,6,5]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>1
[3,1,4,5,2,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[3,1,4,5,6,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,1,4,6,2,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,1,4,6,5,2]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[3,1,5,2,4,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[3,1,5,2,6,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,1,5,4,2,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>[4,5,1,2,3,6]=>0
[3,1,5,4,6,2]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[3,1,5,6,2,4]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>[5,1,2,3,6,4]=>0
[3,1,5,6,4,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,1,6,2,4,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,1,6,2,5,4]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[3,1,6,4,2,5]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[3,1,6,4,5,2]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>[4,5,6,1,2,3]=>0
[3,1,6,5,2,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,1,6,5,4,2]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>[5,4,6,1,2,3]=>1
[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}}=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>0
[3,2,1,4,6,5]=>{{1,3},{2},{4},{5,6}}=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>1
[3,2,1,5,4,6]=>{{1,3},{2},{4,5},{6}}=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>1
[3,2,1,5,6,4]=>{{1,3},{2},{4,5,6}}=>[3,2,1,5,6,4]=>[2,3,1,6,4,5]=>0
[3,2,1,6,4,5]=>{{1,3},{2},{4,5,6}}=>[3,2,1,5,6,4]=>[2,3,1,6,4,5]=>0
[3,2,1,6,5,4]=>{{1,3},{2},{4,6},{5}}=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>0
[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}}=>[3,2,4,1,5,6]=>[2,4,1,3,5,6]=>0
[3,2,4,1,6,5]=>{{1,3,4},{2},{5,6}}=>[3,2,4,1,6,5]=>[2,4,1,3,6,5]=>1
[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>[2,5,1,3,4,6]=>0
[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[3,2,4,6,1,5]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[3,2,4,6,5,1]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>[2,5,6,1,3,4]=>0
[3,2,5,1,4,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>[2,5,1,3,4,6]=>0
[3,2,5,1,6,4]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[3,2,5,4,1,6]=>{{1,3,5},{2},{4},{6}}=>[3,2,5,4,1,6]=>[2,4,5,1,3,6]=>0
[3,2,5,4,6,1]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>[2,4,6,1,3,5]=>0
[3,2,5,6,1,4]=>{{1,3,5},{2},{4,6}}=>[3,2,5,6,1,4]=>[2,5,1,3,6,4]=>0
[3,2,5,6,4,1]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[3,2,6,1,4,5]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[3,2,6,1,5,4]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>[2,5,6,1,3,4]=>0
[3,2,6,4,1,5]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>[2,4,6,1,3,5]=>0
[3,2,6,4,5,1]=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>[2,4,5,6,1,3]=>0
[3,2,6,5,1,4]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[3,2,6,5,4,1]=>{{1,3,6},{2},{4,5}}=>[3,2,6,5,4,1]=>[2,5,4,6,1,3]=>1
[3,4,1,2,5,6]=>{{1,3},{2,4},{5},{6}}=>[3,4,1,2,5,6]=>[3,1,4,2,5,6]=>0
[3,4,1,2,6,5]=>{{1,3},{2,4},{5,6}}=>[3,4,1,2,6,5]=>[3,1,4,2,6,5]=>1
[3,4,1,5,2,6]=>{{1,3},{2,4,5},{6}}=>[3,4,1,5,2,6]=>[3,1,5,2,4,6]=>0
[3,4,1,5,6,2]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>[3,1,6,2,4,5]=>0
[3,4,1,6,2,5]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>[3,1,6,2,4,5]=>0
[3,4,1,6,5,2]=>{{1,3},{2,4,6},{5}}=>[3,4,1,6,5,2]=>[3,1,5,6,2,4]=>0
[3,4,2,1,5,6]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>0
[3,4,2,1,6,5]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>1
[3,4,2,5,1,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[3,4,2,5,6,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,4,2,6,1,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,4,2,6,5,1]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[3,4,5,1,2,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[3,4,5,1,6,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,4,5,2,1,6]=>{{1,3,5},{2,4},{6}}=>[3,4,5,2,1,6]=>[4,2,5,1,3,6]=>0
[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>[4,2,6,1,3,5]=>0
[3,4,5,6,1,2]=>{{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>[5,1,3,6,2,4]=>0
[3,4,5,6,2,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,4,6,1,2,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,4,6,1,5,2]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[3,4,6,2,1,5]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>[4,2,6,1,3,5]=>0
[3,4,6,2,5,1]=>{{1,3,6},{2,4},{5}}=>[3,4,6,2,5,1]=>[4,2,5,6,1,3]=>0
[3,4,6,5,1,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,4,6,5,2,1]=>{{1,3,6},{2,4,5}}=>[3,4,6,5,2,1]=>[5,2,4,6,1,3]=>0
[3,5,1,2,4,6]=>{{1,3},{2,4,5},{6}}=>[3,4,1,5,2,6]=>[3,1,5,2,4,6]=>0
[3,5,1,2,6,4]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>[3,1,6,2,4,5]=>0
[3,5,1,4,2,6]=>{{1,3},{2,5},{4},{6}}=>[3,5,1,4,2,6]=>[3,1,4,5,2,6]=>0
[3,5,1,4,6,2]=>{{1,3},{2,5,6},{4}}=>[3,5,1,4,6,2]=>[3,1,4,6,2,5]=>0
[3,5,1,6,2,4]=>{{1,3},{2,5},{4,6}}=>[3,5,1,6,2,4]=>[3,1,5,2,6,4]=>0
[3,5,1,6,4,2]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>[3,1,6,2,4,5]=>0
[3,5,2,1,4,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[3,5,2,1,6,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,5,2,4,1,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>[4,5,1,2,3,6]=>0
[3,5,2,4,6,1]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[3,5,2,6,1,4]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>[5,1,2,3,6,4]=>0
[3,5,2,6,4,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,5,4,1,2,6]=>{{1,3,4},{2,5},{6}}=>[3,5,4,1,2,6]=>[4,1,3,5,2,6]=>0
[3,5,4,1,6,2]=>{{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>[4,1,3,6,2,5]=>0
[3,5,4,2,1,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[3,5,4,2,6,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,5,4,6,1,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,5,4,6,2,1]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>[5,2,6,1,3,4]=>0
[3,5,6,1,2,4]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>[5,2,6,1,3,4]=>0
[3,5,6,1,4,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,5,6,2,1,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,5,6,2,4,1]=>{{1,3,6},{2,4,5}}=>[3,4,6,5,2,1]=>[5,2,4,6,1,3]=>0
[3,5,6,4,1,2]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[3,5,6,4,2,1]=>{{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>[4,5,2,6,1,3]=>0
[3,6,1,2,4,5]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>[3,1,6,2,4,5]=>0
[3,6,1,2,5,4]=>{{1,3},{2,4,6},{5}}=>[3,4,1,6,5,2]=>[3,1,5,6,2,4]=>0
[3,6,1,4,2,5]=>{{1,3},{2,5,6},{4}}=>[3,5,1,4,6,2]=>[3,1,4,6,2,5]=>0
[3,6,1,4,5,2]=>{{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>[3,1,4,5,6,2]=>0
[3,6,1,5,2,4]=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>[3,1,6,2,4,5]=>0
[3,6,1,5,4,2]=>{{1,3},{2,6},{4,5}}=>[3,6,1,5,4,2]=>[3,1,5,4,6,2]=>1
[3,6,2,1,4,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,6,2,1,5,4]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[3,6,2,4,1,5]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[3,6,2,4,5,1]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>[4,5,6,1,2,3]=>0
[3,6,2,5,1,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,6,2,5,4,1]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>[5,4,6,1,2,3]=>1
[3,6,4,1,2,5]=>{{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>[4,1,3,6,2,5]=>0
[3,6,4,1,5,2]=>{{1,3,4},{2,6},{5}}=>[3,6,4,1,5,2]=>[4,1,3,5,6,2]=>0
[3,6,4,2,1,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,6,4,2,5,1]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[3,6,4,5,1,2]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>[5,1,3,4,6,2]=>0
[3,6,4,5,2,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,6,5,1,2,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,6,5,1,4,2]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>[5,1,3,4,6,2]=>0
[3,6,5,2,1,4]=>{{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>[5,1,3,6,2,4]=>0
[3,6,5,2,4,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[3,6,5,4,1,2]=>{{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>[4,5,1,3,6,2]=>0
[3,6,5,4,2,1]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[4,1,2,3,5,6]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>0
[4,1,2,3,6,5]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>1
[4,1,2,5,3,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[4,1,2,5,6,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,1,2,6,3,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,1,2,6,5,3]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[4,1,3,2,5,6]=>{{1,2,4},{3},{5},{6}}=>[2,4,3,1,5,6]=>[3,4,1,2,5,6]=>0
[4,1,3,2,6,5]=>{{1,2,4},{3},{5,6}}=>[2,4,3,1,6,5]=>[3,4,1,2,6,5]=>1
[4,1,3,5,2,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>[3,5,1,2,4,6]=>0
[4,1,3,5,6,2]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[4,1,3,6,2,5]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[4,1,3,6,5,2]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>[3,5,6,1,2,4]=>0
[4,1,5,2,3,6]=>{{1,2,4},{3,5},{6}}=>[2,4,5,1,3,6]=>[4,1,2,5,3,6]=>0
[4,1,5,2,6,3]=>{{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>[4,1,2,6,3,5]=>0
[4,1,5,3,2,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[4,1,5,3,6,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,1,5,6,2,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,1,5,6,3,2]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>[5,3,6,1,2,4]=>0
[4,1,6,2,3,5]=>{{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>[4,1,2,6,3,5]=>0
[4,1,6,2,5,3]=>{{1,2,4},{3,6},{5}}=>[2,4,6,1,5,3]=>[4,1,2,5,6,3]=>0
[4,1,6,3,2,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,1,6,3,5,2]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[4,1,6,5,2,3]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>[5,1,2,4,6,3]=>0
[4,1,6,5,3,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,2,1,3,5,6]=>{{1,3,4},{2},{5},{6}}=>[3,2,4,1,5,6]=>[2,4,1,3,5,6]=>0
[4,2,1,3,6,5]=>{{1,3,4},{2},{5,6}}=>[3,2,4,1,6,5]=>[2,4,1,3,6,5]=>1
[4,2,1,5,3,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>[2,5,1,3,4,6]=>0
[4,2,1,5,6,3]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[4,2,1,6,3,5]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[4,2,1,6,5,3]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>[2,5,6,1,3,4]=>0
[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}}=>[4,2,3,1,5,6]=>[2,3,4,1,5,6]=>0
[4,2,3,1,6,5]=>{{1,4},{2},{3},{5,6}}=>[4,2,3,1,6,5]=>[2,3,4,1,6,5]=>1
[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}}=>[4,2,3,5,1,6]=>[2,3,5,1,4,6]=>0
[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>[2,3,6,1,4,5]=>0
[4,2,3,6,1,5]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>[2,3,6,1,4,5]=>0
[4,2,3,6,5,1]=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>[2,3,5,6,1,4]=>0
[4,2,5,1,3,6]=>{{1,4},{2},{3,5},{6}}=>[4,2,5,1,3,6]=>[2,4,1,5,3,6]=>0
[4,2,5,1,6,3]=>{{1,4},{2},{3,5,6}}=>[4,2,5,1,6,3]=>[2,4,1,6,3,5]=>0
[4,2,5,3,1,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>[2,5,1,3,4,6]=>0
[4,2,5,3,6,1]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[4,2,5,6,1,3]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[4,2,5,6,3,1]=>{{1,4,6},{2},{3,5}}=>[4,2,5,6,3,1]=>[2,5,3,6,1,4]=>0
[4,2,6,1,3,5]=>{{1,4},{2},{3,5,6}}=>[4,2,5,1,6,3]=>[2,4,1,6,3,5]=>0
[4,2,6,1,5,3]=>{{1,4},{2},{3,6},{5}}=>[4,2,6,1,5,3]=>[2,4,1,5,6,3]=>0
[4,2,6,3,1,5]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[4,2,6,3,5,1]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>[2,5,6,1,3,4]=>0
[4,2,6,5,1,3]=>{{1,4,5},{2},{3,6}}=>[4,2,6,5,1,3]=>[2,5,1,4,6,3]=>0
[4,2,6,5,3,1]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[4,3,1,2,5,6]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>0
[4,3,1,2,6,5]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>1
[4,3,1,5,2,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[4,3,1,5,6,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,3,1,6,2,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,3,1,6,5,2]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}}=>[4,3,2,1,5,6]=>[3,2,4,1,5,6]=>1
[4,3,2,1,6,5]=>{{1,4},{2,3},{5,6}}=>[4,3,2,1,6,5]=>[3,2,4,1,6,5]=>2
[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}}=>[4,3,2,5,1,6]=>[3,2,5,1,4,6]=>1
[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>[3,2,6,1,4,5]=>1
[4,3,2,6,1,5]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>[3,2,6,1,4,5]=>1
[4,3,2,6,5,1]=>{{1,4,6},{2,3},{5}}=>[4,3,2,6,5,1]=>[3,2,5,6,1,4]=>1
[4,3,5,1,2,6]=>{{1,4},{2,3,5},{6}}=>[4,3,5,1,2,6]=>[4,1,5,2,3,6]=>0
[4,3,5,1,6,2]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>[4,1,6,2,3,5]=>0
[4,3,5,2,1,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[4,3,5,2,6,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,3,5,6,1,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,3,5,6,2,1]=>{{1,4,6},{2,3,5}}=>[4,3,5,6,2,1]=>[5,2,3,6,1,4]=>0
[4,3,6,1,2,5]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>[4,1,6,2,3,5]=>0
[4,3,6,1,5,2]=>{{1,4},{2,3,6},{5}}=>[4,3,6,1,5,2]=>[4,1,5,6,2,3]=>0
[4,3,6,2,1,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,3,6,2,5,1]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[4,3,6,5,1,2]=>{{1,4,5},{2,3,6}}=>[4,3,6,5,1,2]=>[5,1,4,6,2,3]=>0
[4,3,6,5,2,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,5,1,2,3,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[4,5,1,2,6,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,5,1,3,2,6]=>{{1,3,4},{2,5},{6}}=>[3,5,4,1,2,6]=>[4,1,3,5,2,6]=>0
[4,5,1,3,6,2]=>{{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>[4,1,3,6,2,5]=>0
[4,5,1,6,2,3]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>[5,2,6,1,3,4]=>0
[4,5,1,6,3,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,5,2,1,3,6]=>{{1,4},{2,3,5},{6}}=>[4,3,5,1,2,6]=>[4,1,5,2,3,6]=>0
[4,5,2,1,6,3]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>[4,1,6,2,3,5]=>0
[4,5,2,3,1,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[4,5,2,3,6,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,5,2,6,1,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,5,2,6,3,1]=>{{1,4,6},{2,3,5}}=>[4,3,5,6,2,1]=>[5,2,3,6,1,4]=>0
[4,5,3,1,2,6]=>{{1,4},{2,5},{3},{6}}=>[4,5,3,1,2,6]=>[3,4,1,5,2,6]=>0
[4,5,3,1,6,2]=>{{1,4},{2,5,6},{3}}=>[4,5,3,1,6,2]=>[3,4,1,6,2,5]=>0
[4,5,3,2,1,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>[3,5,1,2,4,6]=>0
[4,5,3,2,6,1]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[4,5,3,6,1,2]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[4,5,3,6,2,1]=>{{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>[3,5,2,6,1,4]=>0
[4,5,6,1,2,3]=>{{1,4},{2,5},{3,6}}=>[4,5,6,1,2,3]=>[4,1,5,2,6,3]=>0
[4,5,6,1,3,2]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>[4,1,6,2,3,5]=>0
[4,5,6,2,1,3]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>[5,1,2,4,6,3]=>0
[4,5,6,2,3,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,5,6,3,1,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,5,6,3,2,1]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>[5,2,6,1,3,4]=>0
[4,6,1,2,3,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,6,1,2,5,3]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[4,6,1,3,2,5]=>{{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>[4,1,3,6,2,5]=>0
[4,6,1,3,5,2]=>{{1,3,4},{2,6},{5}}=>[3,6,4,1,5,2]=>[4,1,3,5,6,2]=>0
[4,6,1,5,2,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,6,1,5,3,2]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>[5,1,3,4,6,2]=>0
[4,6,2,1,3,5]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>[4,1,6,2,3,5]=>0
[4,6,2,1,5,3]=>{{1,4},{2,3,6},{5}}=>[4,3,6,1,5,2]=>[4,1,5,6,2,3]=>0
[4,6,2,3,1,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,6,2,3,5,1]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[4,6,2,5,1,3]=>{{1,4,5},{2,3,6}}=>[4,3,6,5,1,2]=>[5,1,4,6,2,3]=>0
[4,6,2,5,3,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,6,3,1,2,5]=>{{1,4},{2,5,6},{3}}=>[4,5,3,1,6,2]=>[3,4,1,6,2,5]=>0
[4,6,3,1,5,2]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>[3,4,1,5,6,2]=>0
[4,6,3,2,1,5]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[4,6,3,2,5,1]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>[3,5,6,1,2,4]=>0
[4,6,3,5,1,2]=>{{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>[3,5,1,4,6,2]=>0
[4,6,3,5,2,1]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[4,6,5,1,2,3]=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>[4,1,6,2,3,5]=>0
[4,6,5,1,3,2]=>{{1,4},{2,6},{3,5}}=>[4,6,5,1,3,2]=>[4,1,5,3,6,2]=>0
[4,6,5,2,1,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[4,6,5,2,3,1]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>[5,3,6,1,2,4]=>0
[4,6,5,3,1,2]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>[5,1,3,4,6,2]=>0
[4,6,5,3,2,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,1,2,3,4,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,1,2,4,3,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>[4,5,1,2,3,6]=>0
[5,1,2,4,6,3]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[5,1,2,6,3,4]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>[5,1,2,3,6,4]=>0
[5,1,2,6,4,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,1,3,2,4,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>[3,5,1,2,4,6]=>0
[5,1,3,2,6,4]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[5,1,3,4,2,6]=>{{1,2,5},{3},{4},{6}}=>[2,5,3,4,1,6]=>[3,4,5,1,2,6]=>0
[5,1,3,4,6,2]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>[3,4,6,1,2,5]=>0
[5,1,3,6,2,4]=>{{1,2,5},{3},{4,6}}=>[2,5,3,6,1,4]=>[3,5,1,2,6,4]=>0
[5,1,3,6,4,2]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[5,1,4,2,3,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[5,1,4,2,6,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,1,4,3,2,6]=>{{1,2,5},{3,4},{6}}=>[2,5,4,3,1,6]=>[4,3,5,1,2,6]=>1
[5,1,4,3,6,2]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>[4,3,6,1,2,5]=>1
[5,1,4,6,2,3]=>{{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>[5,1,2,6,3,4]=>0
[5,1,4,6,3,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,1,6,2,3,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,1,6,2,4,3]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>[5,1,2,4,6,3]=>0
[5,1,6,3,2,4]=>{{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>[5,1,2,6,3,4]=>0
[5,1,6,3,4,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,1,6,4,2,3]=>{{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>[4,5,1,2,6,3]=>0
[5,1,6,4,3,2]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[5,2,1,3,4,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>[2,5,1,3,4,6]=>0
[5,2,1,3,6,4]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[5,2,1,4,3,6]=>{{1,3,5},{2},{4},{6}}=>[3,2,5,4,1,6]=>[2,4,5,1,3,6]=>0
[5,2,1,4,6,3]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>[2,4,6,1,3,5]=>0
[5,2,1,6,3,4]=>{{1,3,5},{2},{4,6}}=>[3,2,5,6,1,4]=>[2,5,1,3,6,4]=>0
[5,2,1,6,4,3]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[5,2,3,1,4,6]=>{{1,4,5},{2},{3},{6}}=>[4,2,3,5,1,6]=>[2,3,5,1,4,6]=>0
[5,2,3,1,6,4]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>[2,3,6,1,4,5]=>0
[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>[2,3,4,5,1,6]=>0
[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>[2,3,4,6,1,5]=>0
[5,2,3,6,1,4]=>{{1,5},{2},{3},{4,6}}=>[5,2,3,6,1,4]=>[2,3,5,1,6,4]=>0
[5,2,3,6,4,1]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>[2,3,6,1,4,5]=>0
[5,2,4,1,3,6]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>[2,5,1,3,4,6]=>0
[5,2,4,1,6,3]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[5,2,4,3,1,6]=>{{1,5},{2},{3,4},{6}}=>[5,2,4,3,1,6]=>[2,4,3,5,1,6]=>1
[5,2,4,3,6,1]=>{{1,5,6},{2},{3,4}}=>[5,2,4,3,6,1]=>[2,4,3,6,1,5]=>1
[5,2,4,6,1,3]=>{{1,5},{2},{3,4,6}}=>[5,2,4,6,1,3]=>[2,5,1,6,3,4]=>0
[5,2,4,6,3,1]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[5,2,6,1,3,4]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[5,2,6,1,4,3]=>{{1,4,5},{2},{3,6}}=>[4,2,6,5,1,3]=>[2,5,1,4,6,3]=>0
[5,2,6,3,1,4]=>{{1,5},{2},{3,4,6}}=>[5,2,4,6,1,3]=>[2,5,1,6,3,4]=>0
[5,2,6,3,4,1]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[5,2,6,4,1,3]=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>[2,4,5,1,6,3]=>0
[5,2,6,4,3,1]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>[2,4,6,1,3,5]=>0
[5,3,1,2,4,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[5,3,1,2,6,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,3,1,4,2,6]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>[4,5,1,2,3,6]=>0
[5,3,1,4,6,2]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[5,3,1,6,2,4]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>[5,1,2,3,6,4]=>0
[5,3,1,6,4,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,3,2,1,4,6]=>{{1,4,5},{2,3},{6}}=>[4,3,2,5,1,6]=>[3,2,5,1,4,6]=>1
[5,3,2,1,6,4]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>[3,2,6,1,4,5]=>1
[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}}=>[5,3,2,4,1,6]=>[3,2,4,5,1,6]=>1
[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}}=>[5,3,2,4,6,1]=>[3,2,4,6,1,5]=>1
[5,3,2,6,1,4]=>{{1,5},{2,3},{4,6}}=>[5,3,2,6,1,4]=>[3,2,5,1,6,4]=>1
[5,3,2,6,4,1]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>[3,2,6,1,4,5]=>1
[5,3,4,1,2,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[5,3,4,1,6,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}}=>[5,3,4,2,1,6]=>[4,2,3,5,1,6]=>0
[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}}=>[5,3,4,2,6,1]=>[4,2,3,6,1,5]=>0
[5,3,4,6,1,2]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>[5,1,6,2,3,4]=>0
[5,3,4,6,2,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,3,6,1,2,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,3,6,1,4,2]=>{{1,4,5},{2,3,6}}=>[4,3,6,5,1,2]=>[5,1,4,6,2,3]=>0
[5,3,6,2,1,4]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>[5,1,6,2,3,4]=>0
[5,3,6,2,4,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,3,6,4,1,2]=>{{1,5},{2,3,6},{4}}=>[5,3,6,4,1,2]=>[4,5,1,6,2,3]=>0
[5,3,6,4,2,1]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[5,4,1,2,3,6]=>{{1,3,5},{2,4},{6}}=>[3,4,5,2,1,6]=>[4,2,5,1,3,6]=>0
[5,4,1,2,6,3]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>[4,2,6,1,3,5]=>0
[5,4,1,3,2,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[5,4,1,3,6,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,4,1,6,2,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,4,1,6,3,2]=>{{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>[5,1,3,6,2,4]=>0
[5,4,2,1,3,6]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>0
[5,4,2,1,6,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,4,2,3,1,6]=>{{1,5},{2,3,4},{6}}=>[5,3,4,2,1,6]=>[4,2,3,5,1,6]=>0
[5,4,2,3,6,1]=>{{1,5,6},{2,3,4}}=>[5,3,4,2,6,1]=>[4,2,3,6,1,5]=>0
[5,4,2,6,1,3]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>[5,1,6,2,3,4]=>0
[5,4,2,6,3,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,4,3,1,2,6]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>[3,5,1,2,4,6]=>0
[5,4,3,1,6,2]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}}=>[5,4,3,2,1,6]=>[3,4,2,5,1,6]=>0
[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}}=>[5,4,3,2,6,1]=>[3,4,2,6,1,5]=>0
[5,4,3,6,1,2]=>{{1,5},{2,4,6},{3}}=>[5,4,3,6,1,2]=>[3,5,1,6,2,4]=>0
[5,4,3,6,2,1]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[5,4,6,1,2,3]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>[5,1,2,4,6,3]=>0
[5,4,6,1,3,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,4,6,2,1,3]=>{{1,5},{2,4},{3,6}}=>[5,4,6,2,1,3]=>[4,2,5,1,6,3]=>0
[5,4,6,2,3,1]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>[4,2,6,1,3,5]=>0
[5,4,6,3,1,2]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>[5,1,6,2,3,4]=>0
[5,4,6,3,2,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,6,1,2,3,4]=>{{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>[5,1,3,6,2,4]=>0
[5,6,1,2,4,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,6,1,3,2,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,6,1,3,4,2]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>[5,1,3,4,6,2]=>0
[5,6,1,4,2,3]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[5,6,1,4,3,2]=>{{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>[4,5,1,3,6,2]=>0
[5,6,2,1,3,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,6,2,1,4,3]=>{{1,4,5},{2,3,6}}=>[4,3,6,5,1,2]=>[5,1,4,6,2,3]=>0
[5,6,2,3,1,4]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>[5,1,6,2,3,4]=>0
[5,6,2,3,4,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,6,2,4,1,3]=>{{1,5},{2,3,6},{4}}=>[5,3,6,4,1,2]=>[4,5,1,6,2,3]=>0
[5,6,2,4,3,1]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[5,6,3,1,2,4]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[5,6,3,1,4,2]=>{{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>[3,5,1,4,6,2]=>0
[5,6,3,2,1,4]=>{{1,5},{2,4,6},{3}}=>[5,4,3,6,1,2]=>[3,5,1,6,2,4]=>0
[5,6,3,2,4,1]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[5,6,3,4,1,2]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>[3,4,5,1,6,2]=>0
[5,6,3,4,2,1]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>[3,4,6,1,2,5]=>0
[5,6,4,1,2,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,6,4,1,3,2]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>[5,1,3,4,6,2]=>0
[5,6,4,2,1,3]=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>[5,1,6,2,3,4]=>0
[5,6,4,2,3,1]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[5,6,4,3,1,2]=>{{1,5},{2,6},{3,4}}=>[5,6,4,3,1,2]=>[4,3,5,1,6,2]=>1
[5,6,4,3,2,1]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>[4,3,6,1,2,5]=>1
[6,1,2,3,4,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,1,2,3,5,4]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[6,1,2,4,3,5]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[6,1,2,4,5,3]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>[4,5,6,1,2,3]=>0
[6,1,2,5,3,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,1,2,5,4,3]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>[5,4,6,1,2,3]=>1
[6,1,3,2,4,5]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[6,1,3,2,5,4]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>[3,5,6,1,2,4]=>0
[6,1,3,4,2,5]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>[3,4,6,1,2,5]=>0
[6,1,3,4,5,2]=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>[3,4,5,6,1,2]=>0
[6,1,3,5,2,4]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[6,1,3,5,4,2]=>{{1,2,6},{3},{4,5}}=>[2,6,3,5,4,1]=>[3,5,4,6,1,2]=>1
[6,1,4,2,3,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,1,4,2,5,3]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[6,1,4,3,2,5]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>[4,3,6,1,2,5]=>1
[6,1,4,3,5,2]=>{{1,2,6},{3,4},{5}}=>[2,6,4,3,5,1]=>[4,3,5,6,1,2]=>1
[6,1,4,5,2,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,1,4,5,3,2]=>{{1,2,6},{3,4,5}}=>[2,6,4,5,3,1]=>[5,3,4,6,1,2]=>0
[6,1,5,2,3,4]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>[5,3,6,1,2,4]=>0
[6,1,5,2,4,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,1,5,3,2,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,1,5,3,4,2]=>{{1,2,6},{3,4,5}}=>[2,6,4,5,3,1]=>[5,3,4,6,1,2]=>0
[6,1,5,4,2,3]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[6,1,5,4,3,2]=>{{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>[4,5,3,6,1,2]=>0
[6,2,1,3,4,5]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[6,2,1,3,5,4]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>[2,5,6,1,3,4]=>0
[6,2,1,4,3,5]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>[2,4,6,1,3,5]=>0
[6,2,1,4,5,3]=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>[2,4,5,6,1,3]=>0
[6,2,1,5,3,4]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[6,2,1,5,4,3]=>{{1,3,6},{2},{4,5}}=>[3,2,6,5,4,1]=>[2,5,4,6,1,3]=>1
[6,2,3,1,4,5]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>[2,3,6,1,4,5]=>0
[6,2,3,1,5,4]=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>[2,3,5,6,1,4]=>0
[6,2,3,4,1,5]=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>[2,3,4,6,1,5]=>0
[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>[2,3,4,5,6,1]=>0
[6,2,3,5,1,4]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>[2,3,6,1,4,5]=>0
[6,2,3,5,4,1]=>{{1,6},{2},{3},{4,5}}=>[6,2,3,5,4,1]=>[2,3,5,4,6,1]=>1
[6,2,4,1,3,5]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[6,2,4,1,5,3]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>[2,5,6,1,3,4]=>0
[6,2,4,3,1,5]=>{{1,5,6},{2},{3,4}}=>[5,2,4,3,6,1]=>[2,4,3,6,1,5]=>1
[6,2,4,3,5,1]=>{{1,6},{2},{3,4},{5}}=>[6,2,4,3,5,1]=>[2,4,3,5,6,1]=>1
[6,2,4,5,1,3]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[6,2,4,5,3,1]=>{{1,6},{2},{3,4,5}}=>[6,2,4,5,3,1]=>[2,5,3,4,6,1]=>0
[6,2,5,1,3,4]=>{{1,4,6},{2},{3,5}}=>[4,2,5,6,3,1]=>[2,5,3,6,1,4]=>0
[6,2,5,1,4,3]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[6,2,5,3,1,4]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>0
[6,2,5,3,4,1]=>{{1,6},{2},{3,4,5}}=>[6,2,4,5,3,1]=>[2,5,3,4,6,1]=>0
[6,2,5,4,1,3]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>[2,4,6,1,3,5]=>0
[6,2,5,4,3,1]=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>[2,4,5,3,6,1]=>0
[6,3,1,2,4,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,3,1,2,5,4]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[6,3,1,4,2,5]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[6,3,1,4,5,2]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>[4,5,6,1,2,3]=>0
[6,3,1,5,2,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,3,1,5,4,2]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>[5,4,6,1,2,3]=>1
[6,3,2,1,4,5]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>[3,2,6,1,4,5]=>1
[6,3,2,1,5,4]=>{{1,4,6},{2,3},{5}}=>[4,3,2,6,5,1]=>[3,2,5,6,1,4]=>1
[6,3,2,4,1,5]=>{{1,5,6},{2,3},{4}}=>[5,3,2,4,6,1]=>[3,2,4,6,1,5]=>1
[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}}=>[6,3,2,4,5,1]=>[3,2,4,5,6,1]=>1
[6,3,2,5,1,4]=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>[3,2,6,1,4,5]=>1
[6,3,2,5,4,1]=>{{1,6},{2,3},{4,5}}=>[6,3,2,5,4,1]=>[3,2,5,4,6,1]=>2
[6,3,4,1,2,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,3,4,1,5,2]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[6,3,4,2,1,5]=>{{1,5,6},{2,3,4}}=>[5,3,4,2,6,1]=>[4,2,3,6,1,5]=>0
[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}}=>[6,3,4,2,5,1]=>[4,2,3,5,6,1]=>0
[6,3,4,5,1,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>[5,2,3,4,6,1]=>0
[6,3,5,1,2,4]=>{{1,4,6},{2,3,5}}=>[4,3,5,6,2,1]=>[5,2,3,6,1,4]=>0
[6,3,5,1,4,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,3,5,2,1,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,3,5,2,4,1]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>[5,2,3,4,6,1]=>0
[6,3,5,4,1,2]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[6,3,5,4,2,1]=>{{1,6},{2,3,5},{4}}=>[6,3,5,4,2,1]=>[4,5,2,3,6,1]=>0
[6,4,1,2,3,5]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>[4,2,6,1,3,5]=>0
[6,4,1,2,5,3]=>{{1,3,6},{2,4},{5}}=>[3,4,6,2,5,1]=>[4,2,5,6,1,3]=>0
[6,4,1,3,2,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,4,1,3,5,2]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[6,4,1,5,2,3]=>{{1,3,6},{2,4,5}}=>[3,4,6,5,2,1]=>[5,2,4,6,1,3]=>0
[6,4,1,5,3,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,4,2,1,3,5]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,4,2,1,5,3]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>0
[6,4,2,3,1,5]=>{{1,5,6},{2,3,4}}=>[5,3,4,2,6,1]=>[4,2,3,6,1,5]=>0
[6,4,2,3,5,1]=>{{1,6},{2,3,4},{5}}=>[6,3,4,2,5,1]=>[4,2,3,5,6,1]=>0
[6,4,2,5,1,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,4,2,5,3,1]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>[5,2,3,4,6,1]=>0
[6,4,3,1,2,5]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[6,4,3,1,5,2]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>[3,5,6,1,2,4]=>0
[6,4,3,2,1,5]=>{{1,5,6},{2,4},{3}}=>[5,4,3,2,6,1]=>[3,4,2,6,1,5]=>0
[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>[3,4,2,5,6,1]=>0
[6,4,3,5,1,2]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}}=>[6,4,3,5,2,1]=>[3,5,2,4,6,1]=>0
[6,4,5,1,2,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,4,5,1,3,2]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>[5,3,6,1,2,4]=>0
[6,4,5,2,1,3]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>[4,2,6,1,3,5]=>0
[6,4,5,2,3,1]=>{{1,6},{2,4},{3,5}}=>[6,4,5,2,3,1]=>[4,2,5,3,6,1]=>0
[6,4,5,3,1,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,4,5,3,2,1]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>[5,2,3,4,6,1]=>0
[6,5,1,2,3,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,5,1,2,4,3]=>{{1,3,6},{2,4,5}}=>[3,4,6,5,2,1]=>[5,2,4,6,1,3]=>0
[6,5,1,3,2,4]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>[5,2,6,1,3,4]=>0
[6,5,1,3,4,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,5,1,4,2,3]=>{{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>[4,5,2,6,1,3]=>0
[6,5,1,4,3,2]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[6,5,2,1,3,4]=>{{1,4,6},{2,3,5}}=>[4,3,5,6,2,1]=>[5,2,3,6,1,4]=>0
[6,5,2,1,4,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,5,2,3,1,4]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,5,2,3,4,1]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>[5,2,3,4,6,1]=>0
[6,5,2,4,1,3]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>0
[6,5,2,4,3,1]=>{{1,6},{2,3,5},{4}}=>[6,3,5,4,2,1]=>[4,5,2,3,6,1]=>0
[6,5,3,1,2,4]=>{{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>[3,5,2,6,1,4]=>0
[6,5,3,1,4,2]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[6,5,3,2,1,4]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>0
[6,5,3,2,4,1]=>{{1,6},{2,4,5},{3}}=>[6,4,3,5,2,1]=>[3,5,2,4,6,1]=>0
[6,5,3,4,1,2]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>[3,4,6,1,2,5]=>0
[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>[3,4,5,2,6,1]=>0
[6,5,4,1,2,3]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>[5,2,6,1,3,4]=>0
[6,5,4,1,3,2]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,5,4,2,1,3]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>0
[6,5,4,2,3,1]=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>[5,2,3,4,6,1]=>0
[6,5,4,3,1,2]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>[4,3,6,1,2,5]=>1
[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}}=>[6,5,4,3,2,1]=>[4,3,5,2,6,1]=>1
[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>1
[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>1
[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}=>[1,2,3,6,7,4,5]=>[1,2,3,6,4,7,5]=>0
[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}=>[1,2,4,6,7,3,5]=>[1,2,6,3,4,7,5]=>0
[1,2,6,3,7,4,5]=>{{1},{2},{3,4,6},{5,7}}=>[1,2,4,6,7,3,5]=>[1,2,6,3,4,7,5]=>0
[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>1
[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>1
[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,4,5,7,2,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,3,4,6,2,7,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>[1,6,2,3,4,7,5]=>0
[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,4,7,2,5,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,4,7,2,6,5]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,3,4,7,5,2,6]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>[1,5,6,7,2,3,4]=>0
[1,3,4,7,6,2,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,5,2,4,7,6]=>{{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>1
[1,3,5,2,6,7,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,5,2,7,4,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,5,2,7,6,4]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,3,5,4,7,2,6]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>[1,4,6,7,2,3,5]=>0
[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,5,6,7,2,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,5,7,4,2,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,6,2,4,7,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,6,2,5,7,4]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,3,6,2,7,4,5]=>{{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>[1,6,2,3,4,7,5]=>0
[1,3,6,2,7,5,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,6,4,2,7,5]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,3,6,5,2,7,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}=>[1,3,6,5,7,2,4]=>[1,6,2,3,7,4,5]=>0
[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,6,7,2,4,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,6,7,4,2,5]=>{{1},{2,3,6},{4,5,7}}=>[1,3,6,5,7,2,4]=>[1,6,2,3,7,4,5]=>0
[1,3,6,7,4,5,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,3,7,2,4,5,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,7,2,4,6,5]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,3,7,2,5,4,6]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,3,7,2,5,6,4]=>{{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>[1,5,6,7,2,3,4]=>0
[1,3,7,2,6,4,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,7,4,2,5,6]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,3,7,4,2,6,5]=>{{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>[1,4,6,7,2,3,5]=>0
[1,3,7,4,6,2,5]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,3,7,5,2,4,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,7,5,2,6,4]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,3,7,5,6,2,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,7,6,2,5,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,7,6,4,2,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,3,7,6,5,2,4]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,4,2,5,3,7,6]=>{{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>1
[1,4,2,5,6,7,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,2,5,7,3,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,2,5,7,6,3]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,4,2,6,3,7,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,2,6,5,7,3]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,4,2,6,7,3,5]=>{{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>[1,6,2,3,4,7,5]=>0
[1,4,2,6,7,5,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,2,7,3,5,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,2,7,3,6,5]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,4,2,7,5,3,6]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,4,2,7,5,6,3]=>{{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>[1,5,6,7,2,3,4]=>0
[1,4,2,7,6,3,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,4,3,5,7,2,6]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,4,3,6,2,7,5]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,4,3,7,2,5,6]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,4,3,7,6,2,5]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>1
[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,5,3,7,2,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,4,5,6,2,7,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,5,7,2,3,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,5,7,2,6,3]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,4,5,7,6,2,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,6,3,2,7,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>[1,6,2,3,4,7,5]=>0
[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,6,5,7,2,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,6,7,2,5,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,6,7,3,2,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,6,7,5,2,3]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,4,7,3,2,5,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,7,3,2,6,5]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,4,7,3,5,2,6]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,4,7,3,5,6,2]=>{{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>[1,5,6,7,2,3,4]=>0
[1,4,7,3,6,2,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,7,5,3,2,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,7,5,3,6,2]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,4,7,5,6,3,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,7,6,2,3,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,7,6,3,5,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,4,7,6,5,3,2]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,5,2,3,4,7,6]=>{{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>1
[1,5,2,3,6,7,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,2,3,7,4,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,2,3,7,6,4]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,5,2,4,6,7,3]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,5,2,4,7,3,6]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,5,2,4,7,6,3]=>{{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>[1,4,6,7,2,3,5]=>0
[1,5,2,6,4,7,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,2,6,7,3,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,2,7,4,3,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,2,7,4,6,3]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,5,2,7,6,4,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,3,2,6,7,4]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,5,3,2,7,4,6]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,5,3,6,7,2,4]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,5,3,7,4,2,6]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,5,3,7,6,4,2]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,5,4,2,3,7,6]=>{{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>1
[1,5,4,2,6,7,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,4,2,7,3,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,4,2,7,6,3]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>[1,5,2,7,3,4,6]=>0
[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,4,6,7,2,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,4,7,2,3,6]=>{{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>[1,5,2,7,3,4,6]=>0
[1,5,4,7,3,2,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,6,2,3,7,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,6,2,7,4,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,6,3,2,7,4]=>{{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>[1,5,2,7,3,4,6]=>0
[1,5,6,3,4,7,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,6,3,7,2,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,5,6,4,7,2,3]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>[1,5,2,7,3,4,6]=>0
[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,6,7,4,2,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,7,2,3,4,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,7,2,3,6,4]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,5,7,2,6,3,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,7,3,2,4,6]=>{{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>[1,5,2,7,3,4,6]=>0
[1,5,7,3,4,2,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,7,3,4,6,2]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,5,7,3,6,4,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,7,4,3,2,6]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,5,7,4,3,6,2]=>{{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>[1,4,6,7,2,3,5]=>0
[1,5,7,4,6,3,2]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,5,7,6,2,3,4]=>{{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>[1,5,2,7,3,4,6]=>0
[1,5,7,6,3,2,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,5,7,6,4,3,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,2,3,4,7,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,2,3,5,7,4]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,6,2,3,7,4,5]=>{{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>[1,6,2,3,4,7,5]=>0
[1,6,2,3,7,5,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,2,4,3,7,5]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,6,2,4,7,5,3]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,6,2,5,3,7,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,2,5,7,3,4]=>{{1},{2,3,6},{4,5,7}}=>[1,3,6,5,7,2,4]=>[1,6,2,3,7,4,5]=>0
[1,6,2,5,7,4,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,2,7,3,4,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,2,7,4,3,5]=>{{1},{2,3,6},{4,5,7}}=>[1,3,6,5,7,2,4]=>[1,6,2,3,7,4,5]=>0
[1,6,2,7,4,5,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,2,7,5,4,3]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,6,3,2,4,7,5]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,6,3,2,7,5,4]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,6,3,5,2,7,4]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,6,3,7,2,4,5]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,6,3,7,4,5,2]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,6,4,2,3,7,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,4,2,5,7,3]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,6,4,2,7,3,5]=>{{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>[1,6,2,3,4,7,5]=>0
[1,6,4,2,7,5,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,4,5,2,7,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>[1,6,2,7,3,4,5]=>0
[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,4,7,2,3,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,4,7,3,2,5]=>{{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>[1,6,2,7,3,4,5]=>0
[1,6,4,7,3,5,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}=>[1,6,4,7,5,2,3]=>[1,5,6,2,7,3,4]=>0
[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,6,5,2,4,7,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,5,2,7,3,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,5,3,2,7,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,5,3,7,2,4]=>{{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>[1,6,2,7,3,4,5]=>0
[1,6,5,3,7,4,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,5,4,2,7,3]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,6,5,7,2,4,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>[1,6,2,7,3,4,5]=>0
[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,7,2,3,5,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,7,2,4,3,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,7,2,5,3,4]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,6,7,3,2,4,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,7,3,4,2,5]=>{{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>[1,6,2,7,3,4,5]=>0
[1,6,7,3,4,5,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,7,3,5,2,4]=>{{1},{2,6},{3,4,7},{5}}=>[1,6,4,7,5,2,3]=>[1,5,6,2,7,3,4]=>0
[1,6,7,3,5,4,2]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,6,7,4,2,3,5]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,6,7,4,3,5,2]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,6,7,5,2,3,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,6,7,5,3,2,4]=>{{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>[1,6,2,7,3,4,5]=>0
[1,6,7,5,3,4,2]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,2,3,4,5,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,2,3,4,6,5]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,7,2,3,5,4,6]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,7,2,3,5,6,4]=>{{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>[1,5,6,7,2,3,4]=>0
[1,7,2,3,6,4,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,2,4,3,5,6]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,7,2,4,3,6,5]=>{{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>[1,4,6,7,2,3,5]=>0
[1,7,2,4,6,3,5]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,7,2,5,3,4,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,2,5,3,6,4]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,7,2,5,6,3,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,2,6,3,5,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,2,6,4,3,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,2,6,5,3,4]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,7,3,2,4,5,6]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,7,3,2,6,4,5]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,7,3,5,2,4,6]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,7,3,5,6,2,4]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,7,3,6,2,5,4]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,7,3,6,4,2,5]=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>0
[1,7,4,2,3,5,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,4,2,3,6,5]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,7,4,2,5,3,6]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,7,4,2,5,6,3]=>{{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>[1,5,6,7,2,3,4]=>0
[1,7,4,2,6,3,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,4,5,2,3,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,4,5,2,6,3]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,7,4,5,6,2,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,4,6,2,5,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,4,6,3,2,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,4,6,5,2,3]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,7,5,2,4,3,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,5,2,4,6,3]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,7,5,2,6,4,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,5,3,2,4,6]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,5,3,2,6,4]=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>0
[1,7,5,3,6,2,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,5,4,2,3,6]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,7,5,4,2,6,3]=>{{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>[1,4,6,7,2,3,5]=>0
[1,7,5,4,6,2,3]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,7,5,6,2,3,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,5,6,4,2,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,6,2,3,4,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,6,2,4,5,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,6,2,5,4,3]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,7,6,3,2,5,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,6,3,4,2,5]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,6,3,5,2,4]=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>0
[1,7,6,4,2,5,3]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,7,6,4,3,2,5]=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>0
[1,7,6,5,2,4,3]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[1,7,6,5,3,2,4]=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>0
[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}}=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>1
[2,1,3,4,6,7,5]=>{{1,2},{3},{4},{5,6,7}}=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,5,6]=>1
[2,1,3,4,7,5,6]=>{{1,2},{3},{4},{5,6,7}}=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,5,6]=>1
[2,1,3,5,6,7,4]=>{{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>1
[2,1,3,5,7,4,6]=>{{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>1
[2,1,3,6,4,7,5]=>{{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>1
[2,1,3,6,7,5,4]=>{{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>1
[2,1,3,7,4,5,6]=>{{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>1
[2,1,3,7,6,4,5]=>{{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>1
[2,1,4,5,6,3,7]=>{{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>1
[2,1,4,5,6,7,3]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,4,5,7,3,6]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,4,6,3,5,7]=>{{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>1
[2,1,4,6,3,7,5]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,4,6,7,5,3]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,4,7,3,5,6]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,4,7,6,3,5]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,5,3,6,4,7]=>{{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>1
[2,1,5,3,6,7,4]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,5,3,7,4,6]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,5,6,4,3,7]=>{{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>1
[2,1,5,6,4,7,3]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,5,6,7,3,4]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,5,7,4,3,6]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,5,7,6,4,3]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,6,3,4,5,7]=>{{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>1
[2,1,6,3,4,7,5]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,6,3,7,5,4]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,6,5,3,4,7]=>{{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>1
[2,1,6,5,3,7,4]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,6,5,7,4,3]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,6,7,3,4,5]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,6,7,4,5,3]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,7,3,4,5,6]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,7,3,6,4,5]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,7,5,3,4,6]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,7,5,6,3,4]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,7,6,3,5,4]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,1,7,6,4,3,5]=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>1
[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>0
[2,3,1,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}=>[2,3,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>1
[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>0
[2,3,4,1,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>1
[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[2,3,4,5,1,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,4,5,7,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,3,4,6,1,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,4,6,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[2,3,4,6,7,1,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[2,3,4,6,7,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,4,7,1,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,3,4,7,5,6,1]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[2,3,4,7,6,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,5,1,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[2,3,5,1,4,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[2,3,5,1,6,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,5,1,7,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,3,5,4,6,1,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[2,3,5,6,1,4,7]=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>[5,1,2,3,6,4,7]=>0
[2,3,5,6,1,7,4]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>[5,1,2,3,7,4,6]=>0
[2,3,5,6,4,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,3,5,6,4,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,5,6,7,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,5,7,1,4,6]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>[5,1,2,3,7,4,6]=>0
[2,3,5,7,1,6,4]=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>[5,1,2,3,6,7,4]=>0
[2,3,5,7,4,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,5,7,4,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,3,5,7,6,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,6,1,4,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,3,6,1,4,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,6,1,5,4,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[2,3,6,1,7,4,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[2,3,6,1,7,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,6,4,1,5,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[2,3,6,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>[4,5,6,1,2,3,7]=>0
[2,3,6,4,7,1,5]=>{{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>[4,6,1,2,3,7,5]=>0
[2,3,6,5,1,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,3,6,5,1,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,6,5,7,1,4]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>[6,1,2,3,7,4,5]=>0
[2,3,6,5,7,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,6,7,1,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,6,7,4,1,5]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>[6,1,2,3,7,4,5]=>0
[2,3,6,7,4,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,6,7,5,1,4]=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>[5,6,1,2,3,7,4]=>0
[2,3,7,1,4,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,7,1,4,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,3,7,1,5,6,4]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[2,3,7,1,6,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,7,5,1,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,7,5,1,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,3,7,5,4,6,1]=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>[5,4,6,7,1,2,3]=>1
[2,3,7,5,6,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,7,5,6,4,1]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>0
[2,3,7,6,1,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,7,6,4,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,3,7,6,4,5,1]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>0
[2,4,1,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>0
[2,4,1,3,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>1
[2,4,1,5,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[2,4,1,5,3,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[2,4,1,5,6,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,1,5,7,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,4,1,6,3,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,1,6,5,3,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[2,4,1,6,7,3,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[2,4,1,6,7,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,1,7,3,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,4,1,7,5,6,3]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,3,1,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}=>[2,4,3,1,5,6,7]=>[3,4,1,2,5,6,7]=>0
[2,4,3,5,6,1,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[2,4,3,6,1,5,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[2,4,3,6,5,1,7]=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>[3,5,6,1,2,4,7]=>0
[2,4,5,3,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[2,4,5,3,1,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[2,4,5,3,6,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,4,5,3,6,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,5,3,7,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,5,3,7,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,4,5,6,1,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,4,5,6,1,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,5,6,7,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,5,7,1,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,5,7,1,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,4,5,7,3,6,1]=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>[5,3,6,7,1,2,4]=>0
[2,4,5,7,6,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,6,3,1,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,4,6,3,1,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,6,3,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[2,4,6,3,7,1,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[2,4,6,3,7,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,6,5,3,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,4,6,5,3,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,6,5,7,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,6,7,1,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,6,7,3,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,7,3,1,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,7,3,1,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,4,7,3,5,6,1]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[2,4,7,3,6,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,7,5,3,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,7,5,3,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,4,7,5,6,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,7,6,1,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,4,7,6,3,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,1,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[2,5,1,3,4,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[2,5,1,3,6,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,5,1,3,6,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,1,3,7,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,1,3,7,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,5,1,4,6,3,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[2,5,1,6,3,4,7]=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>[5,1,2,3,6,4,7]=>0
[2,5,1,6,3,7,4]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>[5,1,2,3,7,4,6]=>0
[2,5,1,6,4,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,5,1,6,4,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,1,6,7,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,1,7,3,4,6]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>[5,1,2,3,7,4,6]=>0
[2,5,1,7,3,6,4]=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>[5,1,2,3,6,7,4]=>0
[2,5,1,7,4,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,1,7,4,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,5,1,7,6,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,3,1,6,4,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[2,5,3,6,4,1,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[2,5,4,1,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[2,5,4,1,3,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[2,5,4,1,6,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,5,4,1,6,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,4,1,7,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,5,4,6,1,3,7]=>{{1,2,5},{3,4,6},{7}}=>[2,5,4,6,1,3,7]=>[5,1,2,6,3,4,7]=>0
[2,5,4,6,3,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,5,4,6,3,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,4,6,7,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,4,6,7,3,1]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>0
[2,5,4,7,3,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,4,7,3,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,5,4,7,6,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,6,1,3,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,5,6,1,3,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,6,1,7,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,6,3,1,4,7]=>{{1,2,5},{3,4,6},{7}}=>[2,5,4,6,1,3,7]=>[5,1,2,6,3,4,7]=>0
[2,5,6,3,4,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,5,6,3,4,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,6,3,7,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,6,3,7,4,1]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>0
[2,5,6,4,3,1,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[2,5,6,7,3,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,6,7,4,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,7,1,3,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,7,1,3,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,5,7,1,6,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,7,3,4,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,7,3,4,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,5,7,3,6,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,7,6,3,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,5,7,6,4,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,1,3,4,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,6,1,3,4,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,1,3,5,4,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[2,6,1,3,7,4,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[2,6,1,3,7,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,1,4,3,5,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[2,6,1,4,5,3,7]=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>[4,5,6,1,2,3,7]=>0
[2,6,1,4,7,3,5]=>{{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>[4,6,1,2,3,7,5]=>0
[2,6,1,5,3,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,6,1,5,3,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,1,5,7,3,4]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>[6,1,2,3,7,4,5]=>0
[2,6,1,5,7,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,1,7,3,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,1,7,4,3,5]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>[6,1,2,3,7,4,5]=>0
[2,6,1,7,4,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,1,7,5,3,4]=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>[5,6,1,2,3,7,4]=>0
[2,6,3,1,4,5,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[2,6,3,1,5,4,7]=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>[3,5,6,1,2,4,7]=>0
[2,6,3,5,1,4,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[2,6,4,1,3,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,6,4,1,3,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,4,1,5,3,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[2,6,4,1,7,3,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[2,6,4,1,7,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,4,5,1,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,6,4,5,1,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,4,5,7,1,3]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>[6,1,2,7,3,4,5]=>0
[2,6,4,5,7,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,4,7,1,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,4,7,3,1,5]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>[6,1,2,7,3,4,5]=>0
[2,6,4,7,3,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,5,1,4,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,6,5,1,4,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,5,1,7,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,5,3,1,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[2,6,5,3,1,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,5,3,7,1,4]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>[6,1,2,7,3,4,5]=>0
[2,6,5,3,7,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,5,4,1,3,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[2,6,5,7,1,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,5,7,4,1,3]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>[6,1,2,7,3,4,5]=>0
[2,6,5,7,4,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,7,1,3,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,7,1,4,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,7,3,1,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,7,3,4,1,5]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>[6,1,2,7,3,4,5]=>0
[2,6,7,3,4,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,7,5,1,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,6,7,5,3,1,4]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>[6,1,2,7,3,4,5]=>0
[2,6,7,5,3,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,1,3,4,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,1,3,4,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,7,1,3,5,6,4]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[2,7,1,3,6,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,1,5,3,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,1,5,3,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,7,1,5,4,6,3]=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>[5,4,6,7,1,2,3]=>1
[2,7,1,5,6,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,1,5,6,4,3]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>0
[2,7,1,6,3,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,1,6,4,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,1,6,4,5,3]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>0
[2,7,3,4,5,6,1]=>{{1,2,7},{3},{4},{5},{6}}=>[2,7,3,4,5,6,1]=>[3,4,5,6,7,1,2]=>0
[2,7,4,1,3,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,4,1,3,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,7,4,1,5,6,3]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[2,7,4,1,6,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,4,5,1,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,4,5,1,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,7,4,5,6,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,4,6,1,3,5]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>0
[2,7,4,6,1,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,4,6,3,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,5,1,3,6,4]=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>[5,3,6,7,1,2,4]=>0
[2,7,5,1,4,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,5,1,4,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,7,5,1,6,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,5,3,1,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,5,3,1,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[2,7,5,3,6,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,5,6,1,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,5,6,4,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,6,1,3,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,6,1,4,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,6,3,1,4,5]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>0
[2,7,6,3,1,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,6,3,4,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,6,5,1,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[2,7,6,5,3,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,2,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>0
[3,1,2,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}=>[2,3,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>1
[3,1,4,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>0
[3,1,4,2,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>1
[3,1,4,5,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[3,1,4,5,2,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[3,1,4,5,6,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,1,4,5,6,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,4,5,7,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,1,4,6,2,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,4,6,5,2,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[3,1,4,6,7,2,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[3,1,4,6,7,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,4,7,2,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,4,7,2,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,1,4,7,5,6,2]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[3,1,4,7,6,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,5,2,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[3,1,5,2,4,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[3,1,5,2,6,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,5,2,7,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,1,5,4,6,2,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[3,1,5,6,2,4,7]=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>[5,1,2,3,6,4,7]=>0
[3,1,5,6,2,7,4]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>[5,1,2,3,7,4,6]=>0
[3,1,5,6,4,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,1,5,6,4,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,5,6,7,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,5,7,2,4,6]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>[5,1,2,3,7,4,6]=>0
[3,1,5,7,2,6,4]=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>[5,1,2,3,6,7,4]=>0
[3,1,5,7,4,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,5,7,4,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,1,5,7,6,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,6,2,4,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,1,6,2,4,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,6,2,5,4,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[3,1,6,2,7,4,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[3,1,6,2,7,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,6,4,2,5,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[3,1,6,4,5,2,7]=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>[4,5,6,1,2,3,7]=>0
[3,1,6,4,7,2,5]=>{{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>[4,6,1,2,3,7,5]=>0
[3,1,6,5,2,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,1,6,5,2,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,6,5,7,2,4]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>[6,1,2,3,7,4,5]=>0
[3,1,6,5,7,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,6,7,2,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,6,7,4,2,5]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>[6,1,2,3,7,4,5]=>0
[3,1,6,7,4,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,6,7,5,2,4]=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>[5,6,1,2,3,7,4]=>0
[3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,7,2,4,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,1,7,2,5,6,4]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[3,1,7,2,6,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,7,5,2,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,7,5,2,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,1,7,5,4,6,2]=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>[5,4,6,7,1,2,3]=>1
[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,7,5,6,4,2]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>0
[3,1,7,6,2,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,7,6,4,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,1,7,6,4,5,2]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>0
[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}}=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>0
[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}=>[3,2,4,1,5,6,7]=>[2,4,1,3,5,6,7]=>0
[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>[2,5,1,3,4,6,7]=>0
[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,4,5,7,1,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,4,5,7,6,1]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[3,2,4,6,1,5,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[3,2,4,6,1,7,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,4,6,5,7,1]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[3,2,4,6,7,5,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,4,7,1,5,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,4,7,1,6,5]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[3,2,4,7,5,1,6]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[3,2,4,7,6,1,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,5,1,4,6,7]=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>[2,5,1,3,4,6,7]=>0
[3,2,5,1,6,4,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[3,2,5,1,6,7,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,5,1,7,4,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,5,1,7,6,4]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[3,2,5,6,4,1,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[3,2,5,6,4,7,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,5,6,7,1,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,5,7,4,1,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,5,7,4,6,1]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[3,2,5,7,6,4,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,6,1,4,5,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[3,2,6,1,4,7,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,6,1,5,7,4]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[3,2,6,1,7,5,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,6,5,1,4,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[3,2,6,5,1,7,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,6,5,7,4,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,6,7,1,4,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,6,7,4,5,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,6,7,5,4,1]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[3,2,7,1,4,5,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,7,1,4,6,5]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[3,2,7,1,5,4,6]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[3,2,7,1,6,4,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,7,5,1,4,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,7,5,1,6,4]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[3,2,7,5,6,1,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,7,6,1,5,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,7,6,4,1,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[3,2,7,6,5,1,4]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[3,4,2,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>0
[3,4,2,1,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>1
[3,4,2,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[3,4,2,5,1,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[3,4,2,5,6,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,4,2,5,6,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,2,5,7,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,2,5,7,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,4,2,6,1,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,4,2,6,1,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,2,6,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[3,4,2,6,7,1,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[3,4,2,6,7,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,2,7,1,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,2,7,1,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,4,2,7,5,6,1]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[3,4,2,7,6,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,5,1,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[3,4,5,1,2,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[3,4,5,1,6,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,4,5,1,6,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,5,1,7,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,5,1,7,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,4,5,2,1,6,7]=>{{1,3,5},{2,4},{6},{7}}=>[3,4,5,2,1,6,7]=>[4,2,5,1,3,6,7]=>0
[3,4,5,6,2,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,4,5,6,2,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,5,6,7,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,5,7,2,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,5,7,2,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,4,5,7,6,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,6,1,2,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,4,6,1,2,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,6,1,5,2,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[3,4,6,1,7,2,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[3,4,6,1,7,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,6,5,1,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,4,6,5,1,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,6,5,7,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,6,7,1,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,6,7,2,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,7,1,2,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,7,1,2,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,4,7,1,5,6,2]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[3,4,7,1,6,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,7,5,1,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,7,5,1,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,4,7,5,6,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,7,6,1,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,4,7,6,2,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,2,1,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[3,5,2,1,4,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[3,5,2,1,6,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,5,2,1,6,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,2,1,7,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,2,1,7,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,5,2,4,6,1,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[3,5,2,6,1,4,7]=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>[5,1,2,3,6,4,7]=>0
[3,5,2,6,1,7,4]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>[5,1,2,3,7,4,6]=>0
[3,5,2,6,4,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,5,2,6,4,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,2,6,7,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,2,7,1,4,6]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>[5,1,2,3,7,4,6]=>0
[3,5,2,7,1,6,4]=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>[5,1,2,3,6,7,4]=>0
[3,5,2,7,4,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,2,7,4,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,5,2,7,6,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,4,2,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[3,5,4,2,1,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[3,5,4,2,6,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,5,4,2,6,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,4,2,7,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,4,2,7,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,5,4,6,1,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,5,4,6,1,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,4,6,7,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,4,7,1,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,4,7,1,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,5,4,7,2,6,1]=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>[5,2,6,7,1,3,4]=>0
[3,5,4,7,6,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,6,1,4,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,5,6,1,4,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,6,1,7,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,6,2,1,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,5,6,2,1,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,6,2,7,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,6,4,1,2,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[3,5,6,7,1,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,6,7,4,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,7,1,2,6,4]=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>[5,2,6,7,1,3,4]=>0
[3,5,7,1,4,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,7,1,4,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,5,7,1,6,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,7,2,1,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,7,2,1,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,5,7,2,6,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,7,6,1,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,5,7,6,4,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,2,1,4,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,6,2,1,4,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,2,1,5,4,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[3,6,2,1,7,4,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[3,6,2,1,7,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,2,4,1,5,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[3,6,2,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>[4,5,6,1,2,3,7]=>0
[3,6,2,4,7,1,5]=>{{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>[4,6,1,2,3,7,5]=>0
[3,6,2,5,1,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,6,2,5,1,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,2,5,7,1,4]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>[6,1,2,3,7,4,5]=>0
[3,6,2,5,7,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,2,7,1,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,2,7,4,1,5]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>[6,1,2,3,7,4,5]=>0
[3,6,2,7,4,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,2,7,5,1,4]=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>[5,6,1,2,3,7,4]=>0
[3,6,4,2,1,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,6,4,2,1,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,4,2,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[3,6,4,2,7,1,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[3,6,4,2,7,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,4,5,2,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,6,4,5,2,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,4,5,7,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,4,7,1,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,4,7,2,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,5,1,2,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,6,5,1,2,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,5,1,7,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,5,2,4,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[3,6,5,2,4,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,5,2,7,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,5,4,2,1,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[3,6,5,7,2,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,5,7,4,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,7,1,2,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,7,1,4,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,7,2,1,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,7,2,4,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,7,5,1,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,6,7,5,2,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,2,1,4,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,2,1,4,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,7,2,1,5,6,4]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[3,7,2,1,6,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,2,5,1,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,2,5,1,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,7,2,5,4,6,1]=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>[5,4,6,7,1,2,3]=>1
[3,7,2,5,6,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,2,5,6,4,1]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>0
[3,7,2,6,1,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,2,6,4,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,2,6,4,5,1]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>0
[3,7,4,2,1,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,4,2,1,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,7,4,2,5,6,1]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[3,7,4,2,6,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,4,5,2,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,4,5,2,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,7,4,5,6,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,4,6,1,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,4,6,2,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,5,1,2,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,5,1,2,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,7,5,1,6,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,5,2,4,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,5,2,4,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[3,7,5,2,6,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,5,6,2,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,5,6,4,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,6,1,2,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,6,1,4,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,6,2,1,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,6,2,4,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,6,5,1,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[3,7,6,5,2,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,2,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>0
[4,1,2,3,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>1
[4,1,2,5,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[4,1,2,5,3,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[4,1,2,5,6,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,1,2,5,6,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,2,5,7,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,2,5,7,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,1,2,6,3,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,1,2,6,3,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,2,6,5,3,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[4,1,2,6,7,3,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[4,1,2,6,7,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,2,7,3,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,2,7,3,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,1,2,7,5,6,3]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[4,1,2,7,6,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,3,2,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}=>[2,4,3,1,5,6,7]=>[3,4,1,2,5,6,7]=>0
[4,1,3,5,6,2,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[4,1,3,6,2,5,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[4,1,3,6,5,2,7]=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>[3,5,6,1,2,4,7]=>0
[4,1,5,3,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[4,1,5,3,2,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[4,1,5,3,6,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,1,5,3,6,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,5,3,7,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,5,3,7,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,1,5,6,2,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,1,5,6,2,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,5,6,7,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,5,7,2,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,5,7,2,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,1,5,7,3,6,2]=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>[5,3,6,7,1,2,4]=>0
[4,1,5,7,6,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,6,3,2,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,1,6,3,2,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,6,3,5,2,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[4,1,6,3,7,2,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[4,1,6,3,7,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,6,5,3,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,1,6,5,3,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,6,5,7,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,6,7,2,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,6,7,3,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,7,3,2,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,7,3,2,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,1,7,3,5,6,2]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[4,1,7,3,6,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,7,5,3,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,7,5,3,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,1,7,5,6,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,7,6,2,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,1,7,6,3,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,2,1,3,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}=>[3,2,4,1,5,6,7]=>[2,4,1,3,5,6,7]=>0
[4,2,1,5,3,6,7]=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>[2,5,1,3,4,6,7]=>0
[4,2,1,5,6,3,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[4,2,1,5,6,7,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,1,5,7,3,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,1,5,7,6,3]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[4,2,1,6,3,5,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[4,2,1,6,3,7,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,1,6,5,7,3]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[4,2,1,6,7,5,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,1,7,3,5,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,1,7,3,6,5]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[4,2,1,7,5,3,6]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[4,2,1,7,6,3,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,3,1,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}}=>[4,2,3,1,5,6,7]=>[2,3,4,1,5,6,7]=>0
[4,2,3,1,5,7,6]=>{{1,4},{2},{3},{5},{6,7}}=>[4,2,3,1,5,7,6]=>[2,3,4,1,5,7,6]=>1
[4,2,3,7,5,6,1]=>{{1,4,7},{2},{3},{5},{6}}=>[4,2,3,7,5,6,1]=>[2,3,5,6,7,1,4]=>0
[4,2,5,3,1,6,7]=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>[2,5,1,3,4,6,7]=>0
[4,2,5,3,6,1,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[4,2,5,3,6,7,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,5,3,7,1,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,5,3,7,6,1]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[4,2,5,6,1,3,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[4,2,5,6,1,7,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,5,6,7,3,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,5,7,1,3,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,5,7,1,6,3]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[4,2,5,7,6,1,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,6,3,1,5,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[4,2,6,3,1,7,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,6,3,5,7,1]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[4,2,6,3,7,5,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,6,5,3,1,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[4,2,6,5,3,7,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,6,5,7,1,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,6,7,1,5,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,6,7,3,1,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,6,7,5,1,3]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[4,2,7,3,1,5,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,7,3,1,6,5]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[4,2,7,3,5,1,6]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[4,2,7,3,6,1,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,7,5,3,1,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,7,5,3,6,1]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[4,2,7,5,6,3,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,7,6,1,3,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,7,6,3,5,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[4,2,7,6,5,3,1]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[4,3,1,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>0
[4,3,1,2,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>1
[4,3,1,5,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[4,3,1,5,2,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[4,3,1,5,6,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,3,1,5,6,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,1,5,7,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,1,5,7,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,3,1,6,2,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,3,1,6,2,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,1,6,5,2,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[4,3,1,6,7,2,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[4,3,1,6,7,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,1,7,2,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,1,7,2,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,3,1,7,5,6,2]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,5,1,6,2,7]=>{{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>[4,1,6,2,3,5,7]=>0
[4,3,5,2,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[4,3,5,2,1,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[4,3,5,2,6,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,3,5,2,6,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,5,2,7,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,5,2,7,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,3,5,6,1,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,3,5,6,1,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,5,6,7,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,5,7,1,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,5,7,1,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,3,5,7,6,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,6,1,2,5,7]=>{{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>[4,1,6,2,3,5,7]=>0
[4,3,6,2,1,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,3,6,2,1,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,6,2,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[4,3,6,2,7,1,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[4,3,6,2,7,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,6,5,2,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,3,6,5,2,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,6,5,7,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,6,7,1,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,6,7,2,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,7,2,1,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,7,2,1,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,3,7,2,5,6,1]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[4,3,7,2,6,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,7,5,2,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,7,5,2,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,3,7,5,6,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,7,6,1,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,3,7,6,2,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,1,2,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[4,5,1,2,3,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[4,5,1,2,6,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,5,1,2,6,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,1,2,7,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,1,2,7,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,5,1,6,3,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,5,1,6,3,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,1,6,7,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,1,7,2,6,3]=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>[5,2,6,7,1,3,4]=>0
[4,5,1,7,3,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,1,7,3,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,5,1,7,6,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,2,1,6,3,7]=>{{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>[4,1,6,2,3,5,7]=>0
[4,5,2,3,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[4,5,2,3,1,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[4,5,2,3,6,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,5,2,3,6,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,2,3,7,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,2,3,7,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,5,2,6,1,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,5,2,6,1,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,2,6,7,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,2,7,1,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,2,7,1,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,5,2,7,6,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,3,2,6,1,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[4,5,3,6,1,2,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[4,5,6,1,3,2,7]=>{{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>[4,1,6,2,3,5,7]=>0
[4,5,6,2,3,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,5,6,2,3,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,6,2,7,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,6,3,1,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,5,6,3,1,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,6,3,7,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,6,7,1,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,6,7,3,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,7,2,3,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,7,2,3,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,5,7,2,6,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,7,3,1,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,7,3,1,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,5,7,3,2,6,1]=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>[5,2,6,7,1,3,4]=>0
[4,5,7,3,6,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,7,6,1,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,5,7,6,3,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,1,2,3,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,6,1,2,3,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,1,2,5,3,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[4,6,1,2,7,3,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[4,6,1,2,7,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,1,5,2,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,6,1,5,2,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,1,5,7,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,1,7,2,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,1,7,3,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,2,1,3,5,7]=>{{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>[4,1,6,2,3,5,7]=>0
[4,6,2,3,1,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,6,2,3,1,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,2,3,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[4,6,2,3,7,1,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[4,6,2,3,7,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,2,5,3,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,6,2,5,3,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,2,5,7,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,2,7,1,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,2,7,3,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,3,2,1,5,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[4,6,3,2,5,1,7]=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>[3,5,6,1,2,4,7]=>0
[4,6,3,5,2,1,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[4,6,5,1,2,3,7]=>{{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>[4,1,6,2,3,5,7]=>0
[4,6,5,2,1,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,6,5,2,1,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,5,2,7,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,5,3,2,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[4,6,5,3,2,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,5,3,7,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,5,7,1,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,5,7,2,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,7,2,1,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,7,2,3,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,7,3,1,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,7,3,2,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,7,5,2,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,6,7,5,3,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,1,2,3,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,1,2,3,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,7,1,2,5,6,3]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[4,7,1,2,6,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,1,5,2,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,1,5,2,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,7,1,5,6,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,1,6,2,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,1,6,3,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,2,3,1,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,2,3,1,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,7,2,3,5,6,1]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[4,7,2,3,6,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,2,5,3,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,2,5,3,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,7,2,5,6,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,2,6,1,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,2,6,3,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,5,2,1,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,5,2,1,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,7,5,2,3,6,1]=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>[5,3,6,7,1,2,4]=>0
[4,7,5,2,6,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,5,3,2,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,5,3,2,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[4,7,5,3,6,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,5,6,1,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,5,6,2,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,6,2,1,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,6,2,3,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,6,3,1,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,6,3,2,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,6,5,2,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[4,7,6,5,3,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,2,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[5,1,2,3,4,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[5,1,2,3,6,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,1,2,3,6,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,2,3,7,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,2,3,7,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,1,2,4,6,3,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[5,1,2,6,3,4,7]=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>[5,1,2,3,6,4,7]=>0
[5,1,2,6,3,7,4]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>[5,1,2,3,7,4,6]=>0
[5,1,2,6,4,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,1,2,6,4,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,2,6,7,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,2,7,3,4,6]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>[5,1,2,3,7,4,6]=>0
[5,1,2,7,3,6,4]=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>[5,1,2,3,6,7,4]=>0
[5,1,2,7,4,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,2,7,4,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,1,2,7,6,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,3,2,6,4,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[5,1,3,6,4,2,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[5,1,4,2,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[5,1,4,2,3,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[5,1,4,2,6,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,1,4,2,6,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,4,2,7,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,4,2,7,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,1,4,6,2,3,7]=>{{1,2,5},{3,4,6},{7}}=>[2,5,4,6,1,3,7]=>[5,1,2,6,3,4,7]=>0
[5,1,4,6,3,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,1,4,6,3,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,4,6,7,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,4,6,7,3,2]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>0
[5,1,4,7,3,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,4,7,3,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,1,4,7,6,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,6,2,3,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,1,6,2,3,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,6,2,7,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,6,3,2,4,7]=>{{1,2,5},{3,4,6},{7}}=>[2,5,4,6,1,3,7]=>[5,1,2,6,3,4,7]=>0
[5,1,6,3,4,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,1,6,3,4,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,6,3,7,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,6,3,7,4,2]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>0
[5,1,6,4,3,2,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[5,1,6,7,3,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,6,7,4,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,7,2,3,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,7,2,3,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,1,7,2,6,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,7,3,4,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,7,3,4,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,1,7,3,6,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,7,6,3,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,1,7,6,4,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,2,1,3,4,6,7]=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>[2,5,1,3,4,6,7]=>0
[5,2,1,3,6,4,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[5,2,1,3,6,7,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,1,3,7,4,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,1,3,7,6,4]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[5,2,1,6,4,3,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[5,2,1,6,4,7,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,1,6,7,3,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,1,7,4,3,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,1,7,4,6,3]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[5,2,1,7,6,4,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,3,4,1,6,7]=>{{1,5},{2},{3},{4},{6},{7}}=>[5,2,3,4,1,6,7]=>[2,3,4,5,1,6,7]=>0
[5,2,3,4,1,7,6]=>{{1,5},{2},{3},{4},{6,7}}=>[5,2,3,4,1,7,6]=>[2,3,4,5,1,7,6]=>1
[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>[2,3,4,7,1,5,6]=>0
[5,2,3,4,7,1,6]=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>[2,3,4,7,1,5,6]=>0
[5,2,3,4,7,6,1]=>{{1,5,7},{2},{3},{4},{6}}=>[5,2,3,4,7,6,1]=>[2,3,4,6,7,1,5]=>0
[5,2,4,1,3,6,7]=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>[2,5,1,3,4,6,7]=>0
[5,2,4,1,6,3,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[5,2,4,1,6,7,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,4,1,7,3,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,4,1,7,6,3]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[5,2,4,6,3,1,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[5,2,4,6,3,7,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,4,6,7,1,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,4,7,3,1,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,4,7,3,6,1]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[5,2,4,7,6,3,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,6,1,3,4,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[5,2,6,1,3,7,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,6,1,7,4,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,6,3,4,1,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[5,2,6,3,4,7,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,6,3,7,1,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,6,7,3,4,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,6,7,4,1,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,7,1,3,4,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,7,1,3,6,4]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[5,2,7,1,6,3,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,7,3,4,1,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,7,3,4,6,1]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[5,2,7,3,6,4,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,7,6,3,1,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,2,7,6,4,3,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[5,3,1,2,4,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[5,3,1,2,4,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[5,3,1,2,6,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,3,1,2,6,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,1,2,7,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,1,2,7,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,3,1,4,6,2,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[5,3,1,6,2,4,7]=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>[5,1,2,3,6,4,7]=>0
[5,3,1,6,2,7,4]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>[5,1,2,3,7,4,6]=>0
[5,3,1,6,4,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,3,1,6,4,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,1,6,7,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,1,7,2,4,6]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>[5,1,2,3,7,4,6]=>0
[5,3,1,7,2,6,4]=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>[5,1,2,3,6,7,4]=>0
[5,3,1,7,4,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,1,7,4,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,3,1,7,6,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,4,1,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[5,3,4,1,2,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[5,3,4,1,6,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,3,4,1,6,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,4,1,7,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,4,1,7,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,3,4,6,1,2,7]=>{{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>[5,1,6,2,3,4,7]=>0
[5,3,4,6,2,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,3,4,6,2,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,4,6,7,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,4,7,2,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,4,7,2,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,3,4,7,6,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,6,1,2,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,3,6,1,2,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,6,1,7,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,6,2,1,4,7]=>{{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>[5,1,6,2,3,4,7]=>0
[5,3,6,2,4,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,3,6,2,4,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,6,2,7,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,6,4,1,2,7]=>{{1,5},{2,3,6},{4},{7}}=>[5,3,6,4,1,2,7]=>[4,5,1,6,2,3,7]=>0
[5,3,6,4,2,1,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[5,3,6,7,1,2,4]=>{{1,5},{2,3,6},{4,7}}=>[5,3,6,7,1,2,4]=>[5,1,6,2,3,7,4]=>0
[5,3,6,7,2,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,6,7,4,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,7,1,2,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,7,1,2,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,3,7,1,6,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,7,2,4,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,7,2,4,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,3,7,2,6,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,7,6,2,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,3,7,6,4,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,1,2,3,6,7]=>{{1,3,5},{2,4},{6},{7}}=>[3,4,5,2,1,6,7]=>[4,2,5,1,3,6,7]=>0
[5,4,1,3,2,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[5,4,1,3,2,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[5,4,1,3,6,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,4,1,3,6,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,1,3,7,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,1,3,7,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,4,1,6,2,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,4,1,6,2,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,1,6,7,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,1,7,2,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,1,7,2,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,4,1,7,6,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,2,1,3,6,7]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>0
[5,4,2,1,3,7,6]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>1
[5,4,2,1,6,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,4,2,1,6,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,2,1,7,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,2,1,7,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,4,2,6,1,3,7]=>{{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>[5,1,6,2,3,4,7]=>0
[5,4,2,6,3,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,4,2,6,3,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,2,6,7,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,2,7,3,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,2,7,3,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,4,2,7,6,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,3,1,6,2,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[5,4,3,6,2,1,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[5,4,6,1,3,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,4,6,1,3,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,6,1,7,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,6,3,1,2,7]=>{{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>[5,1,6,2,3,4,7]=>0
[5,4,6,3,2,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,4,6,3,2,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,6,3,7,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,6,7,2,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,6,7,3,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,7,1,3,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,7,1,3,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,4,7,1,6,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,7,3,2,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,7,3,2,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,4,7,3,6,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,7,6,2,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,4,7,6,3,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,1,2,4,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,6,1,2,4,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,1,2,7,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,1,3,2,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,6,1,3,2,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,1,3,7,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,1,4,2,3,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[5,6,1,7,2,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,1,7,4,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,2,1,3,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,6,2,1,3,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,2,1,7,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,2,3,1,4,7]=>{{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>[5,1,6,2,3,4,7]=>0
[5,6,2,3,4,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,6,2,3,4,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,2,3,7,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,2,4,1,3,7]=>{{1,5},{2,3,6},{4},{7}}=>[5,3,6,4,1,2,7]=>[4,5,1,6,2,3,7]=>0
[5,6,2,4,3,1,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[5,6,2,7,1,3,4]=>{{1,5},{2,3,6},{4,7}}=>[5,3,6,7,1,2,4]=>[5,1,6,2,3,7,4]=>0
[5,6,2,7,3,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,2,7,4,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,3,1,2,4,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[5,6,3,2,4,1,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[5,6,4,1,2,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,6,4,1,2,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,4,1,7,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,4,2,1,3,7]=>{{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>[5,1,6,2,3,4,7]=>0
[5,6,4,2,3,1,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[5,6,4,2,3,7,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,4,2,7,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,4,7,2,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,4,7,3,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,7,1,2,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,7,1,3,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,7,2,3,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,7,2,4,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,7,3,2,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,6,7,3,4,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,1,2,4,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,1,2,4,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,7,1,2,6,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,1,3,2,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,1,3,2,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,7,1,3,6,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,1,6,2,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,1,6,4,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,2,1,3,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,2,1,3,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,7,2,1,6,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,2,3,4,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,2,3,4,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,7,2,3,6,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,2,6,3,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,2,6,4,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,4,1,2,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,4,1,2,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,7,4,1,6,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,4,2,3,1,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,4,2,3,6,1]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[5,7,4,2,6,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,4,6,2,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,4,6,2,3,1]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>0
[5,7,4,6,3,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,6,1,2,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,6,1,3,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,6,2,3,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,6,2,4,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,6,3,2,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[5,7,6,3,2,4,1]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>0
[5,7,6,3,4,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,2,3,4,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,1,2,3,4,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,2,3,5,4,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[6,1,2,3,7,4,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[6,1,2,3,7,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,2,4,3,5,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[6,1,2,4,5,3,7]=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>[4,5,6,1,2,3,7]=>0
[6,1,2,4,7,3,5]=>{{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>[4,6,1,2,3,7,5]=>0
[6,1,2,5,3,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,1,2,5,3,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,2,5,7,3,4]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>[6,1,2,3,7,4,5]=>0
[6,1,2,5,7,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,2,7,3,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,2,7,4,3,5]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>[6,1,2,3,7,4,5]=>0
[6,1,2,7,4,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,2,7,5,3,4]=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>[5,6,1,2,3,7,4]=>0
[6,1,3,2,4,5,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[6,1,3,2,5,4,7]=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>[3,5,6,1,2,4,7]=>0
[6,1,3,5,2,4,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[6,1,4,2,3,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,1,4,2,3,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,4,2,5,3,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[6,1,4,2,7,3,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[6,1,4,2,7,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,4,5,2,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,1,4,5,2,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,4,5,7,2,3]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>[6,1,2,7,3,4,5]=>0
[6,1,4,5,7,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,4,7,2,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,4,7,3,2,5]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>[6,1,2,7,3,4,5]=>0
[6,1,4,7,3,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,5,2,4,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,1,5,2,4,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,5,2,7,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,5,3,2,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,1,5,3,2,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,5,3,7,2,4]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>[6,1,2,7,3,4,5]=>0
[6,1,5,3,7,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,5,4,2,3,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[6,1,5,7,2,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,5,7,4,2,3]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>[6,1,2,7,3,4,5]=>0
[6,1,5,7,4,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,7,2,3,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,7,2,4,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,7,3,2,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,7,3,4,2,5]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>[6,1,2,7,3,4,5]=>0
[6,1,7,3,4,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,7,5,2,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,1,7,5,3,2,4]=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>[6,1,2,7,3,4,5]=>0
[6,1,7,5,3,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,2,1,3,4,5,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[6,2,1,3,4,7,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,1,3,5,7,4]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[6,2,1,3,7,5,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,1,5,3,4,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[6,2,1,5,3,7,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,1,5,7,4,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,1,7,3,4,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,1,7,4,5,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,1,7,5,4,3]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[6,2,3,4,1,7,5]=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>[2,3,4,7,1,5,6]=>0
[6,2,3,4,5,1,7]=>{{1,6},{2},{3},{4},{5},{7}}=>[6,2,3,4,5,1,7]=>[2,3,4,5,6,1,7]=>0
[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}}=>[6,2,3,4,5,7,1]=>[2,3,4,5,7,1,6]=>0
[6,2,3,4,7,1,5]=>{{1,6},{2},{3},{4},{5,7}}=>[6,2,3,4,7,1,5]=>[2,3,4,6,1,7,5]=>0
[6,2,3,4,7,5,1]=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>[2,3,4,7,1,5,6]=>0
[6,2,4,1,3,5,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[6,2,4,1,3,7,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,4,1,5,7,3]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[6,2,4,1,7,5,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,4,5,1,3,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[6,2,4,5,1,7,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,4,5,7,1,3]=>{{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>[2,6,1,7,3,4,5]=>0
[6,2,4,5,7,3,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,4,7,1,3,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,4,7,3,1,5]=>{{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>[2,6,1,7,3,4,5]=>0
[6,2,4,7,3,5,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,4,7,5,3,1]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[6,2,5,1,4,3,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[6,2,5,1,4,7,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,5,1,7,3,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,5,3,1,4,7]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>0
[6,2,5,3,1,7,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,5,3,7,1,4]=>{{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>[2,6,1,7,3,4,5]=>0
[6,2,5,3,7,4,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,5,7,1,4,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,5,7,4,1,3]=>{{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>[2,6,1,7,3,4,5]=>0
[6,2,5,7,4,3,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,7,1,3,5,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,7,1,4,3,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,7,1,5,3,4]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[6,2,7,3,1,4,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,7,3,4,1,5]=>{{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>[2,6,1,7,3,4,5]=>0
[6,2,7,3,4,5,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,7,3,5,4,1]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[6,2,7,5,1,3,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,2,7,5,3,1,4]=>{{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>[2,6,1,7,3,4,5]=>0
[6,2,7,5,3,4,1]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[6,3,1,2,4,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,3,1,2,4,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,1,2,5,4,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[6,3,1,2,7,4,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[6,3,1,2,7,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,1,4,2,5,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[6,3,1,4,5,2,7]=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>[4,5,6,1,2,3,7]=>0
[6,3,1,4,7,2,5]=>{{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>[4,6,1,2,3,7,5]=>0
[6,3,1,5,2,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,3,1,5,2,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,1,5,7,2,4]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>[6,1,2,3,7,4,5]=>0
[6,3,1,5,7,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,1,7,2,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,1,7,4,2,5]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>[6,1,2,3,7,4,5]=>0
[6,3,1,7,4,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,1,7,5,2,4]=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>[5,6,1,2,3,7,4]=>0
[6,3,4,1,2,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,3,4,1,2,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,4,1,5,2,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[6,3,4,1,7,2,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[6,3,4,1,7,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,4,5,1,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,3,4,5,1,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,4,5,7,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,4,7,1,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,4,7,2,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,5,1,4,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,3,5,1,4,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,5,1,7,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,5,2,1,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,3,5,2,1,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,5,2,7,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,5,4,1,2,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[6,3,5,7,1,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,5,7,4,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,7,1,2,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,7,1,4,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,7,2,1,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,7,2,4,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,7,5,1,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,3,7,5,2,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,1,3,2,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,4,1,3,2,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,1,3,5,2,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[6,4,1,3,7,2,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[6,4,1,3,7,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,1,5,3,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,4,1,5,3,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,1,5,7,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,1,7,2,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,1,7,3,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,2,1,3,5,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,4,2,1,3,7,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,2,1,5,3,7]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>0
[6,4,2,1,7,3,5]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>0
[6,4,2,1,7,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,2,5,1,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,4,2,5,1,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,2,5,7,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,2,7,1,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,2,7,3,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,3,1,2,5,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[6,4,3,1,5,2,7]=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>[3,5,6,1,2,4,7]=>0
[6,4,3,5,1,2,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[6,4,5,1,2,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,4,5,1,2,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,5,1,7,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,5,3,1,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,4,5,3,1,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,5,3,7,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,5,7,1,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,5,7,2,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,7,1,2,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,7,1,3,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,7,3,1,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,7,3,2,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,7,5,1,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,4,7,5,3,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,1,2,3,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,5,1,2,3,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,1,2,7,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,1,3,4,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,5,1,3,4,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,1,3,7,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,1,4,3,2,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[6,5,1,7,3,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,1,7,4,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,2,1,4,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,5,2,1,4,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,2,1,7,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,2,3,1,4,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,5,2,3,1,7,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,2,3,7,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,2,4,1,3,7]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>0
[6,5,2,7,1,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,2,7,4,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,3,1,4,2,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[6,5,3,2,1,4,7]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>0
[6,5,4,1,3,2,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,5,4,1,3,7,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,4,1,7,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,4,2,1,3,7]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>0
[6,5,4,2,1,7,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,4,2,7,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,4,7,1,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,4,7,3,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,7,1,3,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,7,1,4,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,7,2,1,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,7,2,3,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,7,3,1,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,5,7,3,4,2,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,1,2,3,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,1,2,4,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,1,3,2,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,1,3,4,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,1,5,2,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,1,5,3,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,2,1,3,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,2,1,4,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,2,3,1,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,2,3,4,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,2,5,1,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,2,5,3,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,4,1,2,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,4,1,3,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,4,2,1,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,4,2,3,5,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,4,5,1,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,4,5,2,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,5,1,2,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,5,1,4,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,5,2,1,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,5,2,4,3,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,5,3,1,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[6,7,5,3,2,4,1]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,2,3,4,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,1,2,3,5,6,4]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[7,1,2,3,6,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,2,5,3,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,2,5,3,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,1,2,5,4,6,3]=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>[5,4,6,7,1,2,3]=>1
[7,1,2,5,6,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,2,5,6,4,3]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>0
[7,1,2,6,3,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,2,6,4,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,2,6,4,5,3]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>0
[7,1,3,4,5,6,2]=>{{1,2,7},{3},{4},{5},{6}}=>[2,7,3,4,5,6,1]=>[3,4,5,6,7,1,2]=>0
[7,1,4,2,3,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,4,2,3,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,1,4,2,5,6,3]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[7,1,4,2,6,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,4,5,2,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,4,5,2,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,1,4,5,6,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,4,6,2,3,5]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>0
[7,1,4,6,2,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,4,6,3,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,5,2,3,6,4]=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>[5,3,6,7,1,2,4]=>0
[7,1,5,2,4,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,5,2,4,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,1,5,2,6,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,5,3,2,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,5,3,2,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,1,5,3,6,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,5,6,2,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,5,6,4,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,6,2,3,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,6,2,4,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,6,3,2,4,5]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>0
[7,1,6,3,2,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,6,3,4,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,6,5,2,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,1,6,5,3,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,2,1,3,4,5,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,1,3,4,6,5]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[7,2,1,3,5,4,6]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[7,2,1,3,6,4,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,1,5,3,4,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,1,5,3,6,4]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[7,2,1,5,6,3,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,1,6,3,5,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,1,6,4,3,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,1,6,5,3,4]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[7,2,3,1,5,6,4]=>{{1,4,7},{2},{3},{5},{6}}=>[4,2,3,7,5,6,1]=>[2,3,5,6,7,1,4]=>0
[7,2,3,4,1,5,6]=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>[2,3,4,7,1,5,6]=>0
[7,2,3,4,1,6,5]=>{{1,5,7},{2},{3},{4},{6}}=>[5,2,3,4,7,6,1]=>[2,3,4,6,7,1,5]=>0
[7,2,3,4,5,1,6]=>{{1,6,7},{2},{3},{4},{5}}=>[6,2,3,4,5,7,1]=>[2,3,4,5,7,1,6]=>0
[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}}=>[7,2,3,4,5,6,1]=>[2,3,4,5,6,7,1]=>0
[7,2,3,4,6,1,5]=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>[2,3,4,7,1,5,6]=>0
[7,2,4,1,3,5,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,4,1,3,6,5]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[7,2,4,1,5,3,6]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[7,2,4,1,6,3,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,4,5,1,3,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,4,5,1,6,3]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[7,2,4,5,6,1,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,4,6,1,5,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,4,6,3,1,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,4,6,5,1,3]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[7,2,5,1,4,3,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,5,1,4,6,3]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[7,2,5,1,6,4,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,5,3,1,4,6]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,5,3,1,6,4]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>0
[7,2,5,3,6,1,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,5,6,1,3,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,5,6,4,1,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,6,1,3,4,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,6,1,4,5,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,6,1,5,4,3]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[7,2,6,3,1,5,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,6,3,4,1,5]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,6,3,5,1,4]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>0
[7,2,6,5,1,4,3]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,2,6,5,3,1,4]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>0
[7,3,1,2,4,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,1,2,4,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,3,1,2,5,6,4]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[7,3,1,2,6,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,1,5,2,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,1,5,2,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,3,1,5,4,6,2]=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>[5,4,6,7,1,2,3]=>1
[7,3,1,5,6,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,1,5,6,4,2]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>0
[7,3,1,6,2,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,1,6,4,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,1,6,4,5,2]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>0
[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}}=>[7,3,2,4,5,6,1]=>[3,2,4,5,6,7,1]=>1
[7,3,4,1,2,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,4,1,2,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,3,4,1,5,6,2]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[7,3,4,1,6,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}}=>[7,3,4,2,5,6,1]=>[4,2,3,5,6,7,1]=>0
[7,3,4,5,1,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,4,5,1,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>[5,2,3,4,6,7,1]=>0
[7,3,4,5,6,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,3,4,6,1,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,4,6,2,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,4,6,2,5,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,3,5,1,4,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,5,1,4,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,3,5,1,6,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,5,2,1,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,5,2,1,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,3,5,2,4,6,1]=>{{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>[5,2,3,4,6,7,1]=>0
[7,3,5,2,6,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,5,2,6,4,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,3,5,4,2,6,1]=>{{1,7},{2,3,5},{4},{6}}=>[7,3,5,4,2,6,1]=>[4,5,2,3,6,7,1]=>0
[7,3,5,6,1,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,5,6,4,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,5,6,4,2,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,3,6,1,2,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,6,1,4,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,6,2,1,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,6,2,4,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,6,2,4,5,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,3,6,5,1,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,6,5,2,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,3,6,5,2,4,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,4,1,3,2,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,1,3,2,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,4,1,3,5,6,2]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[7,4,1,3,6,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,1,5,3,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,1,5,3,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,4,1,5,6,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,1,6,2,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,1,6,3,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,2,1,3,5,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,2,1,3,6,5]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,4,2,1,5,6,3]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>0
[7,4,2,1,6,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,2,3,5,6,1]=>{{1,7},{2,3,4},{5},{6}}=>[7,3,4,2,5,6,1]=>[4,2,3,5,6,7,1]=>0
[7,4,2,5,1,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,2,5,1,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,4,2,5,3,6,1]=>{{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>[5,2,3,4,6,7,1]=>0
[7,4,2,5,6,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,2,5,6,3,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,4,2,6,1,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,2,6,3,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,2,6,3,5,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,4,3,2,5,6,1]=>{{1,7},{2,4},{3},{5},{6}}=>[7,4,3,2,5,6,1]=>[3,4,2,5,6,7,1]=>0
[7,4,5,1,2,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,5,1,2,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,4,5,1,3,6,2]=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>[5,3,6,7,1,2,4]=>0
[7,4,5,1,6,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,5,3,1,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,5,3,1,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,4,5,3,2,6,1]=>{{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>[5,2,3,4,6,7,1]=>0
[7,4,5,3,6,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,5,3,6,2,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,4,5,6,1,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,5,6,2,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,5,6,2,3,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,4,6,1,2,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,6,1,3,2,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,6,3,1,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,6,3,2,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,6,3,2,5,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,4,6,5,1,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,6,5,3,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,4,6,5,3,2,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,5,1,2,3,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,1,2,3,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,5,1,2,6,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,1,3,2,6,4]=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>[5,2,6,7,1,3,4]=>0
[7,5,1,3,4,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,1,3,4,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,5,1,3,6,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,1,6,3,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,1,6,4,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,2,1,4,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,2,1,4,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,5,2,1,6,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,2,3,1,4,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,2,3,1,6,4]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,5,2,3,4,6,1]=>{{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>[5,2,3,4,6,7,1]=>0
[7,5,2,3,6,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,2,3,6,4,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,5,2,4,3,6,1]=>{{1,7},{2,3,5},{4},{6}}=>[7,3,5,4,2,6,1]=>[4,5,2,3,6,7,1]=>0
[7,5,2,6,1,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,2,6,4,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,2,6,4,3,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,5,3,4,2,6,1]=>{{1,7},{2,5},{3},{4},{6}}=>[7,5,3,4,2,6,1]=>[3,4,5,2,6,7,1]=>0
[7,5,4,1,2,6,3]=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>[5,2,6,7,1,3,4]=>0
[7,5,4,1,3,2,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,4,1,3,6,2]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,5,4,1,6,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,4,2,1,3,6]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,4,2,1,6,3]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>0
[7,5,4,2,3,6,1]=>{{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>[5,2,3,4,6,7,1]=>0
[7,5,4,2,6,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,4,2,6,3,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,5,4,3,2,6,1]=>{{1,7},{2,5},{3,4},{6}}=>[7,5,4,3,2,6,1]=>[4,3,5,2,6,7,1]=>1
[7,5,4,6,1,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,4,6,1,3,2]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>0
[7,5,4,6,3,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,4,6,3,2,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,5,6,1,3,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,6,1,4,2,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,6,2,1,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,6,2,3,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,6,2,3,4,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,5,6,3,1,2,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,6,3,1,4,2]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>0
[7,5,6,3,4,1,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,5,6,3,4,2,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,6,1,2,3,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,1,2,4,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,1,3,2,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,1,3,4,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,1,5,2,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,1,5,3,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,2,1,3,4,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,2,1,4,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,2,3,1,5,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,2,3,4,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,2,3,4,5,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,6,2,5,1,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,2,5,3,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,2,5,3,4,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}}=>[7,6,3,4,5,2,1]=>[3,4,5,6,2,7,1]=>0
[7,6,4,1,2,3,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,4,1,3,5,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,4,2,1,5,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,4,2,3,1,5]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,4,2,3,5,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,6,4,5,1,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,4,5,2,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,4,5,2,3,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,6,5,1,2,4,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,5,1,4,3,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,5,2,1,3,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,5,2,4,1,3]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,5,2,4,3,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[7,6,5,3,1,4,2]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,5,3,2,1,4]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>0
[7,6,5,3,2,4,1]=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>0
[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}}=>[8,7,6,5,4,3,2,1]=>[5,4,6,3,7,2,8,1]=>1
[7,6,5,8,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,8,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,5,4,8,3,2,1]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[7,6,4,5,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,5,6,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,7,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,8,5,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,6,3,4,2,1]=>{{1,8},{2,7},{3,5},{4,6}}=>[8,7,5,6,3,4,2,1]=>[5,3,6,4,7,2,8,1]=>0
[5,6,7,8,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,4,3,5,2,1]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[7,6,8,3,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,4,6,3,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,7,3,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,4,5,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,4,6,7,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,6,7,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,7,5,4,2,3,1]=>{{1,8},{2,6},{3,7},{4,5}}=>[8,6,7,5,4,2,3,1]=>[5,4,6,2,7,3,8,1]=>1
[6,7,5,8,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,6,8,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,4,5,6,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,4,5,8,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,7,8,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,6,5,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,5,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,7,3,2,4,1]=>{{1,8},{2,6},{3,5},{4,7}}=>[8,6,5,7,3,2,4,1]=>[5,3,6,2,7,4,8,1]=>0
[7,6,8,5,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,5,6,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,6,7,2,3,4,1]=>{{1,8},{2,5},{3,6},{4,7}}=>[8,5,6,7,2,3,4,1]=>[5,2,6,3,7,4,8,1]=>0
[6,7,5,8,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,7,8,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,6,3,4,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,3,4,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,6,2,3,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,2,3,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,4,2,3,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,2,3,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,3,4,2,6,7,1]=>{{1,8},{2,5},{3},{4},{6},{7}}=>[8,5,3,4,2,6,7,1]=>[3,4,5,2,6,7,8,1]=>0
[8,4,3,2,5,6,7,1]=>{{1,8},{2,4},{3},{5},{6},{7}}=>[8,4,3,2,5,6,7,1]=>[3,4,2,5,6,7,8,1]=>0
[8,3,4,2,5,6,7,1]=>{{1,8},{2,3,4},{5},{6},{7}}=>[8,3,4,2,5,6,7,1]=>[4,2,3,5,6,7,8,1]=>0
[8,4,2,3,5,6,7,1]=>{{1,8},{2,3,4},{5},{6},{7}}=>[8,3,4,2,5,6,7,1]=>[4,2,3,5,6,7,8,1]=>0
[8,3,2,4,5,6,7,1]=>{{1,8},{2,3},{4},{5},{6},{7}}=>[8,3,2,4,5,6,7,1]=>[3,2,4,5,6,7,8,1]=>1
[8,2,3,4,5,6,7,1]=>{{1,8},{2},{3},{4},{5},{6},{7}}=>[8,2,3,4,5,6,7,1]=>[2,3,4,5,6,7,8,1]=>0
[6,5,4,7,3,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,3,4,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,5,3,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,3,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,5,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,5,6,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,4,5,2,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,7,2,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,5,3,2,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,2,3,4,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,3,4,5,6,8,1]=>{{1,7,8},{2},{3},{4},{5},{6}}=>[7,2,3,4,5,6,8,1]=>[2,3,4,5,6,8,1,7]=>0
[5,4,6,3,2,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,6,2,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,2,3,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,2,3,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,5,2,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,2,3,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,2,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,4,5,6,7,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,3,4,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,6,5,4,3,1,2]=>{{1,7},{2,8},{3,6},{4,5}}=>[7,8,6,5,4,3,1,2]=>[5,4,6,3,7,1,8,2]=>1
[8,6,5,7,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,5,8,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,7,8,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,5,7,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,4,5,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,7,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,7,8,3,1,2]=>{{1,4,7},{2,5,8},{3,6}}=>[4,5,6,7,8,3,1,2]=>[6,3,7,1,4,8,2,5]=>0
[6,7,8,5,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,5,6,3,4,1,2]=>{{1,7},{2,8},{3,5},{4,6}}=>[7,8,5,6,3,4,1,2]=>[5,3,6,4,7,1,8,2]=>0
[8,5,6,7,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,8,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,7,8,3,4,1,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[8,6,7,3,4,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,4,6,3,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,5,6,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,7,3,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,3,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,5,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,5,6,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,6,7,8,1,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[7,6,8,5,4,2,1,3]=>{{1,7},{2,6},{3,8},{4,5}}=>[7,6,8,5,4,2,1,3]=>[5,4,6,2,7,1,8,3]=>1
[8,7,5,6,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,8,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,6,7,8,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,5,4,1,2,3]=>{{1,6},{2,7},{3,8},{4,5}}=>[6,7,8,5,4,1,2,3]=>[5,4,6,1,7,2,8,3]=>1
[7,8,5,6,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,7,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,6,8,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,8,4,1,2,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[5,6,7,8,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,4,6,1,2,3]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[7,8,4,5,6,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,5,7,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,5,6,7,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,4,6,8,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,7,8,1,2,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[5,6,4,7,8,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,7,8,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,5,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,5,8,3,2,1,4]=>{{1,7},{2,6},{3,5},{4,8}}=>[7,6,5,8,3,2,1,4]=>[5,3,6,2,7,1,8,4]=>0
[8,6,7,5,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,5,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,6,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,6,8,2,3,1,4]=>{{1,7},{2,5},{3,6},{4,8}}=>[7,5,6,8,2,3,1,4]=>[5,2,6,3,7,1,8,4]=>0
[7,8,6,5,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,7,5,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,5,8,3,1,2,4]=>{{1,6},{2,7},{3,5},{4,8}}=>[6,7,5,8,3,1,2,4]=>[5,3,6,1,7,2,8,4]=>0
[8,7,6,5,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,8,5,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,5,2,1,3,4]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,8,5,6,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,7,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,8,2,1,3,4]=>{{1,6},{2,5},{3,7},{4,8}}=>[6,5,7,8,2,1,3,4]=>[5,2,6,1,7,3,8,4]=>0
[7,8,6,5,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,5,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,6,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,5,6,1,2,3,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[8,5,6,7,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,7,8,1,2,3,4]=>{{1,5},{2,6},{3,7},{4,8}}=>[5,6,7,8,1,2,3,4]=>[5,1,6,2,7,3,8,4]=>0
[8,7,6,3,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,7,3,2,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,3,2,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,2,3,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,4,3,1,2,5]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[7,8,6,3,4,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,7,3,4,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,3,2,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,8,3,2,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,3,2,1,4,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,8,6,2,3,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,7,2,3,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,6,3,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,3,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,6,1,2,3,4,5]=>{{1,4,7},{2,5,8},{3,6}}=>[4,5,6,7,8,3,1,2]=>[6,3,7,1,4,8,2,5]=>0
[8,6,7,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,4,5,2,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,3,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,3,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,4,5,1,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,5,3,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,3,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,5,2,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,1,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,4,2,3,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,2,3,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,4,2,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,4,1,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,3,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,2,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,2,3,4,5,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[8,2,3,4,5,6,1,7]=>{{1,7,8},{2},{3},{4},{5},{6}}=>[7,2,3,4,5,6,8,1]=>[2,3,4,5,6,8,1,7]=>0
[8,5,6,3,4,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,5,3,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,5,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,5,6,2,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,3,2,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,6,2,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,6,3,1,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,2,1,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,2,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,2,3,4,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,1,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,5,1,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,4,2,1,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,5,1,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,1,2,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,1,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,1,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,3,4,5,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,1,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,4,3,2,1,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[6,5,4,7,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,4,6,7,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,5,7,3,4,2,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,7,5,4,2,3,1,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[5,6,7,4,2,3,1,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[6,7,4,5,2,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,6,4,7,2,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,6,7,3,2,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,5,7,2,3,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,7,4,2,3,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,7,2,3,4,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,2,3,4,5,6,1,8]=>{{1,7},{2},{3},{4},{5},{6},{8}}=>[7,2,3,4,5,6,1,8]=>[2,3,4,5,6,7,1,8]=>0
[5,4,6,3,2,7,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,3,4,6,2,7,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,4,5,6,2,7,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,5,2,3,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,4,2,5,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,2,4,5,6,7,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[2,3,4,5,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,5,6,4,3,1,2,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[4,5,6,7,3,1,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,4,5,6,7,1,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,6,5,4,2,1,3,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[7,6,4,5,2,1,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,4,6,7,2,1,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,5,6,7,1,2,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,6,5,3,2,1,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,5,6,2,3,1,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,6,7,2,3,1,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,6,5,2,1,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,7,5,1,2,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,6,7,1,2,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,6,4,2,3,1,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,6,2,3,4,1,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,7,2,3,1,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,7,1,2,3,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,4,5,1,2,3,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,5,2,3,1,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,5,1,2,3,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,4,1,2,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,1,2,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,2,1,3,4,5,6,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[7,1,2,3,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,4,6,3,2,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[3,4,5,6,2,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[5,6,2,3,4,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[6,2,3,4,5,1,7,8]=>{{1,6},{2},{3},{4},{5},{7},{8}}=>[6,2,3,4,5,1,7,8]=>[2,3,4,5,6,1,7,8]=>0
[4,3,5,2,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[3,4,2,5,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[3,2,4,5,6,1,7,8]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>0
[2,3,4,5,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[6,4,5,3,1,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[4,3,5,6,1,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[6,5,4,2,1,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[5,6,2,1,3,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[6,4,2,1,3,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[6,3,1,2,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[6,1,2,3,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[4,3,5,2,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[3,4,5,2,1,6,7,8]=>{{1,3,5},{2,4},{6},{7},{8}}=>[3,4,5,2,1,6,7,8]=>[4,2,5,1,3,6,7,8]=>0
[4,5,2,3,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[5,2,3,4,1,6,7,8]=>{{1,5},{2},{3},{4},{6},{7},{8}}=>[5,2,3,4,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>0
[3,4,2,5,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[2,3,4,5,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[5,3,4,1,2,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[3,4,5,1,2,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[5,4,2,1,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[5,4,1,2,3,6,7,8]=>{{1,3,5},{2,4},{6},{7},{8}}=>[3,4,5,2,1,6,7,8]=>[4,2,5,1,3,6,7,8]=>0
[4,5,1,2,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[5,3,1,2,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[5,1,2,3,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[2,1,3,4,5,6,7,8]=>{{1,2},{3},{4},{5},{6},{7},{8}}=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1
[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0
[5,8,7,6,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,8,7,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,8,6,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,8,7,6,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,8,7,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,7,6,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,5,7,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,7,8,6,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,7,8,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,7,8,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,3,8,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,5,6,8,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,6,4,3,8,2,1]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[5,4,7,6,3,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,7,6,4,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,7,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,5,7,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,5,7,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,8,7,6,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,7,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,7,8,6,3,1]=>{{1,2,5,8},{3,4,7},{6}}=>[2,5,4,7,8,6,3,1]=>[6,7,3,4,8,1,2,5]=>0
[2,5,6,4,8,7,3,1]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>[4,7,3,6,8,1,2,5]=>0
[2,4,5,6,8,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,6,7,4,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,5,7,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,6,7,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,6,8,7,5,4,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,5,6,7,8,4,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,3,6,5,8,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,5,6,7,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,6,8,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,7,6,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,2,7,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,3,7,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,2,5,7,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,4,5,7,8,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,3,4,5,7,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,5,3,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,6,3,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,3,6,5,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,4,5,6,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,4,6,5,3,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,5,6,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,4,3,6,5,8,7,1]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[2,4,5,3,6,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,2,5,4,6,8,7,1]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[4,3,2,5,6,8,7,1]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[3,4,2,5,6,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,2,4,5,6,8,7,1]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[2,3,4,5,6,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,7,6,5,3,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,7,4,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,7,6,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,5,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,6,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,5,7,4,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,7,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,6,7,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,7,6,4,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,6,5,7,4,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,3,5,7,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,2,6,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,6,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,4,7,6,8,1]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[2,4,6,5,3,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,6,4,7,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,3,5,6,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,2,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,3,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,8,7,5,4,3,2]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,7,6,8,5,4,3,2]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,5,8,7,6,4,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,5,7,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,6,8,7,5,3,2]=>{{1},{2,4,8},{3,5,6,7}}=>[1,4,5,8,6,7,3,2]=>[1,7,3,5,6,8,2,4]=>0
[1,4,6,7,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,6,7,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,5,4,6,7,8,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,6,8,7,5,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,5,8,7,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,3,5,6,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,3,8,7,6,5,2]=>{{1},{2,4,8},{3},{5,7},{6}}=>[1,4,3,8,7,6,5,2]=>[1,3,6,7,5,8,2,4]=>0
[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,6,5,3,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,4,5,3,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,5,6,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,1,8,7,6,5,4,3]=>{{1,2},{3,8},{4,7},{5,6}}=>[2,1,8,7,6,5,4,3]=>[2,1,6,5,7,4,8,3]=>2
[2,1,6,8,7,5,4,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,1,7,6,8,5,4,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,1,6,5,8,7,4,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,1,5,6,7,8,4,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,1,4,6,8,7,5,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,1,4,5,7,8,6,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,1,5,7,6,4,8,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,1,6,5,7,4,8,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,1,4,6,7,5,8,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,1,5,6,4,7,8,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,1,4,5,6,7,8,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[1,2,4,6,7,8,5,3]=>{{1},{2},{3,4,6,8},{5,7}}=>[1,2,4,6,7,8,5,3]=>[1,2,7,5,8,3,4,6]=>0
[1,2,4,5,8,7,6,3]=>{{1},{2},{3,4,5,8},{6,7}}=>[1,2,4,5,8,7,6,3]=>[1,2,7,6,8,3,4,5]=>1
[1,3,2,6,8,7,5,4]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[1,3,2,7,6,8,5,4]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[1,3,2,5,7,8,6,4]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[1,3,2,6,7,5,8,4]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[1,2,3,6,8,7,5,4]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[4,3,2,1,8,7,6,5]=>{{1,4},{2,3},{5,8},{6,7}}=>[4,3,2,1,8,7,6,5]=>[3,2,4,1,7,6,8,5]=>2
[3,4,2,1,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[3,4,2,1,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[2,4,3,1,6,8,7,5]=>{{1,2,4},{3},{5,6,8},{7}}=>[2,4,3,1,6,8,7,5]=>[3,4,1,2,7,8,5,6]=>0
[2,3,4,1,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[2,3,4,1,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[2,1,4,3,8,7,6,5]=>{{1,2},{3,4},{5,8},{6,7}}=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,7,6,8,5]=>3
[2,1,4,3,7,8,6,5]=>{{1,2},{3,4},{5,6,7,8}}=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>2
[2,1,4,3,6,8,7,5]=>{{1,2},{3,4},{5,6,8},{7}}=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,8,5,6]=>2
[2,1,4,3,6,7,8,5]=>{{1,2},{3,4},{5,6,7,8}}=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>2
[1,3,2,5,4,7,8,6]=>{{1},{2,3},{4,5},{6,7,8}}=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,6,7]=>2
[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}=>[1,3,4,2,5,7,8,6]=>[1,4,2,3,5,8,6,7]=>0
[3,2,1,4,5,8,7,6]=>{{1,3},{2},{4},{5},{6,8},{7}}=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>0
[2,3,1,4,5,7,8,6]=>{{1,2,3},{4},{5},{6,7,8}}=>[2,3,1,4,5,7,8,6]=>[3,1,2,4,5,8,6,7]=>0
[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,6,7]=>0
[6,5,4,3,2,1,8,7]=>{{1,6},{2,5},{3,4},{7,8}}=>[6,5,4,3,2,1,8,7]=>[4,3,5,2,6,1,8,7]=>2
[4,6,5,3,2,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[5,4,6,3,2,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,3,6,5,2,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,4,5,6,2,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,4,6,5,3,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,3,5,6,4,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,5,4,2,6,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,3,5,2,6,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,4,5,3,6,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,4,2,5,6,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,3,4,5,6,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,1,6,5,4,3,8,7]=>{{1,2},{3,6},{4,5},{7,8}}=>[2,1,6,5,4,3,8,7]=>[2,1,5,4,6,3,8,7]=>3
[2,1,5,6,4,3,8,7]=>{{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>2
[2,1,4,6,5,3,8,7]=>{{1,2},{3,4,6},{5},{7,8}}=>[2,1,4,6,5,3,8,7]=>[2,1,5,6,3,4,8,7]=>2
[2,1,4,5,6,3,8,7]=>{{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>2
[4,3,2,1,6,5,8,7]=>{{1,4},{2,3},{5,6},{7,8}}=>[4,3,2,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>3
[3,4,2,1,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>2
[2,4,3,1,6,5,8,7]=>{{1,2,4},{3},{5,6},{7,8}}=>[2,4,3,1,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>2
[2,3,4,1,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>2
[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}}=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>4
[2,1,3,4,5,6,8,7]=>{{1,2},{3},{4},{5},{6},{7,8}}=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>2
[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>1
[5,7,6,4,3,2,1,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[4,7,6,5,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,5,7,6,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,6,7,4,2,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,3,7,6,5,2,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[3,5,6,4,7,2,1,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[2,5,7,6,4,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,5,4,7,6,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,4,5,6,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,2,5,7,6,4,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[3,2,6,5,7,4,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[2,3,6,7,5,4,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[2,3,5,7,6,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,3,6,5,7,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,4,2,6,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,2,4,6,7,5,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[2,3,4,6,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,4,2,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[4,3,5,2,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[3,4,2,5,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[2,3,4,5,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[3,6,5,4,2,7,1,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[2,5,4,6,3,7,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,4,2,6,5,7,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[2,3,4,6,5,7,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[3,5,4,2,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,3,5,4,6,7,1,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>0
[1,4,3,2,7,6,5,8]=>{{1},{2,4},{3},{5,7},{6},{8}}=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>0
[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}=>[1,3,4,2,6,7,5,8]=>[1,4,2,3,7,5,6,8]=>0
[1,3,2,5,4,7,6,8]=>{{1},{2,3},{4,5},{6,7},{8}}=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>3
[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}}=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>2
[4,3,6,5,2,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,4,6,5,3,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,3,5,6,4,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[3,5,4,2,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[1,2,4,3,6,5,7,8]=>{{1},{2},{3,4},{5,6},{7},{8}}=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>2
[3,5,4,2,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[2,4,5,3,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[1,2,3,8,5,6,7,4]=>{{1},{2},{3},{4,8},{5},{6},{7}}=>[1,2,3,8,5,6,7,4]=>[1,2,3,5,6,7,8,4]=>0
[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[2,1,4,5,8,6,7,3]=>{{1,2},{3,4,5,8},{6},{7}}=>[2,1,4,5,8,6,7,3]=>[2,1,6,7,8,3,4,5]=>1
[2,1,4,8,6,5,7,3]=>{{1,2},{3,4,8},{5,6},{7}}=>[2,1,4,8,6,5,7,3]=>[2,1,6,5,7,8,3,4]=>2
[2,1,4,8,6,7,5,3]=>{{1,2},{3,4,8},{5,6,7}}=>[2,1,4,8,6,7,5,3]=>[2,1,7,5,6,8,3,4]=>1
[2,1,8,5,4,7,6,3]=>{{1,2},{3,8},{4,5},{6,7}}=>[2,1,8,5,4,7,6,3]=>[2,1,5,4,7,6,8,3]=>3
[2,3,4,5,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[2,3,4,7,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[2,3,4,8,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[2,3,6,4,5,1,8,7]=>{{1,2,3,6},{4},{5},{7,8}}=>[2,3,6,4,5,1,8,7]=>[4,5,6,1,2,3,8,7]=>1
[2,3,6,4,5,8,7,1]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[2,3,7,4,5,6,8,1]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[2,3,8,5,7,6,4,1]=>{{1,2,3,8},{4,5,7},{6}}=>[2,3,8,5,7,6,4,1]=>[6,7,4,5,8,1,2,3]=>0
[2,4,3,7,5,6,8,1]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[2,5,3,4,6,8,7,1]=>{{1,2,5,6,8},{3},{4},{7}}=>[2,5,3,4,6,8,7,1]=>[3,4,7,8,1,2,5,6]=>0
[2,8,3,4,5,6,7,1]=>{{1,2,8},{3},{4},{5},{6},{7}}=>[2,8,3,4,5,6,7,1]=>[3,4,5,6,7,8,1,2]=>0
[2,8,3,5,4,7,6,1]=>{{1,2,8},{3},{4,5},{6,7}}=>[2,8,3,5,4,7,6,1]=>[3,5,4,7,6,8,1,2]=>2
[2,8,3,5,7,6,4,1]=>{{1,2,8},{3},{4,5,7},{6}}=>[2,8,3,5,7,6,4,1]=>[3,6,7,4,5,8,1,2]=>0
[4,2,3,1,8,6,7,5]=>{{1,4},{2},{3},{5,8},{6},{7}}=>[4,2,3,1,8,6,7,5]=>[2,3,4,1,6,7,8,5]=>0
[6,2,3,4,5,1,8,7]=>{{1,6},{2},{3},{4},{5},{7,8}}=>[6,2,3,4,5,1,8,7]=>[2,3,4,5,6,1,8,7]=>1
[8,2,4,7,6,5,3,1]=>{{1,8},{2},{3,4,7},{5,6}}=>[8,2,4,7,6,5,3,1]=>[2,6,5,7,3,4,8,1]=>1
[6,3,2,5,4,1,8,7]=>{{1,6},{2,3},{4,5},{7,8}}=>[6,3,2,5,4,1,8,7]=>[3,2,5,4,6,1,8,7]=>3
[6,3,2,5,4,7,8,1]=>{{1,6,7,8},{2,3},{4,5}}=>[6,3,2,5,4,7,8,1]=>[3,2,5,4,8,1,6,7]=>2
[8,3,2,5,4,7,6,1]=>{{1,8},{2,3},{4,5},{6,7}}=>[8,3,2,5,4,7,6,1]=>[3,2,5,4,7,6,8,1]=>3
[8,3,2,7,6,5,4,1]=>{{1,8},{2,3},{4,7},{5,6}}=>[8,3,2,7,6,5,4,1]=>[3,2,6,5,7,4,8,1]=>2
[6,3,5,4,2,7,8,1]=>{{1,6,7,8},{2,3,5},{4}}=>[6,3,5,4,2,7,8,1]=>[4,5,2,3,8,1,6,7]=>0
[8,7,3,5,6,4,2,1]=>{{1,8},{2,7},{3},{4,5,6}}=>[8,7,3,5,6,4,2,1]=>[3,6,4,5,7,2,8,1]=>0
[8,5,4,3,2,7,6,1]=>{{1,8},{2,5},{3,4},{6,7}}=>[8,5,4,3,2,7,6,1]=>[4,3,5,2,7,6,8,1]=>2
[8,7,4,3,6,5,2,1]=>{{1,8},{2,7},{3,4},{5,6}}=>[8,7,4,3,6,5,2,1]=>[4,3,6,5,7,2,8,1]=>2
[2,4,1,3,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>2
[2,1,4,6,3,5,8,7]=>{{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>2
[2,4,1,6,3,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,1,4,3,6,8,5,7]=>{{1,2},{3,4},{5,6,7,8}}=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>2
[2,4,1,3,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[2,1,4,6,3,8,5,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,1,6,3,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,4,1,6,3,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,4,1,3,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[2,1,4,6,3,7,8,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,4,6,7,8,3,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,4,1,6,7,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,4,3,7,5,8,6]=>{{1,2},{3,4},{5,6,7,8}}=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>2
[2,4,1,3,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[2,1,4,7,3,5,8,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,4,1,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,4,3,7,8,5,6]=>{{1,2},{3,4},{5,7},{6,8}}=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,7,5,8,6]=>2
[2,4,1,7,3,8,5,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,1,4,7,8,3,5,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,4,1,7,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,8,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,4,5,7,3,8,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,7,1,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,4,5,7,8,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,4,3,8,5,6,7]=>{{1,2},{3,4},{5,6,7,8}}=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>2
[2,4,1,3,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[2,1,4,8,3,5,6,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,4,1,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,4,5,8,3,6,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,1,5,6,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,4,5,6,1,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,1,4,5,6,8,3,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,6,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,1,5,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[2,4,1,5,6,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,4,5,6,1,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,4,1,5,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,4,5,6,1,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,4,1,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,6,1,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,6,7,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,5,3,6,4,8,7]=>{{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>2
[2,5,1,3,6,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,1,5,6,3,4,8,7]=>{{1,2},{3,5},{4,6},{7,8}}=>[2,1,5,6,3,4,8,7]=>[2,1,5,3,6,4,8,7]=>2
[2,5,6,1,3,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,1,5,3,6,8,4,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,5,1,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,6,1,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,5,6,8,3,4,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,5,1,6,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,3,6,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,5,6,1,3,7,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,5,1,6,7,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,1,5,3,6,7,8,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,5,1,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,6,1,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,5,6,7,3,8,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,5,1,6,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,5,6,7,8,3,4]=>{{1,2},{3,5,7},{4,6,8}}=>[2,1,5,6,7,8,3,4]=>[2,1,7,3,5,8,4,6]=>1
[2,5,6,1,7,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,6,7,1,8,3,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[2,5,6,7,8,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,5,3,7,4,8,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,5,1,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,1,3,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,3,7,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,1,5,7,3,8,4,6]=>{{1,2},{3,5},{4,7},{6,8}}=>[2,1,5,7,3,8,4,6]=>[2,1,5,3,7,4,8,6]=>1
[2,5,7,1,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,8,1,3,4,6]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[2,5,1,3,7,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,5,3,8,4,6,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,5,1,3,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,8,1,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,5,1,6,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,5,6,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,3,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[2,3,5,1,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[2,3,5,1,6,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,3,5,6,7,1,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,5,6,7,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,7,3,4,8,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,6,1,7,3,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,3,7,8,4,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,6,1,3,7,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,7,1,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,7,8,3,4,5]=>{{1,2},{3,6},{4,7},{5,8}}=>[2,1,6,7,8,3,4,5]=>[2,1,6,3,7,4,8,5]=>1
[2,6,7,8,1,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,7,3,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,6,1,3,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,3,6,1,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,1,6,3,4,7,8,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,6,1,3,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,1,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,1,7,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,8,3,4,5,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,6,1,8,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,3,4,8,5,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,6,1,3,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,1,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,3,4,5,8,7]=>{{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>2
[2,6,1,3,4,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,3,6,1,4,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,3,4,1,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,3,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,3,6,1,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,3,4,6,1,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,3,4,6,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,6,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,7,3,8,4,5,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,7,1,3,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,7,8,3,4,5,6]=>{{1,2},{3,5,7},{4,6,8}}=>[2,1,5,6,7,8,3,4]=>[2,1,7,3,5,8,4,6]=>1
[2,7,8,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,7,1,4,8,5,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,1,7,3,4,5,8,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,7,1,3,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,7,1,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,1,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[2,3,4,7,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,7,1,8,5,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,3,4,7,8,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,3,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,3,7,1,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,3,4,7,1,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,3,4,5,7,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,5,7,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,1,8,3,4,5,6,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,8,1,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,8,1,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,1,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[2,3,4,8,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,1,4,5,8,6,7]=>{{1,2,3},{4},{5},{6,7,8}}=>[2,3,1,4,5,7,8,6]=>[3,1,2,4,5,8,6,7]=>0
[2,3,4,5,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,5,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,2,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>2
[3,4,1,2,6,5,8,7]=>{{1,3},{2,4},{5,6},{7,8}}=>[3,4,1,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]=>2
[3,1,4,6,2,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,4,6,1,2,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,1,4,2,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,8,1,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,1,2,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,4,6,7,1,2,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,1,4,2,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[3,1,4,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,1,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,7,1,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,6,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,1,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,2,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[3,1,4,7,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,7,1,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,1,2,7,8,5,6]=>{{1,3},{2,4},{5,7},{6,8}}=>[3,4,1,2,7,8,5,6]=>[3,1,4,2,7,5,8,6]=>0
[3,4,7,1,8,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,7,8,1,2,5,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[3,1,4,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,5,7,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[3,4,5,1,7,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[3,1,4,2,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[3,1,4,8,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,1,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,5,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,5,6,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,4,5,1,6,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,1,4,5,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,6,8,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,5,2,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[3,4,5,1,6,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[3,1,4,5,6,7,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,4,5,1,6,7,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,1,4,5,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,1,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,6,7,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,2,6,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,5,1,6,2,4,8,7]=>{{1,3},{2,5},{4,6},{7,8}}=>[3,5,1,6,2,4,8,7]=>[3,1,5,2,6,4,8,7]=>1
[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,6,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,1,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,1,7,2,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,1,5,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,6,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,1,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,7,1,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,2,7,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[3,5,1,7,2,8,4,6]=>{{1,3},{2,5},{4,7},{6,8}}=>[3,5,1,7,2,8,4,6]=>[3,1,5,2,7,4,8,6]=>0
[3,5,7,8,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,2,7,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,3,5,2,7,4,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,5,2,7,8,4,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[3,1,5,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,2,5,4,8,6,7]=>{{1},{2,3},{4,5},{6,7,8}}=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,6,7]=>2
[1,3,2,5,8,4,6,7]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[1,3,5,2,8,4,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,5,2,6,8,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,5,6,8,2,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,6,7,1,2,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,1,7,8,2,4,5]=>{{1,3},{2,6},{4,7},{5,8}}=>[3,6,1,7,8,2,4,5]=>[3,1,6,2,7,4,8,5]=>0
[3,1,6,7,2,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,6,7,1,2,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,1,6,2,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,1,6,2,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,6,2,4,7,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,2,6,7,4,8,5]=>{{1},{2,3},{4,6},{5,7,8}}=>[1,3,2,6,7,4,8,5]=>[1,3,2,6,4,8,5,7]=>1
[1,3,6,2,7,4,8,5]=>{{1},{2,3,4,6},{5,7,8}}=>[1,3,4,6,7,2,8,5]=>[1,6,2,3,4,8,5,7]=>0
[1,3,6,7,2,4,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,2,6,7,8,4,5]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[1,3,6,2,7,8,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,6,8,2,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,8,1,2,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,6,2,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,2,6,4,8,5,7]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[1,3,6,2,4,8,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,2,6,8,4,5,7]=>{{1},{2,3},{4,6},{5,7,8}}=>[1,3,2,6,7,4,8,5]=>[1,3,2,6,4,8,5,7]=>1
[3,1,6,2,4,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[1,3,4,6,8,2,5,7]=>{{1},{2,3,4,6},{5,7,8}}=>[1,3,4,6,7,2,8,5]=>[1,6,2,3,4,8,5,7]=>0
[3,1,6,2,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}=>[1,3,4,6,7,2,8,5]=>[1,6,2,3,4,8,5,7]=>0
[3,1,7,2,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,7,2,4,8,5,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[1,3,7,2,8,4,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,7,2,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,7,2,4,5,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,4,7,2,5,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,4,7,8,2,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,7,2,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,1,2,4,5,7,8,6]=>{{1,2,3},{4},{5},{6,7,8}}=>[2,3,1,4,5,7,8,6]=>[3,1,2,4,5,8,6,7]=>0
[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[3,1,8,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,2,8,4,5,6,7]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[1,3,8,2,4,5,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,4,8,2,5,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,2,4,5,8,6,7]=>{{1,2,3},{4},{5},{6,7,8}}=>[2,3,1,4,5,7,8,6]=>[3,1,2,4,5,8,6,7]=>0
[1,3,4,2,5,8,6,7]=>{{1},{2,3,4},{5},{6,7,8}}=>[1,3,4,2,5,7,8,6]=>[1,4,2,3,5,8,6,7]=>0
[1,3,4,5,8,2,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,4,5,6,8,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,5,1,2,6,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,1,5,6,2,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,5,6,1,2,3,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>[4,5,6,1,2,3,8,7]=>[4,1,5,2,6,3,8,7]=>1
[4,5,1,2,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,5,6,2,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,6,8,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,8,1,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,5,6,2,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[4,5,1,2,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,5,1,6,7,2,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,5,1,2,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,6,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,7,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,5,6,7,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,2,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,2,7,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[4,1,5,7,2,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[4,5,7,1,2,8,3,6]=>{{1,4},{2,5},{3,7},{6,8}}=>[4,5,7,1,2,8,3,6]=>[4,1,5,2,7,3,8,6]=>0
[4,5,1,2,7,3,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,4,5,2,3,7,6,8]=>{{1},{2,4},{3,5},{6,7},{8}}=>[1,4,5,2,3,7,6,8]=>[1,4,2,5,3,7,6,8]=>1
[4,1,2,5,7,3,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,4,5,2,3,7,8,6]=>{{1},{2,4},{3,5},{6,7,8}}=>[1,4,5,2,3,7,8,6]=>[1,4,2,5,3,8,6,7]=>0
[4,1,2,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,5,7,3,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,5,2,7,3,8,6]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[1,4,5,7,2,3,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,1,2,5,7,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[1,4,2,5,7,8,3,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[1,4,5,7,8,2,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,5,1,2,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,5,2,3,8,6,7]=>{{1},{2,4},{3,5},{6,7,8}}=>[1,4,5,2,3,7,8,6]=>[1,4,2,5,3,8,6,7]=>0
[4,1,2,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,5,8,3,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,5,2,8,3,6,7]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[4,1,2,5,6,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,1,2,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,5,6,8,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,5,2,6,8,3,7]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[4,1,2,5,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[4,1,2,5,6,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[4,1,2,5,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,1,2,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,5,6,7,8,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[1,4,5,6,2,7,8,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,5,6,7,8,2,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,6,1,2,7,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,7,1,8,2,3,5]=>{{1,4},{2,6},{3,7},{5,8}}=>[4,6,7,1,8,2,3,5]=>[4,1,6,2,7,3,8,5]=>0
[4,6,1,7,2,3,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,6,1,2,3,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,1,2,6,3,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,1,2,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,6,2,3,7,8,5]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}=>[1,4,6,2,7,3,8,5]=>[1,4,2,6,3,8,5,7]=>0
[1,4,2,6,7,8,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,6,2,7,8,3,5]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[1,4,6,7,2,8,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,6,1,8,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,1,2,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,2,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,6,3,8,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,6,2,3,8,5,7]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[1,4,2,6,8,3,5,7]=>{{1},{2,3,4,6},{5,7,8}}=>[1,3,4,6,7,2,8,5]=>[1,6,2,3,4,8,5,7]=>0
[1,4,6,2,8,3,5,7]=>{{1},{2,4},{3,6},{5,7,8}}=>[1,4,6,2,7,3,8,5]=>[1,4,2,6,3,8,5,7]=>0
[4,6,1,2,3,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,1,2,6,3,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,1,2,3,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>2
[4,1,2,3,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[4,6,1,2,3,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[1,4,2,3,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}=>[1,3,4,2,6,7,5,8]=>[1,4,2,3,7,5,6,8]=>0
[4,1,2,3,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[4,7,1,2,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,7,8,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,1,2,3,8,5,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[1,4,2,7,3,8,5,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[4,1,2,7,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,7,8,3,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,7,2,8,3,5,6]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[1,4,7,8,2,3,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,7,1,2,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,2,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,7,3,5,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,7,2,3,5,8,6]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[4,1,2,3,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[1,2,4,7,3,8,5,6]=>{{1},{2},{3,4,5,7},{6,8}}=>[1,2,4,5,7,8,3,6]=>[1,2,7,3,4,5,8,6]=>0
[4,7,1,2,3,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,1,2,7,3,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,4,2,3,7,5,6,8]=>{{1},{2,3,4},{5,6,7},{8}}=>[1,3,4,2,6,7,5,8]=>[1,4,2,3,7,5,6,8]=>0
[1,4,2,3,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}=>[1,3,4,2,5,7,8,6]=>[1,4,2,3,5,8,6,7]=>0
[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}=>[1,2,4,5,7,8,3,6]=>[1,2,7,3,4,5,8,6]=>0
[4,8,1,2,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,2,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,8,3,5,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,8,2,3,5,6,7]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[4,1,2,3,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[1,4,2,3,5,8,6,7]=>{{1},{2,3,4},{5},{6,7,8}}=>[1,3,4,2,5,7,8,6]=>[1,4,2,3,5,8,6,7]=>0
[5,6,1,2,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,7,1,2,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,1,2,7,8,3,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[5,1,6,7,2,8,3,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[5,1,6,7,8,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,2,3,7,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,1,2,6,7,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}=>[1,5,6,7,2,3,4,8]=>[1,5,2,6,3,7,4,8]=>0
[5,1,6,2,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,6,2,3,7,8,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,2,6,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}=>[1,5,6,7,2,3,8,4]=>[1,5,2,6,3,8,4,7]=>0
[1,5,6,2,7,8,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,6,7,2,8,3,4]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[1,5,6,7,8,2,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,6,1,2,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,8,1,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,2,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,6,2,3,8,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,2,6,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,2,6,8,3,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,6,8,2,3,4,7]=>{{1},{2,5},{3,6},{4,7,8}}=>[1,5,6,7,2,3,8,4]=>[1,5,2,6,3,8,4,7]=>0
[5,1,6,2,3,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[5,1,2,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,2,3,6,8,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,6,2,3,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[5,1,2,3,6,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[5,1,2,3,6,7,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,1,2,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,2,3,6,7,8,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,7,2,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,7,8,2,3,4,6]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[5,7,1,8,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,7,2,3,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[1,5,7,2,3,8,4,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[1,5,7,2,8,3,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,7,8,2,3,4,6]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[5,1,7,2,3,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,7,2,3,4,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,2,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,2,3,7,4,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,2,3,7,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[1,5,2,3,7,8,4,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[1,2,5,3,7,8,4,6]=>{{1},{2},{3,4,5,7},{6,8}}=>[1,2,4,5,7,8,3,6]=>[1,2,7,3,4,5,8,6]=>0
[5,1,7,2,3,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,2,3,5,7,4,8,6]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[5,1,8,2,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,8,2,3,4,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,2,3,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,2,3,8,4,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,2,3,5,8,4,6,7]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[1,2,3,5,6,8,4,7]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[6,1,7,8,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,7,2,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,7,2,3,8,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,7,8,2,3,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,7,1,2,3,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,7,3,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,2,7,3,4,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,2,3,7,4,8,5]=>{{1},{2,3,4,6},{5,7,8}}=>[1,3,4,6,7,2,8,5]=>[1,6,2,3,4,8,5,7]=>0
[6,1,2,3,7,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,2,3,7,8,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,1,2,7,3,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,1,2,3,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,1,2,3,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,2,3,4,7,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,2,3,6,4,7,8,5]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[1,2,3,6,7,8,4,5]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[6,8,1,2,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,8,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,2,8,3,4,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,2,3,8,4,5,7]=>{{1},{2,3,4,6},{5,7,8}}=>[1,3,4,6,7,2,8,5]=>[1,6,2,3,4,8,5,7]=>0
[6,1,2,3,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,2,3,4,8,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,2,3,6,4,8,5,7]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[6,1,2,3,4,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[7,1,8,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,8,2,3,4,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,1,2,3,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,2,3,8,4,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,1,2,3,4,8,5,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[1,7,2,3,4,8,5,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[1,2,7,3,4,8,5,6]=>{{1},{2},{3,4,5,7},{6,8}}=>[1,2,4,5,7,8,3,6]=>[1,2,7,3,4,5,8,6]=>0
[1,2,3,7,8,4,5,6]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[7,1,2,3,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,2,3,4,5,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,2,3,7,4,5,8,6]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[1,8,2,3,4,5,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,2,3,8,4,5,6,7]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[1,2,3,4,5,8,6,7]=>{{1},{2},{3},{4},{5},{6,7,8}}=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,6,7]=>0
[5,3,2,6,1,4,8,7]=>{{1,5},{2,3},{4,6},{7,8}}=>[5,3,2,6,1,4,8,7]=>[3,2,5,1,6,4,8,7]=>2
[7,3,2,5,4,8,1,6]=>{{1,7},{2,3},{4,5},{6,8}}=>[7,3,2,5,4,8,1,6]=>[3,2,5,4,7,1,8,6]=>2
[8,4,5,2,3,7,6,1]=>{{1,8},{2,4},{3,5},{6,7}}=>[8,4,5,2,3,7,6,1]=>[4,2,5,3,7,6,8,1]=>1
[7,4,5,2,3,8,1,6]=>{{1,7},{2,4},{3,5},{6,8}}=>[7,4,5,2,3,8,1,6]=>[4,2,5,3,7,1,8,6]=>0
[6,4,5,2,3,1,8,7]=>{{1,6},{2,4},{3,5},{7,8}}=>[6,4,5,2,3,1,8,7]=>[4,2,5,3,6,1,8,7]=>1
[5,4,6,2,1,3,8,7]=>{{1,5},{2,4},{3,6},{7,8}}=>[5,4,6,2,1,3,8,7]=>[4,2,5,1,6,3,8,7]=>1
[3,6,1,5,4,2,8,7]=>{{1,3},{2,6},{4,5},{7,8}}=>[3,6,1,5,4,2,8,7]=>[3,1,5,4,6,2,8,7]=>2
[4,6,5,1,3,2,8,7]=>{{1,4},{2,6},{3,5},{7,8}}=>[4,6,5,1,3,2,8,7]=>[4,1,5,3,6,2,8,7]=>1
[5,6,4,3,1,2,8,7]=>{{1,5},{2,6},{3,4},{7,8}}=>[5,6,4,3,1,2,8,7]=>[4,3,5,1,6,2,8,7]=>2
[7,5,4,3,2,8,1,6]=>{{1,7},{2,5},{3,4},{6,8}}=>[7,5,4,3,2,8,1,6]=>[4,3,5,2,7,1,8,6]=>1
[8,6,4,3,7,2,5,1]=>{{1,8},{2,6},{3,4},{5,7}}=>[8,6,4,3,7,2,5,1]=>[4,3,6,2,7,5,8,1]=>1
[7,6,4,3,8,2,1,5]=>{{1,7},{2,6},{3,4},{5,8}}=>[7,6,4,3,8,2,1,5]=>[4,3,6,2,7,1,8,5]=>1
[6,7,4,3,8,1,2,5]=>{{1,6},{2,7},{3,4},{5,8}}=>[6,7,4,3,8,1,2,5]=>[4,3,6,1,7,2,8,5]=>1
[5,7,4,3,1,8,2,6]=>{{1,5},{2,7},{3,4},{6,8}}=>[5,7,4,3,1,8,2,6]=>[4,3,5,1,7,2,8,6]=>1
[4,7,5,1,3,8,2,6]=>{{1,4},{2,7},{3,5},{6,8}}=>[4,7,5,1,3,8,2,6]=>[4,1,5,3,7,2,8,6]=>0
[3,7,1,5,4,8,2,6]=>{{1,3},{2,7},{4,5},{6,8}}=>[3,7,1,5,4,8,2,6]=>[3,1,5,4,7,2,8,6]=>1
[2,1,7,5,4,8,3,6]=>{{1,2},{3,7},{4,5},{6,8}}=>[2,1,7,5,4,8,3,6]=>[2,1,5,4,7,3,8,6]=>2
[3,8,1,5,4,7,6,2]=>{{1,3},{2,8},{4,5},{6,7}}=>[3,8,1,5,4,7,6,2]=>[3,1,5,4,7,6,8,2]=>2
[4,8,5,1,3,7,6,2]=>{{1,4},{2,8},{3,5},{6,7}}=>[4,8,5,1,3,7,6,2]=>[4,1,5,3,7,6,8,2]=>1
[5,8,4,3,1,7,6,2]=>{{1,5},{2,8},{3,4},{6,7}}=>[5,8,4,3,1,7,6,2]=>[4,3,5,1,7,6,8,2]=>2
[6,8,4,3,7,1,5,2]=>{{1,6},{2,8},{3,4},{5,7}}=>[6,8,4,3,7,1,5,2]=>[4,3,6,1,7,5,8,2]=>1
[7,8,4,3,6,5,1,2]=>{{1,7},{2,8},{3,4},{5,6}}=>[7,8,4,3,6,5,1,2]=>[4,3,6,5,7,1,8,2]=>2
[6,8,5,7,3,1,4,2]=>{{1,6},{2,8},{3,5},{4,7}}=>[6,8,5,7,3,1,4,2]=>[5,3,6,1,7,4,8,2]=>0
[5,8,6,7,1,3,4,2]=>{{1,5},{2,8},{3,6},{4,7}}=>[5,8,6,7,1,3,4,2]=>[5,1,6,3,7,4,8,2]=>0
[4,8,6,1,7,3,5,2]=>{{1,4},{2,8},{3,6},{5,7}}=>[4,8,6,1,7,3,5,2]=>[4,1,6,3,7,5,8,2]=>0
[3,8,1,6,7,4,5,2]=>{{1,3},{2,8},{4,6},{5,7}}=>[3,8,1,6,7,4,5,2]=>[3,1,6,4,7,5,8,2]=>0
[2,1,8,6,7,4,5,3]=>{{1,2},{3,8},{4,6},{5,7}}=>[2,1,8,6,7,4,5,3]=>[2,1,6,4,7,5,8,3]=>1
[2,1,7,6,8,4,3,5]=>{{1,2},{3,7},{4,6},{5,8}}=>[2,1,7,6,8,4,3,5]=>[2,1,6,4,7,3,8,5]=>1
[3,7,1,6,8,4,2,5]=>{{1,3},{2,7},{4,6},{5,8}}=>[3,7,1,6,8,4,2,5]=>[3,1,6,4,7,2,8,5]=>0
[4,7,6,1,8,3,2,5]=>{{1,4},{2,7},{3,6},{5,8}}=>[4,7,6,1,8,3,2,5]=>[4,1,6,3,7,2,8,5]=>0
[5,7,6,8,1,3,2,4]=>{{1,5},{2,7},{3,6},{4,8}}=>[5,7,6,8,1,3,2,4]=>[5,1,6,3,7,2,8,4]=>0
[5,4,7,2,1,8,3,6]=>{{1,5},{2,4},{3,7},{6,8}}=>[5,4,7,2,1,8,3,6]=>[4,2,5,1,7,3,8,6]=>0
[6,4,7,2,8,1,3,5]=>{{1,6},{2,4},{3,7},{5,8}}=>[6,4,7,2,8,1,3,5]=>[4,2,6,1,7,3,8,5]=>0
[7,4,6,2,8,3,1,5]=>{{1,7},{2,4},{3,6},{5,8}}=>[7,4,6,2,8,3,1,5]=>[4,2,6,3,7,1,8,5]=>0
[8,4,6,2,7,3,5,1]=>{{1,8},{2,4},{3,6},{5,7}}=>[8,4,6,2,7,3,5,1]=>[4,2,6,3,7,5,8,1]=>0
[8,3,2,6,7,4,5,1]=>{{1,8},{2,3},{4,6},{5,7}}=>[8,3,2,6,7,4,5,1]=>[3,2,6,4,7,5,8,1]=>1
[7,3,2,6,8,4,1,5]=>{{1,7},{2,3},{4,6},{5,8}}=>[7,3,2,6,8,4,1,5]=>[3,2,6,4,7,1,8,5]=>1
[6,3,2,7,8,1,4,5]=>{{1,6},{2,3},{4,7},{5,8}}=>[6,3,2,7,8,1,4,5]=>[3,2,6,1,7,4,8,5]=>1
[5,3,2,7,1,8,4,6]=>{{1,5},{2,3},{4,7},{6,8}}=>[5,3,2,7,1,8,4,6]=>[3,2,5,1,7,4,8,6]=>1
[4,3,2,1,7,8,5,6]=>{{1,4},{2,3},{5,7},{6,8}}=>[4,3,2,1,7,8,5,6]=>[3,2,4,1,7,5,8,6]=>1
[3,4,1,2,8,7,6,5]=>{{1,3},{2,4},{5,8},{6,7}}=>[3,4,1,2,8,7,6,5]=>[3,1,4,2,7,6,8,5]=>1
[5,3,2,8,1,7,6,4]=>{{1,5},{2,3},{4,8},{6,7}}=>[5,3,2,8,1,7,6,4]=>[3,2,5,1,7,6,8,4]=>2
[6,3,2,8,7,1,5,4]=>{{1,6},{2,3},{4,8},{5,7}}=>[6,3,2,8,7,1,5,4]=>[3,2,6,1,7,5,8,4]=>1
[7,3,2,8,6,5,1,4]=>{{1,7},{2,3},{4,8},{5,6}}=>[7,3,2,8,6,5,1,4]=>[3,2,6,5,7,1,8,4]=>2
[8,4,7,2,6,5,3,1]=>{{1,8},{2,4},{3,7},{5,6}}=>[8,4,7,2,6,5,3,1]=>[4,2,6,5,7,3,8,1]=>1
[7,4,8,2,6,5,1,3]=>{{1,7},{2,4},{3,8},{5,6}}=>[7,4,8,2,6,5,1,3]=>[4,2,6,5,7,1,8,3]=>1
[6,4,8,2,7,1,5,3]=>{{1,6},{2,4},{3,8},{5,7}}=>[6,4,8,2,7,1,5,3]=>[4,2,6,1,7,5,8,3]=>0
[5,4,8,2,1,7,6,3]=>{{1,5},{2,4},{3,8},{6,7}}=>[5,4,8,2,1,7,6,3]=>[4,2,5,1,7,6,8,3]=>1
[4,5,8,1,2,7,6,3]=>{{1,4},{2,5},{3,8},{6,7}}=>[4,5,8,1,2,7,6,3]=>[4,1,5,2,7,6,8,3]=>1
[3,5,1,8,2,7,6,4]=>{{1,3},{2,5},{4,8},{6,7}}=>[3,5,1,8,2,7,6,4]=>[3,1,5,2,7,6,8,4]=>1
[2,1,5,8,3,7,6,4]=>{{1,2},{3,5},{4,8},{6,7}}=>[2,1,5,8,3,7,6,4]=>[2,1,5,3,7,6,8,4]=>2
[2,1,6,8,7,3,5,4]=>{{1,2},{3,6},{4,8},{5,7}}=>[2,1,6,8,7,3,5,4]=>[2,1,6,3,7,5,8,4]=>1
[3,6,1,8,7,2,5,4]=>{{1,3},{2,6},{4,8},{5,7}}=>[3,6,1,8,7,2,5,4]=>[3,1,6,2,7,5,8,4]=>0
[4,6,8,1,7,2,5,3]=>{{1,4},{2,6},{3,8},{5,7}}=>[4,6,8,1,7,2,5,3]=>[4,1,6,2,7,5,8,3]=>0
[5,6,8,7,1,2,4,3]=>{{1,5},{2,6},{3,8},{4,7}}=>[5,6,8,7,1,2,4,3]=>[5,1,6,2,7,4,8,3]=>0
[6,5,8,7,2,1,4,3]=>{{1,6},{2,5},{3,8},{4,7}}=>[6,5,8,7,2,1,4,3]=>[5,2,6,1,7,4,8,3]=>0
[7,5,8,6,2,4,1,3]=>{{1,7},{2,5},{3,8},{4,6}}=>[7,5,8,6,2,4,1,3]=>[5,2,6,4,7,1,8,3]=>0
[8,5,7,6,2,4,3,1]=>{{1,8},{2,5},{3,7},{4,6}}=>[8,5,7,6,2,4,3,1]=>[5,2,6,4,7,3,8,1]=>0
[5,7,8,6,1,4,2,3]=>{{1,5},{2,7},{3,8},{4,6}}=>[5,7,8,6,1,4,2,3]=>[5,1,6,4,7,2,8,3]=>0
[4,7,8,1,6,5,2,3]=>{{1,4},{2,7},{3,8},{5,6}}=>[4,7,8,1,6,5,2,3]=>[4,1,6,5,7,2,8,3]=>1
[3,7,1,8,6,5,2,4]=>{{1,3},{2,7},{4,8},{5,6}}=>[3,7,1,8,6,5,2,4]=>[3,1,6,5,7,2,8,4]=>1
[2,1,7,8,6,5,3,4]=>{{1,2},{3,7},{4,8},{5,6}}=>[2,1,7,8,6,5,3,4]=>[2,1,6,5,7,3,8,4]=>2
[3,8,1,7,6,5,4,2]=>{{1,3},{2,8},{4,7},{5,6}}=>[3,8,1,7,6,5,4,2]=>[3,1,6,5,7,4,8,2]=>1
[4,8,7,1,6,5,3,2]=>{{1,4},{2,8},{3,7},{5,6}}=>[4,8,7,1,6,5,3,2]=>[4,1,6,5,7,3,8,2]=>1
[5,8,7,6,1,4,3,2]=>{{1,5},{2,8},{3,7},{4,6}}=>[5,8,7,6,1,4,3,2]=>[5,1,6,4,7,3,8,2]=>0
[6,8,7,5,4,1,3,2]=>{{1,6},{2,8},{3,7},{4,5}}=>[6,8,7,5,4,1,3,2]=>[5,4,6,1,7,3,8,2]=>1
[2,1,4,3,6,5,8,7,10,9]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>5
[3,2,6,1,4,5,7,8]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>0
[5,3,6,1,2,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[6,2,4,1,3,5,7,8]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>0
[5,3,7,1,2,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,4,7,1,2,3,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,6,1,2,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,2,8,1,4,5,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,4,8,1,2,3,6,7]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[6,4,8,1,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,8,1,3,4,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,3,8,1,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,4,1,3,5,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,3,6,1,2,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,7,1,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,5,7,1,3,6,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[4,2,5,8,1,3,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,3,5,8,1,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,6,8,1,4,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,4,8,1,3,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,3,4,8,1,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,5,8,1,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,8,1,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,7,8,1,3,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,3,7,8,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,5,8,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,5,8,1,2,3,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[7,4,6,8,1,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,6,1,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,4,7,1,3,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,6,2,5,1,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[3,7,2,5,1,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,7,2,5,1,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,8,2,7,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,5,7,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,4,6,1,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,7,1,3,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,4,2,5,1,3,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,5,2,6,1,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,4,2,8,1,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,4,8,1,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,5,1,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,7,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,5,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,6,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,2,6,7,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,5,7,1,3,4]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,8,4,5,7,1,2,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,8,2,5,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,2,6,8,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,2,7,8,1,3,4]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,4,2,5,8,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,2,6,8,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,2,5,7,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,2,6,1,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,6,2,5,1,4,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[4,3,8,2,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,3,4,1,2,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[5,3,8,2,7,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,3,7,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,8,2,7,1,4,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,5,8,2,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,4,2,6,1,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,5,4,2,8,1,3,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,5,4,2,8,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,5,2,8,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,4,2,6,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,2,4,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,2,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,2,4,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,7,2,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,7,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,7,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,4,6,2,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,3,2,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,3,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,5,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,3,4,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,3,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,2,3,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,2,3,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,3,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,2,8,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,5,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,2,5,3,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,5,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,5,3,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,5,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,2,8,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,2,7,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,5,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,2,5,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,2,5,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,2,8,6,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,5,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,8,2,4,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,8,2,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,7,2,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,2,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,8,2,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,2,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,2,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,4,2,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,2,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,4,2,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,2,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,2,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,2,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,2,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,5,2,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,2,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,2,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,2,6,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,2,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,8,2,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,8,5,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,7,5,2,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,6,5,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,8,5,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,6,5,2,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,5,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,5,2,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,8,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,4,5,2,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,5,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,4,5,2,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,8,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,7,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,8,5,6,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,7,5,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,5,6,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,5,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,5,8,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,8,6,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,8,5,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,5,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,3,4,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,3,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,3,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,3,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,3,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,1,8,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,5,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,5,3,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,5,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,5,3,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,5,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,1,8,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,1,7,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,5,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,5,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,1,5,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,1,8,6,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,5,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,1,2,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,2,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,2,4,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,2,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,2,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,1,2,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,2,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,2,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,1,2,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,8,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,7,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,8,2,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,5,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,1,5,2,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,5,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,5,2,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,6,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,8,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,6,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,1,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,6,2,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,5,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,8,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,7,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,5,6,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,1,5,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,5,7,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,7,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,5,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,5,8,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,8,6,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,5,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,5,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,8,1,4,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,8,1,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,7,1,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,5,1,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,8,1,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,1,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,4,1,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,1,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,1,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,1,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,1,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,1,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,1,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,4,1,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,5,1,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,1,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,1,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,1,6,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,1,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,4,1,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,1,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,1,2,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,1,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,5,1,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,5,1,2,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,5,1,2,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,4,1,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,4,1,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,1,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,4,1,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,1,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,4,1,7,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,5,1,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,4,1,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,4,1,8,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,1,6,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,4,1,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,8,1,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,8,5,1,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,7,5,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,5,1,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,8,5,1,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,5,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,5,1,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,4,5,1,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,8,6,1,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,5,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,5,1,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,5,1,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,4,5,1,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,8,6,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,5,1,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,5,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,5,1,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,8,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,7,6,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,8,5,6,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,7,5,6,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,5,6,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,4,5,6,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,4,5,6,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,5,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,8,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,8,5,6,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,5,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,1,2,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,1,2,3,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,1,2,3,4,5,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,2,3,4,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,1,2,3,4,5,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,1,2,3,4,9,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,1,2,3,4,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,2,3,4,7,5,6,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,1,2,3,4,7,5,9,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,1,2,3,4,7,9,5,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,1,2,3,4,9,8,5,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,2,3,4,7,8,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,1,2,3,4,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,1,2,3,9,4,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,1,2,3,8,4,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,2,3,6,4,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,1,2,3,6,9,8,4,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,1,2,3,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,1,2,8,3,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,1,2,9,3,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,2,5,3,4,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,1,2,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,1,2,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,1,2,9,6,7,8,3,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,2,5,6,7,8,3,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,1,2,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,9,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,8,2,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,9,2,4,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,1,4,2,3,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,4,2,3,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,1,4,2,3,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,8,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,4,9,2,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,4,9,2,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,4,5,2,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,1,4,5,2,3,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,1,9,6,2,3,4,5,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,8,6,2,3,4,5,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,1,8,9,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,8,9,7,2,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,1,4,5,6,2,3,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,1,4,9,7,2,3,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,1,9,7,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,1,4,5,6,2,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,4,5,6,9,2,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,4,5,6,7,2,3,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,1,4,5,6,7,2,9,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,4,5,6,7,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,4,9,6,7,8,2,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,9,5,6,7,8,2,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,4,5,6,7,8,2,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,4,5,6,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,1,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,8,1,3,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,7,1,3,4,5,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,1,3,4,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,7,1,3,4,5,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,6,1,3,4,9,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,1,3,6,7,8,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,5,1,3,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,6,1,5,3,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,8,1,9,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,4,1,5,6,9,8,3,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,1,5,6,7,8,3,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,4,1,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,3,1,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,3,1,2,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,3,1,2,4,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,3,1,2,4,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,3,1,2,6,7,8,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,3,1,2,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,7,1,2,3,4,5,6,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,9,1,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,7,1,2,3,4,5,9,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,7,1,2,3,4,8,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,8,1,2,3,7,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,8,1,2,9,3,4,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,3,1,9,2,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,4,1,8,2,3,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,7,1,6,2,3,4,5,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,7,1,9,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,7,1,6,2,3,4,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,8,1,6,2,7,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,3,1,5,9,2,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,8,1,7,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,3,1,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,3,1,5,8,7,2,9,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,3,1,5,6,7,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,3,1,5,6,9,8,2,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,3,1,5,6,7,8,2,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,3,1,5,6,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,9,1,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,8,1,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,9,1,4,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,9,1,4,7,8,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,8,1,6,7,4,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,9,1,6,7,8,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,4,1,3,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,6,4,1,3,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,8,1,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,4,1,6,3,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,8,1,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,3,4,1,2,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,3,4,1,2,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,3,8,1,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,8,4,1,2,3,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,9,5,1,2,3,4,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,8,5,1,2,3,4,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,7,5,1,2,3,4,9,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,7,9,1,2,3,4,5,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,9,8,1,2,3,4,5,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,7,8,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,7,8,1,2,3,4,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,8,9,1,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,8,5,1,6,2,3,9,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,3,4,1,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,3,4,1,6,7,2,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,5,4,1,8,7,2,3,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,3,4,1,9,7,8,2,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,3,4,1,6,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,9,1,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,9,1,5,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,9,1,7,8,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,9,5,1,4,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,9,5,1,7,4,6,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,4,5,1,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,7,4,5,1,3,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,8,6,1,3,4,5,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,7,8,9,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,8,9,6,1,7,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,3,4,5,1,2,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,3,8,9,1,2,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,8,4,6,1,2,3,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,8,6,5,1,2,3,4,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,8,6,5,1,2,3,9,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,3,9,6,1,7,2,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,3,4,5,1,7,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,3,4,5,1,9,8,2,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,3,4,5,1,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,9,1,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,8,1,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,9,1,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,9,6,1,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,9,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,9,5,6,1,4,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,8,5,6,1,4,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,9,5,6,1,8,4,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,8,4,5,6,1,3,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,8,9,5,7,1,3,4,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,8,9,7,6,1,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,3,4,5,6,1,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,3,9,7,6,1,2,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,9,7,5,6,1,2,3,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,3,4,5,6,1,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,3,4,5,6,1,8,2,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,3,4,5,6,1,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,6,9,1,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,9,7,1,6,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,9,6,7,1,5,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,9,5,6,7,1,4,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,4,5,6,7,1,3,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,8,4,5,6,7,1,9,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,3,4,5,6,7,1,2,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,3,4,5,6,7,1,9,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,6,7,9,1,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,6,9,8,1,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,9,7,8,1,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,9,6,7,8,1,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,9,5,6,7,8,1,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,4,5,6,7,8,1,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,3,4,5,6,7,8,1,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,6,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,5,2,6,4,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,5,2,7,4,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[3,5,2,7,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,7,2,3,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,7,2,3,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[4,5,6,2,3,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,5,6,3,1,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,5,7,3,1,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,1,5,7,4,8,6,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[4,5,7,3,1,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,7,3,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,7,3,8,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,7,8,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,7,8,4,5,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[4,6,7,2,8,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,7,8,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,7,8,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,7,2,8,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,7,2,1,8,6,3]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[5,6,7,8,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,7,8,5,3,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[3,5,2,7,4,9,6,10,8,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,6,7,3,9,5,2,10,8,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,6,8,9,4,3,10,7,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,6,2,8,9,5,10,7,4,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,7,8,3,9,10,6,5,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,6,7,2,1,8,5,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[5,4,1,8,7,2,3,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[4,3,1,2,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[4,3,1,2,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>2
[6,3,1,5,2,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[7,3,1,5,2,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[8,4,5,1,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,5,1,2,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[6,4,5,1,2,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,1,6,5,3,4,8,7]=>{{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>2
[5,6,4,1,2,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[5,7,4,1,2,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,1,8,5,3,7,4,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[5,8,4,1,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,1,7,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,4,1,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,8,6,7,3,4,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[8,4,6,1,7,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,6,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,4,3,8,7,5,6]=>{{1,2},{3,4},{5,6,7,8}}=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>2
[7,3,1,8,6,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,8,1,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,1,2,7,3,6]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[7,5,8,6,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,7,8,6,3,4,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[6,4,7,3,8,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,2,6,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,2,6,7,1,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,4,2,6,8,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,2,7,8,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,2,1,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,2,1,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,2,1,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,4,2,8,7,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,4,2,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,8,2,1,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,8,2,1,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,8,2,1,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,5,6,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,4,1,6,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,8,2,3,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,8,2,3,7,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,2,8,1,3,7,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,6,8,1,3,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,8,1,2,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,1,8,7,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,8,7,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,5,8,7,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,5,8,7,2,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,6,8,2,1,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,8,3,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,2,8,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,5,8,7,1,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,4,5,8,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,3,2,6,5,8,7]=>{{1,2,4},{3},{5,6},{7,8}}=>[2,4,3,1,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>2
[8,1,3,2,5,4,7,6]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[5,1,4,2,6,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,1,6,3,5,4,8,7]=>{{1,2},{3,4,6},{5},{7,8}}=>[2,1,4,6,5,3,8,7]=>[2,1,5,6,3,4,8,7]=>2
[6,2,8,1,4,3,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[6,2,7,1,4,3,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,5,1,4,3,8,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,2,5,1,4,3,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[8,1,5,3,7,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,8,2,6,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,1,8,2,6,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,1,7,3,6,4,8,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[5,1,7,2,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,5,2,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,2,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,1,4,3,8,5,7,6]=>{{1,2},{3,4},{5,6,8},{7}}=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,8,5,6]=>2
[4,1,3,2,8,5,7,6]=>{{1,2,4},{3},{5,6,8},{7}}=>[2,4,3,1,6,8,7,5]=>[3,4,1,2,7,8,5,6]=>0
[8,4,7,1,3,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,8,1,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,2,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,1,5,2,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,1,6,3,8,4,7,5]=>{{1,2},{3,4,6},{5,8},{7}}=>[2,1,4,6,8,3,7,5]=>[2,1,6,3,4,7,8,5]=>1
[6,1,5,2,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,3,7,2,6,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,8,3,7,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,7,3,8,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,6,3,8,1,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,3,6,2,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,6,2,4,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,2,5,8,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,6,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,1,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,6,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,5,3,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,4,8,3,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,5,3,1,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[7,3,5,8,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,4,8,3,1,5,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,4,7,1,8,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,3,1,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,2,8,4,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,1,5,2,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[7,4,2,5,1,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[6,7,4,2,8,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,7,2,1,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,7,8,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,8,2,1,5,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,4,1,7,8,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,7,1,8,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,1,7,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,4,5,8,3,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,4,5,3,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,4,5,6,1,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,1,2,4,5,6,3,7]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[8,5,6,2,1,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,5,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,7,2,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,5,3,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,7,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,4,7,8,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,6,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,1,7,8,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,7,8,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,2,7,8,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,7,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,4,2,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,4,2,1,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,3,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,7,1,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,7,8,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,1,7,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,2,6,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,6,7,8,4,1,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,5,6,7,8,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,2,6,7,8,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,4,7,8,5,2,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,5,2,3,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[1,5,6,3,4,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[3,2,6,7,4,5,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[4,7,2,6,5,3,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[8,7,5,4,1,3,2,6]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[5,8,6,2,4,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,6,7,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,6,8,4,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,7,8,2,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,7,2,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,2,7,8,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,2,7,1,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,6,1,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,7,1,3,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,8,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,8,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,8,2,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,8,3,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,7,3,1,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,2,3,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,8,3,7,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[7,5,1,3,8,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,6,1,4,8,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[5,7,1,2,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,1,7,3,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,8,6,5,3,4,2]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[6,8,1,7,2,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,6,2,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,6,1,2,3,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,1,5,2,4,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,5,1,2,3,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,7,5,3,8,4,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,1,5,2,7,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,1,2,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,6,2,3,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,6,1,7,2,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,6,7,2,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,6,8,3,4,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,8,2,7,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,8,7,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,1,7,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,1,2,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,8,3,7,4,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,8,7,3,4,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,8,7,1,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,6,2,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,5,3,7,1,8,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,1,5,3,6,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,3,5,2,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,2,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,5,7,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,6,1,7,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,3,7,5,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,3,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,6,2,7,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,6,3,7,1,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,6,3,7,5,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,5,1,7,4,8,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,6,1,7,5,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,6,5,7,1,8,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,1,6,3,7,5,8,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[3,1,6,2,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,2,7,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,6,1,7,4,8,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,4,6,1,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,5,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,6,5,7,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,6,3,7,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,5,2,4,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,6,3,2,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,6,7,3,2,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,3,7,5,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,8,6,3,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,6,5,8,7,4,1,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[3,1,5,8,6,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,6,1,4,7,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,7,6,8,1,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,6,7,5,8,2,4]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[2,3,5,7,6,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,5,7,8,3,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[3,2,6,1,4,7,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,3,6,7,2,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,6,5,7,4,1,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,7,2,5,8,6,4,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[3,6,2,4,5,1,8,7]=>{{1,2,3,6},{4},{5},{7,8}}=>[2,3,6,4,5,1,8,7]=>[4,5,6,1,2,3,8,7]=>1
[2,6,1,4,5,3,8,7]=>{{1,2,3,6},{4},{5},{7,8}}=>[2,3,6,4,5,1,8,7]=>[4,5,6,1,2,3,8,7]=>1
[6,1,2,4,5,3,8,7]=>{{1,2,3,6},{4},{5},{7,8}}=>[2,3,6,4,5,1,8,7]=>[4,5,6,1,2,3,8,7]=>1
[5,6,3,2,1,4,8,7]=>{{1,5},{2,4,6},{3},{7,8}}=>[5,4,3,6,1,2,8,7]=>[3,5,1,6,2,4,8,7]=>1
[5,4,3,6,1,2,8,7]=>{{1,5},{2,4,6},{3},{7,8}}=>[5,4,3,6,1,2,8,7]=>[3,5,1,6,2,4,8,7]=>1
[6,3,1,4,5,2,8,7]=>{{1,2,3,6},{4},{5},{7,8}}=>[2,3,6,4,5,1,8,7]=>[4,5,6,1,2,3,8,7]=>1
[3,1,6,4,5,2,8,7]=>{{1,2,3,6},{4},{5},{7,8}}=>[2,3,6,4,5,1,8,7]=>[4,5,6,1,2,3,8,7]=>1
[2,4,8,3,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[4,1,8,3,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[3,8,4,2,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[8,4,1,3,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[7,5,8,4,3,6,1,2]=>{{1,7},{2,3,5,8},{4},{6}}=>[7,3,5,4,8,6,1,2]=>[4,6,7,1,8,2,3,5]=>0
[6,5,3,8,4,1,7,2]=>{{1,6},{2,4,5,8},{3},{7}}=>[6,4,3,5,8,1,7,2]=>[3,6,1,7,8,2,4,5]=>0
[2,1,5,8,4,6,7,3]=>{{1,2},{3,4,5,8},{6},{7}}=>[2,1,4,5,8,6,7,3]=>[2,1,6,7,8,3,4,5]=>1
[2,1,4,8,3,6,7,5]=>{{1,2},{3,4,5,8},{6},{7}}=>[2,1,4,5,8,6,7,3]=>[2,1,6,7,8,3,4,5]=>1
[6,4,3,8,2,1,7,5]=>{{1,6},{2,4,5,8},{3},{7}}=>[6,4,3,5,8,1,7,2]=>[3,6,1,7,8,2,4,5]=>0
[7,3,8,4,2,6,1,5]=>{{1,7},{2,3,5,8},{4},{6}}=>[7,3,5,4,8,6,1,2]=>[4,6,7,1,8,2,3,5]=>0
[8,3,1,2,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[3,1,8,2,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[2,3,8,1,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[4,3,8,2,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[4,8,2,3,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[3,8,2,1,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[2,8,1,3,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[8,1,2,3,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[7,8,2,4,3,6,1,5]=>{{1,7},{2,3,5,8},{4},{6}}=>[7,3,5,4,8,6,1,2]=>[4,6,7,1,8,2,3,5]=>0
[6,8,3,2,4,1,7,5]=>{{1,6},{2,4,5,8},{3},{7}}=>[6,4,3,5,8,1,7,2]=>[3,6,1,7,8,2,4,5]=>0
[2,1,8,3,4,6,7,5]=>{{1,2},{3,4,5,8},{6},{7}}=>[2,1,4,5,8,6,7,3]=>[2,1,6,7,8,3,4,5]=>1
[2,1,7,8,5,4,3,6]=>{{1,2},{3,7},{4,6,8},{5}}=>[2,1,7,6,5,8,3,4]=>[2,1,5,7,3,8,4,6]=>1
[5,7,3,8,1,4,2,6]=>{{1,5},{2,7},{3},{4,6,8}}=>[5,7,3,6,1,8,2,4]=>[3,5,1,7,2,8,4,6]=>0
[7,1,8,4,5,3,2,6]=>{{1,2,7},{3,6,8},{4},{5}}=>[2,7,6,4,5,8,1,3]=>[4,5,7,1,2,8,3,6]=>0
[2,7,8,4,5,3,1,6]=>{{1,2,7},{3,6,8},{4},{5}}=>[2,7,6,4,5,8,1,3]=>[4,5,7,1,2,8,3,6]=>0
[2,4,3,1,8,5,7,6]=>{{1,2,4},{3},{5,6,8},{7}}=>[2,4,3,1,6,8,7,5]=>[3,4,1,2,7,8,5,6]=>0
[4,1,3,2,6,8,7,5]=>{{1,2,4},{3},{5,6,8},{7}}=>[2,4,3,1,6,8,7,5]=>[3,4,1,2,7,8,5,6]=>0
[2,7,6,4,5,8,1,3]=>{{1,2,7},{3,6,8},{4},{5}}=>[2,7,6,4,5,8,1,3]=>[4,5,7,1,2,8,3,6]=>0
[7,1,6,4,5,8,2,3]=>{{1,2,7},{3,6,8},{4},{5}}=>[2,7,6,4,5,8,1,3]=>[4,5,7,1,2,8,3,6]=>0
[5,7,3,6,1,8,2,4]=>{{1,5},{2,7},{3},{4,6,8}}=>[5,7,3,6,1,8,2,4]=>[3,5,1,7,2,8,4,6]=>0
[2,1,7,6,5,8,3,4]=>{{1,2},{3,7},{4,6,8},{5}}=>[2,1,7,6,5,8,3,4]=>[2,1,5,7,3,8,4,6]=>1
[2,1,8,5,3,6,7,4]=>{{1,2},{3,4,5,8},{6},{7}}=>[2,1,4,5,8,6,7,3]=>[2,1,6,7,8,3,4,5]=>1
[6,8,3,5,2,1,7,4]=>{{1,6},{2,4,5,8},{3},{7}}=>[6,4,3,5,8,1,7,2]=>[3,6,1,7,8,2,4,5]=>0
[7,8,5,4,2,6,1,3]=>{{1,7},{2,3,5,8},{4},{6}}=>[7,3,5,4,8,6,1,2]=>[4,6,7,1,8,2,3,5]=>0
[8,1,4,2,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[2,8,4,1,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[4,8,1,2,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[3,4,8,1,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[3,4,2,8,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[2,4,1,8,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[4,1,2,8,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[8,4,2,1,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[7,5,2,4,8,6,1,3]=>{{1,7},{2,3,5,8},{4},{6}}=>[7,3,5,4,8,6,1,2]=>[4,6,7,1,8,2,3,5]=>0
[6,5,3,2,8,1,7,4]=>{{1,6},{2,4,5,8},{3},{7}}=>[6,4,3,5,8,1,7,2]=>[3,6,1,7,8,2,4,5]=>0
[2,1,5,3,8,6,7,4]=>{{1,2},{3,4,5,8},{6},{7}}=>[2,1,4,5,8,6,7,3]=>[2,1,6,7,8,3,4,5]=>1
[6,4,3,5,8,1,7,2]=>{{1,6},{2,4,5,8},{3},{7}}=>[6,4,3,5,8,1,7,2]=>[3,6,1,7,8,2,4,5]=>0
[7,3,5,4,8,6,1,2]=>{{1,7},{2,3,5,8},{4},{6}}=>[7,3,5,4,8,6,1,2]=>[4,6,7,1,8,2,3,5]=>0
[8,3,4,1,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[4,3,1,8,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[3,1,4,8,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0
[3,2,5,1,6,8,4,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,6,5,3,8,1,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,4,2,1,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,1,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,2,8,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,7,5,8,3,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,2,5,8,4,1,3,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,4,5,8,7,3,6,2]=>{{1},{2,4,8},{3,5,6,7}}=>[1,4,5,8,6,7,3,2]=>[1,7,3,5,6,8,2,4]=>0
[1,5,4,8,7,3,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,3,8,7,6,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,5,3,2,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,7,6,3,1,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,5,2,1,7,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,8,6,3,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,6,2,4,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,6,2,4,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,5,7,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,6,8,1,7,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,8,1,5,7,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,8,2,7,4,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[6,5,2,8,1,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,2,7,6,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,7,2,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,4,6,1,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,7,3,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,4,2,6,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,6,3,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,7,6,2,3,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,2,8,6,4,1,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,8,5,2,7,3,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,2,8,7,1,4,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,5,8,2,3,1,4,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[8,5,7,2,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,8,3,1,5,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,4,2,1,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,2,1,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,1,2,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,1,2,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,6,1,4,8,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,7,1,8,4,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,6,1,8,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,8,6,2,3,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,3,5,6,1,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[6,3,7,5,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,2,7,1,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,4,6,2,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,7,2,6,3,5]=>{{1,2,5,8},{3,4,7},{6}}=>[2,5,4,7,8,6,3,1]=>[6,7,3,4,8,1,2,5]=>0
[5,1,4,6,8,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,5,4,6,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,3,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,3,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,3,7,2,6,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,3,8,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,1,6,3,4,2,5]=>{{1,3,5,8},{2,7},{4,6}}=>[3,7,5,6,8,4,2,1]=>[6,4,7,2,8,1,3,5]=>0
[5,3,8,7,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,2,5,8,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[3,1,4,5,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,5,2,1,4,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[8,5,2,7,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,7,5,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,3,4,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,3,8,6,4,1]=>{{1,2,5,8},{3,4,7},{6}}=>[2,5,4,7,8,6,3,1]=>[6,7,3,4,8,1,2,5]=>0
[2,1,8,7,4,3,6,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,8,6,3,1,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,1,6,3,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,1,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,4,2,1,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,5,6,8,4,2,1]=>{{1,3,5,8},{2,7},{4,6}}=>[3,7,5,6,8,4,2,1]=>[6,4,7,2,8,1,3,5]=>0
[8,6,2,5,1,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,1,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,3,7,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,8,1,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[2,8,1,3,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,8,5,3,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,5,8,2,1,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,5,6,2,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,1,2,6,4,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,1,2,8,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,1,2,3,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[6,1,2,8,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,6,8,2,3,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,7,8,6,3,4,2,1]=>{{1,3,5,8},{2,7},{4,6}}=>[3,7,5,6,8,4,2,1]=>[6,4,7,2,8,1,3,5]=>0
[4,1,8,3,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,1,4,8,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,6,5,2,8,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,1,2,5,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,1,2,3,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[4,1,2,6,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,1,2,5,6,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,8,4,2,1,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,2,6,4,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,8,2,6,4,7,5]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[6,1,2,5,8,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,7,6,4,2,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,1,7,5,6,8,4,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[5,6,7,3,8,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,8,6,2,7,3,4]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[5,1,6,3,4,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[6,1,4,2,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,5,8,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,7,6,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,2,1,5,6,3,7]=>{{1,4},{2,3,7,8},{5},{6}}=>[4,3,7,1,5,6,8,2]=>[4,1,5,6,8,2,3,7]=>0
[3,1,7,4,5,6,8,2]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[4,3,7,5,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,6,5,2,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,8,5,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,8,6,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,8,6,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,7,1,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,2,5,1,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,7,1,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,1,5,2,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,5,1,2,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,2,3,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,4,2,3,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[5,8,2,6,3,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,6,2,7,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,7,1,4,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[5,3,7,2,4,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[8,4,6,3,7,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,1,2,7,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,8,2,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,6,1,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,5,6,7,8,1,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[2,3,4,5,7,8,9,1,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,5,6,7,8,9,1,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,4,5,6,7,8,9,1,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,6,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,6,7,8,9,1,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[2,3,4,5,6,7,1,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>0
[2,3,4,5,6,7,8,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,6,8,9,10,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,6,7,8,9,10,1,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,4,5,6,7,8,9,10,1,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,2,6,3,4,7,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,7,3,4,5,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,4,7,6,2,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,2,4,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,1,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,1,7,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,6,3,7,2,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,2,7,3,4,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,8,1,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,6,1,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,1,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,1,5,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,1,3,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,6,3,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,4,5,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,8,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,8,1,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,8,7,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,8,6,1,3,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,1,8,7,3,4,5,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[1,3,8,7,2,4,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,8,3,6,2,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,1,6,7,3,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,5,3,6,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,3,2,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[8,1,5,3,6,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,4,1,3,2,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,4,8,3,2,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,3,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,1,8,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,3,2,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,3,2,8,5,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[7,6,1,8,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,8,3,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,7,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,1,3,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[5,3,7,8,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,7,8,4,3,5,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[1,8,2,5,3,4,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,2,8,3,5,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,2,8,3,6,5,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,4,2,7,3,6,5,8]=>{{1},{2,3,4,5,7},{6},{8}}=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>0
[1,8,2,6,3,5,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,2,5,3,6,4,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,7,2,5,3,6,4,8]=>{{1},{2,3,4,5,7},{6},{8}}=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>0
[1,8,2,3,4,6,5,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,7,2,3,4,6,5,8]=>{{1},{2,3,4,5,7},{6},{8}}=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>0
[1,8,2,3,4,7,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,2,5,3,8,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,2,5,3,8,4,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[1,8,2,5,3,7,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,2,6,3,8,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,2,3,8,4,7,5,6]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[1,3,2,8,4,7,5,6]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[1,4,2,8,3,7,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,2,8,3,7,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,2,8,3,6,4,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[4,6,3,8,5,1,7,2]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[5,6,8,3,4,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,8,3,4,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,6,7,2,4,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,7,8,1,3,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,1,4,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,8,1,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,8,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,5,2,3,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,2,5,4,8,1,7,6]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[3,2,7,8,1,5,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,7,8,1,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,1,2,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,1,3,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,7,8,1,4,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,3,7,5,2,6,4,8]=>{{1},{2,3,4,5,7},{6},{8}}=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>0
[2,8,4,5,6,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,8,5,1,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,7,5,2,1,8,4]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[4,3,7,1,5,6,8,2]=>{{1,4},{2,3,7,8},{5},{6}}=>[4,3,7,1,5,6,8,2]=>[4,1,5,6,8,2,3,7]=>0
[3,6,1,7,5,2,8,4]=>{{1,3},{2,6},{4,7,8},{5}}=>[3,6,1,7,5,2,8,4]=>[3,1,5,6,2,8,4,7]=>0
[3,4,1,2,7,6,8,5]=>{{1,3},{2,4},{5,7,8},{6}}=>[3,4,1,2,7,6,8,5]=>[3,1,4,2,6,8,5,7]=>0
[3,4,2,1,7,5,8,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[6,5,2,7,4,1,8,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[3,5,2,6,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,3,1,8,6,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,2,5,8,3,7,1,4]=>{{1,6,7},{2},{3,5},{4,8}}=>[6,2,5,8,3,7,1,4]=>[2,5,3,7,1,6,8,4]=>0
[1,5,2,7,4,6,3,8]=>{{1},{2,3,4,5,7},{6},{8}}=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>0
[7,1,3,8,4,6,2,5]=>{{1,2,7},{3},{4,5,8},{6}}=>[2,7,3,5,8,6,1,4]=>[3,6,7,1,2,8,4,5]=>0
[2,3,4,8,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,7,3,5,8,6,1,4]=>{{1,2,7},{3},{4,5,8},{6}}=>[2,7,3,5,8,6,1,4]=>[3,6,7,1,2,8,4,5]=>0
[3,2,4,7,8,6,1,5]=>{{1,3,4,7},{2},{5,8},{6}}=>[3,2,4,7,8,6,1,5]=>[2,6,7,1,3,4,8,5]=>0
[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}=>[1,5,4,6,2,7,3,8]=>[1,5,2,7,3,4,6,8]=>0
[5,2,4,7,1,8,3,6]=>{{1,5},{2},{3,4,7},{6,8}}=>[5,2,4,7,1,8,3,6]=>[2,5,1,7,3,4,8,6]=>0
[5,3,6,4,1,8,7,2]=>{{1,5},{2,3,6,8},{4},{7}}=>[5,3,6,4,1,8,7,2]=>[4,5,1,7,8,2,3,6]=>0
[6,3,5,1,8,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,1,5,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,2,4,1,7,8,5,6]=>{{1,3,4},{2},{5,7},{6,8}}=>[3,2,4,1,7,8,5,6]=>[2,4,1,3,7,5,8,6]=>0
[3,1,4,2,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[5,1,4,7,2,8,6,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[3,1,4,6,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,4,5,7,1,8,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[2,5,4,6,1,7,8,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[7,3,4,1,2,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[1,8,4,5,2,3,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[7,2,1,5,6,3,4,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[7,3,6,1,5,4,2,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[6,4,7,5,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,8,5,6,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,8,5,7,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,8,6,7,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,8,6,1,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,1,6,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,7,5,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,6,1,7,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,1,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,5,7,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,7,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,3,2,7,6,5,4]=>{{1},{2,4,8},{3},{5,7},{6}}=>[1,4,3,8,7,6,5,2]=>[1,3,6,7,5,8,2,4]=>0
[1,8,4,7,2,6,5,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[3,6,4,8,2,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,1,5,8,3,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[3,4,6,8,1,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,6,7,5,4,2,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[3,5,7,8,6,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,1,7,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[7,5,6,1,8,3,4,2]=>{{1,4,7},{2,5,8},{3,6}}=>[4,5,6,7,8,3,1,2]=>[6,3,7,1,4,8,2,5]=>0
[4,7,5,6,1,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,5,3,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,1,2,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,1,2,6,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,6,5,8,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,5,2,7,6,8,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,7,6,2,5,8,3,4]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[6,2,4,1,7,5,8,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,5,2,3,7,6,8,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[8,4,2,6,7,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,4,2,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,7,6,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[10,7,8,5,6,9,1,2,3,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,7,8,3,4,9,1,2,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,7,10,5,6,8,1,2,3,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,7,10,3,4,8,1,2,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,6,10,3,4,7,1,2,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,5,10,3,6,7,1,2,4,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,6,10,2,7,8,1,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,6,9,2,7,10,1,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,5,9,2,6,10,1,3,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,7,8,3,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,5,6,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,8,5,6,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,8,2,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,8,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,7,4,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,2,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,5,8,7,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,5,1,7,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,4,1,3,7,5,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[2,6,4,8,3,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,5,8,7,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,5,1,7,3,4,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[6,5,2,1,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,7,3,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,6,7,3,1,5,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[4,7,8,2,3,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,8,3,2,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,5,3,7,1,6,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[4,3,6,7,2,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,7,2,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,2,5,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,7,8,6,4,1,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,8,1,6,3,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,8,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,7,1,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,8,3,4,7,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,5,7,2,3,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,1,2,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,7,2,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,7,3,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,1,7,3,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,7,3,1,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,1,7,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,5,7,1,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,8,1,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,8,3,7,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,7,6,1,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,5,2,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,4,5,7,1,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,5,2,3,7,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,4,2,1,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,2,1,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[6,5,4,1,3,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[8,7,4,1,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,4,1,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,8,7,6,4,3,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[8,7,4,2,6,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,7,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,7,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,4,2,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,2,5,4,7,1,6]=>{{1,6,7,8},{2,3},{4,5}}=>[6,3,2,5,4,7,8,1]=>[3,2,5,4,8,1,6,7]=>2
[8,7,6,5,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,5,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,8,7,6,3,5,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[8,7,6,5,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,4,1,8,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,5,1,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,1,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,5,1,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,1,2,8,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,5,6,8,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,5,7,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,6,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,2,1,6,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,2,4,1,8,5,7,3]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[5,2,1,3,8,7,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,4,1,3,8,5,2,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[7,5,1,3,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,7,1,4,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,7,3,4,1,8,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,2,8,6,7,3,4,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,5,7,3,4,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,8,5,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,7,3,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,5,1,7,3,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,2,4,1,7,3,8,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,5,6,2,3,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,3,8,5,6,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,2,8,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[3,1,6,2,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,1,6,2,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,2,7,3,8,4,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,4,5,1,6,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,1,8,5,6,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,1,7,3,8,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,3,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,1,2,5,7,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[7,8,5,1,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,6,8,3,7,5,2]=>{{1},{2,4,8},{3,5,6,7}}=>[1,4,5,8,6,7,3,2]=>[1,7,3,5,6,8,2,4]=>0
[2,4,8,5,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,5,3,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[6,3,1,2,4,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,6,7,8,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,8,4,5,3,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[3,4,2,8,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,4,7,1,5,2,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[4,1,8,3,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,8,6,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,5,8,1,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,6,5,3,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,1,5,2,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,5,2,4,8,3,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[6,1,5,2,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,5,3,8,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,6,1,2,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,1,4,2,5,3,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[7,4,2,6,5,1,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[7,4,6,3,1,5,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,8,1,2,3,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,5,7,2,3,8,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,8,2,3,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[2,6,4,1,5,7,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[2,5,1,7,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,4,7,8,5,6,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,4,7,6,8,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,8,1,4,6,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[5,3,4,1,8,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[1,4,2,7,5,8,6,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[4,1,8,6,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,7,6,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,3,1,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,8,7,1,3,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,3,8,7,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,1,2,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,5,1,2,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,8,5,2,4,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,8,5,3,1,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,5,1,2,7,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[4,5,1,2,6,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,5,2,7,8,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,7,5,6,2,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[3,1,4,5,8,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[3,5,6,2,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,2,5,6,1,8,7,3]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,1,2,7,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,1,7,5,2,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[1,3,7,2,4,8,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,4,7,5,1,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,8,1,3,7,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,7,2,3,6,8,1,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[5,2,7,3,6,8,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,8,3,6,7,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,4,1,3,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,8,3,1,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,8,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,7,4,1,6,2,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,5,7,8,3,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,5,8,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,7,3,4,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,7,3,4,1,2,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[4,3,8,7,6,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,8,7,6,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,4,6,1,5,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,1,4,6,2,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,8,7,2,6,3,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,3,8,2,7,6,4,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[3,4,1,8,7,6,5,2]=>{{1,3},{2,4,8},{5,7},{6}}=>[3,4,1,8,7,6,5,2]=>[3,1,6,7,5,8,2,4]=>0
[3,8,2,1,7,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,6,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,1,2,7,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,3,7,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,3,7,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,3,7,5,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,2,6,5,8,3,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,5,4,2,6,8,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,4,2,5,8,3,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,5,2,6,4,8,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,1,2,6,3,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,4,5,2,8,7,3,6]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[1,2,5,3,8,7,6,4]=>{{1},{2},{3,4,5,8},{6,7}}=>[1,2,4,5,8,7,6,3]=>[1,2,7,6,8,3,4,5]=>1
[7,3,1,6,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,5,2,7,3,8,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,1,2,8,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,1,8,3,2,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,8,7,3,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,2,8,5,3,7,6,4]=>{{1},{2},{3,4,5,8},{6,7}}=>[1,2,4,5,8,7,6,3]=>[1,2,7,6,8,3,4,5]=>1
[1,6,2,7,3,8,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,2,1,8,6,3,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,4,2,8,7,6,3,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[6,1,4,8,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,8,6,3,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,1,8,2,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,8,5,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,8,6,1,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,8,5,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,7,5,6,1,4,2,3]=>{{1,3,5,8},{2,7},{4,6}}=>[3,7,5,6,8,4,2,1]=>[6,4,7,2,8,1,3,5]=>0
[2,6,4,1,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,1,3,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,1,8,3,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,8,6,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,4,1,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[2,3,8,1,6,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,8,1,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,2,3,4,5,6,7,9,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9}}=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>1
[2,1,3,4,5,6,7,8,9]=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>1
[1,2,3,4,5,6,7,8,10,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>1
[2,1,3,4,5,6,7,8,9,10]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>1
[9,1,2,3,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,8,2,3,4,5,6,9,7]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[7,1,2,3,4,5,6,9,8]=>{{1,2,3,4,5,6,7},{8,9}}=>[2,3,4,5,6,7,1,9,8]=>[7,1,2,3,4,5,6,9,8]=>1
[2,8,1,3,4,5,6,7,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[2,10,1,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,1,3,4,5,6,7,8,9,10,11]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>1
[8,4,3,6,5,1,7,2]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[8,5,6,3,4,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,8,6,2,4,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,1,6,5,2,4,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,2,8,3,7,4,5,6]=>{{1},{2},{3,4,6,8},{5,7}}=>[1,2,4,6,7,8,5,3]=>[1,2,7,5,8,3,4,6]=>0
[7,1,8,2,6,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,8,2,4,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,8,3,2,7,4,6]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[7,5,8,3,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,7,3,1,6,4,2]=>{{1,2,5,8},{3,4,7},{6}}=>[2,5,4,7,8,6,3,1]=>[6,7,3,4,8,1,2,5]=>0
[1,5,4,8,2,7,3,6]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[5,7,1,3,2,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[6,7,1,2,4,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,8,1,3,2,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,2,8,1,4,5,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[7,1,2,3,4,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[8,1,2,3,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,7,4,5,1,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,6,8,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,4,5,7,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,6,7,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,7,1,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,2,7,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,1,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,6,1,8,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,8,6,2,3,7,5]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,5,6,2,8,4,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[2,5,6,3,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,6,8,5,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[2,4,1,6,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,7,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,2,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,2,1,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,2,1,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,1,2,8,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,1,3,4,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,7,3,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,8,7,2,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,5,7,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,3,4,5,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[5,2,7,4,8,6,1,3]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[5,7,2,3,8,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,1,3,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,6,1,3,2,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,1,7,8,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,7,8,4,3,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,2,7,8,4,5,1,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,7,8,1,4,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,2,7,1,8,4,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,1,7,8,5,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,6,7,8,3,5,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,7,8,2,4,1,3,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,7,8,2,4,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,7,8,5,3,4,2]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[6,7,8,4,1,3,2,5]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[6,3,8,5,2,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,2,8,4,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,5,8,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,8,6,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,3,8,5,6,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,4,2,8,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,5,2,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,2,7,4,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,1,4,8,3,2,6]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[5,3,8,7,4,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,1,5,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,4,1,8,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,5,2,8,3,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,8,2,6,4,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,6,3,7,5,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,8,1,6,3,2,5,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[2,8,1,7,3,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,5,7,3,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,1,7,6,8,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,2,8,5,3,4,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[7,1,2,8,3,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,1,5,8,3,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,8,6,4,3,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,3,8,7,4,6,2,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[2,8,6,7,4,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,6,7,4,5,2,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,5,7,4,6,2,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[4,7,3,8,5,6,1,2]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[6,8,1,7,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,5,6,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,5,6,2,7,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,8,2,7,3,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,3,8,4,6,1,5]=>{{1,2,7},{3},{4,5,8},{6}}=>[2,7,3,5,8,6,1,4]=>[3,6,7,1,2,8,4,5]=>0
[1,8,4,7,3,6,2,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[3,8,6,7,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,6,7,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,5,7,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,6,7,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,4,6,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,2,6,1,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,1,6,2,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,5,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,2,6,1,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>0
[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>0
[3,2,4,5,6,7,8,9,1]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>[2,9,1,3,4,5,6,7,8]=>0
[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[6,7,4,8,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,4,5,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,4,6,3,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,8,3,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,6,2,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,5,2,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,8,2,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,5,8,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,5,7,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,4,8,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,7,2,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,5,2,1,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[4,6,5,2,1,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[5,6,4,2,3,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[6,4,5,3,1,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[5,4,6,1,3,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[5,4,7,1,3,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,1,6,8,7,4,3,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,1,7,8,6,4,5,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[5,8,7,6,3,2,1,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[6,7,4,2,8,1,5,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[2,1,8,6,7,5,3,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[7,6,5,8,1,4,3,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[2,1,7,6,8,3,5,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[8,1,3,7,4,6,5,2]=>{{1,2,8},{3},{4,5,7},{6}}=>[2,8,3,5,7,6,4,1]=>[3,6,7,4,5,8,1,2]=>0
[8,1,3,5,4,7,6,2]=>{{1,2,8},{3},{4,5},{6,7}}=>[2,8,3,5,4,7,6,1]=>[3,5,4,7,6,8,1,2]=>2
[6,1,8,3,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,1,3,4,5,6,7,2]=>{{1,2,8},{3},{4},{5},{6},{7}}=>[2,8,3,4,5,6,7,1]=>[3,4,5,6,7,8,1,2]=>0
[8,5,2,1,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,5,2,8,4,1,3,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[3,6,1,8,5,2,4,7]=>{{1,3},{2,6},{4,7,8},{5}}=>[3,6,1,7,5,2,8,4]=>[3,1,5,6,2,8,4,7]=>0
[3,4,1,2,8,6,5,7]=>{{1,3},{2,4},{5,7,8},{6}}=>[3,4,1,2,7,6,8,5]=>[3,1,4,2,6,8,5,7]=>0
[4,3,1,2,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[6,3,8,5,2,1,4,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[8,3,1,5,2,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,8,2,6,1,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,2,5,8,3,1,6,4]=>{{1,6,7},{2},{3,5},{4,8}}=>[6,2,5,8,3,7,1,4]=>[2,5,3,7,1,6,8,4]=>0
[6,1,2,3,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,2,1,3,8,6,4,5]=>{{1,3,4,7},{2},{5,8},{6}}=>[3,2,4,7,8,6,1,5]=>[2,6,7,1,3,4,8,5]=>0
[1,5,7,3,2,4,6,8]=>{{1},{2,5},{3,4,6,7},{8}}=>[1,5,4,6,2,7,3,8]=>[1,5,2,7,3,4,6,8]=>0
[5,2,7,3,1,8,4,6]=>{{1,5},{2},{3,4,7},{6,8}}=>[5,2,4,7,1,8,3,6]=>[2,5,1,7,3,4,8,6]=>0
[5,8,2,4,1,3,7,6]=>{{1,5},{2,3,6,8},{4},{7}}=>[5,3,6,4,1,8,7,2]=>[4,5,1,7,8,2,3,6]=>0
[4,8,1,6,3,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,1,8,6,4,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,2,1,3,7,8,5,6]=>{{1,3,4},{2},{5,7},{6,8}}=>[3,2,4,1,7,8,5,6]=>[2,4,1,3,7,5,8,6]=>0
[2,4,1,3,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[2,5,8,3,1,7,4,6]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[2,8,1,3,6,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,8,2,3,4,1,5,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[5,1,8,3,2,4,6,7]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[8,7,6,5,9,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,8,7,6,10,5,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,7,3,8,5,2,4,6]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[8,2,5,1,7,3,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,1,8,3,4,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[6,2,1,3,7,8,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,6,4,2,3,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,6,4,3,1,7,5]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[6,8,4,1,3,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,8,1,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,6,7,2,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,3,6,1,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,1,2,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[6,3,1,4,2,7,5,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[4,2,5,6,7,8,1,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,7,5,1,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,6,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,8,2,7,3,6]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[1,7,4,5,2,8,3,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[3,7,5,1,2,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[4,1,5,8,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,8,6,7,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}=>[1,4,7,2,6,8,3,5]=>[1,4,2,7,3,8,5,6]=>0
[5,1,4,2,7,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[5,3,7,1,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,7,2,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,8,1,3,4,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[1,2,3,7,8,5,6,4]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[1,4,2,7,3,8,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,1,7,8,3,4,6,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[10,1,2,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,1,2,3,4,5,6,9,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,1,2,9,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,1,10,2,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,1,2,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,1,2,3,4,5,6,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,1,2,3,4,5,10,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,1,10,9,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,9,10,1,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,7,8,3,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,8,3,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,4,7,3,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,2,7,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,4,2,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,2,7,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[3,5,4,2,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,1,5,7,3,6,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[4,5,2,3,7,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,2,5,3,8,1,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,1,5,3,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,8,5,2,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,7,3,2,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,3,1,5,7,2,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,3,1,7,5,2,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[6,3,4,1,2,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,2,4,1,3,7,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,6,1,4,7,5,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[3,6,2,1,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,2,7,4,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[3,6,2,1,5,7,4,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[7,3,1,5,2,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[3,6,5,1,2,7,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,5,2,1,4,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,1,5,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,4,5,1,8,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,4,5,8,2,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,5,6,2,7,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,4,6,3,7,2,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,4,6,8,2,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,2,7,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,6,8,7,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,8,6,7,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,6,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,7,3,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,8,7,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,5,3,7,1,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,5,6,1,8,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,5,6,1,7,3,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[3,6,8,2,4,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,1,7,4,6,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[3,2,5,1,8,4,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,5,7,8,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,5,6,1,7,8,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,5,1,8,7,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,5,1,6,4,7,8]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>0
[3,2,5,1,6,8,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[3,7,6,5,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,1,7,8,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,1,6,7,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,5,1,8,4,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[3,2,5,1,6,7,4,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[6,5,1,7,4,2,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,5,1,8,4,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,6,1,8,4,7,3]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[8,6,1,5,7,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,8,5,1,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,1,7,8,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,8,5,1,6,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,6,8,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,4,1,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,5,1,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,3,8,2,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,2,6,8,1,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[3,2,5,7,8,1,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,5,2,1,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,7,5,3,8,6,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[3,5,2,1,7,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,2,1,7,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,4,1,7,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,7,1,4,8,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,5,8,2,1,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,2,8,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,2,1,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,3,2,8,1,4,7,5]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[4,3,8,2,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,5,2,4,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[6,3,5,1,4,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[8,3,7,2,4,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,1,4,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,3,7,5,6,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,7,1,6,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,7,3,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,7,3,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,7,3,6,1,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,1,8,3,7,4,6,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[8,1,5,2,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,2,7,3,4,1,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,5,7,2,6,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,7,5,6,1,4,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,1,8,3,7,5,6,4]=>{{1,2},{3,4,8},{5,6,7}}=>[2,1,4,8,6,7,5,3]=>[2,1,7,5,6,8,3,4]=>1
[8,1,7,5,6,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,7,2,6,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,7,1,6,4,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,4,7,1,6,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,8,5,7,3,6,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[8,5,7,1,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,7,3,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,8,3,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,5,8,1,3,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,5,8,6,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,5,8,7,3,1,2,4]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[1,5,8,7,3,6,2,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,7,2,8,4,6,5,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[6,7,2,8,4,1,5,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[3,6,2,8,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,1,8,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,8,4,6,1,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,1,8,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,1,6,8,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,6,8,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,7,8,4,1,5,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[1,3,7,8,4,6,5,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,5,7,8,2,4,6,3]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[5,1,7,8,2,4,6,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[4,3,1,2,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[3,4,2,1,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[1,7,3,8,5,4,6,2]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[2,8,1,5,3,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,4,2,8,5,3,6,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,8,4,2,5,3,6,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[8,1,5,3,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,2,8,4,3,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,2,7,8,4,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,2,7,4,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[8,3,5,1,4,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,8,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,1,3,2,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,1,3,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,8,1,7,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,6,1,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,6,2,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,7,6,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,8,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,7,3,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,5,1,8,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,7,3,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[5,6,2,7,3,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,8,4,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,8,3,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,7,3,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[9,2,1,3,4,5,6,7,8]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>[2,9,1,3,4,5,6,7,8]=>0
[10,2,1,3,4,5,6,7,8,9]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[3,4,2,5,6,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,2,4,5,6,7,8,9,10,1]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[2,4,6,8,10,1,3,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,5,6,9,10,1,3,4,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,5,8,9,10,1,3,4,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,7,8,9,10,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,4,7,8,10,1,2,5,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,4,8,9,10,1,2,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,5,7,9,10,1,2,4,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,6,8,9,10,1,2,4,5,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,5,6,9,10,1,2,3,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,5,7,8,10,1,2,3,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,6,7,9,10,1,2,3,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,6,7,8,10,1,2,3,4,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,5,7,3,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,7,3,6,4,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,3,4,7,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,7,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,7,8,6,5,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,5,7,2,8,6,4,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[6,7,4,5,8,1,3,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[3,4,8,7,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,1,8,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,1,2,7,6,5,4]=>{{1,3},{2,4,8},{5,7},{6}}=>[3,4,1,8,7,6,5,2]=>[3,1,6,7,5,8,2,4]=>0
[3,1,4,5,6,7,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,3,4,5,6,7,8,1,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,1,4,5,6,7,8,9,2,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,10,4,5,6,7,8,1,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,3,4,5,6,7,1,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,1,10,5,6,7,8,9,2,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,1,4,5,6,7,8,2,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,6,5,1,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,6,1,8,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,1,8,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,4,6,1,2,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,1,2,5,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,5,1,8,3,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[2,3,6,1,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,2,4,1,3,8,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[6,3,4,1,2,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,4,1,3,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,7,1,2,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,3,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,1,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,5,2,1,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,2,1,3,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,2,1,4,8,7,5]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[7,3,1,2,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,1,3,4,8,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,6,5,8,1,7,3]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,2,6,5,8,1,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,4,6,8,1,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,4,1,6,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,1,4,6,8,5,3,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,4,1,6,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,8,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,8,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,3,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,3,8,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,3,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,1,4,6,8,3,7,5]=>{{1,2},{3,4,6},{5,8},{7}}=>[2,1,4,6,8,3,7,5]=>[2,1,6,3,4,7,8,5]=>1
[2,4,6,8,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,2,8,7,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,1,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,7,3,8,2,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,1,6,3,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,7,3,4,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,7,3,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,8,6,3,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,1,3,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,2,1,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,1,3,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,1,3,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,8,3,6,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,4,8,7,1,3,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,1,4,8,7,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,1,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,7,2,1,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,1,4,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,2,1,4,8,5,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[4,2,8,6,1,7,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,8,1,6,7,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,8,1,7,4,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,8,1,6,4,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[3,2,7,1,6,4,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,7,6,1,3,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,8,6,1,3,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,2,8,7,1,3,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,7,2,1,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,2,1,8,5,4,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[3,2,7,1,8,6,4,5]=>{{1,3,4,7},{2},{5,8},{6}}=>[3,2,4,7,8,6,1,5]=>[2,6,7,1,3,4,8,5]=>0
[4,3,6,8,7,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,6,7,1,8,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,6,1,7,8,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,8,2,5,7,3,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,8,1,5,2,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,5,1,6,4,3,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,1,5,7,4,3,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,5,8,6,4,3,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,8,7,4,3,2,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,6,1,7,4,3,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,1,7,6,4,3,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,8,7,6,4,3,2,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,1,7,5,6,3,8,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[4,2,1,5,6,3,7,8]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>0
[5,4,6,1,3,7,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,1,7,5,2,3,8,6]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[1,8,5,7,4,3,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,5,7,1,4,3,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,5,7,8,4,3,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,4,7,5,1,3,8,6]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[2,6,4,5,1,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[1,6,5,8,4,3,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,6,5,1,4,3,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,4,2,5,6,7,8,9,3]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[6,7,8,9,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,9,6,7,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,5,6,7,8,1,2,3,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,9,5,6,7,1,2,3,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,9,6,7,4,5,1,2,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,7,8,5,6,3,4,1,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,9,10,1,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,7,8,9,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,6,7,8,9,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,10,6,7,8,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,8,9,6,7,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,5,6,7,8,1,2,3,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,9,10,5,6,7,1,2,3,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,10,7,8,4,5,6,1,2,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,2,4,5,1,3,7,8]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>0
[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,5,4,1,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,4,1,7,8,5,3,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[2,5,4,1,6,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,5,2,1,6,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[3,7,5,8,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,6,3,2,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,3,5,2,1,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[3,7,2,8,6,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,7,3,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,2,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,1,6,2,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[5,7,1,6,2,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,6,5,1,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,5,1,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,7,6,1,4,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,5,1,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,7,6,3,8,5,4]=>{{1,2},{3,5,7},{4,6,8}}=>[2,1,5,6,7,8,3,4]=>[2,1,7,3,5,8,4,6]=>1
[2,1,7,6,3,8,4,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[6,3,5,1,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,4,5,8,7,3,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,3,4,8,7,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,5,6,8,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,1,5,8,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,5,8,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,7,8,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,8,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,8,1,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[2,3,4,8,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,8,2,6,1,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,6,7,2,5,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,5,7,2,6,3,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[2,8,6,7,1,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,7,4,6,3,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[2,8,4,7,1,6,3,5]=>{{1,2,5,8},{3,4,7},{6}}=>[2,5,4,7,8,6,3,1]=>[6,7,3,4,8,1,2,5]=>0
[2,8,3,7,5,6,1,4]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[1,6,7,3,8,5,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,4,2,8,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,1,8,4,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,3,6,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,2,3,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,4,7,8,3,6,2,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[5,3,8,2,4,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,8,1,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,8,1,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,1,3,6,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,3,1,6,4,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[4,5,1,7,2,6,3,8]=>{{1,3,4,7},{2,5},{6},{8}}=>[3,5,4,7,2,6,1,8]=>[5,2,6,7,1,3,4,8]=>0
[4,2,5,7,1,8,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,4,5,8,2,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,2,6,8,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,1,2,3,4,5,6,7,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[1,9,2,3,4,5,6,7,8]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[9,1,2,3,4,5,6,7,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[1,10,2,3,4,5,6,7,8,9]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[10,1,2,3,4,5,6,7,8,9,11]=>{{1,2,3,4,5,6,7,8,9,10},{11}}=>[2,3,4,5,6,7,8,9,10,1,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>0
[8,9,1,2,3,4,5,6,7,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[7,1,8,2,3,4,5,6,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[6,8,1,2,3,4,5,7,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[1,8,2,9,3,4,5,6,7]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,7,9,2,3,4,5,6,8]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,9,10,2,3,4,5,6,7,8]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[1,11,2,3,4,5,6,7,8,9,10]=>{{1},{2,3,4,5,6,7,8,9,10,11}}=>[1,3,4,5,6,7,8,9,10,11,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>0
[3,6,4,8,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,8,5,3,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,5,2,7,3,6,4]=>{{1},{2,4,8},{3,5,6,7}}=>[1,4,5,8,6,7,3,2]=>[1,7,3,5,6,8,2,4]=>0
[4,1,7,5,3,2,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,5,1,3,4,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,6,4,1,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,5,8,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,6,7,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,5,7,4,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,7,8,4,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,7,5,3,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[2,4,6,7,3,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,4,6,3,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,4,2,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,8,6,5,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,6,5,1,2,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,7,5,8,2,1,4,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[1,7,5,8,2,6,4,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,3,8,5,7,6,2,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[6,3,8,5,7,1,2,4]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[8,3,1,5,6,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,8,5,2,1,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,8,2,5,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,8,1,5,6,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,1,2,5,6,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,8,2,5,7,6,3,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[5,1,8,6,2,7,3,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[2,5,8,6,1,7,3,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[4,3,1,2,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[1,8,3,6,5,7,2,4]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[5,4,7,3,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,5,8,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,8,6,4,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,8,6,4,7,3,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[5,1,8,7,2,3,6,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[4,2,8,3,1,7,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,4,7,3,6,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,7,6,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,6,8,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,4,5,6,3,7]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[7,8,2,1,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,1,6,4,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,1,7,4,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,6,1,7,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,7,5,8,2,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[6,1,7,5,3,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,5,6,2,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,1,8,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,1,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,2,1,8,5,3,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[1,5,4,2,8,3,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,3,5,8,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,2,8,7,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,5,8,7,3,4,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,5,8,7,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,7,5,6,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,4,3,6,5,7]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[6,2,4,1,3,8,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,6,4,1,3,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[6,4,2,1,3,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[8,4,2,1,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,1,4,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,8,1,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,1,6,3,8,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,1,8,6,3,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,2,1,6,4,3,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,1,4,8,6,3,5,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,4,8,6,1,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,6,1,3,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,6,8,2,1,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,8,1,4,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,8,6,4,3,5,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[6,8,4,2,1,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,5,2,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,3,8,2,6,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,1,8,3,4,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,8,1,3,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,3,6,5,8,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,4,6,1,3,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,1,6,3,4,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,3,5,2,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,2,4,1,7,3,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,8,4,6,1,7,5]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[3,2,7,6,8,1,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,7,1,8,5,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,4,1,8,5,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,1,7,3,8,5,6,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[5,4,6,3,8,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,1,3,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,8,3,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,7,3,8,4,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,4,7,8,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,8,5,3,7,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,6,4,1,3,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,4,6,3,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,4,8,3,7,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,6,3,4,1,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,6,7,3,1,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,8,3,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,1,3,6,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,7,3,5,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,8,2,6,3,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,1,2,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,5,2,6,7,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,2,1,8,6,7,4,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,8,1,6,4,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,8,6,1,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,2,1,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[8,5,2,7,4,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,5,7,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,6,3,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,8,5,7,4,3,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[3,8,6,7,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,8,2,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,6,2,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,6,2,8,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,7,6,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,7,2,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,7,3,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,7,6,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,7,6,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,7,6,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,1,5,7,4,8,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,4,6,7,3,8,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,2,1,6,7,8,4,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,4,5,7,2,1,8,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[5,4,6,7,2,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,2,7,1,8,4]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[4,2,1,5,7,3,8,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,5,6,7,8,4,2,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,4,6,7,1,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,1,6,3,8,5,7,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[2,4,1,6,3,7,5,9,8]=>{{1,2,3,4,5,6,7},{8,9}}=>[2,3,4,5,6,7,1,9,8]=>[7,1,2,3,4,5,6,9,8]=>1
[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,4,1,6,3,7,5,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>0
[2,4,1,6,3,8,5,9,7,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[7,1,2,3,4,5,6,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>0
[1,5,4,8,3,7,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,2,3,8,4,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[5,1,2,3,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,2,8,1,3,5,4,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,5,1,3,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,2,4,8,3,7,6,5]=>{{1},{2},{3,4,5,8},{6,7}}=>[1,2,4,5,8,7,6,3]=>[1,2,7,6,8,3,4,5]=>1
[2,4,8,3,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,2,3,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,8,3,7,2,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,3,8,1,2,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,5,1,2,8,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,6,4,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[5,1,6,2,8,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,5,2,8,7,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,3,1,5,8,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,5,2,8,7,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,1,7,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,4,8,7,2,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,3,6,2,4,7,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,2,6,7,4,8,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,7,6,5,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,6,5,2,4,8,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,7,6,5,3,1,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,1,6,2,4,8,3,7]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[4,7,6,5,2,1,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,7,6,5,2,8,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,6,5,3,2,8,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,2,6,3,4,1,7,8]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>0
[5,1,6,2,4,7,8,3]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[1,7,2,6,8,3,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,7,6,5,2,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,7,6,5,8,2,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,7,6,5,1,2,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,7,6,5,1,4,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,2,1,7,3,5,8,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,3,7,2,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,5,3,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,6,2,4,8,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,2,7,5,3,8,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,7,2,6,1,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,8,3,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,5,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,8,4,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,8,1,7,3,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,5,8,7,1,3,6,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[5,3,8,7,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,7,6,1,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,8,7,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,8,6,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,7,3,6,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,5,1,2,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,8,5,7,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,7,8,4,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,2,6,4,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,1,5,8,7,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,5,8,7,3,4,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[4,7,1,6,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,3,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,7,3,4,8,6,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[6,7,1,4,3,8,2,5]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[7,1,2,3,6,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,2,3,8,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,2,8,3,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,1,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,2,8,3,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,2,3,7,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,2,3,8,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[5,1,2,3,6,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,3,6,8,4,7,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,4,6,1,5,2,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[7,1,4,2,6,3,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,6,4,2,8,3,5,7]=>{{1},{2,3,4,6},{5,7,8}}=>[1,3,4,6,7,2,8,5]=>[1,6,2,3,4,8,5,7]=>0
[1,6,3,8,5,4,2,7]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[1,6,2,3,8,5,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,8,2,7,6,3,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[2,1,6,3,8,5,4,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[3,5,8,7,1,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,7,6,3,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,6,1,2,4,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[1,3,2,5,8,7,4,6]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[4,5,8,3,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,7,6,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,4,8,7,6,2,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[3,2,5,8,7,4,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,8,1,3,7,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,6,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,5,7,1,3,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,8,1,6,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,7,4,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,7,1,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,4,7,1,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,6,8,2,7,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,5,8,2,7,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,4,5,7,2,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,4,2,5,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,5,7,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,5,3,7,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,2,1,8,4,3,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[6,3,4,8,2,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,4,1,8,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,1,4,5,2,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,5,4,2,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,1,6,3,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,4,2,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,4,1,3,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[3,7,4,2,6,1,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,1,7,3,2,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[4,7,5,6,2,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,7,5,6,2,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,7,5,6,1,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,5,4,1,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,1,8,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,8,5,1,7,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,1,8,6,7,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,3,2,8,6,7,4,5]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[2,3,8,6,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,8,6,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,1,7,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,5,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,6,5,1,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,7,5,1,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,6,1,5,4,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[8,7,1,2,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,1,2,4,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,1,2,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,1,3,6,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,6,1,5,3,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,1,4,2,7,3,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,7,8,1,3,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,7,6,4,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,7,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,1,3,8,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,5,3,2,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,5,2,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,7,5,3,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,7,2,6,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,1,2,8,6,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,7,4,6,5,3]=>{{1,2,3,8},{4,5,7},{6}}=>[2,3,8,5,7,6,4,1]=>[6,7,4,5,8,1,2,3]=>0
[1,2,3,5,8,7,4,6]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[1,2,3,6,8,5,4,7]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[7,8,5,3,1,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,6,3,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,6,3,1,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,8,3,6,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,8,6,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,6,8,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,6,3,8,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,6,3,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,3,2,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,6,3,7,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,5,3,2,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,6,3,8,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,2,6,8,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,8,7,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,3,7,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,2,5,4,8,6,1]=>{{1,6,7,8},{2,3},{4,5}}=>[6,3,2,5,4,7,8,1]=>[3,2,5,4,8,1,6,7]=>2
[6,8,5,7,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,5,6,8,7,1,9]=>{{1,2,3,4,5,6,8},{7},{9}}=>[2,3,4,5,6,8,7,1,9]=>[7,8,1,2,3,4,5,6,9]=>0
[6,8,1,2,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,3,6,8,4,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,5,8,2,4,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[5,4,8,3,2,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,2,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,1,7,3,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,6,4,2,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,7,6,2,8,4,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,7,1,8,2,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,2,7,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,7,6,2,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,6,5,2,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,7,3,6,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,6,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,5,1,8,6,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,2,6,4,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,8,7,6,5,2,4,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[8,6,5,3,2,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,6,1,7,4,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,7,2,5,4,6,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,8,5,3,7,2,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,3,1,8,7,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,8,6,3,5,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,4,1,6,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,5,2,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,5,7,2,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,6,2,4,7,5,1,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[7,3,5,2,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,4,1,5,2,3]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[3,8,7,2,1,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,8,2,1,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,5,8,6,4,3,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[7,1,8,6,3,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,7,6,3,5,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,1,2,3,8,5,4,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[2,5,1,7,4,3,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,8,3,1,5,6,4,7]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[4,3,1,7,6,8,2,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[4,2,8,3,6,1,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,8,5,7,2,1,3,4]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,3,5,2,1,7,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,6,5,8,2,4,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,8,2,4,3,7,5]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,6,7,2,4,3,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[1,5,7,8,3,2,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,8,3,2,4,6,7]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[1,7,4,2,8,6,5,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,6,7,5,2,3,8,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,5,2,8,4,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,4,6,2,8,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,8,5,2,3,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,6,4,2,3,7,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,7,3,2,4,8,6]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[1,6,4,2,3,8,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,4,2,3,8,7,5]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[7,4,1,3,8,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,7,3,8,2,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,1,7,3,8,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,3,8,5,6,1,7]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[1,4,8,3,6,2,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,5,8,7,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,7,6,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,7,3,6,2,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,8,7,5,3,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,6,8,3,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,8,4,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,4,7,6,8,2,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,5,4,8,6,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,2,7,5,8,3,4]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,8,4,6,5,7,2,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,8,2,6,5,7,3,4]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,5,2,7,6,8,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,8,5,6,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}=>[1,3,2,7,6,8,4,5]=>[1,3,2,7,4,8,5,6]=>1
[1,7,6,8,2,4,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,8,2,1,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,2,4,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,5,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,5,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,1,6,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,4,5,6,7,1,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,4,5,1,6,7,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,4,5,6,7,1,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,4,5,6,7,1,2,9,8]=>{{1,2,3,4,5,6,7},{8,9}}=>[2,3,4,5,6,7,1,9,8]=>[7,1,2,3,4,5,6,9,8]=>1
[3,4,5,6,7,8,9,1,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,3,7,5,2,6,8,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,4,7,3,2,5,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,5,3,2,8,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,4,6,8,2,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,7,5,1,8,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,8,7,4,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,5,2,4,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[5,7,1,2,4,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,6,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,7,6,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,7,1,2,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,7,3,5,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,4,1,5,8,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,1,5,8,7,4,6,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,4,8,7,3,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,8,3,1,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,8,3,6,7,5,4]=>{{1,2},{3,4,8},{5,6,7}}=>[2,1,4,8,6,7,5,3]=>[2,1,7,5,6,8,3,4]=>1
[4,5,2,7,6,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,8,4,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,1,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,8,4,1,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,8,2,7,3,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,8,7,2,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,2,1,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,1,2,7,3,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,1,3,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,8,6,2,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,5,2,8,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,8,1,4,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,1,2,4,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,6,2,4,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,6,1,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,1,6,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,5,8,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,8,6,2,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,6,1,4,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,8,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,8,2,3,6,7,5]=>{{1},{2,4},{3,5,8},{6},{7}}=>[1,4,5,2,8,6,7,3]=>[1,4,2,6,7,8,3,5]=>0
[3,1,2,7,8,6,4,5]=>{{1,2,3},{4,7},{5,8},{6}}=>[2,3,1,7,8,6,4,5]=>[3,1,2,6,7,4,8,5]=>0
[4,5,8,1,2,3,7,6]=>{{1,4},{2,5},{3,6,8},{7}}=>[4,5,6,1,2,8,7,3]=>[4,1,5,2,7,8,3,6]=>0
[1,4,7,3,2,8,5,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[2,4,1,8,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,4,1,3,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,8,4,5,1,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[7,6,1,2,8,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,8,7,1,3,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,5,1,6,8,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,1,8,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,3,1,5,8,7,2]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[7,4,1,5,3,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,5,3,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[7,4,1,5,3,2,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,6,8,1,4,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,5,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,5,3,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[4,7,5,6,2,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,6,4,5,2,7,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,8,3,6,2,7,4,5]=>{{1},{2,5,8},{3},{4,6,7}}=>[1,5,3,6,8,7,4,2]=>[1,3,7,4,6,8,2,5]=>0
[1,6,4,8,2,7,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,6,4,7,3,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,7,2,5,3,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,4,2,7,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[7,6,1,3,8,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,1,5,2,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,2,7,3,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,7,2,4,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,7,2,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,7,1,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,4,1,2,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,8,6,4,1,3,7]=>{{1,4,5,6},{2},{3,7,8}}=>[4,2,7,5,6,1,8,3]=>[2,6,1,4,5,8,3,7]=>0
[8,4,7,5,1,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,7,3,1,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,1,6,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,1,3,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,5,8,6,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,8,6,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,3,6,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,4,2,8,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,6,7,5,3,4,2]=>{{1,2,8},{3,6},{4,7},{5}}=>[2,8,6,7,5,3,4,1]=>[5,6,3,7,4,8,1,2]=>0
[2,1,4,7,6,3,8,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[8,5,1,6,3,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,2,6,8,4,7,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,4,6,1,3,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,6,7,3,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,4,8,5,7,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,6,1,4,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,2,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,5,8,4,3,7,1]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,8,2,7,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,8,2,7,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,8,2,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,2,1,3,4,7,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,4,8,2,6,3,5,7]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[1,3,8,2,6,4,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,7,2,3,6,4,8]=>{{1},{2,3,4,5,7},{6},{8}}=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>0
[1,7,2,3,5,4,8,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,3,8,2,4,5,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,8,2,3,5,4,6,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,7,8,2,5,3,6,4]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,7,8,2,4,5,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,2,3,6,4,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,2,7,8,3,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,2,3,4,6,7,5]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[1,7,8,2,4,3,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,8,3,1,5,2,7,4]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[6,7,4,5,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,8,1,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,1,7,6,8,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,8,6,5,7,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,7,3,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[2,4,6,3,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,6,5,3,7,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,2,7,6,3,5,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[1,2,3,7,4,8,6,5]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[1,2,3,7,6,4,8,5]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[4,2,6,3,1,8,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,4,2,8,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,8,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,1,8,3,5,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[1,5,2,8,7,3,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,2,3,8,7,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,2,1,8,3,7,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,2,3,8,7,4,6,5]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[2,6,5,7,1,4,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,5,7,1,4,8,6,3]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[3,5,7,6,1,2,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,8,6,7,1,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,6,1,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,2,8,5,6,1,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[3,8,5,7,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,6,2,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,6,7,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,6,7,2,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,6,7,2,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,4,8,6,1,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,8,6,7,2,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,8,5,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[3,8,4,7,1,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,2,6,7,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,8,6,7,3,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,6,7,3,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,7,5,2,8,6,3]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[4,1,6,7,5,2,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[4,8,6,7,2,3,1,5]=>{{1,4,7},{2,5,8},{3,6}}=>[4,5,6,7,8,3,1,2]=>[6,3,7,1,4,8,2,5]=>0
[5,8,6,7,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,6,7,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,7,5,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,5,3,1,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,2,1,6,7,5,3,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[1,3,8,6,2,7,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,7,3,6,4,5,2,1]=>{{1,8},{2,7},{3},{4,5,6}}=>[8,7,3,5,6,4,2,1]=>[3,6,4,5,7,2,8,1]=>0
[2,7,4,1,6,8,3,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[1,5,2,7,4,3,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,7,1,2,8,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,7,2,8,5,6,3]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[6,8,1,5,7,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,8,1,2,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,2,1,6,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,4,1,8,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,4,1,6,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,7,6,8,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,7,6,8,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,7,6,8,2,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,4,2,6,8,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,1,4,2,8,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,2,6,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,2,6,8,5,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,6,8,2,3,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,6,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,1,6,8,5,4,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,1,5,6,7,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,7,2,1,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,2,6,7,3,1,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,3,5,2,7,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,1,7,2,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,6,3,2,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,2,6,3,8,1,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[5,2,8,3,4,1,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,5,8,6,3,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,4,1,8,7,3]=>{{1,5},{2,3,6,8},{4},{7}}=>[5,3,6,4,1,8,7,2]=>[4,5,1,7,8,2,3,6]=>0
[6,1,4,2,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,1,3,7,2,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,1,6,3,4,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[4,8,6,5,3,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,8,3,2,1,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[5,4,8,7,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,6,8,3,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,8,5,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,7,6,3,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,2,6,3,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,7,1,3,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,1,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,8,3,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,2,8,3,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,8,2,6,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,5,8,2,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,4,5,8,3,1,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,4,5,8,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,8,3,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,2,3,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,7,2,3,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,7,5,2,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[4,2,7,6,3,8,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,7,4,1,6,8,5]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[4,2,7,8,6,1,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,2,1,6,3,7,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,8,1,6,7,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,6,8,1,5,4,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,4,7,3,2,1,8,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[5,4,7,3,2,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,3,7,8,2,1,4,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[5,3,7,6,2,1,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,8,3,2,5,1,7,6]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[6,3,7,8,1,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,2,1,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,8,7,2,1,4,5,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[6,5,2,7,1,4,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,4,1,6,7,8,3,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[1,4,5,7,2,6,3,8]=>{{1},{2,3,4,5,7},{6},{8}}=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>0
[3,4,5,6,8,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,7,2,1,3,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,8,7,2,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,1,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,7,6,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,8,1,7,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,8,6,3,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,6,3,8,5,1,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,4,5,6,8,1,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,5,7,8,4,6,2,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,3,5,7,8,6,2,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[3,1,5,6,8,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,5,6,8,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,5,1,6,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,1,2,6,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,5,2,7,8,6,3,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[5,1,7,8,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,5,2,4,1,8,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,7,2,5,3,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,4,5,2,1,8,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[1,6,7,5,3,8,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,7,5,1,4,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,3,7,5,8,2,4]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[2,7,6,1,3,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,5,1,8,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,7,3,8,5,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[3,6,5,1,8,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,6,5,1,8,4,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,1,5,8,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,6,2,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,2,1,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,5,6,8,3,1,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,5,6,1,8,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,5,6,8,3,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,5,6,3,8,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,7,3,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,7,4,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,1,7,3,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,3,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,2,1,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,3,1,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,1,3,2,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,6,3,7,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,6,3,1,7,8,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[6,3,7,2,8,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,7,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,5,8,1,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,1,7,3,8,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,7,1,8,5,4,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,3,2,1,8,4,7,6]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[2,4,6,5,8,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,4,6,5,8,2,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[8,1,4,2,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,2,5,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[3,7,4,8,2,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,6,8,7,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,1,8,5,6,7,3,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[8,2,1,6,7,3,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,5,2,7,4,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,7,1,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,4,6,7,1,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,8,2,3,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,6,5,8,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,1,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,2,1,8,5,7,4]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[8,6,4,2,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,4,8,5,7,2,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[5,4,8,7,6,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,5,8,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[5,4,2,1,6,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,3,1,2,8,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[5,2,1,3,6,8,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[6,3,8,2,7,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,3,6,4,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[3,4,8,7,2,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,8,7,4,1,2,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[8,6,4,2,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,5,7,2,6,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,5,3,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,5,7,8,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,1,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,7,8,3,5,4,6,2]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[3,4,5,1,8,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[3,5,6,2,8,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,7,2,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,1,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,7,2,8,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,2,1,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,2,8,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,1,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,3,8,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,7,3,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,7,3,2,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,8,3,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,7,3,2,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,2,3,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,7,8,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,2,3,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,2,3,4,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,3,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,8,3,4,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,2,3,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,2,8,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,8,3,4,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,1,2,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,5,8,6,1,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,6,8,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,2,7,5,3,1,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,8,1,5,3,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,7,5,3,2,4,8]=>{{1},{2,6},{3,4,5,7},{8}}=>[1,6,4,5,7,2,3,8]=>[1,6,2,7,3,4,5,8]=>0
[5,9,8,7,6,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,10,9,8,7,5,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,8,5,6,7,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,4,5,6,2,1]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[1,8,7,6,5,3,2,4]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,6,3,2,5,8,4,7]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[2,5,1,8,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,5,4,2,6,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,5,1,8,4,3,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,7,3,2,5,4,8,6]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[8,3,6,4,5,1,7,2]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[3,4,7,8,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,3,8,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,6,3,2,5,8,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,5,3,6,2,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[3,6,2,1,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,7,8,2,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,4,1,6,8,7,3]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,3,5,6,1,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,4,2,5,8,3,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,4,2,7,8,5,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,1,2,6,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,5,8,7,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,8,2,6,7,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,6,2,4,8,7,5]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,3,7,6,2,8,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,3,8,7,4,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,6,7,3,4,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,2,4,7,6,3,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,6,2,1,7,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,4,5,8,7,3]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[5,4,2,7,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,2,7,8,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,7,4,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,6,1,3,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,2,3,8,6,4,5,7]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[5,2,4,1,7,8,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,1,4,2,8,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[1,2,3,8,6,7,4,5]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[1,2,3,8,7,5,4,6]=>{{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0
[3,1,6,2,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,7,3,6,5,4,1]=>{{1,8},{2},{3,4,7},{5,6}}=>[8,2,4,7,6,5,3,1]=>[2,6,5,7,3,4,8,1]=>1
[6,8,1,3,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,2,5,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,7,6,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,4,3,7,5,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[2,6,5,8,1,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,5,3,7,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,8,4,7,1,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,6,8,2,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,2,6,1,5,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,6,5,8,4,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,2,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,2,8,4,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,7,8,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,7,3,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,4,7,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,8,2,4,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,8,2,4,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,2,5,1,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,5,8,7,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,2,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,2,3,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,5,3,8,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,5,3,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,7,3,1,8,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,4,5,3,7,1,8,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[5,7,4,2,3,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,4,2,5,1,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,3,7,2,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,3,4,7,2,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[5,3,4,6,7,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,7,3,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,6,5,1,8,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,7,8,3,2,9,6,5,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,6,7,8,2,1,9,5,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,5,6,7,8,2,9,4,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,4,6,7,1,8,3,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,4,5,6,7,8,1,9,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,3,8,7,2,1,10,9,6,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,7,8,9,3,2,10,6,5,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,3,6,5,8,7,10,9,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,6,7,8,9,3,10,5,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,6,2,1,9,5,4,10,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,6,8,2,9,5,1,10,7,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,5,6,7,8,9,2,10,4,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,4,5,6,7,8,9,10,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,4,6,7,8,1,9,3,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,3,8,2,4,6,5,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,7,2,3,6,4,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,2,5,3,4,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,8,2,3,6,4,7,5]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,3,5,2,8,4,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,5,8,2,3,7,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,8,2,3,5,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,3,6,1,2,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[7,1,5,8,4,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,5,8,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,7,5,8,3,4,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[8,7,1,6,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,7,1,2,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,6,1,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,3,7,5,1,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,6,1,2,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,1,7,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,3,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,1,5,8,3,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,3,6,8,7,4,2,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,2,8,7,4,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,1,3,7,5,6,8,2]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[4,1,7,3,8,5,2,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[1,4,7,2,8,5,3,6]=>{{1},{2,4},{3,7},{5,6,8}}=>[1,4,7,2,6,8,3,5]=>[1,4,2,7,3,8,5,6]=>0
[7,2,8,4,1,6,3,5]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[1,3,6,5,2,8,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,6,4,5,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,5,6,3,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,8,7,2,6,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,7,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,5,3,6,2,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,7,2,4,3,8,6]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[6,8,2,5,3,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,1,7,2,8,5,4,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[5,2,6,8,3,4,7,1]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[5,8,1,2,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,6,8,3,2,7,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,5,7,2,8,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,1,2,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,3,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,8,2,7,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,5,8,2,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,6,4,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,5,1,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,6,1,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,1,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,4,6,8,3,2,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,5,4,6,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,4,7,6,8,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,2,5,8,4,7,6,3]=>{{1},{2},{3,4,5,8},{6,7}}=>[1,2,4,5,8,7,6,3]=>[1,2,7,6,8,3,4,5]=>1
[1,3,5,8,7,2,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,4,5,7,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,4,7,2,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[5,3,6,2,7,1,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,7,4,5,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,3,6,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,2,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,2,8,4,5,7,1]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[6,4,1,3,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,5,2,3,6,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,7,3,4,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,1,6,2,3,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,1,6,2,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,5,7,2,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,8,2,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,8,3,4,5,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,7,8,3,4,5,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,2,8,4,5,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[6,4,5,8,7,1,2,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[5,3,4,8,7,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,8,2,6,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,6,1,3,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,6,1,3,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,8,6,2,3,4,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,8,7,2,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,8,7,2,3,6,4]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[8,7,6,1,3,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,8,5,3,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,4,5,7,1,6,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>0
[2,3,4,5,6,8,1,7,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[3,8,5,2,7,4,1,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[3,1,4,6,2,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,4,5,8,7,2,1,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[6,1,4,8,7,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,1,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,6,3,8,1,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[7,1,6,3,4,2,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,8,7,1,4,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,5,1,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,5,6,7,2,1,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[8,5,6,1,4,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}=>[1,6,4,5,7,2,3,8]=>[1,6,2,7,3,4,5,8]=>0
[1,7,5,3,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,2,1,5,8,7,3,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,5,3,6,8,7,4,2]=>{{1},{2,5,8},{3},{4,6,7}}=>[1,5,3,6,8,7,4,2]=>[1,3,7,4,6,8,2,5]=>0
[3,5,4,6,1,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,7,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}=>[1,3,4,6,7,2,8,5]=>[1,6,2,3,4,8,5,7]=>0
[1,7,3,6,5,2,8,4]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[1,3,4,7,6,2,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,8,5,2,6,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,1,8,6,2,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,1,8,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,8,6,1,7,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,4,6,7,1,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,5,1,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[1,3,2,7,4,8,6,5]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[5,6,7,1,2,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,1,2,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,2,3,8,6,5,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[4,1,5,3,8,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,5,4,2,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,4,1,7,2,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[6,5,3,4,8,2,7,1]=>{{1,2,5,6,8},{3},{4},{7}}=>[2,5,3,4,6,8,7,1]=>[3,4,7,8,1,2,5,6]=>0
[8,6,2,5,7,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,6,2,5,4,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[1,7,6,8,3,2,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,2,8,5,3,4,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,1,5,8,4,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,4,8,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,8,7,3,4,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,4,7,5,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,6,8,2,7,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,6,5,3,2,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,4,7,5,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,3,2,5,4,7,1]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[2,5,4,7,1,8,6,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[5,8,4,7,2,6,3,1]=>{{1,2,5,8},{3,4,7},{6}}=>[2,5,4,7,8,6,3,1]=>[6,7,3,4,8,1,2,5]=>0
[3,5,4,7,1,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[7,5,2,1,10,4,3,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,4,2,1,8,7,3,10,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,4,2,1,10,7,3,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,6,2,1,10,5,3,9,4,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,3,7,2,6,1,5,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>0
[7,1,8,2,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,5,2,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,8,2,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,8,2,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,1,7,2,8,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,7,2,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,5,2,4,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,8,2,6,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,4,2,6,3,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,1,7,3,2,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,1,7,2,6,8,4,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[4,1,6,3,2,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,3,1,6,2,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[6,5,1,7,3,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,8,6,1,5,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,4,2,7,3,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[6,3,1,7,8,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,1,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,2,6,3,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,2,1,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,8,1,2,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,7,1,3,5,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,2,8,3,1,7,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,3,1,2,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[1,5,4,6,8,2,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,7,3,2,4,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,2,4,7,8,1,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,5,7,6,1,8,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,5,2,8,6,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,1,8,3,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,1,5,7,6,2,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,4,2,1,8,7,5,6]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[7,6,5,8,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,5,3,2,1,9,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,7,6,5,9,2,1,4,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,6,5,8,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,8,7,6,4,3,2,1,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,6,3,2,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,3,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,7,3,1,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,2,7,3,1,4,5,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[5,1,4,6,7,2,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,4,6,7,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,4,6,7,1,3,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[2,5,4,6,7,1,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,1,7,3,2,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,4,1,6,2,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,4,1,5,6,2,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[7,6,5,4,1,3,2,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[7,3,4,1,5,2,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[1,3,4,5,8,7,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,3,4,5,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,7,5,4,6,8,2,1]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[3,7,5,2,6,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,5,2,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[2,7,4,6,1,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,4,5,8,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,4,5,8,6,2,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,3,4,5,8,2,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[6,3,4,5,8,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,5,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,4,5,8,1,2,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,3,4,5,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,10,6,9,4,8,2,5,1,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,10,5,9,4,7,2,6,1,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,10,5,9,4,8,2,7,1,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,10,6,9,3,7,2,5,1,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,10,4,9,3,7,2,6,1,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,10,4,9,3,8,2,7,1,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,1,8,6,3,5,4,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,7,3,1,5,6,8,4]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[2,1,6,8,3,7,4,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[8,2,4,1,7,5,3,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,1,7,3,4,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,1,8,3,6,4,5,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[2,1,8,3,6,7,4,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[6,1,5,8,2,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,1,6,2,8,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,7,8,6,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,7,2,4,5,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,1,6,3,2,5,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,7,6,3,1,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,1,4,3,5,2,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[7,4,1,3,5,2,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[7,3,1,2,4,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[3,6,2,1,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,7,4,3,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,4,5,2,6,7,3]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[5,6,7,3,2,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,7,8,1,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,7,8,1,4,5,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[7,4,5,8,2,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,5,2,4,6,3,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,8,4,2,3,5,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[6,4,2,8,3,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,8,2,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,5,6,8,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,8,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,7,8,1,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,8,3,1,4,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[2,5,7,8,3,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,3,8,1,5,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,3,2,5,4,8,1,7]=>{{1,6,7,8},{2,3},{4,5}}=>[6,3,2,5,4,7,8,1]=>[3,2,5,4,8,1,6,7]=>2
[5,4,7,3,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,7,8,1,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,7,8,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,7,8,1,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,5,6,7,8,9,10,1,11]=>{{1,2,3,4,5,6,7,8,9,10},{11}}=>[2,3,4,5,6,7,8,9,10,1,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>0
[3,4,5,6,7,8,9,1,2,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[2,4,5,6,7,8,1,3,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[1,4,5,6,7,8,2,9,3]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,4,5,6,7,8,9,10,2,3]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[1,3,4,5,6,7,8,9,10,11,2]=>{{1},{2,3,4,5,6,7,8,9,10,11}}=>[1,3,4,5,6,7,8,9,10,11,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>0
[4,2,8,6,1,5,3,7]=>{{1,4,5,6},{2},{3,7,8}}=>[4,2,7,5,6,1,8,3]=>[2,6,1,4,5,8,3,7]=>0
[1,3,4,8,2,7,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,4,8,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,3,1,6,2,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,8,6,2,1,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,7,5,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,5,1,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,1,3,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,8,2,3,5,7,4,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[4,7,5,2,6,1,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,6,2,8,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,2,7,1,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,5,1,2,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,2,7,4,8,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,2,1,7,8,5,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,5,8,3,6,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,3,7,1,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,8,2,3,6,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,8,1,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,6,4,8,1,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,5,1,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,6,5,1,2,4,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,6,5,1,2,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,3,6,1,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[3,6,4,2,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,4,2,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,6,4,5,1,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[7,6,5,1,4,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,5,1,2,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,5,1,8,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,5,1,4,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,7,6,2,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,1,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,5,3,1,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,6,4,5,7,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,5,6,8,1,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,3,4,2,8,7,5]=>{{1,2,5,6,8},{3},{4},{7}}=>[2,5,3,4,6,8,7,1]=>[3,4,7,8,1,2,5,6]=>0
[2,4,5,6,1,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,8,7,1,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,8,7,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,5,8,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,1,3,4,8,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[6,5,4,2,8,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,6,2,8,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,8,7,4,5,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,3,8,5,7,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,4,8,7,5,3,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[3,6,8,2,4,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,8,6,2,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,5,3,6,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,9,6,7,4,5,2,3,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[10,7,9,5,8,3,6,1,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,7,4,2,5,3,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[7,6,4,8,3,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,8,5,6,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,7,5,6,3,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[4,1,8,5,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,8,5,3,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,5,3,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,6,5,3,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,6,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,2,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,6,5,1,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,4,6,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,5,6,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,2,1,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,7,3,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,2,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,1,3,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,2,3,6,8,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[6,8,4,1,2,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,1,3,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,5,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,4,1,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,6,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,1,3,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,1,3,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,5,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,1,4,2,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,6,8,5,1,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,3,6,2,1,5,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,7,5,3,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,8,7,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,8,6,3,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,4,2,5,7,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,2,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,8,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,8,6,3,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,5,3,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,6,3,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,6,4,1,8,7,5]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[5,4,2,1,7,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,2,7,1,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,7,2,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,1,2,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,1,3,6,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,1,5,2,7,4,9,6,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[4,6,7,3,1,5,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,2,4,8,1,5,3,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,3,1,6,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,7,8,9,2,3,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,6,7,8,9,1,2,3,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,7,8,9,2,3,4,5,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,5,6,7,8,9,10,1,2,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,8,7,6,1,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,7,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,1,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,3,1,10,9,6,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,7,5,2,1,10,8,6,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,6,5,2,1,10,9,7,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,7,4,2,1,10,9,6,5,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,5,4,2,1,10,9,7,6,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,1,4,2,3,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,8,2,3,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,6,2,4,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,3,6,4,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,3,8,2,4,1,5,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[1,6,4,2,7,5,8,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,2,5,3,6,1,7,8]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>0
[7,1,5,3,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,5,2,4,8,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[4,6,2,3,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,7,2,8,3,9,4,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,1,7,8,9,10,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,4,8,6,2,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,1,8,2,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,1,3,6,5,8,7,2]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[4,2,1,6,3,5,7,8]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>0
[6,2,1,3,8,5,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[8,2,1,6,3,5,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[8,2,1,4,3,5,7,6]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[8,2,4,1,3,5,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[8,4,1,6,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,6,4,8,3,5,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[6,4,8,1,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,2,8,1,3,5,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[2,6,8,1,3,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,6,1,8,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,4,6,3,8,5,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[2,4,1,8,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,1,8,3,6,5,7,4]=>{{1,2},{3,4,8},{5,6},{7}}=>[2,1,4,8,6,5,7,3]=>[2,1,6,5,7,8,3,4]=>2
[2,8,1,6,3,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,4,8,6,3,5,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[4,1,8,6,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,8,4,1,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,4,1,3,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[8,6,4,1,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,4,2,1,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,8,6,5,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,6,1,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,1,8,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,7,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,2,7,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,1,4,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,8,1,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,8,7,6,4,3,2,1,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,7,4,6,3,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,8,7,6,3,5,2,1,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[10,9,8,7,6,4,3,2,1,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,5,4,7,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,8,5,7,4,3,2,1,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,8,6,2,3,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,8,2,6,3,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,6,2,5,8,4,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,8,6,5,1,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,2,8,3,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,7,8,3,1,2,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,3,4,8,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,8,3,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,8,5,1,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[6,4,8,7,3,1,5,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[3,4,8,7,1,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,8,5,1,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,5,6,1,4,7,8,3]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[1,8,7,6,3,2,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,7,8,6,2,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,6,1,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,1,7,2,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,3,4,7,6,1,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,5,8,4,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,4,5,2,7,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,3,5,4,7,2,1,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[1,8,4,5,2,6,3,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[6,4,8,5,3,1,2,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[2,3,4,7,5,1,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[2,3,4,7,1,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[2,3,4,6,1,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,5,8,4,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,8,4,5,2,3,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,4,8,5,3,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,8,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,8,4,6,3,7,1]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[3,2,8,6,1,5,4,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,6,1,2,4,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,6,2,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,7,2,5,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,8,6,2,3,4,7]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[3,7,6,1,8,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,4,1,3,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[8,5,4,7,1,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,7,6,1,8,5,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[3,5,2,6,7,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,7,5,1,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,8,3,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,7,2,5,6,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,3,2,5,7,4,6]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[6,5,1,7,4,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,1,7,3,5,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,6,4,7,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,8,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,4,7,8,1,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,1,6,7,4,2,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,4,7,6,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,6,8,1,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,8,4,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,4,7,6,1,5,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[8,5,6,7,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,7,5,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,7,1,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,4,6,1,5,7,8]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>0
[7,8,6,5,1,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,8,5,2,3,6,7]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[5,4,1,3,6,7,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,7,1,2,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,2,1,5,3,4,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[2,6,4,1,7,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,6,5,7,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,4,1,8,5,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,1,5,8,4,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,8,4,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,2,6,1,4,5,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,8,1,4,5,3,7]=>{{1,4,5,6},{2},{3,7,8}}=>[4,2,7,5,6,1,8,3]=>[2,6,1,4,5,8,3,7]=>0
[7,1,2,5,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,5,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,8,5,1,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,5,6,4,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,6,1,4,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,3,7,2,8,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,4,5,1,3,6,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[6,2,4,5,1,8,7,3]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[1,6,4,5,2,8,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[3,7,4,5,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,4,5,2,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,4,8,6,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,1,5,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,3,6,1,2,7]=>{{1,5,6},{2,7,8},{3,4}}=>[5,7,4,3,6,1,8,2]=>[4,3,6,1,5,8,2,7]=>1
[4,3,8,2,1,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,4,2,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,5,6,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,6,8,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,8,2,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,8,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,5,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,2,1,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,5,6,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,5,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,8,5,6,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,1,5,6,7,3,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[1,4,5,8,6,7,3,2]=>{{1},{2,4,8},{3,5,6,7}}=>[1,4,5,8,6,7,3,2]=>[1,7,3,5,6,8,2,4]=>0
[4,3,5,8,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,8,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,5,6,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,5,6,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,5,2,6,7,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,6,3,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,4,6,2,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,2,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,5,1,8,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,6,3,1,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,7,4,2,3,1,8,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,7,5,3,1,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,5,4,1,8,2,3]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[10,3,1,2,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,7,1,2,3,4,5,6,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,10,1,2,3,4,5,6,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,10,1,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,3,1,10,2,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,7,1,2,3,4,5,10,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,9,1,2,3,4,5,6,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,2,1,6,3,7,5,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[4,2,1,6,3,7,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,8,1,7,4,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,1,8,3,5,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,1,6,3,8,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[3,7,6,8,4,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,1,7,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,1,4,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,7,5,2,1,3,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,5,6,1,4,8,3,7]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[7,1,6,8,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,5,6,4,2,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,7,4,6,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,8,6,1,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,6,1,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,8,5,2,1,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[1,8,4,6,2,5,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,2,8,5,7,1,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,1,8,4,7,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,3,1,5,6,2,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,7,5,1,6,2,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,7,8,2,6,4,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,1,4,2,3,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,5,7,3,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,1,2,3,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,1,5,2,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,8,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,1,2,8,6,3]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[6,7,4,1,2,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,1,2,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,1,2,3,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[6,7,4,1,2,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,4,6,3,5,7,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[8,6,2,5,3,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,5,8,2,3,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,1,8,3,7,5,4,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[4,5,2,8,1,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[6,2,5,8,1,4,7,3]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[1,3,8,2,5,7,4,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[2,8,7,1,6,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,5,6,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,4,8,6,2,7,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,5,1,3,2,6,4,8]=>{{1,3,4,7},{2,5},{6},{8}}=>[3,5,4,7,2,6,1,8]=>[5,2,6,7,1,3,4,8]=>0
[6,7,1,4,2,5,3,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[2,7,1,3,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[8,6,1,2,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,8,1,3,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[1,7,5,3,2,8,4,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[1,3,4,8,2,5,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,5,7,6,2,3,4,8]=>{{1},{2,5},{3,4,6,7},{8}}=>[1,5,4,6,2,7,3,8]=>[1,5,2,7,3,4,6,8]=>0
[1,4,8,3,2,5,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[3,8,2,5,6,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,2,8,6,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,1,6,8,3,4,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,2,6,8,4,1,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,5,6,8,3,4,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,5,7,3,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,1,3,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,6,3,7,8,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,1,8,3,4,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,4,1,8,3,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,4,8,6,1,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,5,7,2,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,8,2,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,4,7,1,8,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,3,7,1,8,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,1,2,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,7,1,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,6,5,3,7,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,5,4,8,3,7,1]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[3,5,2,4,7,1,6,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[4,2,6,7,3,8,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,5,6,8,1,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[6,4,2,5,8,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,5,3,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,8,2,7,4,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,5,8,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,8,7,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,7,2,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,8,2,7,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,8,7,3,6,2,5,1,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,4,8,3,7,2,6,1,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,9,4,8,3,7,1,2,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,8,5,7,1,2,3,4,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,4,6,8,1,2,3,5,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,5,7,9,1,2,4,6,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[10,9,4,8,3,7,2,6,1,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,10,5,9,2,4,8,1,3,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,4,6,8,1,2,3,5,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,10,6,9,1,2,3,4,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,3,5,7,9,1,2,4,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,5,1,8,3,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,7,8,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,6,7,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,4,7,2,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,1,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,7,5,1,8,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,8,2,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,6,4,2,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,7,8,2,1,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,2,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,2,6,8,3,1,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,1,2,5,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,2,5,3,8,1,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[3,4,5,1,8,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,8,2,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,3,2,5,8,1,7,6]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[3,2,4,5,8,7,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,7,5,3,8,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,8,2,6,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,5,8,2,7,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,5,7,2,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,7,6,2,8,4,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[2,5,7,6,3,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,3,1,5,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,3,7,5,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[2,7,4,5,8,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,7,1,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,5,3,8,4,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,2,4,7,8,5,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,8,2,1,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,3,4,5,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,6,8,3,2,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,8,5,1,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,5,8,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,6,3,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,1,3,8,7,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,7,6,8,1,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,8,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,2,7,3,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,1,6,5,2,7,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,7,4,2,1,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,2,4,8,6,7,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,4,6,1,8,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,7,5,1,2,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[4,1,7,3,6,2,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,2,7,3,6,1,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,8,6,5,3,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,1,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,2,7,5,6,3,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,7,5,6,1,8,3]=>{{1,4,5,6},{2},{3,7,8}}=>[4,2,7,5,6,1,8,3]=>[2,6,1,4,5,8,3,7]=>0
[2,8,7,3,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,7,5,3,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,7,5,6,3,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,6,5,2,7,8,1,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[3,2,8,6,7,1,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,8,7,2,3,5,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,7,2,5,3,4,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[4,5,7,6,8,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,6,8,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,8,4,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,7,4,8,1,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,8,2,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,8,5,2,1,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,2,6,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,3,7,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,1,6,3,5,4,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[2,7,1,6,3,5,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,1,5,6,2,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,3,1,6,2,5,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,7,1,2,5,4,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[5,6,2,1,3,7,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,2,6,1,3,7,4,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[5,7,1,6,2,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,6,1,2,7,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,8,6,4,1,2,7,3]=>{{1,5},{2,3,6,8},{4},{7}}=>[5,3,6,4,1,8,7,2]=>[4,5,1,7,8,2,3,6]=>0
[5,8,7,3,2,6,4,1]=>{{1,2,5,8},{3,4,7},{6}}=>[2,5,4,7,8,6,3,1]=>[6,7,3,4,8,1,2,5]=>0
[4,8,1,5,2,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[7,1,3,5,8,6,2,4]=>{{1,2,7},{3},{4,5,8},{6}}=>[2,7,3,5,8,6,1,4]=>[3,6,7,1,2,8,4,5]=>0
[5,1,3,4,6,8,7,2]=>{{1,2,5,6,8},{3},{4},{7}}=>[2,5,3,4,6,8,7,1]=>[3,4,7,8,1,2,5,6]=>0
[5,6,3,4,8,1,7,2]=>{{1,2,5,6,8},{3},{4},{7}}=>[2,5,3,4,6,8,7,1]=>[3,4,7,8,1,2,5,6]=>0
[3,4,8,1,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,6,5,1,4,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,1,7,6,3,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,5,1,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,1,5,2,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,6,7,5,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,5,1,8,3,4,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,6,5,2,8,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,5,1,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,8,6,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,8,6,7,4,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,1,5,3,8,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[2,7,5,8,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,8,1,4,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,4,8,7,5,6,3]=>{{1,2},{3,4,8},{5,6,7}}=>[2,1,4,8,6,7,5,3]=>[2,1,7,5,6,8,3,4]=>1
[3,6,8,2,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,5,8,2,6,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,8,1,6,7,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,1,8,2,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,1,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,8,6,4,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,7,3,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,8,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,8,6,1,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,1,5,2,4,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[1,5,4,8,3,2,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[5,4,7,1,3,2,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,7,4,8,2,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,5,8,1,2,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[8,6,4,2,1,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,1,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,8,7,5,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,8,4,1,2,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,8,1,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,2,1,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,8,7,6,2,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,4,1,8,7,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,5,8,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,6,7,3,4,2,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,2,8,4,7,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,2,8,5,7,3,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,8,4,7,3,5,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,5,6,2,3,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,2,8,4,6,3,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,6,2,8,4,5,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,3,4,6,7,5,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,8,6,2,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,1,6,3,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,8,2,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,1,2,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,2,8,6,3,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,4,1,8,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,1,3,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,8,2,7,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,6,5,2,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[3,4,7,1,6,8,2,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[3,4,7,1,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,1,7,5,3,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[6,4,2,7,5,3,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[4,8,3,2,5,6,1,7]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[3,4,7,1,6,2,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,4,7,1,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,3,6,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,3,6,1,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,4,7,3,6,2,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,5,2,8,4,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,5,3,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,5,6,3,8,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,3,4,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,5,8,3,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,8,3,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,3,7,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,3,7,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,3,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,6,2,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,5,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,3,1,5,7,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,5,7,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[4,2,1,6,8,7,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,1,6,8,5,7,3]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,2,1,6,8,5,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,2,6,1,8,4,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,2,6,1,8,7,4,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,3,1,6,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,1,7,8,6,3,5]=>{{1,3,4,7},{2},{5,8},{6}}=>[3,2,4,7,8,6,1,5]=>[2,6,7,1,3,4,8,5]=>0
[6,7,2,1,8,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,7,1,8,3,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,1,7,8,3,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,3,8,5,2,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,8,4,5,6,2,1]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[6,3,8,2,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,8,2,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,8,2,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[6,3,8,2,4,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,4,2,6,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,2,3,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,2,4,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,3,6,8,2,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,6,4,2,1,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[5,8,6,3,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,1,7,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,1,5,7,8,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,7,8,6,3,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,5,6,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,4,2,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,8,6,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,2,3,8,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,1,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,6,1,8,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,5,8,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,8,3,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,5,8,4,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[7,5,8,9,4,3,2,1,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,7,6,5,10,4,3,2,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,5,4,8,6,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[5,9,8,7,4,3,2,1,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,7,5,9,10,4,3,2,1,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,4,8,9,6,3,2,1,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,3,7,2,5,4,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[7,6,5,3,2,8,4,1,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[8,7,6,5,3,9,10,2,1,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,4,2,6,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,7,6,3,4,2,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,6,3,2,5,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[7,8,5,2,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,8,6,4,1,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[5,1,7,3,4,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,6,3,2,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,8,7,1,5,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,6,8,1,3,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,7,1,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,1,3,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[6,7,1,2,4,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,2,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,1,3,2,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,3,8,2,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,8,7,3,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,7,8,4,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,8,2,6,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,1,5,8,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,8,5,6,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,7,8,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,5,6,3,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[4,8,1,5,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,1,8,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,8,6,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,3,8,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,8,7,4,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,3,7,5,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,3,6,7,8,5,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,1,6,3,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,4,1,6,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,1,8,4,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,8,3,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,6,1,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,1,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,5,7,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[1,3,5,7,4,8,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,5,7,8,4,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,7,2,5,4,8,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,3,7,5,2,4,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,5,2,7,8,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,8,2,4,3,7]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[3,2,4,8,1,5,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,6,7,8,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,4,8,3,1,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,3,8,7,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,8,7,3,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,8,7,2,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,7,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,7,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,4,8,2,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,8,6,2,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,3,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,7,6,4,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,5,3,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,5,3,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,5,1,8,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,1,5,8,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,8,5,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,8,3,1,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,3,6,8,1,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,3,1,6,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,3,6,8,1,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,3,8,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,6,3,8,7,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,6,1,8,3,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,8,5,7,3,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,4,8,7,1,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,4,8,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,5,6,8,9,7,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,4,5,6,7,8,9,3,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,7,8,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,7,1,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,5,6,7,10,1,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,4,7,6,2,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,6,4,8,2,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,3,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,7,2,3,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[4,6,2,3,5,7,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[3,5,2,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,8,2,7,4,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,2,3,4,8,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,1,2,3,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,1,2,3,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,7,1,4,3,5,2,6]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[8,3,2,1,4,5,7,6]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[7,4,1,8,3,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,4,3,1,6,7]=>{{1,6,7,8},{2,3,5},{4}}=>[6,3,5,4,2,7,8,1]=>[4,5,2,3,8,1,6,7]=>0
[8,3,2,5,4,1,6,7]=>{{1,6,7,8},{2,3},{4,5}}=>[6,3,2,5,4,7,8,1]=>[3,2,5,4,8,1,6,7]=>2
[1,8,7,3,5,4,2,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[5,1,8,2,7,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,1,3,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,2,3,4,6,8,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,6,2,3,4,8,7,5]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[7,6,2,3,4,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,2,3,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,7,2,3,4,1,8,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[8,6,2,3,4,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,1,2,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[5,2,8,1,6,3,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[2,8,7,6,3,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,1,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,7,1,6,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,7,2,6,8,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,8,7,6,4,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,6,1,2,5,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[3,8,7,6,2,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,7,6,1,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,6,4,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,6,8,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,1,5,7,2,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[1,3,6,5,7,8,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,8,3,4,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[3,4,8,6,2,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,2,1,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,5,7,2,6,8,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[7,3,5,2,6,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,3,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,5,8,7,3,2,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,2,8,4,7,6,1,5]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[5,6,8,2,3,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,2,8,7,5,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,4,8,7,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,1,4,8,6,5,3]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[7,6,1,2,3,8,5,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[3,4,2,6,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,7,3,5,4,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[4,7,1,2,8,5,3,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[4,8,1,2,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,3,6,8,4,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[7,4,3,1,5,6,8,2]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[4,6,1,2,7,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,6,1,2,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,4,2,7,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,6,4,2,1,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,2,7,5,1,3,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,2,6,1,7,4,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,8,1,6,7,2,3,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[3,5,2,6,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,3,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,4,6,8,1,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,3,5,2,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,7,1,5,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,7,3,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,1,3,5,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,7,3,4,5,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,3,6,1,2,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,6,1,3,7,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,3,7,2,4,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,7,2,8,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,4,5,7,3,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,4,5,1,7,8,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[5,6,4,1,2,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,5,1,2,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,4,2,1,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[5,6,7,2,3,8,1,4]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[3,7,8,5,6,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,8,5,6,3,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,7,8,6,3,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,7,8,3,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[7,1,8,5,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,7,3,8,6,4,2]=>{{1,2,5,8},{3,4,7},{6}}=>[2,5,4,7,8,6,3,1]=>[6,7,3,4,8,1,2,5]=>0
[1,7,5,3,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,7,8,5,3,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[5,7,8,6,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,8,6,1,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,8,1,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,1,8,6,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,3,8,5,6,4,2]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[3,7,5,1,2,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,3,8,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,5,8,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,6,3,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[6,2,7,8,3,4,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,5,3,4,8,1,7,6]=>{{1,2,5,6,8},{3},{4},{7}}=>[2,5,3,4,6,8,7,1]=>[3,4,7,8,1,2,5,6]=>0
[5,1,8,2,3,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,7,6,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,7,6,3,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,4,5,8,1,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[7,4,6,3,2,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,1,7,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,8,1,3,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,1,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,2,1,5,6,8,4,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,7,2,6,4,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,7,3,6,8,5,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[6,4,1,5,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,3,7,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,8,3,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,2,8,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,2,8,7,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,4,2,5,1,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,5,1,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,4,8,7,1,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,2,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,7,2,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,5,6,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,2,6,4,1,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,2,6,3,4,1,5,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[1,6,5,2,8,3,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[6,8,5,3,2,1,4,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[4,1,7,3,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,7,3,6,5,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[8,1,2,7,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,8,7,1,4,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,4,8,3,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,2,7,1,5,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,4,2,5,8,6,7,3]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[7,6,2,1,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,5,8,6,4,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,5,7,1,3,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,7,6,4,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,1,2,3,4,9,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,1,2,9,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[1,8,4,2,3,5,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,4,8,5,1,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,1,4,5,6,3,2]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[8,7,4,5,6,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,5,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,1,2,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,8,5,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,1,2,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,8,7,1,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,8,5,7,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,8,6,7,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,8,6,7,5,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,3,8,6,7,5,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,2,8,4,7,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,8,5,7,2,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,1,8,2,3,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,7,1,6,3,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,8,7,2,3,6,4,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,8,7,2,6,3,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,3,1,6,7,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,1,6,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,2,8,6,7,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,1,3,7,5,6,2,4]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[1,2,8,6,7,3,5,4]=>{{1},{2},{3,4,6,8},{5,7}}=>[1,2,4,6,7,8,5,3]=>[1,2,7,5,8,3,4,6]=>0
[8,1,7,2,6,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,8,2,3,6,5,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[3,1,8,5,7,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,1,7,6,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,7,6,2,3,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,5,8,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,5,2,1,4,3,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[7,5,2,3,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,5,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,6,5,8,1,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,1,4,2,3,6,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[5,8,1,3,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,7,2,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,2,6,1,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,4,2,5,6,1,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,3,8,2,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,8,6,7,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,8,6,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,8,1,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,2,4,3,7,8,1]=>{{1,6,7,8},{2,3,5},{4}}=>[6,3,5,4,2,7,8,1]=>[4,5,2,3,8,1,6,7]=>0
[4,6,8,5,7,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,6,8,2,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,8,6,2,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,6,2,5,7,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,2,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,5,2,8,6,3,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[3,6,4,8,1,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,5,7,1,2,6,4,8]=>{{1,3,4,7},{2,5},{6},{8}}=>[3,5,4,7,2,6,1,8]=>[5,2,6,7,1,3,4,8]=>0
[7,5,1,2,3,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,4,5,1,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,1,3,2,5,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,8,2,3,1,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,1,4,2,7,3,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[6,7,2,4,3,5,1,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[2,4,1,6,5,7,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[2,5,1,6,4,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,6,2,4,3,7,1,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[4,5,2,6,1,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,5,1,6,3,7,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,6,1,3,2,7,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,6,5,7,1,3,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,4,6,1,7,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,2,6,4,7,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,4,2,6,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,6,2,3,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,6,1,7,3,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,2,7,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,7,1,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,5,6,8,7,3,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[3,6,5,2,7,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,7,8,4,2,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,5,6,8,1,7,4,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[4,5,6,3,1,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,3,6,2,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,5,1,7,3,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,1,4,3,8,6]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[4,3,5,7,6,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,4,7,5,3,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[4,6,1,7,5,3,2,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[4,2,6,3,1,7,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,6,1,3,7,5,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,1,6,2,7,4,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,2,1,6,4,3,7,8]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>0
[5,4,2,1,6,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[5,4,2,6,3,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[5,4,1,6,2,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,4,2,1,5,6,3,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[4,3,7,2,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[6,7,1,4,3,2,5,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[1,7,8,2,5,4,3,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[2,5,6,4,7,1,3,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[1,4,5,3,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[5,4,2,1,7,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[4,7,6,2,1,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,6,2,1,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,7,6,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,1,4,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,4,1,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,8,5,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,7,8,4,3,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,3,1,7,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,7,6,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,4,6,2,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,7,4,5,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,6,2,7,1,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,7,1,6,2,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,8,5,6,4,7,2,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,4,2,7,1,8,5,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[4,7,2,3,1,8,5,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[5,2,6,8,3,7,4,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,8,2,5,3,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,8,3,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,8,2,7,3,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,6,4,7,8,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,7,4,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,8,3,4,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,8,4,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,7,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,6,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,5,8,6,2,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,5,8,6,2,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,6,7,2,3,5,8,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,8,1,2,3,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,8,2,3,5,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,4,5,7,6,2,8,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,8,1,2,3,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,1,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,6,5,2,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,4,5,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,8,5,3,1,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,4,8,3,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,5,3,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,7,8,4,3,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,1,8,4,5,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,7,2,8,4,5,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,7,1,2,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,5,8,7,3,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,1,8,7,6,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,1,7,3,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,1,6,3,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,1,6,3,2,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,1,2,3,7,5,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,8,1,5,3,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,2,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,7,3,4,8,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,1,2,3,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[7,6,2,4,3,1,5,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[1,5,7,3,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[6,1,2,3,5,7,4,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[5,1,2,3,7,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[1,5,6,3,4,7,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,6,5,2,4,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,2,5,3,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,7,3,2,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,3,1,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[6,8,1,3,4,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,7,2,3,8,5,1,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[6,8,2,3,1,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,5,2,8,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,6,3,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,2,7,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,4,8,1,3,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,1,8,6,7,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,8,3,4,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,6,3,8,1,4,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,3,8,4,1,2,7,6]=>{{1,5},{2,3,6,8},{4},{7}}=>[5,3,6,4,1,8,7,2]=>[4,5,1,7,8,2,3,6]=>0
[6,1,5,2,4,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,4,1,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,6,7,4,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,6,2,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,5,7,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,8,2,4,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,6,8,2,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,7,5,1,4,8,3]=>{{1,4,5,6},{2},{3,7,8}}=>[4,2,7,5,6,1,8,3]=>[2,6,1,4,5,8,3,7]=>0
[6,3,7,8,4,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,4,8,6,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,8,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,8,7,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,5,6,3,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,2,5,3,6,7,4]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[1,5,2,6,4,7,8,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,2,5,7,1,4,8,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,2,8,3,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,2,7,8,5,6,4]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[6,5,2,1,8,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,5,3,8,4,7,1]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[5,1,6,3,8,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,8,7,6,2,5,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,5,1,9,8,2,3,4,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,6,1,8,2,3,4,5,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,1,7,2,9,3,4,6,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,1,9,2,3,4,5,6,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,5,2,1,10,9,4,3,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,6,5,1,9,8,2,3,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,2,1,4,3,6,5,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,6,1,8,2,3,4,5,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,3,1,7,6,2,10,9,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,4,1,10,6,2,9,3,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,7,1,9,2,3,4,5,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,1,8,2,10,3,4,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,4,8,5,3,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,2,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,6,3,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,2,1,7,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,1,5,6,7,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,1,8,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,6,2,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,7,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,7,8,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,2,1,4,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,1,3,4,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,6,3,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,6,3,4,7,2,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,8,6,3,4,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,6,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,2,7,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,5,2,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,8,6,4,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,2,5,1,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[7,3,6,5,2,1,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,3,6,5,2,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,3,6,5,2,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,5,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,2,1,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,5,8,6,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,6,3,1,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,5,8,7,6,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,5,2,1,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,4,2,5,1,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,6,8,1,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,3,8,5,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,2,1,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,8,1,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,5,7,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,5,8,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,5,8,6,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,5,1,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,8,7,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,7,1,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,8,3,7,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,1,2,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,5,7,4,1,2,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[4,1,7,5,3,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[1,8,4,2,3,6,7,5]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[2,5,8,3,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,6,2,7,5,1,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[3,2,7,6,4,1,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,7,5,2,1,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[6,4,2,1,7,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,3,8,7,2,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,5,8,4,7,3,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[4,3,1,6,2,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,4,1,7,2,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,2,1,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,2,8,3,7,4,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,8,6,5,7,2,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,4,2,7,3,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[6,2,8,3,7,4,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,4,2,7,3,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,8,2,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,1,7,8,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,2,7,1,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,6,1,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,5,6,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,7,5,6,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,5,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,1,7,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,7,1,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,6,1,3,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,2,1,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,5,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,5,2,8,6,7,3]=>{{1},{2,4},{3,5,8},{6},{7}}=>[1,4,5,2,8,6,7,3]=>[1,4,2,6,7,8,3,5]=>0
[2,3,1,7,8,6,4,5]=>{{1,2,3},{4,7},{5,8},{6}}=>[2,3,1,7,8,6,4,5]=>[3,1,2,6,7,4,8,5]=>0
[4,5,6,1,2,8,7,3]=>{{1,4},{2,5},{3,6,8},{7}}=>[4,5,6,1,2,8,7,3]=>[4,1,5,2,7,8,3,6]=>0
[1,5,4,2,7,8,3,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[5,1,8,3,4,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[5,7,4,3,6,1,8,2]=>{{1,5,6},{2,7,8},{3,4}}=>[5,7,4,3,6,1,8,2]=>[4,3,6,1,5,8,2,7]=>1
[7,4,1,8,3,2,5,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[6,2,1,7,8,4,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,4,6,5,1,7,8,3]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[1,4,7,5,6,8,2,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,7,6,5,8,2,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[4,8,1,2,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,6,8,1,2,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,8,5,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,2,3,6,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,5,1,6,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,5,1,3,6,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,6,1,3,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,7,1,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,4,6,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,2,5,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,5,8,2,3,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[2,6,5,1,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,8,4,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,7,5,8,2,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,4,2,6,7,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,2,1,6,3,5,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,6,8,1,2,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,5,8,1,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,8,1,7,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,7,2,8,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,7,8,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,7,4,8,3,6,2]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>[4,7,3,6,8,1,2,5]=>0
[4,7,2,6,3,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,2,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,1,8,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,6,7,5,3,4,1]=>{{1,2,8},{3,6},{4,7},{5}}=>[2,8,6,7,5,3,4,1]=>[5,6,3,7,4,8,1,2]=>0
[3,6,5,8,2,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,2,1,8,7,3,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,5,2,7,4,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,5,2,7,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,7,1,8,3,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,1,6,2,3,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,6,5,3,1,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[2,4,1,7,6,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,5,6,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,4,7,8,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,4,7,8,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,4,7,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,7,1,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,4,7,2,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,4,7,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,8,4,1,3,7,2]=>{{1,5},{2,3,6,8},{4},{7}}=>[5,3,6,4,1,8,7,2]=>[4,5,1,7,8,2,3,6]=>0
[8,5,4,7,1,6,3,2]=>{{1,2,5,8},{3,4,7},{6}}=>[2,5,4,7,8,6,3,1]=>[6,7,3,4,8,1,2,5]=>0
[3,8,5,2,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[2,8,3,4,1,5,7,6]=>{{1,2,5,6,8},{3},{4},{7}}=>[2,5,3,4,6,8,7,1]=>[3,4,7,8,1,2,5,6]=>0
[6,8,3,4,1,2,7,5]=>{{1,2,5,6,8},{3},{4},{7}}=>[2,5,3,4,6,8,7,1]=>[3,4,7,8,1,2,5,6]=>0
[2,5,1,3,8,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,5,1,2,8,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[5,4,8,1,3,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[6,1,5,7,2,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,5,1,2,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,7,6,2,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,6,5,7,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,6,3,5,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,7,6,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,5,2,1,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,2,3,6,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,2,3,7,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,1,5,4,8,3,2]=>{{1,3,7},{2,6,8},{4,5}}=>[3,6,7,5,4,8,1,2]=>[5,4,7,1,3,8,2,6]=>1
[4,8,7,6,1,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,6,1,3,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,6,7,4,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,8,7,3,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,2,6,8,1,7,5]=>{{1,4,6},{2,3},{5,8},{7}}=>[4,3,2,6,8,1,7,5]=>[3,2,6,1,4,7,8,5]=>1
[3,5,4,2,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,8,7,4,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,8,1,7,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,6,8,7,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,6,8,2,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,8,3,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,1,3,7,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,7,1,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,2,3,6,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,3,4,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,1,8,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,4,1,6,3,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,1,3,4,5,8,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,9,8,7,5,4,3,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,6,9,8,1,5,4,3,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,1,10,9,8,7,5,4,3,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,5,8,7,4,1,3,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,1,4,8,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,5,6,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,4,1,2,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,2,5,3,8,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[6,7,4,2,1,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,7,4,5,6,1,2]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[6,8,4,2,3,1,5,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[3,7,5,2,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,2,7,3,1,5,6,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[8,3,7,2,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,5,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,1,3,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,7,4,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,7,2,3,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,7,3,8,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,6,3,8,5,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[6,4,2,5,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,4,5,6,1,8,3,2]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[8,6,5,1,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,4,1,3,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,7,1,8,2,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,6,7,2,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,8,6,4,7,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,8,6,5,3,7,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,2,5,3,6,7,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,4,6,5,7,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,2,6,8,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,4,5,2,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,5,7,8,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,1,8,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,1,4,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[6,4,2,5,1,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[6,8,2,3,7,1,4,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[8,6,2,7,4,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,8,3,7,1,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,1,5,8,4,3,6,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[5,1,8,3,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,1,6,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,4,2,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,2,8,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,5,2,7,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,5,2,6,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,7,5,2,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,4,8,2,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,4,2,1,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[6,7,5,8,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,1,2,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,7,4,8,1,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,7,5,1,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,5,8,4,1,3,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,7,4,8,2,1,3,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[6,7,4,8,1,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,6,3,4,8,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,3,6,5,8,2,7]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[5,1,7,3,4,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[5,8,6,2,3,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,7,4,3,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,3,1,5,7,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,5,1,7,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,8,5,7,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,7,8,6,3,4,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,1,7,8,6,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,2,6,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,5,1,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[3,5,8,1,4,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,2,6,8,1,5,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,4,2,8,1,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,1,8,4,5,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,5,7,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,2,8,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,8,7,5,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,1,6,5,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,6,1,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,1,5,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,6,5,3,2,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,1,6,4,2,5,3,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[5,3,6,4,2,7,1,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[7,4,2,8,6,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,6,1,8,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,5,3,8,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,8,6,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,2,5,8,6,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,8,5,2,7,4,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,5,2,1,7,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,6,3,8,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,1,5,7,8,4,3,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[4,6,2,7,3,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,2,8,7,1,10,9,6,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,5,1,8,4,3,10,9,7,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,5,2,8,4,1,10,9,7,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,7,2,8,6,1,10,9,5,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,3,4,8,1,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,8,1,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,2,8,6,7,1,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,8,5,7,6,2,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,6,7,5,2,3,4]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[5,7,6,4,8,1,2,3]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[5,4,2,7,6,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,1,8,7,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,5,2,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,2,8,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,2,3,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,1,5,6,4,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,6,8,2,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,8,4,6,1,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,6,2,7,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,5,7,6,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,7,6,1,5,8,3]=>{{1,4,5,6},{2},{3,7,8}}=>[4,2,7,5,6,1,8,3]=>[2,6,1,4,5,8,3,7]=>0
[5,8,4,7,3,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,8,3,7,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,8,3,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,5,8,4,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,3,6,1,8,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,6,2,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,7,2,3,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,8,2,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,7,4,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[8,2,4,1,6,3,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[6,1,7,3,2,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,1,5,3,8,4,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,5,3,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,6,3,4,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,5,8,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,7,3,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,8,3,1,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,3,7,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[6,2,7,1,4,8,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,7,4,2,1,8,5,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[7,2,5,3,1,8,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,5,4,1,3,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,5,3,8,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,6,8,4,1,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,4,8,3,2,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,3,7,2,1,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[3,6,8,2,1,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,3,1,8,6,4,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,8,1,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,8,6,2,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,8,4,3,1,2,6]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[5,1,6,3,4,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,6,3,4,7,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[2,3,6,7,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,6,5,3,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,6,5,2,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,6,2,4,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[1,7,4,2,6,3,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,7,4,1,2,3,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,7,6,3,8,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,5,2,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,5,1,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,6,1,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,6,8,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,6,5,8,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,8,7,6,4,3,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,2,7,6,1,5,4,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,5,6,2,3,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,3,8,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,7,2,4,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,1,5,2,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,6,1,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,7,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,6,2,8,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,7,5,8,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,5,1,7,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,7,4,2,3,6,5]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>[4,7,3,6,8,1,2,5]=>0
[1,8,7,2,3,5,6,4]=>{{1},{2,4,8},{3,5,6,7}}=>[1,4,5,8,6,7,3,2]=>[1,7,3,5,6,8,2,4]=>0
[6,3,2,1,8,4,7,5]=>{{1,4,6},{2,3},{5,8},{7}}=>[4,3,2,6,8,1,7,5]=>[3,2,6,1,4,7,8,5]=>1
[6,4,1,3,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,8,5,1,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,1,5,8,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,7,6,2,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,5,3,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,3,8,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,7,2,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,4,6,1,5,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,5,7,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,6,8,3,1,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,7,6,2,4,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,2,7,1,4,5,8,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,1,5,3,8,7,4,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[1,2,7,5,3,8,4,6]=>{{1},{2},{3,4,5,7},{6,8}}=>[1,2,4,5,7,8,3,6]=>[1,2,7,3,4,5,8,6]=>0
[5,3,4,8,7,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,8,3,7,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,7,8,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,8,6,4,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,8,6,4,7,3,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,8,5,6,7,3,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,7,8,4,5,6,3,1]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[7,5,1,3,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,5,2,8,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,6,3,7,1,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,5,7,1,3,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,8,1,6,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,8,5,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,7,5,2,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,8,7,1,2,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,8,2,7,5,3,6]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[7,8,2,1,6,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,7,5,4,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[5,1,7,3,6,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,1,5,7,4,3,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[5,7,4,1,2,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[4,8,1,2,6,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,8,5,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,7,4,6,5,3]=>{{1,2,3,8},{4,5,7},{6}}=>[2,3,8,5,7,6,4,1]=>[6,7,4,5,8,1,2,3]=>0
[1,3,4,8,7,5,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,4,7,8,5,2,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[4,8,2,3,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,7,4,1,8,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,7,3,6,2,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,8,2,6,4,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,4,5,6,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,8,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,8,4,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,2,5,7,4,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[2,5,8,1,7,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,7,4,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,4,8,1,5,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[2,4,8,3,1,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,8,1,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,6,5,2,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,2,6,3,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[7,3,6,5,2,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,2,3,4,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,5,3,8,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,6,1,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,2,8,1,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,5,6,4,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,8,7,6,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,7,6,3,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,9,8,5,7,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,8,7,6,2,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,9,8,7,6,3,5,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,7,10,5,8,3,6,2,4,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,5,4,7,2,6,1,8]=>{{1,3,4,7},{2,5},{6},{8}}=>[3,5,4,7,2,6,1,8]=>[5,2,6,7,1,3,4,8]=>0
[3,5,4,7,6,1,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,4,7,6,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,7,4,6,1,2,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[3,5,2,7,6,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,7,2,6,1,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,7,2,1,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[5,3,7,1,6,2,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,7,1,4,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[3,5,7,1,4,2,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,7,2,1,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,2,5,7,4,1,6,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[3,5,2,7,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,7,4,1,2,6,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[3,5,4,7,1,2,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,4,2,7,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,4,7,1,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,7,4,1,8,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,5,7,2,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,7,1,4,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,2,5,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,7,5,1,8,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,7,2,5,1,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,1,7,5,8,4,6,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[1,3,4,5,6,7,9,2,8]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[2,3,4,5,6,7,1,9,8]=>{{1,2,3,4,5,6,7},{8,9}}=>[2,3,4,5,6,7,1,9,8]=>[7,1,2,3,4,5,6,9,8]=>1
[3,1,4,5,6,7,8,2,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[5,8,7,2,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,7,6,1,5,4,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[3,2,8,7,6,1,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,5,8,1,7,3,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,7,3,2,5,6,1,4]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[2,6,5,7,1,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,8,3,4,5,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[6,4,2,7,3,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,8,7,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,7,2,1,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,5,6,7,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,5,2,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,2,1,5,6,7,8,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,4,6,5,1,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,2,4,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[3,7,5,2,4,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[3,2,7,5,1,4,6,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[3,7,5,1,2,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,1,2,5,4,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[5,3,1,2,7,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,1,5,2,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,7,1,3,2,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,7,2,1,5,4,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[3,1,7,2,5,4,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[3,1,7,5,2,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,1,5,3,2,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,3,9,2,4,5,6,7,8]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,9,8,7,6,2,5,4,3]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[4,9,8,7,6,1,2,5,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,10,9,8,7,1,6,5,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,9,8,7,4,2,6,5,3]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[4,9,8,7,6,3,2,1,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,10,9,8,7,1,2,6,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,9,8,7,4,1,2,6,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[1,9,6,2,8,7,5,4,3]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[7,10,9,1,2,8,6,5,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,7,6,3,4,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,2,3,6,8,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,4,2,8,5,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,6,5,8,2,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,6,5,1,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,1,4,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,1,3,4,5,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,1,5,3,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,5,8,3,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,4,6,8,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,7,3,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,7,1,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,2,3,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,7,1,8,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,2,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[5,4,1,3,2,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[6,2,4,5,1,8,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,6,8,2,3,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,6,4,5,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,7,5,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}=>[1,6,7,5,8,2,3,4]=>[1,6,2,7,3,8,4,5]=>0
[4,6,5,3,7,1,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,5,4,7,3,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[7,2,8,3,4,1,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,6,2,7,3,1,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,2,6,5,7,8,3,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,1,8,3,6,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,6,5,8,7,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,8,2,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,8,1,7,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,1,3,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,2,1,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,7,6,4,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,2,7,5,3,6,4]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[7,5,2,1,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,2,1,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,4,7,5,2,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[8,5,7,6,3,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,2,1,6,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,6,3,5,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,4,6,3,1,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,7,5,3,8,2]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[6,3,5,2,8,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,2,7,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,7,4,2,6,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,4,5,8,1,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[7,6,8,3,1,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,2,8,1,5,4]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,5,2,8,6,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,7,2,8,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,6,5,3,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,4,1,6,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,8,5,7,4,2,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,7,5,3,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,8,7,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,8,7,3,5,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,6,8,5,7,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,7,2,5,3,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[5,7,4,1,2,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,1,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,1,2,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,2,7,8,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,6,4,1,7,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,3,2,5,6,8,4]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[3,2,6,5,8,4,7,1]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[5,2,6,4,8,1,7,3]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[5,4,8,1,6,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,1,7,8,6,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,7,3,8,5,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,5,2,6,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,1,3,2,5,6,4,7]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[8,1,2,4,5,3,7,6]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[10,1,3,2,5,4,7,6,9,8]=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>[2,4,3,6,5,8,7,10,9,1]=>[3,5,7,9,10,1,2,4,6,8]=>0
[12,1,3,2,5,4,7,6,9,8,11,10]=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>[2,4,3,6,5,8,7,10,9,12,11,1]=>[3,5,7,9,11,12,1,2,4,6,8,10]=>0
[7,4,5,1,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,6,8,4,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,7,8,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,7,8,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,8,1,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,7,6,1,8,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,6,8,1,7,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,3,6,2,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,3,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,2,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[5,8,3,4,2,1,7,6]=>{{1,2,5,6,8},{3},{4},{7}}=>[2,5,3,4,6,8,7,1]=>[3,4,7,8,1,2,5,6]=>0
[6,8,4,2,3,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,2,8,4,6,7,3]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[1,5,2,7,4,6,8,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[4,1,2,8,3,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[6,1,8,2,3,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,1,7,2,3,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,7,3,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,6,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,5,7,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,4,5,1,3,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[3,8,4,2,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,2,7,8,5,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,5,2,6,7,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,1,7,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,7,1,5,3,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,7,8,9,1,2,3,4,5,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[6,7,8,1,2,3,4,5,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[1,7,8,9,2,3,4,5,6]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,7,8,9,10,2,3,4,5,6]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[5,6,7,8,9,1,2,3,4,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[1,6,7,8,9,10,2,3,4,5]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[8,2,4,5,7,3,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,1,3,5,7,6,4,2]=>{{1,2,8},{3},{4,5,7},{6}}=>[2,8,3,5,7,6,4,1]=>[3,6,7,4,5,8,1,2]=>0
[8,2,7,1,4,5,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,8,3,7,4,6,5,1]=>{{1,2,8},{3},{4,5,7},{6}}=>[2,8,3,5,7,6,4,1]=>[3,6,7,4,5,8,1,2]=>0
[8,2,7,3,1,5,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,1,8,7,5,4,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,8,6,3,2,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,7,1,3,2,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,1,3,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,8,2,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,8,2,3,5,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,5,8,2,3,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,5,4,2,1,8,6]=>{{1,6,7,8},{2,3,5},{4}}=>[6,3,5,4,2,7,8,1]=>[4,5,2,3,8,1,6,7]=>0
[6,7,4,2,1,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,6,3,2,8,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,4,2,1,7,3,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,5,8,1,7,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,2,3,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,8,2,6,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,7,6,2,8,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,2,6,3,5,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,1,2,7,8,5,3,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[3,8,5,6,4,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,2,7,5,8,3,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,6,2,7,3,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,3,8,5,4,7,2]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[7,3,5,1,4,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[3,4,6,5,1,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[4,5,1,7,6,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,7,5,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,2,3,4,5,6,7,8,1]=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}=>[9,2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,9,1]=>0
[8,2,3,4,5,6,7,1,9]=>{{1,8},{2},{3},{4},{5},{6},{7},{9}}=>[8,2,3,4,5,6,7,1,9]=>[2,3,4,5,6,7,8,1,9]=>0
[7,2,3,4,5,6,1,8,9]=>{{1,7},{2},{3},{4},{5},{6},{8},{9}}=>[7,2,3,4,5,6,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>0
[1,4,5,3,8,2,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,8,2,4,3,6,7]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[1,5,4,8,2,3,6,7]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[5,6,8,1,3,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,1,2,5,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,4,8,1,7,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,7,1,8,4,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,1,8,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,5,6,8,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,2,8,1,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,2,5,3,8,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,6,5,2,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,5,1,8,3,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,8,7,4,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,1,3,2,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,7,6,3,5,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,4,7,6,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,8,3,2,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,8,3,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,1,3,5,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,2,7,4,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,6,7,1,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,7,2,1,5,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[2,6,7,3,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,5,7,4,3,8,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[1,5,8,7,4,3,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,4,1,3,8,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,1,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,1,2,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,3,1,5,6,7,8,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,6,1,5,3,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,3,4,1,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,8,1,6,7,4,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,3,4,5,1,8,2,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,10,1,7,8,9,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,2,1,3,4,5,6,7,9]=>{{1,3,4,5,6,7,8},{2},{9}}=>[3,2,4,5,6,7,8,1,9]=>[2,8,1,3,4,5,6,7,9]=>0
[3,2,4,5,6,7,8,1,9]=>{{1,3,4,5,6,7,8},{2},{9}}=>[3,2,4,5,6,7,8,1,9]=>[2,8,1,3,4,5,6,7,9]=>0
[8,3,1,2,4,5,6,7,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[6,10,5,9,8,7,2,4,1,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,10,4,9,3,8,2,7,6,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,2,8,1,6,4,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,4,2,8,6,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,5,1,6,4,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,8,5,6,7,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,1,2,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,7,2,8,6,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,1,3,6,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,6,3,1,5,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,4,6,2,8,7,5,3]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[8,1,4,7,6,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,6,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,8,6,2,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,5,3,8,4,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[8,2,1,5,3,7,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,7,1,5,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,2,7,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,2,6,8,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,5,7,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,2,3,4,5,6,7,8,1,10]=>{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}=>[9,2,3,4,5,6,7,8,1,10]=>[2,3,4,5,6,7,8,9,1,10]=>0
[7,8,6,3,1,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,3,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,8,2,5,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,8,6,1,4,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,7,3,2,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,4,5,7,8,1,3,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[1,6,4,8,3,5,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,4,8,6,3,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[4,8,2,5,3,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,4,5,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[5,7,8,4,6,3,2,1]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[5,3,2,8,6,4,7,1]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[6,8,1,2,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,5,4,2,8,6,1]=>{{1,6,7,8},{2,3,5},{4}}=>[6,3,5,4,2,7,8,1]=>[4,5,2,3,8,1,6,7]=>0
[5,6,1,3,2,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,5,1,3,7,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,2,1,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,7,2,1,3,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,6,2,3,1,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[3,1,6,4,7,5,2,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[3,6,2,7,5,4,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[2,4,7,5,3,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[2,5,7,3,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,3,5,8,6,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,5,7,2,3,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,8,7,4,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,4,7,1,3,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,3,5,1,4,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,1,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,1,7,4,3,8,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,7,6,2,3,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,1,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,7,5,3,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,5,7,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,4,5,8,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,1,8,5,3,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,1,5,6,8,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,9,1,2,3,4,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[1,3,8,5,2,7,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,8,6,7,2,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,2,6,7,8,1,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,5,6,8,1,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,5,8,6,1,2,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,2,6,8,7,1,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,4,6,8,7,2,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,5,4,8,1,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,7,5,2,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,7,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,6,5,2,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,7,5,2,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,6,7,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,6,3,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,3,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,8,7,2,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,4,1,3,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,4,3,1,6,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[4,2,1,8,6,3,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[3,1,7,2,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[3,7,5,4,2,1,6,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[2,8,6,1,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,6,1,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,1,2,7,5,6,3,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[8,2,1,5,6,3,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[2,8,5,1,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,1,8,6,3,7,5,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[4,3,8,5,7,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,2,8,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,7,8,2,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,4,1,2,5,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[7,4,5,1,8,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,4,8,3,7,5,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[1,5,2,6,4,8,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,6,2,5,3,8,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,8,2,6,3,7,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,2,6,4,8,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,2,7,4,8,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,8,2,1,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,8,3,1,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[2,7,8,6,4,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,5,1,7,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,8,3,7,4,2,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,6,3,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,2,6,4,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,7,6,4,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,6,3,8,5,4,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,5,2,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,6,3,8,2,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,2,4,7,3,8,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,4,8,7,3,6,5,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[3,7,2,8,1,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,8,1,4,3,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,3,4,5,6,7,9,8,2]=>{{1},{2,3,4,5,6,7,9},{8}}=>[1,3,4,5,6,7,9,8,2]=>[1,8,9,2,3,4,5,6,7]=>0
[2,3,4,5,6,7,9,8,1,10]=>{{1,2,3,4,5,6,7,9},{8},{10}}=>[2,3,4,5,6,7,9,8,1,10]=>[8,9,1,2,3,4,5,6,7,10]=>0
[2,3,4,5,7,6,8,1,9]=>{{1,2,3,4,5,7,8},{6},{9}}=>[2,3,4,5,7,6,8,1,9]=>[6,8,1,2,3,4,5,7,9]=>0
[1,3,4,5,6,8,7,9,2]=>{{1},{2,3,4,5,6,8,9},{7}}=>[1,3,4,5,6,8,7,9,2]=>[1,7,9,2,3,4,5,6,8]=>0
[1,3,4,5,6,7,8,10,9,2]=>{{1},{2,3,4,5,6,7,8,10},{9}}=>[1,3,4,5,6,7,8,10,9,2]=>[1,9,10,2,3,4,5,6,7,8]=>0
[1,5,8,6,2,3,4,7]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[1,3,2,8,6,4,5,7]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[1,7,5,8,2,3,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,7,5,2,3,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,5,4,2,6,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,2,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,7,5,3,1,8,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,3,2,5,4,1,8,6]=>{{1,6,7,8},{2,3},{4,5}}=>[6,3,2,5,4,7,8,1]=>[3,2,5,4,8,1,6,7]=>2
[2,7,5,3,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,5,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,5,2,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[8,4,5,3,7,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,3,2,4,5,6,7,8,1]=>{{1,9},{2,3},{4},{5},{6},{7},{8}}=>[9,3,2,4,5,6,7,8,1]=>[3,2,4,5,6,7,8,9,1]=>1
[10,2,3,4,5,6,7,8,9,1]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}=>[10,2,3,4,5,6,7,8,9,1]=>[2,3,4,5,6,7,8,9,10,1]=>0
[8,7,5,6,1,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,6,5,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,6,2,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,7,5,2,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,2,8,7,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,5,8,2,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,1,6,2,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,5,2,4,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[7,5,8,1,6,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,9,1,2,3,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,10,1,2,3,4,5,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,8,1,2,3,9,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,10,1,2,3,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,4,6,1,3,2,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,5,2,6,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,7,6,8,5,2,4,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[7,8,6,1,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,5,3,6,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,7,8,1,2,9,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,5,6,7,1,2,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,5,1,2,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,8,2,3,4,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,8,5,2,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,6,2,8,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,8,3,7,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,1,5,6,8,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,1,8,3,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,3,6,2,1,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,1,4,5,2,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,5,4,1,6,3,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,5,4,8,6,3,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,5,4,1,6,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,5,6,7,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,3,6,8,2,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,8,3,6,7,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,2,5,6,7,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,1,7,2,8,3,9,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,5,8,7,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,2,1,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,5,3,7,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,8,4,1,5,2,6]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[1,8,5,7,2,4,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,6,8,5,4,2,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[7,2,8,5,6,3,4,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,2,8,4,3,1,7,6]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[3,2,5,7,6,8,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,1,8,6,4,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,8,3,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,4,8,3,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,5,6,2,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,8,7,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,8,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,5,6,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,1,5,8,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,6,1,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,5,6,1,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,5,6,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,8,6,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,8,6,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,5,8,6,7,4,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[3,4,5,8,7,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,1,5,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,7,1,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,8,6,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,1,5,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,4,7,2,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,4,6,1,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,5,6,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,4,5,6,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,6,5,2,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,5,2,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,6,5,1,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,1,7,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,6,7,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,7,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,5,3,7,8,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[6,1,4,7,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,2,3,8,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,2,1,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,3,1,4,8,6]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[6,7,1,8,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,7,6,1,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,4,7,1,5,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,5,6,7,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,7,6,4,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,3,7,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,4,6,1,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,6,7,3,8,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,2,1,6,4,8,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,3,7,6,4,8,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,8,7,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,1,6,5,3,2,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[8,5,7,1,4,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,1,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,6,3,4,2,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,6,4,5,8,7,2]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[1,8,7,5,3,2,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,8,1,5,4,2,3,6]=>{{1,3,7},{2,6,8},{4,5}}=>[3,6,7,5,4,8,1,2]=>[5,4,7,1,3,8,2,6]=>1
[6,3,5,7,1,4,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,7,5,2,6,4,8,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,7,4,1,3,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,2,8,4,3,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,4,1,6,7,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,5,3,7,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[8,4,6,5,1,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,1,2,3,4,5,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,7,1,2,3,4,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,1,2,3,4,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,1,2,3,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,7,2,8,6,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,5,8,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,8,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,8,5,1,7,3,6]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[7,3,1,2,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[1,8,4,2,7,6,3,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[2,4,1,8,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,8,2,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,1,5,3,2,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[4,7,5,8,2,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,4,2,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,4,1,6,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,6,7,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,2,6,1,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[8,4,6,7,2,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,6,7,3,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,1,2,6,3,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,7,6,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,2,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,1,7,5,3,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>0
[6,2,5,4,1,8,7,3]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[8,2,5,4,7,6,1,3]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[3,2,5,4,8,6,1,7]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[5,8,1,3,7,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,5,1,8,3,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,1,5,8,4,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,3,1,5,2,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,6,1,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,1,2,4,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,1,3,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,1,4,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,1,3,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,5,8,6,1,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,6,7,2,1,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,8,3,2,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,8,5,3,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,6,5,2,7,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,2,3,4,5,6,7,1,8]=>{{1,8,9},{2},{3},{4},{5},{6},{7}}=>[8,2,3,4,5,6,7,9,1]=>[2,3,4,5,6,7,9,1,8]=>0
[1,3,5,8,6,4,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[7,2,8,3,6,4,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,7,5,1,4,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,8,7,3,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,2,6,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,8,6,3,7,1,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,7,5,3,1,2,4]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,3,6,1,4,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,8,4,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,8,2,6,4,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,8,6,3,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,7,2,3,5,8,6,4]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[6,5,8,7,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,6,8,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,8,2,4,3,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,2,5,3,4,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[10,3,4,5,6,7,8,9,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,3,4,5,6,7,8,1,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,3,4,5,6,7,1,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,3,4,5,6,1,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,3,4,5,1,7,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,3,4,1,6,7,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,3,1,5,6,7,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,3,4,5,1,7,8,9,2,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,3,4,1,6,10,8,9,2,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,3,1,5,6,7,10,9,2,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,1,4,5,6,7,8,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,1,5,6,2,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,6,1,3,4,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,7,5,1,3,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,7,5,6,2,3,8,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,8,1,3,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,7,8,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,7,3,8,5,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,5,8,7,1,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,8,5,7,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,5,1,4,8,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,5,4,1,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,4,2,8,1,7]=>{{1,6,7,8},{2,3,5},{4}}=>[6,3,5,4,2,7,8,1]=>[4,5,2,3,8,1,6,7]=>0
[1,3,8,7,4,2,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,5,4,1,3,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,2,1,4,7,6,3,5]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[8,3,1,7,4,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,7,3,1,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,5,7,1,6,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,8,1,7,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,7,6,8,1,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[8,5,2,1,4,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,2,6,3,8,5,7,1]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[8,3,5,4,2,7,1,6]=>{{1,6,7,8},{2,3,5},{4}}=>[6,3,5,4,2,7,8,1]=>[4,5,2,3,8,1,6,7]=>0
[8,3,1,5,2,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,3,4,6,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,4,6,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,2,8,1,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,5,2,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,7,6,4,8,1,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,1,6,3,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,8,1,4,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,6,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,7,8,2,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,8,2,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,5,2,4,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[6,4,7,3,2,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,6,2,3,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,10,4,5,6,7,8,9,1,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,4,6,3,8,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,5,8,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,8,3,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,5,8,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,4,6,8,7,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,5,1,8,3,7]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[2,4,6,5,3,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,6,8,7,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,6,5,3,2,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[6,1,2,7,8,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,6,2,3,7,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,6,8,2,7,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,2,8,5,4,3,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,4,8,3,2,5,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,2,5,8,3,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,2,3,4,5,6,7,9,1]=>{{1,8,9},{2},{3},{4},{5},{6},{7}}=>[8,2,3,4,5,6,7,9,1]=>[2,3,4,5,6,7,9,1,8]=>0
[2,6,4,5,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,6,7,4,5,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,7,3,6,4,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,7,5,2,1,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,7,3,1,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,8,3,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,7,4,6,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,5,2,3,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,2,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,2,8,5,1,4,3,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,8,7,1,4,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,5,3,1,4,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[4,8,6,2,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,4,7,3,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>0
[3,7,5,6,2,1,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,2,1,7,4,5,3,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[8,5,4,2,1,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[6,7,5,1,4,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,6,8,4,2,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[7,5,4,1,8,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,1,8,2,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,5,3,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[6,8,5,3,7,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,5,7,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,1,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[7,3,1,2,8,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,2,3,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,3,5,6,1,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,2,6,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,6,4,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,6,7,5,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,6,7,1,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,6,1,2,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,6,7,2,8,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,7,1,3,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,4,2,7,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,4,8,7,1,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,5,1,7,6,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,2,8,3,1,4,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,8,5,2,4,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,2,3,1,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,6,1,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,4,8,6,2,7,5]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[4,6,8,2,3,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,7,2,3,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[6,7,2,3,4,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,8,5,2,6,7,4]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[8,1,2,5,3,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,2,5,8,6,7,1,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,1,7,2,4,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,8,2,4,7,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,7,2,4,6,5,8]=>{{1},{2,3,4,5,7},{6},{8}}=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>0
[3,2,6,5,1,7,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,3,8,6,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,4,2,6,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,7,8,6,4,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,7,5,6,8,4,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,5,4,2,1,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,2,1,7,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[4,1,6,5,2,7,8,3]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[6,8,5,3,1,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,6,3,8,7,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,4,8,2,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,6,3,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,1,5,2,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,7,3,5,4,8,2]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,7,8,3,6,4,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,8,5,7,6,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,5,1,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,5,3,1,4,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[1,5,2,8,4,3,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,6,7,2,5,8,4,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,5,8,3,2,7,4,6]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[1,4,5,8,2,6,3,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,5,2,7,6,4,8,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,5,3,2,8,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,3,2,8,7,5,4,6]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[7,1,4,8,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,5,2,4,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,1,7,8,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,7,6,4,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[9,7,5,3,1,8,6,4,2,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[8,6,4,2,1,7,5,3,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[8,7,5,3,1,6,4,2,9]=>{{1,2,3,4,5,7,8},{6},{9}}=>[2,3,4,5,7,6,8,1,9]=>[6,8,1,2,3,4,5,7,9]=>0
[7,6,5,3,1,4,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,9,7,5,3,2,8,6,4]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,8,7,6,4,2,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,9,8,6,4,2,7,5,3]=>{{1},{2,3,4,5,6,8,9},{7}}=>[1,3,4,5,6,8,7,9,2]=>[1,7,9,2,3,4,5,6,8]=>0
[1,10,8,6,4,2,9,7,5,3]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[1,4,8,6,7,5,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,6,2,5,8,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,6,4,3,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,5,7,2,8,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,2,5,8,1,4,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,2,1,5,3,8,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,1,8,7,3,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,5,1,4,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,8,7,5,3,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,4,8,7,3,6,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[4,8,7,3,1,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,1,2,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,7,3,4,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,7,5,6,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,7,5,3,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,7,5,6,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,7,5,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[11,2,3,4,5,6,7,8,9,10,1]=>{{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}}=>[11,2,3,4,5,6,7,8,9,10,1]=>[2,3,4,5,6,7,8,9,10,11,1]=>0
[10,3,2,4,5,6,7,8,9,1]=>{{1,10},{2,3},{4},{5},{6},{7},{8},{9}}=>[10,3,2,4,5,6,7,8,9,1]=>[3,2,4,5,6,7,8,9,10,1]=>1
[9,4,3,2,5,6,7,8,1]=>{{1,9},{2,4},{3},{5},{6},{7},{8}}=>[9,4,3,2,5,6,7,8,1]=>[3,4,2,5,6,7,8,9,1]=>0
[1,9,2,3,4,5,6,8,7]=>{{1},{2,3,4,5,6,7,9},{8}}=>[1,3,4,5,6,7,9,8,2]=>[1,8,9,2,3,4,5,6,7]=>0
[1,10,2,3,4,5,6,7,9,8]=>{{1},{2,3,4,5,6,7,8,10},{9}}=>[1,3,4,5,6,7,8,10,9,2]=>[1,9,10,2,3,4,5,6,7,8]=>0
[5,7,2,1,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,8,7,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,1,3,2,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,1,3,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,8,2,1,3,6,7]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[1,3,4,5,6,7,8,10,2,9]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[1,5,7,3,6,8,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,4,7,6,8,2,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[5,1,7,3,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,6,2,4,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,5,6,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,7,5,4,3,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[3,5,7,1,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,7,6,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,6,8,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,7,5,6,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,8,6,7,3,2,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,4,8,6,7,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,8,7,5,4,2,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[8,2,7,6,4,3,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,1,7,6,4,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,8,6,7,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,7,5,6,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,1,6,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,5,6,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,1,4,7,6,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,2,8,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,6,2,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,4,2,8,5,1,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[7,3,4,1,6,8,2,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[2,7,1,3,6,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,1,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,1,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,4,2,1,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,4,6,2,1,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,5,8,7,6,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,7,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,5,1,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,7,4,1,2,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,5,3,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[8,2,6,4,1,5,7,3]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[4,1,8,5,3,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,6,4,2,7,3,5]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>[4,7,3,6,8,1,2,5]=>0
[7,4,8,6,1,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,8,1,6,4,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,8,4,1,2,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,1,2,5,3,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,4,6,2,8,5,3,7]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[1,5,6,2,8,4,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,5,8,6,1,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,7,8,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,5,6,3,7,1]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[1,8,7,3,2,5,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,8,6,2,4,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,1,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,5,2,1,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[1,3,5,7,9,10,8,6,4,2]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[7,4,1,8,2,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,2,5,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,4,5,7,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,7,1,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,2,5,6,1,7,4]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[6,8,7,2,1,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,8,5,2,6,3,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,5,7,3,8,6,2,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[6,7,5,1,8,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,1,2,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,6,1,4,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,4,1,2,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,7,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,5,7,4,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,5,3,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,5,6,8,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,5,3,6,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,3,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,5,3,1,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,2,1,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,2,8,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,7,3,8,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,8,3,2,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,8,3,1,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,7,3,2,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,5,8,7,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,2,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,1,2,8,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,8,7,1,6,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,6,1,7,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,6,1,3,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,5,7,8,3,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,7,8,2,4,3,6]=>{{1},{2,5},{3,7},{4,6,8}}=>[1,5,7,6,2,8,3,4]=>[1,5,2,7,3,8,4,6]=>0
[6,8,4,7,3,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,4,6,3,2,7,5]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[6,4,8,5,3,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,1,4,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,6,5,7,8,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,7,8,2,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,1,6,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,3,8,7,2,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,1,8,2,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,6,3,4,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,7,1,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,6,2,3,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,5,1,2,3,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,1,5,3,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,2,1,8,6,4,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,3,8,6,4,7,2,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,5,1,8,7,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,1,8,7,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,1,7,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,1,8,2,3,4,5,6,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,7,1,2,3,4,5,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,10,1,9,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,10,8,1,3,4,5,6,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,6,5,7,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,8,5,7,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,5,8,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,6,7,1,8,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,7,1,3,8,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,5,2,4,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,8,7,2,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,1,2,7,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,6,1,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,5,7,9,1,2,4,6,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[4,1,2,6,8,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,8,7,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,5,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,2,8,5,7,1,3,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,1,4,2,5,6,3,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[7,4,1,3,5,6,2,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[4,8,2,5,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,5,8,2,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[2,4,8,5,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[5,3,2,6,4,8,7,1]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[2,4,5,3,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,3,5,2,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,8,5,3,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[3,5,4,2,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[7,5,2,4,3,8,6,1]=>{{1,6,7,8},{2,3,5},{4}}=>[6,3,5,4,2,7,8,1]=>[4,5,2,3,8,1,6,7]=>0
[4,3,2,6,8,5,7,1]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[3,7,6,4,8,5,2,1]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[2,3,5,8,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[3,5,2,8,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[3,4,5,8,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[5,4,2,8,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[5,3,4,8,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[2,5,4,8,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[6,3,2,5,8,4,7,1]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[5,4,8,3,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[5,8,2,3,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[7,4,6,8,3,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,7,6,3,2,8,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,5,2,1,4,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,8,5,1,3,4,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,7,8,6,1,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,8,2,5,1,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,1,6,5,3,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,4,6,3,8,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,7,1,8,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,1,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,6,2,4,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,5,4,8,7,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,8,7,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,8,1,7,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,6,1,7,5,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[1,6,5,2,7,8,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,7,8,5,6,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,7,8,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,1,4,6,3,2,5]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[1,6,3,2,5,7,8,4]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[1,5,6,3,2,8,4,7]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[4,1,8,6,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,6,3,2,7,8,4]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[1,8,4,7,5,3,2,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[6,8,5,2,1,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,2,6,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,6,2,7,1,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,2,8,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,4,2,1,6,7]=>{{1,6,7,8},{2,3,5},{4}}=>[6,3,5,4,2,7,8,1]=>[4,5,2,3,8,1,6,7]=>0
[8,7,6,1,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,1,4,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,5,8,6,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,3,7,8,4,6,2]=>{{1},{2,5,8},{3},{4,6,7}}=>[1,5,3,6,8,7,4,2]=>[1,3,7,4,6,8,2,5]=>0
[1,5,7,3,8,2,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,4,7,3,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[5,7,6,1,3,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,6,1,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,4,1,7,2,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[2,5,6,1,7,4,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,7,6,1,8,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,1,6,3,5,7,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[8,6,4,2,9,1,3,5,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,6,4,2,7,1,3,5,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,7,5,3,1,2,4,6,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[10,8,6,2,1,4,3,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,6,4,2,1,8,3,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,4,2,7,1,3,5,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>0
[8,6,4,2,9,1,3,5,7,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[6,2,8,3,1,4,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[9,6,4,2,7,1,3,5,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[9,6,7,2,3,1,4,5,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,7,4,5,1,2,3,6,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,7,5,3,1,2,4,6,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[1,8,5,3,2,6,7,4]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[1,7,5,2,4,8,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,8,6,2,3,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,4,5,6,7,2,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,6,7,4,2,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,7,8,4,2,3,5]=>{{1},{2,6},{3,7},{4,5,8}}=>[1,6,7,5,8,2,3,4]=>[1,6,2,7,3,8,4,5]=>0
[1,6,7,8,3,4,2,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,4,2,3,8,5,6]=>{{1},{2,3,4,5,7},{6,8}}=>[1,3,4,5,7,8,2,6]=>[1,7,2,3,4,5,8,6]=>0
[1,7,8,3,4,2,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,4,5,6,2,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,8,2,7,3,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,7,2,3,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,8,3,6,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,7,5,6,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,5,2,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,5,2,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,4,2,1,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[8,1,6,7,3,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,8,6,3,7,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,9,1,2,3,4,8,5,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,1,9,2,3,4,8,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[1,7,2,3,4,5,9,8,6]=>{{1},{2,3,4,5,6,7,9},{8}}=>[1,3,4,5,6,7,9,8,2]=>[1,8,9,2,3,4,5,6,7]=>0
[5,7,1,2,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,2,3,6,8,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[7,3,1,2,8,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,4,5,3,8,1,6]=>{{1,7},{2},{3,4,5},{6,8}}=>[7,2,4,5,3,8,1,6]=>[2,5,3,4,7,1,8,6]=>0
[3,7,2,1,6,8,4,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[8,2,5,6,7,1,4,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0
[4,5,7,3,1,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[3,5,7,6,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,8,7,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,2,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,4,7,5,8,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,8,3,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,6,8,1,4,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,7,1,8,3,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,5,2,7,1,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,3,5,2,7,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,8,4,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[6,5,4,7,8,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[6,5,7,8,9,3,2,1,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,5,4,7,8,9,2,1,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,2,5,3,7,4,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[4,2,6,3,7,5,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[5,2,7,3,6,4,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[5,2,8,3,6,4,1,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,2,5,4,1,6,3,7]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[1,4,8,3,7,5,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,2,1,4,8,6,3,7]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[4,2,8,3,7,5,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,3,7,2,6,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,7,3,8,4,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,5,3,8,4,1,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,2,5,3,7,4,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,5,1,3,6,4,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,5,3,1,7,4,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[4,2,6,3,1,7,5,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[7,2,6,3,1,5,4,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[8,4,1,3,7,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,1,5,3,7,4,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[8,7,6,5,3,2,1,4,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[8,7,6,3,4,2,1,5,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[9,8,7,6,4,3,2,1,5,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[8,6,2,3,1,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,4,2,7,3,6,8,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,8,5,3,2,4,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[3,2,4,6,7,8,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,1,5,2,6,4,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,3,5,2,6,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,7,6,1,8,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,4,8,6,3,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,3,8,2,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,8,5,2,7,3,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,8,2,1,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,4,7,3,1,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,1,7,6,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,7,1,8,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,1,7,2,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,8,4,5,6,3,2]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[6,1,8,4,5,3,7,2]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[8,5,1,2,6,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,5,8,7,4,6,3,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[3,7,2,6,8,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,4,7,8,6,2,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[7,3,1,6,8,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,8,7,6,4,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,1,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,10,1,2,3,4,8,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,1,2,5,3,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,1,2,3,10,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,7,1,2,3,4,8,5,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,8,4,9,1,2,3,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,10,1,5,3,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,1,5,2,10,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,1,2,10,3,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,8,9,1,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,6,7,1,8,9,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,5,4,2,1,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,2,4,6,3,7,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,5,7,4,3,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,7,6,8,5,1,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,8,5,1,3,6,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,6,3,1,8,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[8,7,4,2,1,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,5,8,4,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,6,8,3,7,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,8,5,1,4,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,8,5,3,4,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,8,3,6,4,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[6,3,8,1,4,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,1,4,2,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,1,8,3,7,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,1,6,3,2,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,1,4,6,2,5,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[3,7,6,5,8,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,3,6,5,8,7,10,9,1]=>{{1,2,4,6,8,10},{3},{5},{7},{9}}=>[2,4,3,6,5,8,7,10,9,1]=>[3,5,7,9,10,1,2,4,6,8]=>0
[5,4,7,3,8,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,3,6,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,2,7,3,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,7,3,4,5,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,6,1,3,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,8,7,3,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,2,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[3,1,7,5,8,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,5,6,4,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,8,2,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,2,7,5,3,8,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,4,5,1,8,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,8,3,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,2,8,1,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,6,8,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,3,8,5,6,2,1]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[7,2,6,5,1,8,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,8,5,6,3,1,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,5,3,8,7,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,5,3,8,4,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,5,8,2,7,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,3,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,7,8,3,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,3,2,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[5,6,1,3,2,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[3,6,8,5,2,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,4,8,3,2,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,6,7,8,2,9,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,3,4,8,1,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,3,1,5,8,7,4]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[1,3,5,8,4,7,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,3,5,6,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,8,2,7,6,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,4,6,3,7,5]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[1,5,2,8,7,6,4,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[4,2,5,6,8,7,3,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,3,4,5,1,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[1,3,7,8,5,4,6,2]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,3,2,7,8,5,4,6]=>{{1},{2,3},{4,7},{5,6,8}}=>[1,3,2,7,6,8,4,5]=>[1,3,2,7,4,8,5,6]=>1
[5,2,4,1,8,3,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,4,2,6,3,8,5,10,7,9]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[1,4,2,10,7,3,9,5,6,8]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[1,8,5,2,7,3,4,10,6,9]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[1,10,5,2,9,8,3,4,6,7]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[1,10,7,6,2,3,9,4,5,8]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[4,2,6,5,3,1,7,8]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>0
[1,3,8,5,7,4,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,2,8,6,3,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,1,4,7,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,5,8,6,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,6,3,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,2,3,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,7,5,3,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,4,8,3,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,7,8,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,5,8,2,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,6,7,8,1,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,1,5,3,2,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,6,1,3,2,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,8,5,3,2,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,2,7,6,4,1,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,8,2,7,3,1,5,4]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[8,2,6,3,4,1,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,8,5,7,1,3,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,2,7,1,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,2,8,7,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,1,3,8,4,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[5,2,7,8,4,1,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,7,8,3,5,4,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,1,2,8,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,7,8,3,2,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,2,6,4,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,1,8,4,3,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,1,3,7,5,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,4,7,2,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,7,2,4,8,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,4,5,6,2,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[8,2,5,3,1,7,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,3,5,8,1,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,8,6,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,5,2,3,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,5,1,4,8,3,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[5,7,6,1,2,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,5,2,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,1,8,6,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,8,1,2,4,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,5,3,7,4,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,5,6,2,8,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,8,1,2,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,2,8,7,4,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,4,2,3,5,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,4,8,5,2,3,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,6,8,7,5,3,2,4]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,4,2,6,8,7,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,8,6,3,2,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,7,4,6,3,2,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,8,6,4,2,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,5,8,7,1,4,3,6]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[3,4,6,5,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,2,4,1,6,7,8,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,3,6,7,2,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,5,6,4,8,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,6,1,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,8,6,7,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,6,8,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,7,3,8,2,9,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,3,4,8,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,4,5,8,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,6,4,7,3,8,2,9,1,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[8,1,4,7,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,8,5,2,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,6,3,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,1,3,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,7,6,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,8,5,6,7,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,8,6,1,2,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,1,6,7,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,5,2,7,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,1,2,6,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,1,7,4,2,3,5,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[6,1,7,2,5,3,4,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[5,1,7,2,6,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,1,8,2,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,3,5,1,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[2,4,8,6,3,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,1,2,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,1,4,2,3,5,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[8,7,5,1,4,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,5,2,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,5,1,6,4,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,5,4,1,6,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[4,6,1,5,2,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,6,5,3,7,2,4,8]=>{{1},{2,6},{3,4,5,7},{8}}=>[1,6,4,5,7,2,3,8]=>[1,6,2,7,3,4,5,8]=>0
[5,8,6,2,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,5,8,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,7,4,5,6,2,3]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[2,1,7,8,4,5,6,3]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[5,4,1,6,2,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,8,6,7,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,2,8,6,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,3,5,1,6,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,7,6,2,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,7,1,3,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,5,1,4,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,6,5,8,4,3,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,5,1,3,4,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,6,7,8,4,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,8,5,3,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,7,3,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[7,4,8,6,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,6,3,5,2,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[1,6,5,8,7,4,2,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,4,5,2,8,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,5,4,2,1,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,1,7,5,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,2,6,3,1,5,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[7,1,2,3,6,8,4,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[8,1,6,7,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,1,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,6,7,1,4,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,7,5,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,10,1,2,3,4,5,9,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,7,1,2,3,4,5,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,10,1,5,6,7,8,9,3,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,4,5,1,2,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,1,8,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,4,2,3,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,5,1,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,2,3,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,5,2,1,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,7,6,1,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,7,5,2,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,6,8,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,1,6,8,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,7,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,1,8,6,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,1,7,3,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,8,3,7,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,2,8,4,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,3,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,8,7,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,2,7,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,9,2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,7,3,2,5,6,8,1]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[2,3,6,5,1,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,3,1,2,6,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,5,4,2,6,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,2,6,8,7,4,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,3,7,5,1,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,8,1,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,8,4,5,1,7,2]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[8,6,1,7,2,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,8,3,1,4,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[1,6,8,3,2,4,7,5]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[8,4,1,7,3,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,6,2,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,8,4,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,8,3,1,4,6,7]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[5,4,7,8,3,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,5,8,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,5,7,6,3,8]=>{{1},{2,3,4,5,7},{6},{8}}=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>0
[1,4,2,6,8,5,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,8,3,5,4,2,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,5,8,7,6,3,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,7,5,2,4,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,5,2,4,6,3,8]=>{{1},{2,3,4,5,7},{6},{8}}=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>0
[1,8,4,7,5,2,6,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,4,6,3,2,8,7,5]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[5,3,8,2,6,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,5,7,1,4,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,6,1,2,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,6,2,4,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,1,5,2,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[1,8,7,3,4,5,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,9,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,3,7,8,4,5,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,8,6,2,3,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,2,1,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,6,4,5,1,7,3]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[3,2,6,7,8,4,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,5,2,3,6,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,8,6,1,5,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[3,7,2,5,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,5,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,5,6,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,8,2,5,4,6,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,6,8,7,2,3,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,8,2,3,6,7,4]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[1,3,2,6,8,5,4,7]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[1,8,4,2,3,6,5,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,4,2,7,5,3,8,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,8,4,7,3,2,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,4,8,3,2,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,8,3,2,7,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,5,2,1,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,1,3,7,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,7,3,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,7,3,4,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,1,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,5,3,7,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,1,3,4,7,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,4,5,6,8,9,1,2,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,4,5,6,8,1,2,7,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[3,4,5,1,6,7,8,2,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[1,3,5,2,6,7,8,9,4]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[3,4,6,1,7,8,9,10,2,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,2,5,8,7,3,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,4,8,5,7,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,8,7,1,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,7,1,3,6,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,8,6,3,2,5,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,8,7,2,6,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,7,2,6,3,5,4]=>{{1},{2,4,8},{3,5,6,7}}=>[1,4,5,8,6,7,3,2]=>[1,7,3,5,6,8,2,4]=>0
[8,7,2,1,4,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,7,1,6,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,8,7,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,3,1,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,5,3,8,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,1,2,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[6,8,4,1,7,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,4,6,7,5,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,4,6,1,7,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,3,9,5,1,7,4,10,6,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,3,7,5,1,8,9,10,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,3,9,5,6,7,1,10,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,3,7,8,6,10,9,2,5,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,3,5,6,7,8,9,10,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,3,4,5,9,7,1,10,6,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,3,4,5,7,8,9,10,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,5,4,6,7,1,9,10,3,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,7,4,8,6,1,9,5,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,5,4,6,7,8,9,1,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,3,4,5,6,7,9,10,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,7,4,5,6,8,9,1,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,6,5,7,8,1,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,4,7,6,3,1,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,6,4,8,1,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,6,5,7,1,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,1,4,8,2,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,7,8,3,5,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,4,1,7,3,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,6,8,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,8,6,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,8,6,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,8,2,3,4,5,9,6,7]=>{{1},{2,3,4,5,6,8},{7,9}}=>[1,3,4,5,6,8,9,2,7]=>[1,8,2,3,4,5,6,9,7]=>0
[1,3,4,5,6,8,9,2,7]=>{{1},{2,3,4,5,6,8},{7,9}}=>[1,3,4,5,6,8,9,2,7]=>[1,8,2,3,4,5,6,9,7]=>0
[8,4,7,3,6,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,7,5,6,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,2,3,6,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,3,6,2,4,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,7,4,5,2,3,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,5,2,3,6,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,3,6,2,4,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,7,8,9,2,3,4,5,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,7,4,5,2,3,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,3,8,9,10,2,4,5,6,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,5,9,3,6,10,2,4,7,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,9,6,7,4,5,2,3,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,5,6,3,8,2,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,5,6,3,7,2,8,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,5,3,6,2,8,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,7,3,4,2,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,8,3,4,2,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,4,5,3,7,2,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,5,3,8,2,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[3,1,9,6,2,8,4,5,7,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[7,4,1,6,2,3,9,5,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[9,4,1,8,7,2,3,5,6,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[9,6,5,1,2,8,3,4,7,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[5,2,8,1,7,4,3,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,5,6,8,2,7,4,3]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[1,3,7,2,6,4,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,8,6,7,3,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}=>[1,5,7,6,2,8,3,4]=>[1,5,2,7,3,8,4,6]=>0
[8,9,2,3,4,5,1,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,8,9,2,3,1,4,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,6,1,2,3,5,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,8,7,5,1,2,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,8,3,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,3,8,5,4,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[7,1,2,3,4,5,8,6,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[6,1,2,3,4,7,5,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>0
[7,1,2,6,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,4,6,1,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,4,8,3,1,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,5,3,1,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[7,2,5,1,6,8,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,1,7,4,8,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,7,5,8,2,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,4,5,7,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,8,6,3,7,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,4,1,8,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,1,2,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,7,8,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,5,6,8,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,4,5,8,7,1]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[3,6,4,5,2,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,4,6,7,3,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[3,1,6,5,2,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,8,2,4,5,3,7,1]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[1,5,2,8,6,4,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,7,8,5,2,1,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,5,2,8,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,2,1,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,7,1,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,1,2,5,3,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[6,8,4,1,3,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,1,8,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,1,6,7,3,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,5,4,1,6,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,1,6,4,7,8,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,6,2,3,5,7,8,4]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,3,4,8,5,2,6,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,5,7,2,3,6,8,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[3,2,5,7,8,4,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,5,1,7,4,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,8,3,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,8,4,7,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,8,3,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,1,5,4,6,2,3,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[7,4,1,3,6,2,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,6,8,3,1,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,8,1,7,3,6]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[7,8,2,6,3,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,5,3,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[7,6,2,5,3,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,6,1,3,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,6,7,4,8,3,5]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[7,2,6,8,4,5,3,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,7,5,8,2,4,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,5,2,8,1,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,6,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,8,3,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,6,8,1,2,3,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,6,1,2,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,7,3,5,2,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[8,1,5,2,6,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,1,5,6,3,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,3,1,8,6,2,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,1,8,7,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,8,6,3,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,4,2,8,6,3,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[8,3,1,6,4,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,6,4,1,7,3,5]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>[4,7,3,6,8,1,2,5]=>0
[1,8,4,2,7,5,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,1,8,7,6,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,2,6,3,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,5,7,1,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[6,4,1,5,3,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[4,5,2,7,1,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[4,1,8,5,3,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[6,3,8,4,5,2,7,1]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[2,8,1,9,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,2,6,8,4,1,7,3]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[2,6,8,5,7,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,8,7,6,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,1,6,3,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,6,3,4,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,8,1,7,5,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,6,2,7,8,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,3,6,5,8,7,10,9,12,11,1]=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}=>[2,4,3,6,5,8,7,10,9,12,11,1]=>[3,5,7,9,11,12,1,2,4,6,8,10]=>0
[4,7,2,5,6,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,4,1,3,7,8,2,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[7,2,1,6,8,3,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,6,4,1,8,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,9,3,4,5,6,2,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,1,10,3,4,5,6,7,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,2,1,9,4,5,6,3,8]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>[2,9,1,3,4,5,6,7,8]=>0
[5,1,2,6,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,2,3,7,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,10,4,5,6,7,3,9]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[6,1,2,7,4,5,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,5,2,8,6,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,7,2,3,8,5,6,1,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,3,8,5,2,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,8,4,7,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,5,8,1,3,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,6,1,2,3,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,1,7,8,3,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,2,8,6,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,8,1,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,3,8,5,1,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[1,8,2,7,3,5,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,7,4,2,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[3,7,8,6,1,4,2,5]=>{{1,3,5,8},{2,7},{4,6}}=>[3,7,5,6,8,4,2,1]=>[6,4,7,2,8,1,3,5]=>0
[8,1,2,6,3,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,3,8,7,1,2,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,4,5,7,6,2,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[6,3,4,8,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,8,7,4,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,7,8,6,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,8,2,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,5,3,8,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,8,5,1,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,3,4,5,6,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,2,6,5,8,4,1,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,6,5,8,7,1,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,3,7,2,8,5,1,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[4,3,6,2,8,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,6,8,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,7,6,8,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,7,3,8,6,1,5]=>{{1,3,4,7},{2},{5,8},{6}}=>[3,2,4,7,8,6,1,5]=>[2,6,7,1,3,4,8,5]=>0
[5,2,7,6,8,3,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,7,5,8,4,1,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,7,1,3,2,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,5,2,6,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,2,5,3,4,8,1,6]=>{{1,7},{2},{3,4,5},{6,8}}=>[7,2,4,5,3,8,1,6]=>[2,5,3,4,7,1,8,6]=>0
[4,2,5,3,7,8,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,3,6,2,4,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[7,5,6,2,3,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,5,7,6,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,6,3,8,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,3,7,5,6,2,1]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[5,7,2,8,3,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,8,6,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,6,2,8,4,7,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,8,3,6,4,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,5,8,3,6,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,5,3,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,3,4,5,8,7,9,6,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,6,5,7,8,9,4,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,6,9,8,10,7,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,4,5,6,7,1,2,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>0
[1,7,2,5,6,8,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,7,6,8,3,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,7,1,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,5,4,2,3,6,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[4,5,1,7,6,3,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,4,2,1,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,5,6,8,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[7,5,2,8,6,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,6,3,7,5,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,6,2,7,8,4,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,8,2,7,5,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,8,6,4,2,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,2,8,6,4,1,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,7,5,6,1,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,6,4,8,5,7,1]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[7,2,8,1,6,3,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,7,5,8,4,6,3,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[7,1,4,2,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,2,4,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,6,5,2,4,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[6,8,5,2,4,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,2,8,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,2,5,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,2,7,8,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[10,3,1,5,6,7,8,9,2,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,5,1,2,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,8,2,1,3,5,7,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[4,2,5,7,9,1,3,6,8]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>[2,9,1,3,4,5,6,7,8]=>0
[4,2,6,8,10,1,3,5,7,9]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[6,4,2,8,1,3,5,7,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[4,6,2,8,10,1,3,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,6,8,9,2,1,3,5,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,6,8,10,2,1,3,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,8,2,5,9,1,3,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[1,4,5,7,9,2,3,6,8]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[8,6,4,9,7,5,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,6,4,2,9,7,5,3,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,8,5,3,1,9,6,4,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,6,7,8,3,9,4,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,6,7,2,8,3,9,4,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,6,1,7,2,8,3,9,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,7,5,3,10,8,6,4,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,5,9,6,3,1,10,7,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,7,8,3,9,4,10,5,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,6,7,8,9,3,1,10,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,7,2,8,3,9,4,10,5,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,5,7,6,8,2,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,6,3,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,3,5,6,1,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,8,6,3,5,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,3,5,4,1,2,6,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[3,1,5,4,7,2,6,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[5,7,6,3,8,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,2,3,7,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,2,1,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,4,1,3,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,1,7,3,2,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,2,7,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,4,7,3,5,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[1,4,8,5,3,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[2,5,6,3,1,8,4,7]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[4,5,1,2,7,8,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,8,1,4,5,3,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,4,7,3,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,6,3,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,5,8,6,4,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,7,8,6,4,2,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,3,5,2,8,7,9,6,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,3,6,5,8,7,9,2,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,3,7,6,8,5,9,2,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,4,6,3,8,7,9,2,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,4,7,6,8,3,9,2,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,8,2,6,5,3,4,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[8,6,1,5,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,1,2,3,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,1,2,3,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,5,3,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,7,5,4,1,3,6,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[6,8,7,5,2,1,4,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[1,6,4,8,5,7,3,2]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,6,8,5,2,7,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,9,6,2,3,4,5,8,7]=>{{1},{2,3,4,5,6,7,9},{8}}=>[1,3,4,5,6,7,9,8,2]=>[1,8,9,2,3,4,5,6,7]=>0
[1,5,8,2,3,4,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[2,3,4,5,6,9,10,1,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,3,8,7,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,1,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,5,2,1,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,5,7,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,2,1,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[4,5,8,2,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,8,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,8,3,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,6,8,4,7,2,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,8,6,3,2,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,1,6,3,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,1,7,3,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,6,7,8,9,2,3,4]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,7,2,8,9,3,4,5,6]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,6,2,7,8,9,3,4,5]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,5,2,6,7,8,9,3,4]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[6,3,7,5,2,4,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,2,4,5,7,3,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[1,3,8,2,4,6,7,5]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[2,8,7,6,3,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,5,7,4,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}=>[1,6,4,5,7,2,3,8]=>[1,6,2,7,3,4,5,8]=>0
[6,8,7,3,2,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,8,6,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,5,6,7,10,9,1,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,6,10,8,9,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,6,10,8,1,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,6,10,1,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,10,7,8,9,1,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,10,7,8,1,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,10,7,1,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,10,7,1,6,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,10,1,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,10,6,7,8,1,5,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,10,6,7,1,9,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,10,6,7,1,5,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,10,6,1,8,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,10,6,1,5,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,10,1,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,10,5,6,1,8,9,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,10,5,6,1,8,4,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,10,5,6,1,4,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,10,5,1,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,10,5,1,7,4,6,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,10,5,1,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,10,4,1,6,3,8,5,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,10,4,1,6,3,5,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,10,4,1,3,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,8,7,2,6,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,5,2,7,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,8,1,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,8,7,1,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,8,7,6,2,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,2,5,3,1,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,3,1,7,6,2,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,1,6,3,2,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,5,4,1,3,2,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,4,8,5,6,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,6,3,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[1,2,8,3,4,7,6,5]=>{{1},{2},{3,4,5,8},{6,7}}=>[1,2,4,5,8,7,6,3]=>[1,2,7,6,8,3,4,5]=>1
[7,6,4,5,2,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,4,7,6,3,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,1,7,3,6,4,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,3,1,5,2,7]=>{{1,5,6},{2,7,8},{3,4}}=>[5,7,4,3,6,1,8,2]=>[4,3,6,1,5,8,2,7]=>1
[4,2,5,3,6,7,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,5,4,2,8,7,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,8,6,5,2,4,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[1,4,7,3,2,8,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,6,5,2,4,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,7,5,3,2,6,4,8]=>{{1},{2,3,4,5,7},{6},{8}}=>[1,3,4,5,7,6,2,8]=>[1,6,7,2,3,4,5,8]=>0
[1,8,3,7,2,4,6,5]=>{{1},{2,5,8},{3},{4,6,7}}=>[1,5,3,6,8,7,4,2]=>[1,3,7,4,6,8,2,5]=>0
[6,8,5,2,7,1,4,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,1,4,5,2,3,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,1,2,3,7,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,6,1,2,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,3,1,2,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,1,2,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,1,5,6,7,8,9,2,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,3,8,5,6,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,6,8,2,3,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,1,3,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,5,3,1,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,3,4,1,2,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,4,1,3,2,5,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,6,7,3,2,8,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,6,5,3,1,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,4,7,3,6,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[2,6,1,5,7,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,1,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,5,7,4,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,1,6,5,2,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[4,5,2,7,6,1,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,4,2,6,3,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,5,7,1,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,1,6,5,3,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,5,7,6,1,3,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[5,4,2,6,3,7,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,6,5,2,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,6,5,2,1,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,5,8,2,1,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,4,6,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,6,2,1,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,6,2,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,8,4,6,7,5,2,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,7,1,6,3,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,2,5,8,4,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[4,3,1,7,8,5,2,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[5,6,8,2,4,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,2,5,6,8,1,4,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,1,5,3,4,8,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,5,8,7,3,1,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,8,7,6,4,2,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,8,5,1,7,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,4,6,3,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,6,9,1,2,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,1,6,7,8,9,2,3,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,1,8,6,3,7,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,2,1,5,7,3,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[3,1,5,8,7,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,7,4,3,6,8,1]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[3,1,5,7,8,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,1,8,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,1,5,3,8,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[7,3,5,1,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,4,3,7,1,6]=>{{1,6,7,8},{2,3,5},{4}}=>[6,3,5,4,2,7,8,1]=>[4,5,2,3,8,1,6,7]=>0
[2,6,5,7,1,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,1,6,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,6,3,7,2,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,3,1,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,4,2,3,7,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,9,10,5,6,7,1,3,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,9,10,5,6,3,4,7,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,9,5,6,10,3,4,7,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,9,10,5,6,3,1,2,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,9,5,6,10,3,1,2,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,9,5,10,1,3,6,2,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,9,5,3,6,10,1,2,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,5,1,2,3,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,5,1,7,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,7,6,4,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,6,8,2,5,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,5,2,6,8,3,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[5,8,2,1,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,2,8,3,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,1,10,8,6,7,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,1,8,9,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,1,9,10,8,7,2,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,1,8,9,10,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,7,6,5,2,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,7,8,6,2,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,4,5,6,7,1,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,3,1,2,7,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,3,8,5,2,7,6]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[1,8,3,2,5,4,6,7]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[5,7,8,1,3,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,4,1,6,7,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,2,7,5,3,4,1,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,3,1,2,8,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,2,7,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,2,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,2,1,7,8,3]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[6,8,7,2,3,1,4,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[5,7,2,1,3,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,3,4,8,6,7,9,5,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,8,4,5,6,7,9,3,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,3,4,5,6,7,9,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,9,7,8,10,6,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,9,5,6,7,8,10,4,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,4,7,5,6,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,9,4,5,6,7,8,10,3,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,2,4,5,6,7,9,1,8]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>[2,9,1,3,4,5,6,7,8]=>0
[2,3,4,7,6,9,8,5,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,7,6,5,2,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,5,8,6,7,9,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,5,4,8,6,7,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,4,1,6,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,8,5,6,7,9,1,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,1,5,6,4,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,1,5,3,7,8,6,4]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[5,1,4,7,6,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,2,4,5,6,8,3]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[2,8,7,1,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,1,3,4,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,2,5,7,8,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[5,8,2,1,7,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,7,2,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,4,1,3,8,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,2,7,4,5,8,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,4,2,6,1,5,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,7,6,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,6,2,1,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,5,7,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,1,3,5,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,3,1,6,4,7,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,6,2,1,3,7,4,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>0
[5,2,6,3,7,8,4,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,4,1,3,7,8,6,5]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[8,4,6,3,7,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,7,5,8,1,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,8,7,3,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,1,2,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,4,5,1,2,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,4,6,1,3,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,6,4,1,3,7,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,4,5,1,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,7,1,8,4,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,2,7,6,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,4,7,6,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,8,1,4,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,6,5,2,8,7,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,3,4,8,6,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,8,1,3,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,2,8,3,5,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[1,5,2,8,6,4,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[5,1,6,7,4,2,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,4,2,8,6,7,3]=>{{1},{2,3,4,5,8},{6},{7}}=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0
[5,8,4,1,6,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,7,8,1,2,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,6,4,2,1,3,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[6,5,7,4,1,3,2,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[4,6,1,8,3,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,6,8,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,1,8,3,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,6,1,8,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,6,3,8,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,4,5,8,3,7,1]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[6,8,4,2,7,1,3,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[4,5,2,3,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,2,3,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,5,2,3,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,2,3,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,6,2,3,1,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,7,3,4,5,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,2,7,3,4,5,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[3,8,4,5,2,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,7,5,1,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,1,2,3,4,5,9,8]=>{{1,2,3,4,5,6,7},{8,9}}=>[2,3,4,5,6,7,1,9,8]=>[7,1,2,3,4,5,6,9,8]=>1
[9,7,5,3,1,8,6,4,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,5,1,8,4,7,3,6,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,4,7,3,6,2,9,5,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,3,7,2,9,4,5,6,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,3,10,5,7,2,9,4,6,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,2,9,3,10,4,5,6,7,1]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[6,5,9,3,8,2,10,4,7,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,4,7,5,10,3,9,2,8,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,4,7,5,9,2,10,3,8,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,2,1,3,6,7,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,5,2,6,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,5,2,7,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,6,2,7,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,3,6,4,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,4,2,8,1,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[3,5,2,8,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,8,7,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,3,5,7,2,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[7,2,5,8,6,1,4,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,6,2,4,1,7,5,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[2,5,4,1,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0
[6,5,7,3,1,4,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,7,4,3,1,5,8,2]=>{{1,5,6},{2,7,8},{3,4}}=>[5,7,4,3,6,1,8,2]=>[4,3,6,1,5,8,2,7]=>1
[3,1,6,7,8,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,5,6,2,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,5,6,7,8,9,10,1,3]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[3,7,5,6,2,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,8,2,3,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,8,7,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,5,3,7,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,2,6,3,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,1,3,2,7,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,6,3,8,7,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,5,2,6,7,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,5,3,1,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,5,1,2,3,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,3,2,6,1,5,7,4]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[3,1,4,7,6,2,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,3,4,1,6,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,7,1,4,6,3,5,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[7,3,1,6,5,2,4,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[7,1,5,2,4,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[6,1,4,5,2,7,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,1,5,8,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,2,3,6,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,4,6,3,7,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,6,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,4,6,8,5,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,8,3,4,1,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,6,5,2,7,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,5,6,8,7,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,1,5,7,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,8,2,4,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,7,8,5,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,2,1,6,4,7,5]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[6,7,2,5,8,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,7,8,2,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,7,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,8,1,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,3,1,5,8,4,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,7,5,8,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,8,5,6,1,4,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,5,8,1,4,6,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,7,5,8,1,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,5,8,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,7,3,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[4,5,6,7,9,1,2,3,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,5,4,7,6,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,4,5,8,1,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,4,1,6,2,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,6,8,2,4,7,5]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[7,8,6,2,1,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,7,5,8,4,9,3,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[3,4,5,6,7,8,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[4,5,6,7,8,1,2,3,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[4,8,1,6,3,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,4,1,6,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,7,8,3,6,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,7,8,6,3,5,2]=>{{1},{2,4,8},{3,5,6,7}}=>[1,4,5,8,6,7,3,2]=>[1,7,3,5,6,8,2,4]=>0
[8,3,6,1,2,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,6,1,2,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,7,6,2,1,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,6,1,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,9,4,5,6,10,2,3,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,9,4,5,2,3,6,10,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,4,5,9,2,3,6,10,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,9,4,5,2,10,1,3,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,4,5,9,2,10,1,3,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,4,9,10,2,5,1,3,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,4,2,5,9,10,1,3,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,8,2,5,9,1,3,6,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,1,8,2,4,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,8,2,5,3,4,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[4,1,3,8,5,6,2,7]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[1,7,8,6,3,2,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,6,7,1,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,1,6,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,8,3,1,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,3,1,8,4,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,2,8,7,4,6,5]=>{{1},{2,3},{4,5,6,7,8}}=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>1
[8,5,1,6,3,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,8,7,2,5,6,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,5,4,1,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,7,5,3,1,2,4,6,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[6,3,1,2,4,8,7,5,9]=>{{1,2,3,4,5,6,8},{7},{9}}=>[2,3,4,5,6,8,7,1,9]=>[7,8,1,2,3,4,5,6,9]=>0
[10,9,7,5,3,1,2,4,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,4,3,8,5,7,2,6]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[2,5,7,4,8,3,6,1]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>[4,7,3,6,8,1,2,5]=>0
[3,8,6,2,7,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,1,6,2,5,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,4,2,5,7,3,6]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[7,1,4,2,6,8,3,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[1,5,8,7,2,4,3,6]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
[1,5,4,2,8,3,7,6]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[8,7,1,3,2,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,8,7,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,5,2,8,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,4,8,7,3,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,8,5,7,4,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,6,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,6,7,1,4,8,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[4,7,5,3,2,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[5,8,1,2,7,4,3,6]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0
[6,3,1,8,2,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,1,8,4,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,1,4,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[9,3,4,5,6,7,1,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,7,2,8,3,9,4,10,5,6]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[1,7,8,2,3,9,10,4,5,6]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[1,7,8,9,2,3,10,4,5,6]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[7,1,2,8,3,9,4,10,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,1,8,2,3,9,10,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,1,8,9,2,3,10,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,1,8,9,10,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,1,2,3,9,4,10,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,1,9,2,3,4,10,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,9,1,2,3,10,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,9,1,10,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,5,1,8,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,3,6,8,1,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[8,5,7,6,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,5,6,1,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,2,8,7,1,4,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[2,6,1,3,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,1,8,3,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}=>[1,5,4,6,2,7,3,8]=>[1,5,2,7,3,4,6,8]=>0
[5,6,1,2,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,1,2,7,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,8,7,2,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,4,6,1,8,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[3,6,7,5,4,8,1,2]=>{{1,3,7},{2,6,8},{4,5}}=>[3,6,7,5,4,8,1,2]=>[5,4,7,1,3,8,2,6]=>1
[4,5,7,2,6,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,5,7,8,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,8,3,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,3,6,2,5,8,4,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[4,8,1,2,6,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,6,2,3,7,5,8,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,4,2,7,3,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,1,4,7,3,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,1,8,3,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,2,1,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,7,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,2,1,3,8,5,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[1,7,5,3,2,4,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,7,6,2,3,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,6,8,7,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,3,1,5,4,7,6]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[1,4,5,6,7,8,9,3,2]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,7,6,8,9,5,4,3,2]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[8,4,6,7,3,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,5,3,2,4,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,7,3,4,2,5,8]=>{{1},{2,6},{3,4,5,7},{8}}=>[1,6,4,5,7,2,3,8]=>[1,6,2,7,3,4,5,8]=>0
[1,8,7,5,3,4,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,2,8,9,10,1,3,4,5,6]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[9,10,5,6,2,1,4,3,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,7,5,8,2,1,4,6,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,9,5,10,2,1,4,7,6,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,6,7,10,2,1,5,4,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,10,6,3,4,2,1,5,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,7,8,3,4,2,1,6,5,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,8,5,3,6,2,4,1,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,7,5,3,10,2,4,6,8,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,9,4,5,10,3,2,7,6,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,6,4,7,10,3,5,2,8,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,4,9,10,3,6,5,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,5,6,9,10,4,3,7,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,3,4,5,6,7,1,9,2,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,7,8,3,4,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,8,4,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[6,5,8,3,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,6,1,4,8,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,4,8,6,1,7,5]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[4,6,7,2,3,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,6,5,7,8,1,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,5,8,4,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,6,8,5,7,2,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[2,8,5,1,6,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,5,1,2,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,2,5,3,8,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,5,2,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,6,5,1,8,4,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,3,7,1,6,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,8,7,2,1,5,4]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,2,8,6,3,1,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,8,3,6,1,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,4,5,3,8,1,2,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,2,4,6,3,8,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,6,5,3,8,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,2,6,5,1,4,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,8,6,5,7,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,1,7,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,5,2,6,8,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[10,8,7,6,4,2,1,3,5,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,8,7,6,4,2,1,3,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,5,9,7,4,2,1,6,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,8,6,4,3,2,1,5,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,8,7,6,4,3,2,1,5,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,5,7,6,8,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,7,2,6,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,5,7,2,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,4,7,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,7,4,8,6,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,5,7,8,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,5,6,7,8,9,1,4]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>[2,9,1,3,4,5,6,7,8]=>0
[4,2,5,6,7,3,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,2,5,6,7,8,9,3,1]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>[2,9,1,3,4,5,6,7,8]=>0
[8,2,5,4,1,3,7,6]=>{{1,3,5,6,8},{2},{4},{7}}=>[3,2,5,4,6,8,7,1]=>[2,4,7,8,1,3,5,6]=>0
[4,7,5,8,2,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,7,2,4,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,6,2,4,5,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,7,1,6,2,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,1,6,5,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,1,5,2,7,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,1,8,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[4,2,5,8,1,3,7,6]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[7,1,6,2,4,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,8,1,4,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,1,3,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,1,8,5,3,4,6,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[8,4,1,3,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,1,2,3,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,5,2,4,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,6,3,1,5,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,2,8,4,1,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,6,3,8,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,5,6,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,8,1,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,1,7,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,2,3,5,8,4,7]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[4,6,5,7,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,3,6,7,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,5,3,8,4,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[7,6,2,3,5,1,4,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[2,3,6,5,8,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,5,2,6,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,5,3,6,1,4,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,4,6,5,7,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,8,9,10,1,4,5,6,7]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[3,5,2,1,7,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,1,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,4,1,3,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,5,1,6,4,3,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[4,5,7,6,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,2,8,5,1,4,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,4,7,5,8,6,2,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[6,4,5,3,1,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,5,6,4,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,7,8,9,1,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,5,6,7,8,9,1,3,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,7,8,9,10,1,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,6,7,8,9,10,1,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,5,6,3,4,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,3,5,8,7,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,5,8,3,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,3,7,8,1,5,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,7,5,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,8,5,1,4,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,8,1,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,8,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,6,5,3,1,4,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[1,3,8,2,7,4,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,5,4,1,6,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,2,5,1,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[4,6,7,3,1,5,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,5,1,8,7,3,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,1,5,2,4,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,8,1,4,2,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,4,7,3,1,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,6,8,3,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,1,6,2,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[2,7,8,1,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,2,8,7,3,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,8,1,2,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,7,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,1,7,4,5,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,4,5,1,7,3,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,3,7,1,4,5,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,3,6,1,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,7,1,3,4,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,2,4,7,3,1,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,2,7,6,3,1,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,5,7,2,6,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,2,7,3,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,3,7,6,4,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,3,5,6,4,8,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,1,2,3,4,5,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,4,8,5,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,6,2,5,4,8,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[5,6,1,7,4,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,5,6,4,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[3,7,5,6,4,2,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,8,6,4,5,2,7,1]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[3,7,4,5,2,8,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,5,2,6,8,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,4,5,9,6,7,2,8,3]=>{{1},{2,3,4,5,6,7,9},{8}}=>[1,3,4,5,6,7,9,8,2]=>[1,8,9,2,3,4,5,6,7]=>0
[3,4,5,6,8,7,1,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,2,6,3,4,1,5,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,6,5,8,2,1,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,6,7,10,8,1,9,2,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,6,7,2,4,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,3,2,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[5,7,1,8,4,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,7,6,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,6,3,1,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,2,5,4,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[2,7,1,5,3,4,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,6,4,5,8,3,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,5,2,8,1,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,8,7,4,2,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,5,2,4,8,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,8,2,3,6,4,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[5,8,9,1,2,3,4,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,4,1,5,7,2,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,4,1,6,3,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,7,8,2,4,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,7,8,3,2,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,8,2,3,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,7,2,1,5,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,6,1,3,8,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,2,5,6,1,3,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,9,7,5,6,1,2,3,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,9,10,8,6,7,1,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,9,5,1,2,3,4,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,9,1,6,2,3,4,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,8,9,10,6,1,3,4,5,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,8,9,10,1,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,8,1,7,2,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,5,2,1,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[2,6,4,7,1,8,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,5,3,7,6,2,4]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[6,1,4,2,7,8,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,1,3,7,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,1,4,6,8,2,3]=>{{1,3,5,6,8},{2,7},{4}}=>[3,7,5,4,6,8,2,1]=>[4,7,2,8,1,3,5,6]=>0
[2,4,1,7,5,6,3,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[3,7,2,8,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,4,1,7,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,6,3,1,8,4,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,4,2,1,6,8,5,7]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0
[3,4,7,1,5,6,2,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[8,5,2,3,1,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,3,2,6,4,1,7,5]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[8,4,1,5,3,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,3,5,1,4,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,5,1,3,4,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,3,2,5,1,4,7,6]=>{{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>[3,2,7,8,1,4,5,6]=>1
[8,4,5,1,2,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,1,5,3,2,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,1,5,2,4,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[8,6,4,7,1,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,5,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,5,7,3,4,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[8,5,9,3,6,1,2,4,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,7,1,5,8,3,6,2,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,9,4,5,10,1,2,3,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,6,4,10,3,7,1,2,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,1,8,9,6,7,4,5,2,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,8,5,6,1,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,5,6,8,7,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,5,1,2,4,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,7,6,2,8,5,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,8,3,2,4,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,2,5,3,7,4,8,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,4,6,5,8,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,8,6,4,3,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[6,4,2,5,7,1,8,3]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[5,6,3,4,2,8,7,1]=>{{1,2,5,6,8},{3},{4},{7}}=>[2,5,3,4,6,8,7,1]=>[3,4,7,8,1,2,5,6]=>0
[4,5,2,8,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,6,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,1,3,7,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,5,1,2,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0
[6,8,1,3,2,5,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,4,8,5,7,2,3,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,7,3,2,4,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,6,2,7,3,4,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,6,7,3,4,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[8,6,1,7,3,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,7,5,1,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,5,4,8,6,3,1]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[8,5,7,1,4,2,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,8,3,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,2,4,8,6,7,3,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,5,6,7,8,9,1,4,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,4,5,6,7,9,10,1,8,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,8,6,1,7,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,7,8,2,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,3,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,5,6,2,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,7,8,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,7,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,8,6,2,1,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,8,6,2,1,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,7,6,2,5,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,6,7,8,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,8,6,4,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,5,3,2,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,8,1,3,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,5,3,1,7,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,4,5,3,1,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,8,7,2,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,8,6,4,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,7,5,1,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,2,6,7,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,6,3,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,7,4,1,8,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,6,8,3,2,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,4,2,8,1,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,4,8,7,1,2,5]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[3,4,7,8,6,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,8,2,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,8,5,6,4,2,3,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,4,8,5,7,3,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,1,5,3,8,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,3,8,5,1,7,6]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[2,5,8,1,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,8,3,4,5,1,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,5,7,2,8,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,7,6,5,3,2,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[2,3,6,7,1,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,1,4,5,7,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[3,8,5,1,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,1,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,5,8,1,4,2,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,8,5,7,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,2,6,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,8,6,7,3,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,8,3,2,6,5,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[6,7,8,5,2,4,10,1,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,4,5,3,8,2,6,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,8,6,3,2,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,6,8,2,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,2,7,4,1,6,5,3]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[3,2,8,4,1,6,5,7]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0
[6,5,2,7,8,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,6,5,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,5,2,6,8,7,3,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,2,6,1,4,7,8,9,5]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>[2,9,1,3,4,5,6,7,8]=>0
[8,5,6,3,4,1,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,9,4,7,2,5,1,3,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,5,1,3,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,7,8,1,2,3,4,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,3,4,1,2,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,2,6,1,4,7,8,9,10,5]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[2,7,8,9,1,3,4,5,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,3,4,9,10,1,2,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,5,6,3,4,1,2,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,3,9,2,6,10,1,4,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,9,4,7,2,5,1,3,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,7,8,5,6,3,4,1,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,3,4,7,2,1,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[4,2,6,3,1,5,7,8]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>[2,6,1,3,4,5,7,8]=>0
[4,6,3,2,5,8,7,1]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[5,9,1,8,2,7,3,6,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,8,2,7,3,6,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,4,6,3,9,1,8,2,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,6,4,8,2,9,1,7,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,5,10,1,9,2,8,3,7,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,4,7,3,6,2,9,1,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,6,4,7,3,8,2,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,3,1,5,6,8,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,10,1,3,4,5,6,9,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,9,1,3,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,3,1,2,4,5,6,9,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,1,10,2,4,5,6,9,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,3,1,2,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,1,9,2,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,7,8,1,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,2,7,3,8,5]=>{{1},{2,3,4,6},{5,7,8}}=>[1,3,4,6,7,2,8,5]=>[1,6,2,3,4,8,5,7]=>0
[1,4,2,5,8,6,3,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[5,2,7,1,6,3,4,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[5,1,7,3,6,4,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,2,7,5,6,1,4,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[3,2,7,1,6,4,5,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[6,3,1,7,5,4,2,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[9,8,2,3,4,5,6,1,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,2,8,7,3,4,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[9,4,5,6,7,8,2,1,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[10,9,2,3,4,5,6,7,1,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,3,6,8,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,8,3,5,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,2,4,8,3,1,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,4,8,7,3,5,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,4,2,3,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[6,5,1,8,3,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,7,1,2,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,5,7,2,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,1,3,4,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,7,1,3,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[7,3,5,1,4,2,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,3,5,2,1,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[4,6,5,2,1,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>0
[1,7,8,2,4,6,3,5]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[7,5,4,8,1,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,1,8,4,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,7,5,1,6,8,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,5,3,2,7,4,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,4,7,2,3,5,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,2,8,1,7,5,4,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,1,5,6,2,3,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,6,8,2,7,3,4,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,4,5,8,9,1,2,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,4,7,8,9,1,2,5,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[1,3,7,8,9,2,4,5,6]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[3,7,8,2,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,1,5,6,2,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,4,1,7,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,8,2,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,2,4,5,6,8,3,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,7,4,5,6,8,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,8,3,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,4,5,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,6,5,8,2,7,3]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[7,1,8,2,4,5,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,8,2,3,4,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,1,2,3,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[8,6,2,1,3,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,7,8,2,1,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,7,2,1,5,6,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,8,4,1,2,7]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[7,8,6,2,1,4,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[10,5,2,7,4,9,6,1,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,5,2,9,4,1,6,7,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,7,2,9,4,5,6,1,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,2,1,8,5,4,7,6,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,2,1,4,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,7,2,3,4,9,6,1,8,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,2,3,4,1,6,7,8,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,6,3,2,5,4,1,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,1,6,3,8,5,2,7,4,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,1,8,3,2,5,6,7,4,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,2,3,4,5,6,1,8,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,1,8,3,4,5,2,7,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,1,2,7,4,3,6,5,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,2,4,6,1,8,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,1,3,4,8,2,7,6]=>{{1,2,5,6,8},{3},{4},{7}}=>[2,5,3,4,6,8,7,1]=>[3,4,7,8,1,2,5,6]=>0
[6,5,1,8,3,4,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,5,6,1,3,4,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,3,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,8,7,3,5,2,6,4]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[5,6,2,8,4,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,5,8,3,4,6,2,7]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,4,7,6,2,3,8,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,4,6,7,2,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,7,1,6,4,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,6,3,2,8,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,2,6,7,4,1,8,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,5,6,4,1,7,3,2]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>[4,7,3,6,8,1,2,5]=>0
[5,8,2,6,3,1,7,4]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,1,4,6,2,5,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,5,8,3,4,7,2,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,5,6,7,1,8,2,9,4]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[1,9,8,7,6,4,3,2,5]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,9,8,7,4,5,3,2,6]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,10,9,8,7,5,4,3,2,6]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[4,8,7,3,6,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,9,2,3,4,5,1,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,7,8,9,2,3,1,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,8,2,4,5,1,7,6]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[3,7,2,1,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[2,5,7,8,4,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,5,3,2,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,1,8,7,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,2,6,7,8,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,6,2,3,8,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,3,7,5,8,4,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,2,1,6,4,3,8,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,4,8,7,2,3,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,6,5,2,7,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,6,2,7,4,3,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,6,7,5,8,4,2,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,8,7,3,2,1,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,5,6,8,3,4,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,6,5,7,8,3,2,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,8,5,2,7,3,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,1,3,2,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[7,1,6,3,2,8,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,2,6,4,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,1,3,2,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,2,7,6,3,5,4]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[9,4,8,5,10,1,3,2,7,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,7,6,2,3,1,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,2,1,3,6,8,5,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,1,4,6,3,2,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,4,5,8,6,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,3,7,5,2,6,4]=>{{1},{2,4,6,7,8},{3},{5}}=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0
[8,1,3,6,5,2,7,4]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[8,6,2,4,5,1,7,3]=>{{1,2,3,6,8},{4},{5},{7}}=>[2,3,6,4,5,8,7,1]=>[4,5,7,8,1,2,3,6]=>0
[8,6,7,5,2,1,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,5,3,6,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,5,4,8,3,2,6,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,1,7,8,3,5,4,6]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[4,7,6,5,8,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,1,2,3,4,8,6,5,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,2,3,8,5,6,4,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,1,8,3,4,5,6,2,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[10,1,2,3,4,5,9,7,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,1,2,3,4,9,6,7,5,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,1,2,9,4,5,6,7,3,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,1,9,3,4,5,6,7,2,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,2,1,3,4,5,6,9,7]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>[2,9,1,3,4,5,6,7,8]=>0
[9,1,2,3,8,5,4,7,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,8,2,1,4,5,6,7,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,1,7,3,2,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,5,6,1,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,5,1,6,4,3,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,5,2,1,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,7,2,8,5,4,6,3]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[4,1,7,3,2,8,5,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[4,3,7,8,6,1,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,2,6,3,7,8,5,4]=>{{1},{2},{3,4,6,8},{5,7}}=>[1,2,4,6,7,8,5,3]=>[1,2,7,5,8,3,4,6]=>0
[2,6,4,7,5,3,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[3,1,6,7,2,8,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,7,5,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,7,3,6,4,2,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,7,5,8,2,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,5,8,2,6,3,4,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,1,5,7,2,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[5,7,2,1,3,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[7,1,10,9,2,3,4,5,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,7,9,1,2,3,4,5,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,8,1,9,10,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,7,1,10,2,3,4,5,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,1,5,6,4,8,3,7]=>{{1,2},{3,4,5,6,7,8}}=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1
[1,6,7,2,8,5,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,8,7,5,2,9,6,3,10,4]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[7,6,4,1,8,5,2,9,3,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[9,6,2,1,3,7,4,10,8,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,5,8,2,1,7,3,6]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[5,7,9,8,6,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,6,8,5,9,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[7,6,2,8,4,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,1,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,3,8,7,4,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,2,6,4,3,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,1,2,6,5,3,4,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[5,4,7,8,6,2,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,4,8,3,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,3,7,4,6,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,5,8,2,3,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,8,2,3,6,4,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,4,1,3,7,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[8,1,6,2,3,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,5,3,8,1,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[2,4,7,6,3,8,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,5,7,1,3,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,7,6,1,8,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,8,5,3,2,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,10,2,1,6,4,3,5,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,9,1,10,7,4,3,5,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,8,1,9,3,10,5,4,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,2,1,8,3,9,4,10,5,6]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[9,3,1,10,7,4,2,5,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,3,1,9,2,10,5,4,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,1,8,3,2,9,4,10,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,7,1,8,4,2,5,3,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,1,9,2,10,5,3,6,4,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,1,8,2,9,3,10,5,4,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,2,6,7,4,8,3,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[7,2,4,1,6,3,5,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[2,6,1,5,3,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,8,7,3,1,4,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,1,2,4,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,7,6,3,1,2,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,5,3,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,6,3,1,5,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,3,1,4,5,6,8,2]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[3,1,6,5,2,4,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[2,5,1,6,4,3,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[4,1,2,5,7,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>[6,7,1,2,3,4,5,8]=>0
[4,6,5,8,1,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,1,6,8,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,1,8,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[3,8,7,2,6,1,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,5,1,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,8,6,1,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,5,6,4,1,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,4,7,8,1,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,9,1,3,4,5,6,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,1,2,9,3,4,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,2,6,1,4,7,8,5,9]=>{{1,3,4,5,6,7,8},{2},{9}}=>[3,2,4,5,6,7,8,1,9]=>[2,8,1,3,4,5,6,7,9]=>0
[4,3,7,2,1,5,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,5,7,2,1,8,6,4,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[4,6,8,3,2,1,9,7,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,3,7,2,1,5,8,9,6,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[5,4,8,3,2,1,6,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,6,8,3,2,1,9,7,5,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[4,5,6,3,7,2,8,1,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[1,5,6,7,4,8,3,9,2]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[6,4,7,5,1,3,2,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,1,6,3,2,7,8,4]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[5,2,1,6,4,7,3,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[5,4,1,6,2,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,8,3,6,2,7,5]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[3,6,2,5,7,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,4,1,6,8,5,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,1,6,8,7,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,7,5,3,1,8,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,5,8,6,7,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,5,7,2,1,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,7,5,6,1,10,9,4,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,10,6,9,8,5,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,6,5,9,10,8,4,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,9,5,8,7,4,1,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,5,4,9,6,10,8,3,1,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,5,4,8,9,7,3,1,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,3,7,1,4,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,4,6,7,8,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,5,6,7,3,8,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,4,6,2,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,5,3,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,6,5,3,7,4,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,2,8,5,3,6]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[2,6,8,1,7,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,6,5,3,8,2,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,6,8,7,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,2,3,1,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,5,7,6,1,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,7,2,6,4,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,7,2,1,6,4,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,4,7,6,2,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[8,7,1,6,4,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,4,6,3,8,1,7,2,9]=>{{1,2,3,4,5,6,8},{7},{9}}=>[2,3,4,5,6,8,7,1,9]=>[7,8,1,2,3,4,5,6,9]=>0
[1,6,5,7,4,9,2,8,3]=>{{1},{2,3,4,5,6,7,9},{8}}=>[1,3,4,5,6,7,9,8,2]=>[1,8,9,2,3,4,5,6,7]=>0
[5,4,8,1,6,3,7,2,9]=>{{1,2,3,4,5,6,8},{7},{9}}=>[2,3,4,5,6,8,7,1,9]=>[7,8,1,2,3,4,5,6,9]=>0
[1,6,5,9,2,7,4,8,3]=>{{1},{2,3,4,5,6,7,9},{8}}=>[1,3,4,5,6,7,9,8,2]=>[1,8,9,2,3,4,5,6,7]=>0
[4,5,6,7,1,2,8,3,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[1,3,6,7,8,9,2,4,5]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[4,5,1,8,7,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,8,5,2,6,7,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,7,4,5,1,3,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,2,5,3,1,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,7,3,1,2,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,8,5,3,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,7,2,3,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,4,2,8,5,6,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,2,5,7,1,4,3,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[3,1,8,7,6,2,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,4,6,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,4,5,7,8,6,9,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,5,7,9,8,6,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,5,6,3,7,8,9,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,4,5,6,2,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,5,6,4,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,1,5,2,6,4,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,3,4,7,6,2,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,6,8,2,4,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,4,6,8,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,5,1,6,4,8,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,4,8,5,7,6,3,2]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[4,5,2,6,7,3,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,3,10,1,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,3,1,9,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,1,4,10,2,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,6,7,1,4,3,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,7,2,1,3,5,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,5,4,2,7,3,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[5,6,1,7,2,4,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[2,3,7,1,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[4,6,1,5,2,8,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[4,6,1,5,2,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,8,2,7,5,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,6,3,4,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[10,7,1,2,3,4,8,9,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,6,8,2,1,5,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,6,8,3,2,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,3,5,7,4,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,1,6,4,7,3,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[2,7,3,8,5,6,4,1]=>{{1,2,4,7,8},{3},{5},{6}}=>[2,4,3,7,5,6,8,1]=>[3,5,6,8,1,2,4,7]=>0
[6,1,8,7,4,5,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,5,8,6,4,3,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[2,6,1,8,4,7,5,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,2,1,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,4,6,2,7,8,3]=>{{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>[5,1,2,8,3,4,6,7]=>0
[2,8,5,3,1,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,2,3,7,1,8,4]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[4,2,7,5,6,8,1,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,2,9,1,4,5,6,7,8]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>[2,9,1,3,4,5,6,7,8]=>0
[2,8,1,3,4,5,6,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,7,1,2,3,4,5,9,6,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,6,4,2,8,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,7,1,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,6,10,9,5,4,3,7,1]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[10,6,8,2,7,1,9,5,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,8,2,6,7,1,9,5,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,8,2,5,6,7,1,9,4,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,5,7,1,9,4,2,6,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,4,2,5,6,7,1,10,8,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,5,7,1,8,3,9,4,2,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,1,7,3,8,4,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,8,7,2,3,4,6,5]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,5,7,6,3,8,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,1,5,3,7,8,4]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,2,8,5,1,3,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[7,3,9,6,1,2,4,10,8,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,8,4,9,7,3,6,1,2,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,3,10,8,4,9,6,1,2,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,6,1,3,7,2,4,8,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,3,6,1,4,10,9,7,2,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,3,4,6,7,8,9,1,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[1,7,5,8,4,3,6,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,8,1,6,4,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,4,7,5,1,8,6,3]=>{{1,2,4,5},{3,6,7,8}}=>[2,4,6,5,1,7,8,3]=>[5,1,2,4,8,3,6,7]=>0
[2,3,7,1,8,5,6,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,1,2,7,4,8,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,5,1,8,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,4,7,6,8,1,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[3,1,5,7,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,8,6,7,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,2,7,1,4,3,5,8]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>[2,7,1,3,4,5,6,8]=>0
[10,3,4,1,2,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,6,3,2,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,8,2,3,5,7]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,8,5,6,4,1,7,3]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[1,4,7,3,5,8,6,2]=>{{1},{2,3,4,6,7,8},{5}}=>[1,3,4,6,5,7,8,2]=>[1,5,8,2,3,4,6,7]=>0
[7,3,8,2,4,1,5,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,6,1,5,2,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,1,8,6,7,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,1,6,8,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,4,2,1,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,7,5,3,4,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,8,7,4,5,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,4,7,5,3,2,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,8,7,2,3,5,4,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,6,1,8,2,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,6,5,7,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,7,8,5,1,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,6,4,2,9,8,7,5,3]=>{{1},{2,3,4,5,6,8,9},{7}}=>[1,3,4,5,6,8,7,9,2]=>[1,7,9,2,3,4,5,6,8]=>0
[4,3,1,6,2,5,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[7,5,2,1,8,4,3,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,5,8,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,6,8,5,1,4,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,2,4,1,6,8,3,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,7,1,2,5,6,3,8]=>{{1,2,3,4,7},{5},{6},{8}}=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0
[5,4,1,3,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,3,1,8,4,2,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,8,7,4,1,3,6,5]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>[4,7,3,6,8,1,2,5]=>0
[6,8,2,3,1,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,2,7,3,1,4,5,6]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[4,8,3,6,5,2,7,1]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[2,6,3,8,5,4,7,1]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[6,1,3,2,5,8,7,4]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0
[1,4,2,5,6,7,9,8,3]=>{{1},{2,3,4,5,6,7,9},{8}}=>[1,3,4,5,6,7,9,8,2]=>[1,8,9,2,3,4,5,6,7]=>0
[3,5,4,6,1,2,8,7]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>1
[1,4,2,5,6,7,8,10,9,3]=>{{1},{2,3,4,5,6,7,8,10},{9}}=>[1,3,4,5,6,7,8,10,9,2]=>[1,9,10,2,3,4,5,6,7,8]=>0
[1,3,4,5,6,7,8,9,11,2,10]=>{{1},{2,3,4,5,6,7,8,9,10,11}}=>[1,3,4,5,6,7,8,9,10,11,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>0
[4,5,1,7,6,8,2,9,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,5,1,6,7,9,8,10,2,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,7,6,3,4,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,6,7,2,3,5,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,8,7,2,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,8,3,9,4,10,5,1,6]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[7,2,8,9,3,4,10,1,5,6]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[7,2,8,9,10,3,4,1,5,6]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[7,8,2,3,9,4,10,5,1,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,2,9,3,4,10,1,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,2,9,10,3,4,1,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,2,9,10,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,9,2,3,4,10,5,1,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,9,2,10,3,4,5,1,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,9,10,2,3,4,1,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,8,9,10,2,1,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[5,9,8,7,6,4,3,2,1,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[10,9,8,6,1,7,5,4,3,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,8,5,6,2,3,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[4,5,8,3,6,1,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[5,7,1,3,6,2,4,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[5,7,1,3,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,8,2,5,7,3,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,6,3,4,7,2,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,7,3,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,6,4,8,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[10,7,8,1,2,3,4,5,6,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,7,10,1,2,3,4,5,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,10,2,3,4,7,5,6,8,9]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[3,8,2,6,4,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,5,8,6,2,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[6,5,1,7,4,8,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,4,1,7,2,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[7,6,5,3,2,1,4,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>0
[5,7,6,3,4,2,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[3,1,4,5,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,8,6,2,4,7,5,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,1,8,2,3,4,5,9,6]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[6,8,1,2,3,4,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,8,4,1,6,3,7,5,9]=>{{1,2,3,4,5,6,8},{7},{9}}=>[2,3,4,5,6,8,7,1,9]=>[7,8,1,2,3,4,5,6,9]=>0
[5,3,6,8,2,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,2,5,3,8,4,6]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>0
[5,3,7,8,4,2,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,6,8,1,5,4,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,5,8,2,3,4,1,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,8,2,3,7,4,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,7,6,8,4,5,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[7,1,8,6,4,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[1,4,7,6,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[5,7,1,6,4,2,3,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,7,5,2,4,3,8,6]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[2,8,5,1,4,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,7,2,3,5,1,6,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[4,8,2,3,7,5,1,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,1,7,5,6,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,2,1,4,5,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,4,8,7,6,3,5,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,6,7,5,2,3,1,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[6,2,5,3,1,8,7,4]=>{{1,3,4,5,6,8},{2},{7}}=>[3,2,4,5,6,8,7,1]=>[2,7,8,1,3,4,5,6]=>0
[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,6,5,3,8,7,1,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,5,3,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,2,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[7,3,4,5,1,2,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,3,4,5,6,1,2,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,4,5,8,1,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,6,7,8,9,10,1,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,5,6,9,7,4,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,6,2,1,3,4,9,7,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,4,2,6,1,7,5,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>0
[3,5,2,6,7,1,8,4,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[4,3,5,2,7,1,8,6,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[4,3,6,2,7,8,1,9,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,3,6,2,7,8,1,9,5,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[1,6,2,3,8,5,7,4]=>{{1},{2,3,4,5,6,8},{7}}=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0
[3,4,2,6,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[7,4,1,3,6,8,2,5]=>{{1,2,3,4,7},{5,6,8}}=>[2,3,4,7,6,8,1,5]=>[7,1,2,3,4,8,5,6]=>0
[1,6,8,5,7,4,3,2]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[3,1,8,4,5,6,2,7]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[4,2,7,8,6,3,1,5]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,1,4,8,2,3,7,5]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[2,5,7,8,6,4,1,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,1,4,5,6,2,3]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[6,7,8,9,1,4,5,2,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,1,5,3,7,4,2,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[9,5,8,7,6,4,3,1,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,2,1,3,8,4,6,7]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[6,5,1,3,8,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,6,1,4,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,6,4,5,1,3,7,2]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0
[8,5,4,7,6,1,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[2,3,7,8,1,4,6,5]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,2,6,3,8,5,9,7,1]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>[2,9,1,3,4,5,6,7,8]=>0
[4,2,6,3,8,5,1,7,9]=>{{1,3,4,5,6,7,8},{2},{9}}=>[3,2,4,5,6,7,8,1,9]=>[2,8,1,3,4,5,6,7,9]=>0
[4,2,6,3,9,5,1,7,8]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>[2,9,1,3,4,5,6,7,8]=>0
[4,2,6,3,8,5,10,7,1,9]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[7,4,2,6,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,4,1,6,3,5,2,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,3,4,1,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,6,8,3,4,5,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[5,8,6,1,2,4,3,7]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,7,2,1,6,8,4,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,9,5,6,7,8,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,9,4,5,6,7,8,1,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,2,8,5,6,7,1,9,4]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>[2,9,1,3,4,5,6,7,8]=>0
[4,3,10,5,6,7,8,9,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,2,9,5,6,7,8,1,10,4]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>[2,10,1,3,4,5,6,7,8,9]=>0
[4,3,5,7,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,3,4,9,6,7,2,5,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,3,7,4,6,2,1,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[5,7,6,3,2,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,5,1,6,8,3,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,3,1,7,6,8,2,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,1,5,3,2,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[8,1,2,5,3,4,6,7,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[7,1,5,2,4,3,6,8]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0
[1,9,2,3,6,4,5,7,8]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[9,1,2,3,6,4,5,7,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>0
[8,1,2,6,4,3,5,7,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[8,1,2,6,3,5,4,7,9]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>0
[1,9,2,3,7,5,4,6,8]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,9,2,3,7,4,6,5,8]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[6,7,8,9,3,4,1,2,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[10,9,1,2,3,7,8,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,9,1,10,8,7,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[6,5,8,3,7,1,4,2]=>{{1,6},{2,3,4,5,7,8}}=>[6,3,4,5,7,1,8,2]=>[6,1,8,2,3,4,5,7]=>0
[9,6,1,7,2,8,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,8,6,1,7,2,3,4,5]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,6,4,1,9,7,5,2,3]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,8,7,5,3,1,6,4,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,7,1,10,8,2,3,4,5,6]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,6,1,7,2,8,3,9,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,6,1,7,2,8,3,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,7,4,1,10,8,5,2,6,3]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[10,9,7,5,3,1,8,6,4,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[9,1,2,8,4,3,5,6,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[9,8,2,1,3,5,6,4,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[8,1,9,2,4,5,6,3,7]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[2,3,4,10,6,7,8,9,1,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,10,5,6,7,8,9,1,4]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,6,10,1,9,7,8]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,4,5,10,1,8,9,6,7]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[2,3,10,1,6,7,8,9,4,5]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[1,5,2,6,4,8,7,9,3]=>{{1},{2,3,4,5,6,8,9},{7}}=>[1,3,4,5,6,8,7,9,2]=>[1,7,9,2,3,4,5,6,8]=>0
[1,5,2,7,4,8,6,9,3]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,5,2,7,4,9,6,8,3]=>{{1},{2,3,4,5,6,7,9},{8}}=>[1,3,4,5,6,7,9,8,2]=>[1,8,9,2,3,4,5,6,7]=>0
[1,5,2,7,4,8,6,10,9,3]=>{{1},{2,3,4,5,6,7,8,10},{9}}=>[1,3,4,5,6,7,8,10,9,2]=>[1,9,10,2,3,4,5,6,7,8]=>0
[1,5,2,8,4,9,6,7,3]=>{{1},{2,3,4,5,6,7,8,9}}=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>0
[1,5,2,7,4,9,6,10,8,3]=>{{1},{2,3,4,5,6,7,8,9,10}}=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>0
[4,5,6,7,9,8,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,4,6,7,8,9,3,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,5,6,7,8,10,9,3,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,5,6,7,3,9,8,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[4,3,6,7,8,9,5,2,1]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[5,4,6,7,8,9,10,3,2,1]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[4,5,6,7,8,9,3,1,2]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>0
[3,4,5,6,8,9,10,7,1,2]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[3,7,8,4,5,6,1,2]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0
[7,6,4,2,3,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,8,7,3,2,5,6,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,4,2,6,8,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,4,8,7,3,2,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[5,6,2,8,7,4,3,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[3,7,5,6,4,2,8,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,8,2,6,4,3,5,1]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,10,5,1,2,3,4,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>0
[8,3,6,5,2,7,1,4]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[6,1,2,4,7,5,3,8]=>{{1,2,3,5,6,7},{4},{8}}=>[2,3,5,4,6,7,1,8]=>[4,7,1,2,3,5,6,8]=>0
[6,4,5,1,8,7,3,2]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[4,3,6,2,5,7,1,8]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>[5,7,1,2,3,4,6,8]=>0
[8,2,6,5,1,7,4,3]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,8,5,2,7,6,4,3]=>{{1},{2,3,4,5,7,8},{6}}=>[1,3,4,5,7,6,8,2]=>[1,6,8,2,3,4,5,7]=>0
[1,7,6,8,2,5,4,3]=>{{1},{2,3,4,5,6,7,8}}=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0
[4,6,5,7,1,8,2,3]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0
[7,2,5,6,4,8,3,1]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0
[1,5,7,6,2,3,8,4]=>{{1},{2,5},{3,4,6,7,8}}=>[1,5,4,6,2,7,8,3]=>[1,5,2,8,3,4,6,7]=>0
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Description
The number of adjacencies of a permutation.
An adjacency of a permutation $\pi$ is an index $i$ such that $\pi(i)-1 = \pi(i+1)$. Adjacencies are also known as small descents.
This can be also described as an occurrence of the bivincular pattern ([2,1], {((0,1),(1,0),(1,1),(1,2),(2,1)}), i.e., the middle row and the middle column are shaded, see [3].
An adjacency of a permutation $\pi$ is an index $i$ such that $\pi(i)-1 = \pi(i+1)$. Adjacencies are also known as small descents.
This can be also described as an occurrence of the bivincular pattern ([2,1], {((0,1),(1,0),(1,1),(1,2),(2,1)}), i.e., the middle row and the middle column are shaded, see [3].
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
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
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