Identifier
Mp00249:
Set partitions
—Callan switch⟶
Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
=>
Cc0009;cc-rep-0Cc0009;cc-rep-1
{{1}}=>{{1}}=>[1]=>
{{1,2}}=>{{1,2}}=>[2,1]=>0
{{1},{2}}=>{{1},{2}}=>[1,2]=>1
{{1,2,3}}=>{{1,3},{2}}=>[3,2,1]=>00
{{1,2},{3}}=>{{1,2},{3}}=>[2,1,3]=>01
{{1,3},{2}}=>{{1,2,3}}=>[2,3,1]=>00
{{1},{2,3}}=>{{1},{2,3}}=>[1,3,2]=>10
{{1},{2},{3}}=>{{1},{2},{3}}=>[1,2,3]=>11
{{1,2,3,4}}=>{{1,4},{2},{3}}=>[4,2,3,1]=>000
{{1,2,3},{4}}=>{{1,3},{2},{4}}=>[3,2,1,4]=>001
{{1,2,4},{3}}=>{{1,3,4},{2}}=>[3,2,4,1]=>000
{{1,2},{3,4}}=>{{1,2},{3,4}}=>[2,1,4,3]=>010
{{1,2},{3},{4}}=>{{1,2},{3},{4}}=>[2,1,3,4]=>011
{{1,3,4},{2}}=>{{1,2,4},{3}}=>[2,4,3,1]=>000
{{1,3},{2,4}}=>{{1,3},{2,4}}=>[3,4,1,2]=>000
{{1,3},{2},{4}}=>{{1,2,3},{4}}=>[2,3,1,4]=>001
{{1,4},{2,3}}=>{{1,4},{2,3}}=>[4,3,2,1]=>000
{{1},{2,3,4}}=>{{1},{2,3,4}}=>[1,3,4,2]=>100
{{1},{2,3},{4}}=>{{1},{2,3},{4}}=>[1,3,2,4]=>101
{{1,4},{2},{3}}=>{{1,2,3,4}}=>[2,3,4,1]=>000
{{1},{2,4},{3}}=>{{1},{2,4},{3}}=>[1,4,3,2]=>100
{{1},{2},{3,4}}=>{{1},{2},{3,4}}=>[1,2,4,3]=>110
{{1},{2},{3},{4}}=>{{1},{2},{3},{4}}=>[1,2,3,4]=>111
{{1,2,3,4,5}}=>{{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>0000
{{1,2,3,4},{5}}=>{{1,4},{2},{3},{5}}=>[4,2,3,1,5]=>0001
{{1,2,3,5},{4}}=>{{1,4,5},{2},{3}}=>[4,2,3,5,1]=>0000
{{1,2,3},{4,5}}=>{{1,3},{2},{4,5}}=>[3,2,1,5,4]=>0010
{{1,2,3},{4},{5}}=>{{1,3},{2},{4},{5}}=>[3,2,1,4,5]=>0011
{{1,2,4,5},{3}}=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>0000
{{1,2,4},{3,5}}=>{{1,4},{2},{3,5}}=>[4,2,5,1,3]=>0000
{{1,2,4},{3},{5}}=>{{1,3,4},{2},{5}}=>[3,2,4,1,5]=>0001
{{1,2,5},{3,4}}=>{{1,5},{2},{3,4}}=>[5,2,4,3,1]=>0000
{{1,2},{3,4,5}}=>{{1,2},{3,4,5}}=>[2,1,4,5,3]=>0100
{{1,2},{3,4},{5}}=>{{1,2},{3,4},{5}}=>[2,1,4,3,5]=>0101
{{1,2,5},{3},{4}}=>{{1,3,5},{2},{4}}=>[3,2,5,4,1]=>0000
{{1,2},{3,5},{4}}=>{{1,2},{3,5},{4}}=>[2,1,5,4,3]=>0100
{{1,2},{3},{4,5}}=>{{1,2},{3},{4,5}}=>[2,1,3,5,4]=>0110
{{1,2},{3},{4},{5}}=>{{1,2},{3},{4},{5}}=>[2,1,3,4,5]=>0111
{{1,3,4,5},{2}}=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>0000
{{1,3,4},{2,5}}=>{{1,4},{2,5},{3}}=>[4,5,3,1,2]=>0000
{{1,3,4},{2},{5}}=>{{1,2,4},{3},{5}}=>[2,4,3,1,5]=>0001
{{1,3,5},{2,4}}=>{{1,5},{2,4},{3}}=>[5,4,3,2,1]=>0000
{{1,3},{2,4,5}}=>{{1,3},{2,4,5}}=>[3,4,1,5,2]=>0000
{{1,3},{2,4},{5}}=>{{1,3},{2,4},{5}}=>[3,4,1,2,5]=>0001
{{1,3,5},{2},{4}}=>{{1,2,5},{3},{4}}=>[2,5,3,4,1]=>0000
{{1,3},{2,5},{4}}=>{{1,3},{2,5},{4}}=>[3,5,1,4,2]=>0000
{{1,3},{2},{4,5}}=>{{1,2,3},{4,5}}=>[2,3,1,5,4]=>0010
{{1,3},{2},{4},{5}}=>{{1,2,3},{4},{5}}=>[2,3,1,4,5]=>0011
{{1,4,5},{2,3}}=>{{1,4,5},{2,3}}=>[4,3,2,5,1]=>0000
{{1,4},{2,3,5}}=>{{1,4},{2,3,5}}=>[4,3,5,1,2]=>0000
{{1,4},{2,3},{5}}=>{{1,4},{2,3},{5}}=>[4,3,2,1,5]=>0001
{{1,5},{2,3,4}}=>{{1,5},{2,3,4}}=>[5,3,4,2,1]=>0000
{{1},{2,3,4,5}}=>{{1},{2,3,4,5}}=>[1,3,4,5,2]=>1000
{{1},{2,3,4},{5}}=>{{1},{2,3,4},{5}}=>[1,3,4,2,5]=>1001
{{1,5},{2,3},{4}}=>{{1,5},{2,3},{4}}=>[5,3,2,4,1]=>0000
{{1},{2,3,5},{4}}=>{{1},{2,3,5},{4}}=>[1,3,5,4,2]=>1000
{{1},{2,3},{4,5}}=>{{1},{2,3},{4,5}}=>[1,3,2,5,4]=>1010
{{1},{2,3},{4},{5}}=>{{1},{2,3},{4},{5}}=>[1,3,2,4,5]=>1011
{{1,4,5},{2},{3}}=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>0000
{{1,4},{2,5},{3}}=>{{1,3,4},{2,5}}=>[3,5,4,1,2]=>0000
{{1,4},{2},{3,5}}=>{{1,2,4},{3,5}}=>[2,4,5,1,3]=>0000
{{1,4},{2},{3},{5}}=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>0001
{{1,5},{2,4},{3}}=>{{1,3,5},{2,4}}=>[3,4,5,2,1]=>0000
{{1},{2,4,5},{3}}=>{{1},{2,4,5},{3}}=>[1,4,3,5,2]=>1000
{{1},{2,4},{3,5}}=>{{1},{2,4},{3,5}}=>[1,4,5,2,3]=>1000
{{1},{2,4},{3},{5}}=>{{1},{2,4},{3},{5}}=>[1,4,3,2,5]=>1001
{{1,5},{2},{3,4}}=>{{1,2,5},{3,4}}=>[2,5,4,3,1]=>0000
{{1},{2,5},{3,4}}=>{{1},{2,5},{3,4}}=>[1,5,4,3,2]=>1000
{{1},{2},{3,4,5}}=>{{1},{2},{3,4,5}}=>[1,2,4,5,3]=>1100
{{1},{2},{3,4},{5}}=>{{1},{2},{3,4},{5}}=>[1,2,4,3,5]=>1101
{{1,5},{2},{3},{4}}=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000
{{1},{2,5},{3},{4}}=>{{1},{2,5},{3},{4}}=>[1,5,3,4,2]=>1000
{{1},{2},{3,5},{4}}=>{{1},{2},{3,5},{4}}=>[1,2,5,4,3]=>1100
{{1},{2},{3},{4,5}}=>{{1},{2},{3},{4,5}}=>[1,2,3,5,4]=>1110
{{1},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5}}=>[1,2,3,4,5]=>1111
{{1,2,3,4,5,6}}=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>00000
{{1,2,3,4,5},{6}}=>{{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>00001
{{1,2,3,4,6},{5}}=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>00000
{{1,2,3,4},{5,6}}=>{{1,4},{2},{3},{5,6}}=>[4,2,3,1,6,5]=>00010
{{1,2,3,4},{5},{6}}=>{{1,4},{2},{3},{5},{6}}=>[4,2,3,1,5,6]=>00011
{{1,2,3,5,6},{4}}=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>00000
{{1,2,3,5},{4,6}}=>{{1,5},{2},{3},{4,6}}=>[5,2,3,6,1,4]=>00000
{{1,2,3,5},{4},{6}}=>{{1,4,5},{2},{3},{6}}=>[4,2,3,5,1,6]=>00001
{{1,2,3,6},{4,5}}=>{{1,6},{2},{3},{4,5}}=>[6,2,3,5,4,1]=>00000
{{1,2,3},{4,5,6}}=>{{1,3},{2},{4,5,6}}=>[3,2,1,5,6,4]=>00100
{{1,2,3},{4,5},{6}}=>{{1,3},{2},{4,5},{6}}=>[3,2,1,5,4,6]=>00101
{{1,2,3,6},{4},{5}}=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>00000
{{1,2,3},{4,6},{5}}=>{{1,3},{2},{4,6},{5}}=>[3,2,1,6,5,4]=>00100
{{1,2,3},{4},{5,6}}=>{{1,3},{2},{4},{5,6}}=>[3,2,1,4,6,5]=>00110
{{1,2,3},{4},{5},{6}}=>{{1,3},{2},{4},{5},{6}}=>[3,2,1,4,5,6]=>00111
{{1,2,4,5,6},{3}}=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000
{{1,2,4,5},{3,6}}=>{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>00000
{{1,2,4,5},{3},{6}}=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>00001
{{1,2,4,6},{3,5}}=>{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>00000
{{1,2,4},{3,5,6}}=>{{1,4},{2},{3,5,6}}=>[4,2,5,1,6,3]=>00000
{{1,2,4},{3,5},{6}}=>{{1,4},{2},{3,5},{6}}=>[4,2,5,1,3,6]=>00001
{{1,2,4,6},{3},{5}}=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>00000
{{1,2,4},{3,6},{5}}=>{{1,4},{2},{3,6},{5}}=>[4,2,6,1,5,3]=>00000
{{1,2,4},{3},{5,6}}=>{{1,3,4},{2},{5,6}}=>[3,2,4,1,6,5]=>00010
{{1,2,4},{3},{5},{6}}=>{{1,3,4},{2},{5},{6}}=>[3,2,4,1,5,6]=>00011
{{1,2,5,6},{3,4}}=>{{1,5,6},{2},{3,4}}=>[5,2,4,3,6,1]=>00000
{{1,2,5},{3,4,6}}=>{{1,5},{2},{3,4,6}}=>[5,2,4,6,1,3]=>00000
{{1,2,5},{3,4},{6}}=>{{1,5},{2},{3,4},{6}}=>[5,2,4,3,1,6]=>00001
{{1,2,6},{3,4,5}}=>{{1,6},{2},{3,4,5}}=>[6,2,4,5,3,1]=>00000
{{1,2},{3,4,5,6}}=>{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>01000
{{1,2},{3,4,5},{6}}=>{{1,2},{3,4,5},{6}}=>[2,1,4,5,3,6]=>01001
{{1,2,6},{3,4},{5}}=>{{1,6},{2},{3,4},{5}}=>[6,2,4,3,5,1]=>00000
{{1,2},{3,4,6},{5}}=>{{1,2},{3,4,6},{5}}=>[2,1,4,6,5,3]=>01000
{{1,2},{3,4},{5,6}}=>{{1,2},{3,4},{5,6}}=>[2,1,4,3,6,5]=>01010
{{1,2},{3,4},{5},{6}}=>{{1,2},{3,4},{5},{6}}=>[2,1,4,3,5,6]=>01011
{{1,2,5,6},{3},{4}}=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>00000
{{1,2,5},{3,6},{4}}=>{{1,4,5},{2},{3,6}}=>[4,2,6,5,1,3]=>00000
{{1,2,5},{3},{4,6}}=>{{1,3,5},{2},{4,6}}=>[3,2,5,6,1,4]=>00000
{{1,2,5},{3},{4},{6}}=>{{1,3,5},{2},{4},{6}}=>[3,2,5,4,1,6]=>00001
{{1,2,6},{3,5},{4}}=>{{1,4,6},{2},{3,5}}=>[4,2,5,6,3,1]=>00000
{{1,2},{3,5,6},{4}}=>{{1,2},{3,5,6},{4}}=>[2,1,5,4,6,3]=>01000
{{1,2},{3,5},{4,6}}=>{{1,2},{3,5},{4,6}}=>[2,1,5,6,3,4]=>01000
{{1,2},{3,5},{4},{6}}=>{{1,2},{3,5},{4},{6}}=>[2,1,5,4,3,6]=>01001
{{1,2,6},{3},{4,5}}=>{{1,3,6},{2},{4,5}}=>[3,2,6,5,4,1]=>00000
{{1,2},{3,6},{4,5}}=>{{1,2},{3,6},{4,5}}=>[2,1,6,5,4,3]=>01000
{{1,2},{3},{4,5,6}}=>{{1,2},{3},{4,5,6}}=>[2,1,3,5,6,4]=>01100
{{1,2},{3},{4,5},{6}}=>{{1,2},{3},{4,5},{6}}=>[2,1,3,5,4,6]=>01101
{{1,2,6},{3},{4},{5}}=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>00000
{{1,2},{3,6},{4},{5}}=>{{1,2},{3,6},{4},{5}}=>[2,1,6,4,5,3]=>01000
{{1,2},{3},{4,6},{5}}=>{{1,2},{3},{4,6},{5}}=>[2,1,3,6,5,4]=>01100
{{1,2},{3},{4},{5,6}}=>{{1,2},{3},{4},{5,6}}=>[2,1,3,4,6,5]=>01110
{{1,2},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6}}=>[2,1,3,4,5,6]=>01111
{{1,3,4,5,6},{2}}=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000
{{1,3,4,5},{2,6}}=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>00000
{{1,3,4,5},{2},{6}}=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>00001
{{1,3,4,6},{2,5}}=>{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>00000
{{1,3,4},{2,5,6}}=>{{1,4},{2,5,6},{3}}=>[4,5,3,1,6,2]=>00000
{{1,3,4},{2,5},{6}}=>{{1,4},{2,5},{3},{6}}=>[4,5,3,1,2,6]=>00001
{{1,3,4,6},{2},{5}}=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>00000
{{1,3,4},{2,6},{5}}=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>00000
{{1,3,4},{2},{5,6}}=>{{1,2,4},{3},{5,6}}=>[2,4,3,1,6,5]=>00010
{{1,3,4},{2},{5},{6}}=>{{1,2,4},{3},{5},{6}}=>[2,4,3,1,5,6]=>00011
{{1,3,5,6},{2,4}}=>{{1,5,6},{2,4},{3}}=>[5,4,3,2,6,1]=>00000
{{1,3,5},{2,4,6}}=>{{1,5},{2,4,6},{3}}=>[5,4,3,6,1,2]=>00000
{{1,3,5},{2,4},{6}}=>{{1,5},{2,4},{3},{6}}=>[5,4,3,2,1,6]=>00001
{{1,3,6},{2,4,5}}=>{{1,6},{2,4,5},{3}}=>[6,4,3,5,2,1]=>00000
{{1,3},{2,4,5,6}}=>{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>00000
{{1,3},{2,4,5},{6}}=>{{1,3},{2,4,5},{6}}=>[3,4,1,5,2,6]=>00001
{{1,3,6},{2,4},{5}}=>{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>00000
{{1,3},{2,4,6},{5}}=>{{1,3},{2,4,6},{5}}=>[3,4,1,6,5,2]=>00000
{{1,3},{2,4},{5,6}}=>{{1,3},{2,4},{5,6}}=>[3,4,1,2,6,5]=>00010
{{1,3},{2,4},{5},{6}}=>{{1,3},{2,4},{5},{6}}=>[3,4,1,2,5,6]=>00011
{{1,3,5,6},{2},{4}}=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>00000
{{1,3,5},{2,6},{4}}=>{{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>00000
{{1,3,5},{2},{4,6}}=>{{1,2,5},{3},{4,6}}=>[2,5,3,6,1,4]=>00000
{{1,3,5},{2},{4},{6}}=>{{1,2,5},{3},{4},{6}}=>[2,5,3,4,1,6]=>00001
{{1,3,6},{2,5},{4}}=>{{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>00000
{{1,3},{2,5,6},{4}}=>{{1,3},{2,5,6},{4}}=>[3,5,1,4,6,2]=>00000
{{1,3},{2,5},{4,6}}=>{{1,3},{2,5},{4,6}}=>[3,5,1,6,2,4]=>00000
{{1,3},{2,5},{4},{6}}=>{{1,3},{2,5},{4},{6}}=>[3,5,1,4,2,6]=>00001
{{1,3,6},{2},{4,5}}=>{{1,2,6},{3},{4,5}}=>[2,6,3,5,4,1]=>00000
{{1,3},{2,6},{4,5}}=>{{1,3},{2,6},{4,5}}=>[3,6,1,5,4,2]=>00000
{{1,3},{2},{4,5,6}}=>{{1,2,3},{4,5,6}}=>[2,3,1,5,6,4]=>00100
{{1,3},{2},{4,5},{6}}=>{{1,2,3},{4,5},{6}}=>[2,3,1,5,4,6]=>00101
{{1,3,6},{2},{4},{5}}=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>00000
{{1,3},{2,6},{4},{5}}=>{{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>00000
{{1,3},{2},{4,6},{5}}=>{{1,2,3},{4,6},{5}}=>[2,3,1,6,5,4]=>00100
{{1,3},{2},{4},{5,6}}=>{{1,2,3},{4},{5,6}}=>[2,3,1,4,6,5]=>00110
{{1,3},{2},{4},{5},{6}}=>{{1,2,3},{4},{5},{6}}=>[2,3,1,4,5,6]=>00111
{{1,4,5,6},{2,3}}=>{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>00000
{{1,4,5},{2,3,6}}=>{{1,5},{2,3,6},{4}}=>[5,3,6,4,1,2]=>00000
{{1,4,5},{2,3},{6}}=>{{1,4,5},{2,3},{6}}=>[4,3,2,5,1,6]=>00001
{{1,4,6},{2,3,5}}=>{{1,6},{2,3,5},{4}}=>[6,3,5,4,2,1]=>00000
{{1,4},{2,3,5,6}}=>{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>00000
{{1,4},{2,3,5},{6}}=>{{1,4},{2,3,5},{6}}=>[4,3,5,1,2,6]=>00001
{{1,4,6},{2,3},{5}}=>{{1,4,6},{2,3},{5}}=>[4,3,2,6,5,1]=>00000
{{1,4},{2,3,6},{5}}=>{{1,4},{2,3,6},{5}}=>[4,3,6,1,5,2]=>00000
{{1,4},{2,3},{5,6}}=>{{1,4},{2,3},{5,6}}=>[4,3,2,1,6,5]=>00010
{{1,4},{2,3},{5},{6}}=>{{1,4},{2,3},{5},{6}}=>[4,3,2,1,5,6]=>00011
{{1,5,6},{2,3,4}}=>{{1,5,6},{2,3,4}}=>[5,3,4,2,6,1]=>00000
{{1,5},{2,3,4,6}}=>{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>00000
{{1,5},{2,3,4},{6}}=>{{1,5},{2,3,4},{6}}=>[5,3,4,2,1,6]=>00001
{{1,6},{2,3,4,5}}=>{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>00000
{{1},{2,3,4,5,6}}=>{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000
{{1},{2,3,4,5},{6}}=>{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>10001
{{1,6},{2,3,4},{5}}=>{{1,6},{2,3,4},{5}}=>[6,3,4,2,5,1]=>00000
{{1},{2,3,4,6},{5}}=>{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>10000
{{1},{2,3,4},{5,6}}=>{{1},{2,3,4},{5,6}}=>[1,3,4,2,6,5]=>10010
{{1},{2,3,4},{5},{6}}=>{{1},{2,3,4},{5},{6}}=>[1,3,4,2,5,6]=>10011
{{1,5,6},{2,3},{4}}=>{{1,5,6},{2,3},{4}}=>[5,3,2,4,6,1]=>00000
{{1,5},{2,3,6},{4}}=>{{1,4,5},{2,3,6}}=>[4,3,6,5,1,2]=>00000
{{1,5},{2,3},{4,6}}=>{{1,5},{2,3},{4,6}}=>[5,3,2,6,1,4]=>00000
{{1,5},{2,3},{4},{6}}=>{{1,5},{2,3},{4},{6}}=>[5,3,2,4,1,6]=>00001
{{1,6},{2,3,5},{4}}=>{{1,4,6},{2,3,5}}=>[4,3,5,6,2,1]=>00000
{{1},{2,3,5,6},{4}}=>{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>10000
{{1},{2,3,5},{4,6}}=>{{1},{2,3,5},{4,6}}=>[1,3,5,6,2,4]=>10000
{{1},{2,3,5},{4},{6}}=>{{1},{2,3,5},{4},{6}}=>[1,3,5,4,2,6]=>10001
{{1,6},{2,3},{4,5}}=>{{1,6},{2,3},{4,5}}=>[6,3,2,5,4,1]=>00000
{{1},{2,3,6},{4,5}}=>{{1},{2,3,6},{4,5}}=>[1,3,6,5,4,2]=>10000
{{1},{2,3},{4,5,6}}=>{{1},{2,3},{4,5,6}}=>[1,3,2,5,6,4]=>10100
{{1},{2,3},{4,5},{6}}=>{{1},{2,3},{4,5},{6}}=>[1,3,2,5,4,6]=>10101
{{1,6},{2,3},{4},{5}}=>{{1,6},{2,3},{4},{5}}=>[6,3,2,4,5,1]=>00000
{{1},{2,3,6},{4},{5}}=>{{1},{2,3,6},{4},{5}}=>[1,3,6,4,5,2]=>10000
{{1},{2,3},{4,6},{5}}=>{{1},{2,3},{4,6},{5}}=>[1,3,2,6,5,4]=>10100
{{1},{2,3},{4},{5,6}}=>{{1},{2,3},{4},{5,6}}=>[1,3,2,4,6,5]=>10110
{{1},{2,3},{4},{5},{6}}=>{{1},{2,3},{4},{5},{6}}=>[1,3,2,4,5,6]=>10111
{{1,4,5,6},{2},{3}}=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000
{{1,4,5},{2,6},{3}}=>{{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>00000
{{1,4,5},{2},{3,6}}=>{{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>00000
{{1,4,5},{2},{3},{6}}=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>00001
{{1,4,6},{2,5},{3}}=>{{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>00000
{{1,4},{2,5,6},{3}}=>{{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>00000
{{1,4},{2,5},{3,6}}=>{{1,4},{2,5},{3,6}}=>[4,5,6,1,2,3]=>00000
{{1,4},{2,5},{3},{6}}=>{{1,3,4},{2,5},{6}}=>[3,5,4,1,2,6]=>00001
{{1,4,6},{2},{3,5}}=>{{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>00000
{{1,4},{2,6},{3,5}}=>{{1,4},{2,6},{3,5}}=>[4,6,5,1,3,2]=>00000
{{1,4},{2},{3,5,6}}=>{{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>00000
{{1,4},{2},{3,5},{6}}=>{{1,2,4},{3,5},{6}}=>[2,4,5,1,3,6]=>00001
{{1,4,6},{2},{3},{5}}=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>00000
{{1,4},{2,6},{3},{5}}=>{{1,3,4},{2,6},{5}}=>[3,6,4,1,5,2]=>00000
{{1,4},{2},{3,6},{5}}=>{{1,2,4},{3,6},{5}}=>[2,4,6,1,5,3]=>00000
{{1,4},{2},{3},{5,6}}=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>00010
{{1,4},{2},{3},{5},{6}}=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>00011
{{1,5,6},{2,4},{3}}=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>00000
{{1,5},{2,4,6},{3}}=>{{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>00000
{{1,5},{2,4},{3,6}}=>{{1,5},{2,4},{3,6}}=>[5,4,6,2,1,3]=>00000
{{1,5},{2,4},{3},{6}}=>{{1,3,5},{2,4},{6}}=>[3,4,5,2,1,6]=>00001
{{1,6},{2,4,5},{3}}=>{{1,3,6},{2,4,5}}=>[3,4,6,5,2,1]=>00000
{{1},{2,4,5,6},{3}}=>{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>10000
{{1},{2,4,5},{3,6}}=>{{1},{2,4,5},{3,6}}=>[1,4,6,5,2,3]=>10000
{{1},{2,4,5},{3},{6}}=>{{1},{2,4,5},{3},{6}}=>[1,4,3,5,2,6]=>10001
{{1,6},{2,4},{3,5}}=>{{1,6},{2,4},{3,5}}=>[6,4,5,2,3,1]=>00000
{{1},{2,4,6},{3,5}}=>{{1},{2,4,6},{3,5}}=>[1,4,5,6,3,2]=>10000
{{1},{2,4},{3,5,6}}=>{{1},{2,4},{3,5,6}}=>[1,4,5,2,6,3]=>10000
{{1},{2,4},{3,5},{6}}=>{{1},{2,4},{3,5},{6}}=>[1,4,5,2,3,6]=>10001
{{1,6},{2,4},{3},{5}}=>{{1,3,6},{2,4},{5}}=>[3,4,6,2,5,1]=>00000
{{1},{2,4,6},{3},{5}}=>{{1},{2,4,6},{3},{5}}=>[1,4,3,6,5,2]=>10000
{{1},{2,4},{3,6},{5}}=>{{1},{2,4},{3,6},{5}}=>[1,4,6,2,5,3]=>10000
{{1},{2,4},{3},{5,6}}=>{{1},{2,4},{3},{5,6}}=>[1,4,3,2,6,5]=>10010
{{1},{2,4},{3},{5},{6}}=>{{1},{2,4},{3},{5},{6}}=>[1,4,3,2,5,6]=>10011
{{1,5,6},{2},{3,4}}=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>00000
{{1,5},{2,6},{3,4}}=>{{1,5},{2,6},{3,4}}=>[5,6,4,3,1,2]=>00000
{{1,5},{2},{3,4,6}}=>{{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>00000
{{1,5},{2},{3,4},{6}}=>{{1,2,5},{3,4},{6}}=>[2,5,4,3,1,6]=>00001
{{1,6},{2,5},{3,4}}=>{{1,6},{2,5},{3,4}}=>[6,5,4,3,2,1]=>00000
{{1},{2,5,6},{3,4}}=>{{1},{2,5,6},{3,4}}=>[1,5,4,3,6,2]=>10000
{{1},{2,5},{3,4,6}}=>{{1},{2,5},{3,4,6}}=>[1,5,4,6,2,3]=>10000
{{1},{2,5},{3,4},{6}}=>{{1},{2,5},{3,4},{6}}=>[1,5,4,3,2,6]=>10001
{{1,6},{2},{3,4,5}}=>{{1,2,6},{3,4,5}}=>[2,6,4,5,3,1]=>00000
{{1},{2,6},{3,4,5}}=>{{1},{2,6},{3,4,5}}=>[1,6,4,5,3,2]=>10000
{{1},{2},{3,4,5,6}}=>{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>11000
{{1},{2},{3,4,5},{6}}=>{{1},{2},{3,4,5},{6}}=>[1,2,4,5,3,6]=>11001
{{1,6},{2},{3,4},{5}}=>{{1,2,6},{3,4},{5}}=>[2,6,4,3,5,1]=>00000
{{1},{2,6},{3,4},{5}}=>{{1},{2,6},{3,4},{5}}=>[1,6,4,3,5,2]=>10000
{{1},{2},{3,4,6},{5}}=>{{1},{2},{3,4,6},{5}}=>[1,2,4,6,5,3]=>11000
{{1},{2},{3,4},{5,6}}=>{{1},{2},{3,4},{5,6}}=>[1,2,4,3,6,5]=>11010
{{1},{2},{3,4},{5},{6}}=>{{1},{2},{3,4},{5},{6}}=>[1,2,4,3,5,6]=>11011
{{1,5,6},{2},{3},{4}}=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000
{{1,5},{2,6},{3},{4}}=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>00000
{{1,5},{2},{3,6},{4}}=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>00000
{{1,5},{2},{3},{4,6}}=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>00000
{{1,5},{2},{3},{4},{6}}=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001
{{1,6},{2,5},{3},{4}}=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>00000
{{1},{2,5,6},{3},{4}}=>{{1},{2,5,6},{3},{4}}=>[1,5,3,4,6,2]=>10000
{{1},{2,5},{3,6},{4}}=>{{1},{2,5},{3,6},{4}}=>[1,5,6,4,2,3]=>10000
{{1},{2,5},{3},{4,6}}=>{{1},{2,5},{3},{4,6}}=>[1,5,3,6,2,4]=>10000
{{1},{2,5},{3},{4},{6}}=>{{1},{2,5},{3},{4},{6}}=>[1,5,3,4,2,6]=>10001
{{1,6},{2},{3,5},{4}}=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>00000
{{1},{2,6},{3,5},{4}}=>{{1},{2,6},{3,5},{4}}=>[1,6,5,4,3,2]=>10000
{{1},{2},{3,5,6},{4}}=>{{1},{2},{3,5,6},{4}}=>[1,2,5,4,6,3]=>11000
{{1},{2},{3,5},{4,6}}=>{{1},{2},{3,5},{4,6}}=>[1,2,5,6,3,4]=>11000
{{1},{2},{3,5},{4},{6}}=>{{1},{2},{3,5},{4},{6}}=>[1,2,5,4,3,6]=>11001
{{1,6},{2},{3},{4,5}}=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>00000
{{1},{2,6},{3},{4,5}}=>{{1},{2,6},{3},{4,5}}=>[1,6,3,5,4,2]=>10000
{{1},{2},{3,6},{4,5}}=>{{1},{2},{3,6},{4,5}}=>[1,2,6,5,4,3]=>11000
{{1},{2},{3},{4,5,6}}=>{{1},{2},{3},{4,5,6}}=>[1,2,3,5,6,4]=>11100
{{1},{2},{3},{4,5},{6}}=>{{1},{2},{3},{4,5},{6}}=>[1,2,3,5,4,6]=>11101
{{1,6},{2},{3},{4},{5}}=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000
{{1},{2,6},{3},{4},{5}}=>{{1},{2,6},{3},{4},{5}}=>[1,6,3,4,5,2]=>10000
{{1},{2},{3,6},{4},{5}}=>{{1},{2},{3,6},{4},{5}}=>[1,2,6,4,5,3]=>11000
{{1},{2},{3},{4,6},{5}}=>{{1},{2},{3},{4,6},{5}}=>[1,2,3,6,5,4]=>11100
{{1},{2},{3},{4},{5,6}}=>{{1},{2},{3},{4},{5,6}}=>[1,2,3,4,6,5]=>11110
{{1},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5},{6}}=>[1,2,3,4,5,6]=>11111
{{1,2,3,4,5,6,7}}=>{{1,7},{2},{3},{4},{5},{6}}=>[7,2,3,4,5,6,1]=>000000
{{1,2,3,4,5,6},{7}}=>{{1,6},{2},{3},{4},{5},{7}}=>[6,2,3,4,5,1,7]=>000001
{{1,2,3,4,5,7},{6}}=>{{1,6,7},{2},{3},{4},{5}}=>[6,2,3,4,5,7,1]=>000000
{{1,2,3,4,5},{6,7}}=>{{1,5},{2},{3},{4},{6,7}}=>[5,2,3,4,1,7,6]=>000010
{{1,2,3,4,5},{6},{7}}=>{{1,5},{2},{3},{4},{6},{7}}=>[5,2,3,4,1,6,7]=>000011
{{1,2,3,4,6,7},{5}}=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>000000
{{1,2,3,4,6},{5,7}}=>{{1,6},{2},{3},{4},{5,7}}=>[6,2,3,4,7,1,5]=>000000
{{1,2,3,4,6},{5},{7}}=>{{1,5,6},{2},{3},{4},{7}}=>[5,2,3,4,6,1,7]=>000001
{{1,2,3,4,7},{5,6}}=>{{1,7},{2},{3},{4},{5,6}}=>[7,2,3,4,6,5,1]=>000000
{{1,2,3,4},{5,6,7}}=>{{1,4},{2},{3},{5,6,7}}=>[4,2,3,1,6,7,5]=>000100
{{1,2,3,4},{5,6},{7}}=>{{1,4},{2},{3},{5,6},{7}}=>[4,2,3,1,6,5,7]=>000101
{{1,2,3,4,7},{5},{6}}=>{{1,5,7},{2},{3},{4},{6}}=>[5,2,3,4,7,6,1]=>000000
{{1,2,3,4},{5,7},{6}}=>{{1,4},{2},{3},{5,7},{6}}=>[4,2,3,1,7,6,5]=>000100
{{1,2,3,4},{5},{6,7}}=>{{1,4},{2},{3},{5},{6,7}}=>[4,2,3,1,5,7,6]=>000110
{{1,2,3,4},{5},{6},{7}}=>{{1,4},{2},{3},{5},{6},{7}}=>[4,2,3,1,5,6,7]=>000111
{{1,2,3,5,6,7},{4}}=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000
{{1,2,3,5,6},{4,7}}=>{{1,6},{2},{3},{4,7},{5}}=>[6,2,3,7,5,1,4]=>000000
{{1,2,3,5,6},{4},{7}}=>{{1,4,5,6},{2},{3},{7}}=>[4,2,3,5,6,1,7]=>000001
{{1,2,3,5,7},{4,6}}=>{{1,7},{2},{3},{4,6},{5}}=>[7,2,3,6,5,4,1]=>000000
{{1,2,3,5},{4,6,7}}=>{{1,5},{2},{3},{4,6,7}}=>[5,2,3,6,1,7,4]=>000000
{{1,2,3,5},{4,6},{7}}=>{{1,5},{2},{3},{4,6},{7}}=>[5,2,3,6,1,4,7]=>000001
{{1,2,3,5,7},{4},{6}}=>{{1,4,5,7},{2},{3},{6}}=>[4,2,3,5,7,6,1]=>000000
{{1,2,3,5},{4,7},{6}}=>{{1,5},{2},{3},{4,7},{6}}=>[5,2,3,7,1,6,4]=>000000
{{1,2,3,5},{4},{6,7}}=>{{1,4,5},{2},{3},{6,7}}=>[4,2,3,5,1,7,6]=>000010
{{1,2,3,5},{4},{6},{7}}=>{{1,4,5},{2},{3},{6},{7}}=>[4,2,3,5,1,6,7]=>000011
{{1,2,3,6,7},{4,5}}=>{{1,6,7},{2},{3},{4,5}}=>[6,2,3,5,4,7,1]=>000000
{{1,2,3,6},{4,5,7}}=>{{1,6},{2},{3},{4,5,7}}=>[6,2,3,5,7,1,4]=>000000
{{1,2,3,6},{4,5},{7}}=>{{1,6},{2},{3},{4,5},{7}}=>[6,2,3,5,4,1,7]=>000001
{{1,2,3,7},{4,5,6}}=>{{1,7},{2},{3},{4,5,6}}=>[7,2,3,5,6,4,1]=>000000
{{1,2,3},{4,5,6,7}}=>{{1,3},{2},{4,5,6,7}}=>[3,2,1,5,6,7,4]=>001000
{{1,2,3},{4,5,6},{7}}=>{{1,3},{2},{4,5,6},{7}}=>[3,2,1,5,6,4,7]=>001001
{{1,2,3,7},{4,5},{6}}=>{{1,7},{2},{3},{4,5},{6}}=>[7,2,3,5,4,6,1]=>000000
{{1,2,3},{4,5,7},{6}}=>{{1,3},{2},{4,5,7},{6}}=>[3,2,1,5,7,6,4]=>001000
{{1,2,3},{4,5},{6,7}}=>{{1,3},{2},{4,5},{6,7}}=>[3,2,1,5,4,7,6]=>001010
{{1,2,3},{4,5},{6},{7}}=>{{1,3},{2},{4,5},{6},{7}}=>[3,2,1,5,4,6,7]=>001011
{{1,2,3,6,7},{4},{5}}=>{{1,4,6,7},{2},{3},{5}}=>[4,2,3,6,5,7,1]=>000000
{{1,2,3,6},{4,7},{5}}=>{{1,5,6},{2},{3},{4,7}}=>[5,2,3,7,6,1,4]=>000000
{{1,2,3,6},{4},{5,7}}=>{{1,4,6},{2},{3},{5,7}}=>[4,2,3,6,7,1,5]=>000000
{{1,2,3,6},{4},{5},{7}}=>{{1,4,6},{2},{3},{5},{7}}=>[4,2,3,6,5,1,7]=>000001
{{1,2,3,7},{4,6},{5}}=>{{1,5,7},{2},{3},{4,6}}=>[5,2,3,6,7,4,1]=>000000
{{1,2,3},{4,6,7},{5}}=>{{1,3},{2},{4,6,7},{5}}=>[3,2,1,6,5,7,4]=>001000
{{1,2,3},{4,6},{5,7}}=>{{1,3},{2},{4,6},{5,7}}=>[3,2,1,6,7,4,5]=>001000
{{1,2,3},{4,6},{5},{7}}=>{{1,3},{2},{4,6},{5},{7}}=>[3,2,1,6,5,4,7]=>001001
{{1,2,3,7},{4},{5,6}}=>{{1,4,7},{2},{3},{5,6}}=>[4,2,3,7,6,5,1]=>000000
{{1,2,3},{4,7},{5,6}}=>{{1,3},{2},{4,7},{5,6}}=>[3,2,1,7,6,5,4]=>001000
{{1,2,3},{4},{5,6,7}}=>{{1,3},{2},{4},{5,6,7}}=>[3,2,1,4,6,7,5]=>001100
{{1,2,3},{4},{5,6},{7}}=>{{1,3},{2},{4},{5,6},{7}}=>[3,2,1,4,6,5,7]=>001101
{{1,2,3,7},{4},{5},{6}}=>{{1,4,7},{2},{3},{5},{6}}=>[4,2,3,7,5,6,1]=>000000
{{1,2,3},{4,7},{5},{6}}=>{{1,3},{2},{4,7},{5},{6}}=>[3,2,1,7,5,6,4]=>001000
{{1,2,3},{4},{5,7},{6}}=>{{1,3},{2},{4},{5,7},{6}}=>[3,2,1,4,7,6,5]=>001100
{{1,2,3},{4},{5},{6,7}}=>{{1,3},{2},{4},{5},{6,7}}=>[3,2,1,4,5,7,6]=>001110
{{1,2,3},{4},{5},{6},{7}}=>{{1,3},{2},{4},{5},{6},{7}}=>[3,2,1,4,5,6,7]=>001111
{{1,2,4,5,6,7},{3}}=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000
{{1,2,4,5,6},{3,7}}=>{{1,6},{2},{3,7},{4},{5}}=>[6,2,7,4,5,1,3]=>000000
{{1,2,4,5,6},{3},{7}}=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001
{{1,2,4,5,7},{3,6}}=>{{1,7},{2},{3,6},{4},{5}}=>[7,2,6,4,5,3,1]=>000000
{{1,2,4,5},{3,6,7}}=>{{1,5},{2},{3,6,7},{4}}=>[5,2,6,4,1,7,3]=>000000
{{1,2,4,5},{3,6},{7}}=>{{1,5},{2},{3,6},{4},{7}}=>[5,2,6,4,1,3,7]=>000001
{{1,2,4,5,7},{3},{6}}=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000
{{1,2,4,5},{3,7},{6}}=>{{1,5},{2},{3,7},{4},{6}}=>[5,2,7,4,1,6,3]=>000000
{{1,2,4,5},{3},{6,7}}=>{{1,3,4,5},{2},{6,7}}=>[3,2,4,5,1,7,6]=>000010
{{1,2,4,5},{3},{6},{7}}=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>000011
{{1,2,4,6,7},{3,5}}=>{{1,6,7},{2},{3,5},{4}}=>[6,2,5,4,3,7,1]=>000000
{{1,2,4,6},{3,5,7}}=>{{1,6},{2},{3,5,7},{4}}=>[6,2,5,4,7,1,3]=>000000
{{1,2,4,6},{3,5},{7}}=>{{1,6},{2},{3,5},{4},{7}}=>[6,2,5,4,3,1,7]=>000001
{{1,2,4,7},{3,5,6}}=>{{1,7},{2},{3,5,6},{4}}=>[7,2,5,4,6,3,1]=>000000
{{1,2,4},{3,5,6,7}}=>{{1,4},{2},{3,5,6,7}}=>[4,2,5,1,6,7,3]=>000000
{{1,2,4},{3,5,6},{7}}=>{{1,4},{2},{3,5,6},{7}}=>[4,2,5,1,6,3,7]=>000001
{{1,2,4,7},{3,5},{6}}=>{{1,7},{2},{3,5},{4},{6}}=>[7,2,5,4,3,6,1]=>000000
{{1,2,4},{3,5,7},{6}}=>{{1,4},{2},{3,5,7},{6}}=>[4,2,5,1,7,6,3]=>000000
{{1,2,4},{3,5},{6,7}}=>{{1,4},{2},{3,5},{6,7}}=>[4,2,5,1,3,7,6]=>000010
{{1,2,4},{3,5},{6},{7}}=>{{1,4},{2},{3,5},{6},{7}}=>[4,2,5,1,3,6,7]=>000011
{{1,2,4,6,7},{3},{5}}=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000
{{1,2,4,6},{3,7},{5}}=>{{1,5,6},{2},{3,7},{4}}=>[5,2,7,4,6,1,3]=>000000
{{1,2,4,6},{3},{5,7}}=>{{1,3,4,6},{2},{5,7}}=>[3,2,4,6,7,1,5]=>000000
{{1,2,4,6},{3},{5},{7}}=>{{1,3,4,6},{2},{5},{7}}=>[3,2,4,6,5,1,7]=>000001
{{1,2,4,7},{3,6},{5}}=>{{1,5,7},{2},{3,6},{4}}=>[5,2,6,4,7,3,1]=>000000
{{1,2,4},{3,6,7},{5}}=>{{1,4},{2},{3,6,7},{5}}=>[4,2,6,1,5,7,3]=>000000
{{1,2,4},{3,6},{5,7}}=>{{1,4},{2},{3,6},{5,7}}=>[4,2,6,1,7,3,5]=>000000
{{1,2,4},{3,6},{5},{7}}=>{{1,4},{2},{3,6},{5},{7}}=>[4,2,6,1,5,3,7]=>000001
{{1,2,4,7},{3},{5,6}}=>{{1,3,4,7},{2},{5,6}}=>[3,2,4,7,6,5,1]=>000000
{{1,2,4},{3,7},{5,6}}=>{{1,4},{2},{3,7},{5,6}}=>[4,2,7,1,6,5,3]=>000000
{{1,2,4},{3},{5,6,7}}=>{{1,3,4},{2},{5,6,7}}=>[3,2,4,1,6,7,5]=>000100
{{1,2,4},{3},{5,6},{7}}=>{{1,3,4},{2},{5,6},{7}}=>[3,2,4,1,6,5,7]=>000101
{{1,2,4,7},{3},{5},{6}}=>{{1,3,4,7},{2},{5},{6}}=>[3,2,4,7,5,6,1]=>000000
{{1,2,4},{3,7},{5},{6}}=>{{1,4},{2},{3,7},{5},{6}}=>[4,2,7,1,5,6,3]=>000000
{{1,2,4},{3},{5,7},{6}}=>{{1,3,4},{2},{5,7},{6}}=>[3,2,4,1,7,6,5]=>000100
{{1,2,4},{3},{5},{6,7}}=>{{1,3,4},{2},{5},{6,7}}=>[3,2,4,1,5,7,6]=>000110
{{1,2,4},{3},{5},{6},{7}}=>{{1,3,4},{2},{5},{6},{7}}=>[3,2,4,1,5,6,7]=>000111
{{1,2,5,6,7},{3,4}}=>{{1,5,6,7},{2},{3,4}}=>[5,2,4,3,6,7,1]=>000000
{{1,2,5,6},{3,4,7}}=>{{1,6},{2},{3,4,7},{5}}=>[6,2,4,7,5,1,3]=>000000
{{1,2,5,6},{3,4},{7}}=>{{1,5,6},{2},{3,4},{7}}=>[5,2,4,3,6,1,7]=>000001
{{1,2,5,7},{3,4,6}}=>{{1,7},{2},{3,4,6},{5}}=>[7,2,4,6,5,3,1]=>000000
{{1,2,5},{3,4,6,7}}=>{{1,5},{2},{3,4,6,7}}=>[5,2,4,6,1,7,3]=>000000
{{1,2,5},{3,4,6},{7}}=>{{1,5},{2},{3,4,6},{7}}=>[5,2,4,6,1,3,7]=>000001
{{1,2,5,7},{3,4},{6}}=>{{1,5,7},{2},{3,4},{6}}=>[5,2,4,3,7,6,1]=>000000
{{1,2,5},{3,4,7},{6}}=>{{1,5},{2},{3,4,7},{6}}=>[5,2,4,7,1,6,3]=>000000
{{1,2,5},{3,4},{6,7}}=>{{1,5},{2},{3,4},{6,7}}=>[5,2,4,3,1,7,6]=>000010
{{1,2,5},{3,4},{6},{7}}=>{{1,5},{2},{3,4},{6},{7}}=>[5,2,4,3,1,6,7]=>000011
{{1,2,6,7},{3,4,5}}=>{{1,6,7},{2},{3,4,5}}=>[6,2,4,5,3,7,1]=>000000
{{1,2,6},{3,4,5,7}}=>{{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>000000
{{1,2,6},{3,4,5},{7}}=>{{1,6},{2},{3,4,5},{7}}=>[6,2,4,5,3,1,7]=>000001
{{1,2,7},{3,4,5,6}}=>{{1,7},{2},{3,4,5,6}}=>[7,2,4,5,6,3,1]=>000000
{{1,2},{3,4,5,6,7}}=>{{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000
{{1,2},{3,4,5,6},{7}}=>{{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>010001
{{1,2,7},{3,4,5},{6}}=>{{1,7},{2},{3,4,5},{6}}=>[7,2,4,5,3,6,1]=>000000
{{1,2},{3,4,5,7},{6}}=>{{1,2},{3,4,5,7},{6}}=>[2,1,4,5,7,6,3]=>010000
{{1,2},{3,4,5},{6,7}}=>{{1,2},{3,4,5},{6,7}}=>[2,1,4,5,3,7,6]=>010010
{{1,2},{3,4,5},{6},{7}}=>{{1,2},{3,4,5},{6},{7}}=>[2,1,4,5,3,6,7]=>010011
{{1,2,6,7},{3,4},{5}}=>{{1,6,7},{2},{3,4},{5}}=>[6,2,4,3,5,7,1]=>000000
{{1,2,6},{3,4,7},{5}}=>{{1,5,6},{2},{3,4,7}}=>[5,2,4,7,6,1,3]=>000000
{{1,2,6},{3,4},{5,7}}=>{{1,6},{2},{3,4},{5,7}}=>[6,2,4,3,7,1,5]=>000000
{{1,2,6},{3,4},{5},{7}}=>{{1,6},{2},{3,4},{5},{7}}=>[6,2,4,3,5,1,7]=>000001
{{1,2,7},{3,4,6},{5}}=>{{1,5,7},{2},{3,4,6}}=>[5,2,4,6,7,3,1]=>000000
{{1,2},{3,4,6,7},{5}}=>{{1,2},{3,4,6,7},{5}}=>[2,1,4,6,5,7,3]=>010000
{{1,2},{3,4,6},{5,7}}=>{{1,2},{3,4,6},{5,7}}=>[2,1,4,6,7,3,5]=>010000
{{1,2},{3,4,6},{5},{7}}=>{{1,2},{3,4,6},{5},{7}}=>[2,1,4,6,5,3,7]=>010001
{{1,2,7},{3,4},{5,6}}=>{{1,7},{2},{3,4},{5,6}}=>[7,2,4,3,6,5,1]=>000000
{{1,2},{3,4,7},{5,6}}=>{{1,2},{3,4,7},{5,6}}=>[2,1,4,7,6,5,3]=>010000
{{1,2},{3,4},{5,6,7}}=>{{1,2},{3,4},{5,6,7}}=>[2,1,4,3,6,7,5]=>010100
{{1,2},{3,4},{5,6},{7}}=>{{1,2},{3,4},{5,6},{7}}=>[2,1,4,3,6,5,7]=>010101
{{1,2,7},{3,4},{5},{6}}=>{{1,7},{2},{3,4},{5},{6}}=>[7,2,4,3,5,6,1]=>000000
{{1,2},{3,4,7},{5},{6}}=>{{1,2},{3,4,7},{5},{6}}=>[2,1,4,7,5,6,3]=>010000
{{1,2},{3,4},{5,7},{6}}=>{{1,2},{3,4},{5,7},{6}}=>[2,1,4,3,7,6,5]=>010100
{{1,2},{3,4},{5},{6,7}}=>{{1,2},{3,4},{5},{6,7}}=>[2,1,4,3,5,7,6]=>010110
{{1,2},{3,4},{5},{6},{7}}=>{{1,2},{3,4},{5},{6},{7}}=>[2,1,4,3,5,6,7]=>010111
{{1,2,5,6,7},{3},{4}}=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000
{{1,2,5,6},{3,7},{4}}=>{{1,4,5,6},{2},{3,7}}=>[4,2,7,5,6,1,3]=>000000
{{1,2,5,6},{3},{4,7}}=>{{1,3,5,6},{2},{4,7}}=>[3,2,5,7,6,1,4]=>000000
{{1,2,5,6},{3},{4},{7}}=>{{1,3,5,6},{2},{4},{7}}=>[3,2,5,4,6,1,7]=>000001
{{1,2,5,7},{3,6},{4}}=>{{1,4,5,7},{2},{3,6}}=>[4,2,6,5,7,3,1]=>000000
{{1,2,5},{3,6,7},{4}}=>{{1,4,5},{2},{3,6,7}}=>[4,2,6,5,1,7,3]=>000000
{{1,2,5},{3,6},{4,7}}=>{{1,5},{2},{3,6},{4,7}}=>[5,2,6,7,1,3,4]=>000000
{{1,2,5},{3,6},{4},{7}}=>{{1,4,5},{2},{3,6},{7}}=>[4,2,6,5,1,3,7]=>000001
{{1,2,5,7},{3},{4,6}}=>{{1,3,5,7},{2},{4,6}}=>[3,2,5,6,7,4,1]=>000000
{{1,2,5},{3,7},{4,6}}=>{{1,5},{2},{3,7},{4,6}}=>[5,2,7,6,1,4,3]=>000000
{{1,2,5},{3},{4,6,7}}=>{{1,3,5},{2},{4,6,7}}=>[3,2,5,6,1,7,4]=>000000
{{1,2,5},{3},{4,6},{7}}=>{{1,3,5},{2},{4,6},{7}}=>[3,2,5,6,1,4,7]=>000001
{{1,2,5,7},{3},{4},{6}}=>{{1,3,5,7},{2},{4},{6}}=>[3,2,5,4,7,6,1]=>000000
{{1,2,5},{3,7},{4},{6}}=>{{1,4,5},{2},{3,7},{6}}=>[4,2,7,5,1,6,3]=>000000
{{1,2,5},{3},{4,7},{6}}=>{{1,3,5},{2},{4,7},{6}}=>[3,2,5,7,1,6,4]=>000000
{{1,2,5},{3},{4},{6,7}}=>{{1,3,5},{2},{4},{6,7}}=>[3,2,5,4,1,7,6]=>000010
{{1,2,5},{3},{4},{6},{7}}=>{{1,3,5},{2},{4},{6},{7}}=>[3,2,5,4,1,6,7]=>000011
{{1,2,6,7},{3,5},{4}}=>{{1,4,6,7},{2},{3,5}}=>[4,2,5,6,3,7,1]=>000000
{{1,2,6},{3,5,7},{4}}=>{{1,4,6},{2},{3,5,7}}=>[4,2,5,6,7,1,3]=>000000
{{1,2,6},{3,5},{4,7}}=>{{1,6},{2},{3,5},{4,7}}=>[6,2,5,7,3,1,4]=>000000
{{1,2,6},{3,5},{4},{7}}=>{{1,4,6},{2},{3,5},{7}}=>[4,2,5,6,3,1,7]=>000001
{{1,2,7},{3,5,6},{4}}=>{{1,4,7},{2},{3,5,6}}=>[4,2,5,7,6,3,1]=>000000
{{1,2},{3,5,6,7},{4}}=>{{1,2},{3,5,6,7},{4}}=>[2,1,5,4,6,7,3]=>010000
{{1,2},{3,5,6},{4,7}}=>{{1,2},{3,5,6},{4,7}}=>[2,1,5,7,6,3,4]=>010000
{{1,2},{3,5,6},{4},{7}}=>{{1,2},{3,5,6},{4},{7}}=>[2,1,5,4,6,3,7]=>010001
{{1,2,7},{3,5},{4,6}}=>{{1,7},{2},{3,5},{4,6}}=>[7,2,5,6,3,4,1]=>000000
{{1,2},{3,5,7},{4,6}}=>{{1,2},{3,5,7},{4,6}}=>[2,1,5,6,7,4,3]=>010000
{{1,2},{3,5},{4,6,7}}=>{{1,2},{3,5},{4,6,7}}=>[2,1,5,6,3,7,4]=>010000
{{1,2},{3,5},{4,6},{7}}=>{{1,2},{3,5},{4,6},{7}}=>[2,1,5,6,3,4,7]=>010001
{{1,2,7},{3,5},{4},{6}}=>{{1,4,7},{2},{3,5},{6}}=>[4,2,5,7,3,6,1]=>000000
{{1,2},{3,5,7},{4},{6}}=>{{1,2},{3,5,7},{4},{6}}=>[2,1,5,4,7,6,3]=>010000
{{1,2},{3,5},{4,7},{6}}=>{{1,2},{3,5},{4,7},{6}}=>[2,1,5,7,3,6,4]=>010000
{{1,2},{3,5},{4},{6,7}}=>{{1,2},{3,5},{4},{6,7}}=>[2,1,5,4,3,7,6]=>010010
{{1,2},{3,5},{4},{6},{7}}=>{{1,2},{3,5},{4},{6},{7}}=>[2,1,5,4,3,6,7]=>010011
{{1,2,6,7},{3},{4,5}}=>{{1,3,6,7},{2},{4,5}}=>[3,2,6,5,4,7,1]=>000000
{{1,2,6},{3,7},{4,5}}=>{{1,6},{2},{3,7},{4,5}}=>[6,2,7,5,4,1,3]=>000000
{{1,2,6},{3},{4,5,7}}=>{{1,3,6},{2},{4,5,7}}=>[3,2,6,5,7,1,4]=>000000
{{1,2,6},{3},{4,5},{7}}=>{{1,3,6},{2},{4,5},{7}}=>[3,2,6,5,4,1,7]=>000001
{{1,2,7},{3,6},{4,5}}=>{{1,7},{2},{3,6},{4,5}}=>[7,2,6,5,4,3,1]=>000000
{{1,2},{3,6,7},{4,5}}=>{{1,2},{3,6,7},{4,5}}=>[2,1,6,5,4,7,3]=>010000
{{1,2},{3,6},{4,5,7}}=>{{1,2},{3,6},{4,5,7}}=>[2,1,6,5,7,3,4]=>010000
{{1,2},{3,6},{4,5},{7}}=>{{1,2},{3,6},{4,5},{7}}=>[2,1,6,5,4,3,7]=>010001
{{1,2,7},{3},{4,5,6}}=>{{1,3,7},{2},{4,5,6}}=>[3,2,7,5,6,4,1]=>000000
{{1,2},{3,7},{4,5,6}}=>{{1,2},{3,7},{4,5,6}}=>[2,1,7,5,6,4,3]=>010000
{{1,2},{3},{4,5,6,7}}=>{{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>011000
{{1,2},{3},{4,5,6},{7}}=>{{1,2},{3},{4,5,6},{7}}=>[2,1,3,5,6,4,7]=>011001
{{1,2,7},{3},{4,5},{6}}=>{{1,3,7},{2},{4,5},{6}}=>[3,2,7,5,4,6,1]=>000000
{{1,2},{3,7},{4,5},{6}}=>{{1,2},{3,7},{4,5},{6}}=>[2,1,7,5,4,6,3]=>010000
{{1,2},{3},{4,5,7},{6}}=>{{1,2},{3},{4,5,7},{6}}=>[2,1,3,5,7,6,4]=>011000
{{1,2},{3},{4,5},{6,7}}=>{{1,2},{3},{4,5},{6,7}}=>[2,1,3,5,4,7,6]=>011010
{{1,2},{3},{4,5},{6},{7}}=>{{1,2},{3},{4,5},{6},{7}}=>[2,1,3,5,4,6,7]=>011011
{{1,2,6,7},{3},{4},{5}}=>{{1,3,6,7},{2},{4},{5}}=>[3,2,6,4,5,7,1]=>000000
{{1,2,6},{3,7},{4},{5}}=>{{1,4,6},{2},{3,7},{5}}=>[4,2,7,6,5,1,3]=>000000
{{1,2,6},{3},{4,7},{5}}=>{{1,3,6},{2},{4,7},{5}}=>[3,2,6,7,5,1,4]=>000000
{{1,2,6},{3},{4},{5,7}}=>{{1,3,6},{2},{4},{5,7}}=>[3,2,6,4,7,1,5]=>000000
{{1,2,6},{3},{4},{5},{7}}=>{{1,3,6},{2},{4},{5},{7}}=>[3,2,6,4,5,1,7]=>000001
{{1,2,7},{3,6},{4},{5}}=>{{1,4,7},{2},{3,6},{5}}=>[4,2,6,7,5,3,1]=>000000
{{1,2},{3,6,7},{4},{5}}=>{{1,2},{3,6,7},{4},{5}}=>[2,1,6,4,5,7,3]=>010000
{{1,2},{3,6},{4,7},{5}}=>{{1,2},{3,6},{4,7},{5}}=>[2,1,6,7,5,3,4]=>010000
{{1,2},{3,6},{4},{5,7}}=>{{1,2},{3,6},{4},{5,7}}=>[2,1,6,4,7,3,5]=>010000
{{1,2},{3,6},{4},{5},{7}}=>{{1,2},{3,6},{4},{5},{7}}=>[2,1,6,4,5,3,7]=>010001
{{1,2,7},{3},{4,6},{5}}=>{{1,3,7},{2},{4,6},{5}}=>[3,2,7,6,5,4,1]=>000000
{{1,2},{3,7},{4,6},{5}}=>{{1,2},{3,7},{4,6},{5}}=>[2,1,7,6,5,4,3]=>010000
{{1,2},{3},{4,6,7},{5}}=>{{1,2},{3},{4,6,7},{5}}=>[2,1,3,6,5,7,4]=>011000
{{1,2},{3},{4,6},{5,7}}=>{{1,2},{3},{4,6},{5,7}}=>[2,1,3,6,7,4,5]=>011000
{{1,2},{3},{4,6},{5},{7}}=>{{1,2},{3},{4,6},{5},{7}}=>[2,1,3,6,5,4,7]=>011001
{{1,2,7},{3},{4},{5,6}}=>{{1,3,7},{2},{4},{5,6}}=>[3,2,7,4,6,5,1]=>000000
{{1,2},{3,7},{4},{5,6}}=>{{1,2},{3,7},{4},{5,6}}=>[2,1,7,4,6,5,3]=>010000
{{1,2},{3},{4,7},{5,6}}=>{{1,2},{3},{4,7},{5,6}}=>[2,1,3,7,6,5,4]=>011000
{{1,2},{3},{4},{5,6,7}}=>{{1,2},{3},{4},{5,6,7}}=>[2,1,3,4,6,7,5]=>011100
{{1,2},{3},{4},{5,6},{7}}=>{{1,2},{3},{4},{5,6},{7}}=>[2,1,3,4,6,5,7]=>011101
{{1,2,7},{3},{4},{5},{6}}=>{{1,3,7},{2},{4},{5},{6}}=>[3,2,7,4,5,6,1]=>000000
{{1,2},{3,7},{4},{5},{6}}=>{{1,2},{3,7},{4},{5},{6}}=>[2,1,7,4,5,6,3]=>010000
{{1,2},{3},{4,7},{5},{6}}=>{{1,2},{3},{4,7},{5},{6}}=>[2,1,3,7,5,6,4]=>011000
{{1,2},{3},{4},{5,7},{6}}=>{{1,2},{3},{4},{5,7},{6}}=>[2,1,3,4,7,6,5]=>011100
{{1,2},{3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5},{6,7}}=>[2,1,3,4,5,7,6]=>011110
{{1,2},{3},{4},{5},{6},{7}}=>{{1,2},{3},{4},{5},{6},{7}}=>[2,1,3,4,5,6,7]=>011111
{{1,3,4,5,6,7},{2}}=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000
{{1,3,4,5,6},{2,7}}=>{{1,6},{2,7},{3},{4},{5}}=>[6,7,3,4,5,1,2]=>000000
{{1,3,4,5,6},{2},{7}}=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001
{{1,3,4,5,7},{2,6}}=>{{1,7},{2,6},{3},{4},{5}}=>[7,6,3,4,5,2,1]=>000000
{{1,3,4,5},{2,6,7}}=>{{1,5},{2,6,7},{3},{4}}=>[5,6,3,4,1,7,2]=>000000
{{1,3,4,5},{2,6},{7}}=>{{1,5},{2,6},{3},{4},{7}}=>[5,6,3,4,1,2,7]=>000001
{{1,3,4,5,7},{2},{6}}=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000
{{1,3,4,5},{2,7},{6}}=>{{1,5},{2,7},{3},{4},{6}}=>[5,7,3,4,1,6,2]=>000000
{{1,3,4,5},{2},{6,7}}=>{{1,2,4,5},{3},{6,7}}=>[2,4,3,5,1,7,6]=>000010
{{1,3,4,5},{2},{6},{7}}=>{{1,2,4,5},{3},{6},{7}}=>[2,4,3,5,1,6,7]=>000011
{{1,3,4,6,7},{2,5}}=>{{1,6,7},{2,5},{3},{4}}=>[6,5,3,4,2,7,1]=>000000
{{1,3,4,6},{2,5,7}}=>{{1,6},{2,5,7},{3},{4}}=>[6,5,3,4,7,1,2]=>000000
{{1,3,4,6},{2,5},{7}}=>{{1,6},{2,5},{3},{4},{7}}=>[6,5,3,4,2,1,7]=>000001
{{1,3,4,7},{2,5,6}}=>{{1,7},{2,5,6},{3},{4}}=>[7,5,3,4,6,2,1]=>000000
{{1,3,4},{2,5,6,7}}=>{{1,4},{2,5,6,7},{3}}=>[4,5,3,1,6,7,2]=>000000
{{1,3,4},{2,5,6},{7}}=>{{1,4},{2,5,6},{3},{7}}=>[4,5,3,1,6,2,7]=>000001
{{1,3,4,7},{2,5},{6}}=>{{1,7},{2,5},{3},{4},{6}}=>[7,5,3,4,2,6,1]=>000000
{{1,3,4},{2,5,7},{6}}=>{{1,4},{2,5,7},{3},{6}}=>[4,5,3,1,7,6,2]=>000000
{{1,3,4},{2,5},{6,7}}=>{{1,4},{2,5},{3},{6,7}}=>[4,5,3,1,2,7,6]=>000010
{{1,3,4},{2,5},{6},{7}}=>{{1,4},{2,5},{3},{6},{7}}=>[4,5,3,1,2,6,7]=>000011
{{1,3,4,6,7},{2},{5}}=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000
{{1,3,4,6},{2,7},{5}}=>{{1,5,6},{2,7},{3},{4}}=>[5,7,3,4,6,1,2]=>000000
{{1,3,4,6},{2},{5,7}}=>{{1,2,4,6},{3},{5,7}}=>[2,4,3,6,7,1,5]=>000000
{{1,3,4,6},{2},{5},{7}}=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>000001
{{1,3,4,7},{2,6},{5}}=>{{1,5,7},{2,6},{3},{4}}=>[5,6,3,4,7,2,1]=>000000
{{1,3,4},{2,6,7},{5}}=>{{1,4},{2,6,7},{3},{5}}=>[4,6,3,1,5,7,2]=>000000
{{1,3,4},{2,6},{5,7}}=>{{1,4},{2,6},{3},{5,7}}=>[4,6,3,1,7,2,5]=>000000
{{1,3,4},{2,6},{5},{7}}=>{{1,4},{2,6},{3},{5},{7}}=>[4,6,3,1,5,2,7]=>000001
{{1,3,4,7},{2},{5,6}}=>{{1,2,4,7},{3},{5,6}}=>[2,4,3,7,6,5,1]=>000000
{{1,3,4},{2,7},{5,6}}=>{{1,4},{2,7},{3},{5,6}}=>[4,7,3,1,6,5,2]=>000000
{{1,3,4},{2},{5,6,7}}=>{{1,2,4},{3},{5,6,7}}=>[2,4,3,1,6,7,5]=>000100
{{1,3,4},{2},{5,6},{7}}=>{{1,2,4},{3},{5,6},{7}}=>[2,4,3,1,6,5,7]=>000101
{{1,3,4,7},{2},{5},{6}}=>{{1,2,4,7},{3},{5},{6}}=>[2,4,3,7,5,6,1]=>000000
{{1,3,4},{2,7},{5},{6}}=>{{1,4},{2,7},{3},{5},{6}}=>[4,7,3,1,5,6,2]=>000000
{{1,3,4},{2},{5,7},{6}}=>{{1,2,4},{3},{5,7},{6}}=>[2,4,3,1,7,6,5]=>000100
{{1,3,4},{2},{5},{6,7}}=>{{1,2,4},{3},{5},{6,7}}=>[2,4,3,1,5,7,6]=>000110
{{1,3,4},{2},{5},{6},{7}}=>{{1,2,4},{3},{5},{6},{7}}=>[2,4,3,1,5,6,7]=>000111
{{1,3,5,6,7},{2,4}}=>{{1,5,6,7},{2,4},{3}}=>[5,4,3,2,6,7,1]=>000000
{{1,3,5,6},{2,4,7}}=>{{1,6},{2,4,7},{3},{5}}=>[6,4,3,7,5,1,2]=>000000
{{1,3,5,6},{2,4},{7}}=>{{1,5,6},{2,4},{3},{7}}=>[5,4,3,2,6,1,7]=>000001
{{1,3,5,7},{2,4,6}}=>{{1,7},{2,4,6},{3},{5}}=>[7,4,3,6,5,2,1]=>000000
{{1,3,5},{2,4,6,7}}=>{{1,5},{2,4,6,7},{3}}=>[5,4,3,6,1,7,2]=>000000
{{1,3,5},{2,4,6},{7}}=>{{1,5},{2,4,6},{3},{7}}=>[5,4,3,6,1,2,7]=>000001
{{1,3,5,7},{2,4},{6}}=>{{1,5,7},{2,4},{3},{6}}=>[5,4,3,2,7,6,1]=>000000
{{1,3,5},{2,4,7},{6}}=>{{1,5},{2,4,7},{3},{6}}=>[5,4,3,7,1,6,2]=>000000
{{1,3,5},{2,4},{6,7}}=>{{1,5},{2,4},{3},{6,7}}=>[5,4,3,2,1,7,6]=>000010
{{1,3,5},{2,4},{6},{7}}=>{{1,5},{2,4},{3},{6},{7}}=>[5,4,3,2,1,6,7]=>000011
{{1,3,6,7},{2,4,5}}=>{{1,6,7},{2,4,5},{3}}=>[6,4,3,5,2,7,1]=>000000
{{1,3,6},{2,4,5,7}}=>{{1,6},{2,4,5,7},{3}}=>[6,4,3,5,7,1,2]=>000000
{{1,3,6},{2,4,5},{7}}=>{{1,6},{2,4,5},{3},{7}}=>[6,4,3,5,2,1,7]=>000001
{{1,3,7},{2,4,5,6}}=>{{1,7},{2,4,5,6},{3}}=>[7,4,3,5,6,2,1]=>000000
{{1,3},{2,4,5,6,7}}=>{{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000
{{1,3},{2,4,5,6},{7}}=>{{1,3},{2,4,5,6},{7}}=>[3,4,1,5,6,2,7]=>000001
{{1,3,7},{2,4,5},{6}}=>{{1,7},{2,4,5},{3},{6}}=>[7,4,3,5,2,6,1]=>000000
{{1,3},{2,4,5,7},{6}}=>{{1,3},{2,4,5,7},{6}}=>[3,4,1,5,7,6,2]=>000000
{{1,3},{2,4,5},{6,7}}=>{{1,3},{2,4,5},{6,7}}=>[3,4,1,5,2,7,6]=>000010
{{1,3},{2,4,5},{6},{7}}=>{{1,3},{2,4,5},{6},{7}}=>[3,4,1,5,2,6,7]=>000011
{{1,3,6,7},{2,4},{5}}=>{{1,6,7},{2,4},{3},{5}}=>[6,4,3,2,5,7,1]=>000000
{{1,3,6},{2,4,7},{5}}=>{{1,5,6},{2,4,7},{3}}=>[5,4,3,7,6,1,2]=>000000
{{1,3,6},{2,4},{5,7}}=>{{1,6},{2,4},{3},{5,7}}=>[6,4,3,2,7,1,5]=>000000
{{1,3,6},{2,4},{5},{7}}=>{{1,6},{2,4},{3},{5},{7}}=>[6,4,3,2,5,1,7]=>000001
{{1,3,7},{2,4,6},{5}}=>{{1,5,7},{2,4,6},{3}}=>[5,4,3,6,7,2,1]=>000000
{{1,3},{2,4,6,7},{5}}=>{{1,3},{2,4,6,7},{5}}=>[3,4,1,6,5,7,2]=>000000
{{1,3},{2,4,6},{5,7}}=>{{1,3},{2,4,6},{5,7}}=>[3,4,1,6,7,2,5]=>000000
{{1,3},{2,4,6},{5},{7}}=>{{1,3},{2,4,6},{5},{7}}=>[3,4,1,6,5,2,7]=>000001
{{1,3,7},{2,4},{5,6}}=>{{1,7},{2,4},{3},{5,6}}=>[7,4,3,2,6,5,1]=>000000
{{1,3},{2,4,7},{5,6}}=>{{1,3},{2,4,7},{5,6}}=>[3,4,1,7,6,5,2]=>000000
{{1,3},{2,4},{5,6,7}}=>{{1,3},{2,4},{5,6,7}}=>[3,4,1,2,6,7,5]=>000100
{{1,3},{2,4},{5,6},{7}}=>{{1,3},{2,4},{5,6},{7}}=>[3,4,1,2,6,5,7]=>000101
{{1,3,7},{2,4},{5},{6}}=>{{1,7},{2,4},{3},{5},{6}}=>[7,4,3,2,5,6,1]=>000000
{{1,3},{2,4,7},{5},{6}}=>{{1,3},{2,4,7},{5},{6}}=>[3,4,1,7,5,6,2]=>000000
{{1,3},{2,4},{5,7},{6}}=>{{1,3},{2,4},{5,7},{6}}=>[3,4,1,2,7,6,5]=>000100
{{1,3},{2,4},{5},{6,7}}=>{{1,3},{2,4},{5},{6,7}}=>[3,4,1,2,5,7,6]=>000110
{{1,3},{2,4},{5},{6},{7}}=>{{1,3},{2,4},{5},{6},{7}}=>[3,4,1,2,5,6,7]=>000111
{{1,3,5,6,7},{2},{4}}=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000
{{1,3,5,6},{2,7},{4}}=>{{1,4,5,6},{2,7},{3}}=>[4,7,3,5,6,1,2]=>000000
{{1,3,5,6},{2},{4,7}}=>{{1,2,5,6},{3},{4,7}}=>[2,5,3,7,6,1,4]=>000000
{{1,3,5,6},{2},{4},{7}}=>{{1,2,5,6},{3},{4},{7}}=>[2,5,3,4,6,1,7]=>000001
{{1,3,5,7},{2,6},{4}}=>{{1,4,5,7},{2,6},{3}}=>[4,6,3,5,7,2,1]=>000000
{{1,3,5},{2,6,7},{4}}=>{{1,4,5},{2,6,7},{3}}=>[4,6,3,5,1,7,2]=>000000
{{1,3,5},{2,6},{4,7}}=>{{1,5},{2,6},{3},{4,7}}=>[5,6,3,7,1,2,4]=>000000
{{1,3,5},{2,6},{4},{7}}=>{{1,4,5},{2,6},{3},{7}}=>[4,6,3,5,1,2,7]=>000001
{{1,3,5,7},{2},{4,6}}=>{{1,2,5,7},{3},{4,6}}=>[2,5,3,6,7,4,1]=>000000
{{1,3,5},{2,7},{4,6}}=>{{1,5},{2,7},{3},{4,6}}=>[5,7,3,6,1,4,2]=>000000
{{1,3,5},{2},{4,6,7}}=>{{1,2,5},{3},{4,6,7}}=>[2,5,3,6,1,7,4]=>000000
{{1,3,5},{2},{4,6},{7}}=>{{1,2,5},{3},{4,6},{7}}=>[2,5,3,6,1,4,7]=>000001
{{1,3,5,7},{2},{4},{6}}=>{{1,2,5,7},{3},{4},{6}}=>[2,5,3,4,7,6,1]=>000000
{{1,3,5},{2,7},{4},{6}}=>{{1,4,5},{2,7},{3},{6}}=>[4,7,3,5,1,6,2]=>000000
{{1,3,5},{2},{4,7},{6}}=>{{1,2,5},{3},{4,7},{6}}=>[2,5,3,7,1,6,4]=>000000
{{1,3,5},{2},{4},{6,7}}=>{{1,2,5},{3},{4},{6,7}}=>[2,5,3,4,1,7,6]=>000010
{{1,3,5},{2},{4},{6},{7}}=>{{1,2,5},{3},{4},{6},{7}}=>[2,5,3,4,1,6,7]=>000011
{{1,3,6,7},{2,5},{4}}=>{{1,4,6,7},{2,5},{3}}=>[4,5,3,6,2,7,1]=>000000
{{1,3,6},{2,5,7},{4}}=>{{1,4,6},{2,5,7},{3}}=>[4,5,3,6,7,1,2]=>000000
{{1,3,6},{2,5},{4,7}}=>{{1,6},{2,5},{3},{4,7}}=>[6,5,3,7,2,1,4]=>000000
{{1,3,6},{2,5},{4},{7}}=>{{1,4,6},{2,5},{3},{7}}=>[4,5,3,6,2,1,7]=>000001
{{1,3,7},{2,5,6},{4}}=>{{1,4,7},{2,5,6},{3}}=>[4,5,3,7,6,2,1]=>000000
{{1,3},{2,5,6,7},{4}}=>{{1,3},{2,5,6,7},{4}}=>[3,5,1,4,6,7,2]=>000000
{{1,3},{2,5,6},{4,7}}=>{{1,3},{2,5,6},{4,7}}=>[3,5,1,7,6,2,4]=>000000
{{1,3},{2,5,6},{4},{7}}=>{{1,3},{2,5,6},{4},{7}}=>[3,5,1,4,6,2,7]=>000001
{{1,3,7},{2,5},{4,6}}=>{{1,7},{2,5},{3},{4,6}}=>[7,5,3,6,2,4,1]=>000000
{{1,3},{2,5,7},{4,6}}=>{{1,3},{2,5,7},{4,6}}=>[3,5,1,6,7,4,2]=>000000
{{1,3},{2,5},{4,6,7}}=>{{1,3},{2,5},{4,6,7}}=>[3,5,1,6,2,7,4]=>000000
{{1,3},{2,5},{4,6},{7}}=>{{1,3},{2,5},{4,6},{7}}=>[3,5,1,6,2,4,7]=>000001
{{1,3,7},{2,5},{4},{6}}=>{{1,4,7},{2,5},{3},{6}}=>[4,5,3,7,2,6,1]=>000000
{{1,3},{2,5,7},{4},{6}}=>{{1,3},{2,5,7},{4},{6}}=>[3,5,1,4,7,6,2]=>000000
{{1,3},{2,5},{4,7},{6}}=>{{1,3},{2,5},{4,7},{6}}=>[3,5,1,7,2,6,4]=>000000
{{1,3},{2,5},{4},{6,7}}=>{{1,3},{2,5},{4},{6,7}}=>[3,5,1,4,2,7,6]=>000010
{{1,3},{2,5},{4},{6},{7}}=>{{1,3},{2,5},{4},{6},{7}}=>[3,5,1,4,2,6,7]=>000011
{{1,3,6,7},{2},{4,5}}=>{{1,2,6,7},{3},{4,5}}=>[2,6,3,5,4,7,1]=>000000
{{1,3,6},{2,7},{4,5}}=>{{1,6},{2,7},{3},{4,5}}=>[6,7,3,5,4,1,2]=>000000
{{1,3,6},{2},{4,5,7}}=>{{1,2,6},{3},{4,5,7}}=>[2,6,3,5,7,1,4]=>000000
{{1,3,6},{2},{4,5},{7}}=>{{1,2,6},{3},{4,5},{7}}=>[2,6,3,5,4,1,7]=>000001
{{1,3,7},{2,6},{4,5}}=>{{1,7},{2,6},{3},{4,5}}=>[7,6,3,5,4,2,1]=>000000
{{1,3},{2,6,7},{4,5}}=>{{1,3},{2,6,7},{4,5}}=>[3,6,1,5,4,7,2]=>000000
{{1,3},{2,6},{4,5,7}}=>{{1,3},{2,6},{4,5,7}}=>[3,6,1,5,7,2,4]=>000000
{{1,3},{2,6},{4,5},{7}}=>{{1,3},{2,6},{4,5},{7}}=>[3,6,1,5,4,2,7]=>000001
{{1,3,7},{2},{4,5,6}}=>{{1,2,7},{3},{4,5,6}}=>[2,7,3,5,6,4,1]=>000000
{{1,3},{2,7},{4,5,6}}=>{{1,3},{2,7},{4,5,6}}=>[3,7,1,5,6,4,2]=>000000
{{1,3},{2},{4,5,6,7}}=>{{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000
{{1,3},{2},{4,5,6},{7}}=>{{1,2,3},{4,5,6},{7}}=>[2,3,1,5,6,4,7]=>001001
{{1,3,7},{2},{4,5},{6}}=>{{1,2,7},{3},{4,5},{6}}=>[2,7,3,5,4,6,1]=>000000
{{1,3},{2,7},{4,5},{6}}=>{{1,3},{2,7},{4,5},{6}}=>[3,7,1,5,4,6,2]=>000000
{{1,3},{2},{4,5,7},{6}}=>{{1,2,3},{4,5,7},{6}}=>[2,3,1,5,7,6,4]=>001000
{{1,3},{2},{4,5},{6,7}}=>{{1,2,3},{4,5},{6,7}}=>[2,3,1,5,4,7,6]=>001010
{{1,3},{2},{4,5},{6},{7}}=>{{1,2,3},{4,5},{6},{7}}=>[2,3,1,5,4,6,7]=>001011
{{1,3,6,7},{2},{4},{5}}=>{{1,2,6,7},{3},{4},{5}}=>[2,6,3,4,5,7,1]=>000000
{{1,3,6},{2,7},{4},{5}}=>{{1,4,6},{2,7},{3},{5}}=>[4,7,3,6,5,1,2]=>000000
{{1,3,6},{2},{4,7},{5}}=>{{1,2,6},{3},{4,7},{5}}=>[2,6,3,7,5,1,4]=>000000
{{1,3,6},{2},{4},{5,7}}=>{{1,2,6},{3},{4},{5,7}}=>[2,6,3,4,7,1,5]=>000000
{{1,3,6},{2},{4},{5},{7}}=>{{1,2,6},{3},{4},{5},{7}}=>[2,6,3,4,5,1,7]=>000001
{{1,3,7},{2,6},{4},{5}}=>{{1,4,7},{2,6},{3},{5}}=>[4,6,3,7,5,2,1]=>000000
{{1,3},{2,6,7},{4},{5}}=>{{1,3},{2,6,7},{4},{5}}=>[3,6,1,4,5,7,2]=>000000
{{1,3},{2,6},{4,7},{5}}=>{{1,3},{2,6},{4,7},{5}}=>[3,6,1,7,5,2,4]=>000000
{{1,3},{2,6},{4},{5,7}}=>{{1,3},{2,6},{4},{5,7}}=>[3,6,1,4,7,2,5]=>000000
{{1,3},{2,6},{4},{5},{7}}=>{{1,3},{2,6},{4},{5},{7}}=>[3,6,1,4,5,2,7]=>000001
{{1,3,7},{2},{4,6},{5}}=>{{1,2,7},{3},{4,6},{5}}=>[2,7,3,6,5,4,1]=>000000
{{1,3},{2,7},{4,6},{5}}=>{{1,3},{2,7},{4,6},{5}}=>[3,7,1,6,5,4,2]=>000000
{{1,3},{2},{4,6,7},{5}}=>{{1,2,3},{4,6,7},{5}}=>[2,3,1,6,5,7,4]=>001000
{{1,3},{2},{4,6},{5,7}}=>{{1,2,3},{4,6},{5,7}}=>[2,3,1,6,7,4,5]=>001000
{{1,3},{2},{4,6},{5},{7}}=>{{1,2,3},{4,6},{5},{7}}=>[2,3,1,6,5,4,7]=>001001
{{1,3,7},{2},{4},{5,6}}=>{{1,2,7},{3},{4},{5,6}}=>[2,7,3,4,6,5,1]=>000000
{{1,3},{2,7},{4},{5,6}}=>{{1,3},{2,7},{4},{5,6}}=>[3,7,1,4,6,5,2]=>000000
{{1,3},{2},{4,7},{5,6}}=>{{1,2,3},{4,7},{5,6}}=>[2,3,1,7,6,5,4]=>001000
{{1,3},{2},{4},{5,6,7}}=>{{1,2,3},{4},{5,6,7}}=>[2,3,1,4,6,7,5]=>001100
{{1,3},{2},{4},{5,6},{7}}=>{{1,2,3},{4},{5,6},{7}}=>[2,3,1,4,6,5,7]=>001101
{{1,3,7},{2},{4},{5},{6}}=>{{1,2,7},{3},{4},{5},{6}}=>[2,7,3,4,5,6,1]=>000000
{{1,3},{2,7},{4},{5},{6}}=>{{1,3},{2,7},{4},{5},{6}}=>[3,7,1,4,5,6,2]=>000000
{{1,3},{2},{4,7},{5},{6}}=>{{1,2,3},{4,7},{5},{6}}=>[2,3,1,7,5,6,4]=>001000
{{1,3},{2},{4},{5,7},{6}}=>{{1,2,3},{4},{5,7},{6}}=>[2,3,1,4,7,6,5]=>001100
{{1,3},{2},{4},{5},{6,7}}=>{{1,2,3},{4},{5},{6,7}}=>[2,3,1,4,5,7,6]=>001110
{{1,3},{2},{4},{5},{6},{7}}=>{{1,2,3},{4},{5},{6},{7}}=>[2,3,1,4,5,6,7]=>001111
{{1,4,5,6,7},{2,3}}=>{{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000
{{1,4,5,6},{2,3,7}}=>{{1,6},{2,3,7},{4},{5}}=>[6,3,7,4,5,1,2]=>000000
{{1,4,5,6},{2,3},{7}}=>{{1,4,5,6},{2,3},{7}}=>[4,3,2,5,6,1,7]=>000001
{{1,4,5,7},{2,3,6}}=>{{1,7},{2,3,6},{4},{5}}=>[7,3,6,4,5,2,1]=>000000
{{1,4,5},{2,3,6,7}}=>{{1,5},{2,3,6,7},{4}}=>[5,3,6,4,1,7,2]=>000000
{{1,4,5},{2,3,6},{7}}=>{{1,5},{2,3,6},{4},{7}}=>[5,3,6,4,1,2,7]=>000001
{{1,4,5,7},{2,3},{6}}=>{{1,4,5,7},{2,3},{6}}=>[4,3,2,5,7,6,1]=>000000
{{1,4,5},{2,3,7},{6}}=>{{1,5},{2,3,7},{4},{6}}=>[5,3,7,4,1,6,2]=>000000
{{1,4,5},{2,3},{6,7}}=>{{1,4,5},{2,3},{6,7}}=>[4,3,2,5,1,7,6]=>000010
{{1,4,5},{2,3},{6},{7}}=>{{1,4,5},{2,3},{6},{7}}=>[4,3,2,5,1,6,7]=>000011
{{1,4,6,7},{2,3,5}}=>{{1,6,7},{2,3,5},{4}}=>[6,3,5,4,2,7,1]=>000000
{{1,4,6},{2,3,5,7}}=>{{1,6},{2,3,5,7},{4}}=>[6,3,5,4,7,1,2]=>000000
{{1,4,6},{2,3,5},{7}}=>{{1,6},{2,3,5},{4},{7}}=>[6,3,5,4,2,1,7]=>000001
{{1,4,7},{2,3,5,6}}=>{{1,7},{2,3,5,6},{4}}=>[7,3,5,4,6,2,1]=>000000
{{1,4},{2,3,5,6,7}}=>{{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000
{{1,4},{2,3,5,6},{7}}=>{{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>000001
{{1,4,7},{2,3,5},{6}}=>{{1,7},{2,3,5},{4},{6}}=>[7,3,5,4,2,6,1]=>000000
{{1,4},{2,3,5,7},{6}}=>{{1,4},{2,3,5,7},{6}}=>[4,3,5,1,7,6,2]=>000000
{{1,4},{2,3,5},{6,7}}=>{{1,4},{2,3,5},{6,7}}=>[4,3,5,1,2,7,6]=>000010
{{1,4},{2,3,5},{6},{7}}=>{{1,4},{2,3,5},{6},{7}}=>[4,3,5,1,2,6,7]=>000011
{{1,4,6,7},{2,3},{5}}=>{{1,4,6,7},{2,3},{5}}=>[4,3,2,6,5,7,1]=>000000
{{1,4,6},{2,3,7},{5}}=>{{1,5,6},{2,3,7},{4}}=>[5,3,7,4,6,1,2]=>000000
{{1,4,6},{2,3},{5,7}}=>{{1,4,6},{2,3},{5,7}}=>[4,3,2,6,7,1,5]=>000000
{{1,4,6},{2,3},{5},{7}}=>{{1,4,6},{2,3},{5},{7}}=>[4,3,2,6,5,1,7]=>000001
{{1,4,7},{2,3,6},{5}}=>{{1,5,7},{2,3,6},{4}}=>[5,3,6,4,7,2,1]=>000000
{{1,4},{2,3,6,7},{5}}=>{{1,4},{2,3,6,7},{5}}=>[4,3,6,1,5,7,2]=>000000
{{1,4},{2,3,6},{5,7}}=>{{1,4},{2,3,6},{5,7}}=>[4,3,6,1,7,2,5]=>000000
{{1,4},{2,3,6},{5},{7}}=>{{1,4},{2,3,6},{5},{7}}=>[4,3,6,1,5,2,7]=>000001
{{1,4,7},{2,3},{5,6}}=>{{1,4,7},{2,3},{5,6}}=>[4,3,2,7,6,5,1]=>000000
{{1,4},{2,3,7},{5,6}}=>{{1,4},{2,3,7},{5,6}}=>[4,3,7,1,6,5,2]=>000000
{{1,4},{2,3},{5,6,7}}=>{{1,4},{2,3},{5,6,7}}=>[4,3,2,1,6,7,5]=>000100
{{1,4},{2,3},{5,6},{7}}=>{{1,4},{2,3},{5,6},{7}}=>[4,3,2,1,6,5,7]=>000101
{{1,4,7},{2,3},{5},{6}}=>{{1,4,7},{2,3},{5},{6}}=>[4,3,2,7,5,6,1]=>000000
{{1,4},{2,3,7},{5},{6}}=>{{1,4},{2,3,7},{5},{6}}=>[4,3,7,1,5,6,2]=>000000
{{1,4},{2,3},{5,7},{6}}=>{{1,4},{2,3},{5,7},{6}}=>[4,3,2,1,7,6,5]=>000100
{{1,4},{2,3},{5},{6,7}}=>{{1,4},{2,3},{5},{6,7}}=>[4,3,2,1,5,7,6]=>000110
{{1,4},{2,3},{5},{6},{7}}=>{{1,4},{2,3},{5},{6},{7}}=>[4,3,2,1,5,6,7]=>000111
{{1,5,6,7},{2,3,4}}=>{{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000
{{1,5,6},{2,3,4,7}}=>{{1,6},{2,3,4,7},{5}}=>[6,3,4,7,5,1,2]=>000000
{{1,5,6},{2,3,4},{7}}=>{{1,5,6},{2,3,4},{7}}=>[5,3,4,2,6,1,7]=>000001
{{1,5,7},{2,3,4,6}}=>{{1,7},{2,3,4,6},{5}}=>[7,3,4,6,5,2,1]=>000000
{{1,5},{2,3,4,6,7}}=>{{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000
{{1,5},{2,3,4,6},{7}}=>{{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>000001
{{1,5,7},{2,3,4},{6}}=>{{1,5,7},{2,3,4},{6}}=>[5,3,4,2,7,6,1]=>000000
{{1,5},{2,3,4,7},{6}}=>{{1,5},{2,3,4,7},{6}}=>[5,3,4,7,1,6,2]=>000000
{{1,5},{2,3,4},{6,7}}=>{{1,5},{2,3,4},{6,7}}=>[5,3,4,2,1,7,6]=>000010
{{1,5},{2,3,4},{6},{7}}=>{{1,5},{2,3,4},{6},{7}}=>[5,3,4,2,1,6,7]=>000011
{{1,6,7},{2,3,4,5}}=>{{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000
{{1,6},{2,3,4,5,7}}=>{{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000
{{1,6},{2,3,4,5},{7}}=>{{1,6},{2,3,4,5},{7}}=>[6,3,4,5,2,1,7]=>000001
{{1,7},{2,3,4,5,6}}=>{{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000
{{1},{2,3,4,5,6,7}}=>{{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000
{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001
{{1,7},{2,3,4,5},{6}}=>{{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>000000
{{1},{2,3,4,5,7},{6}}=>{{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000
{{1},{2,3,4,5},{6,7}}=>{{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>100010
{{1},{2,3,4,5},{6},{7}}=>{{1},{2,3,4,5},{6},{7}}=>[1,3,4,5,2,6,7]=>100011
{{1,6,7},{2,3,4},{5}}=>{{1,6,7},{2,3,4},{5}}=>[6,3,4,2,5,7,1]=>000000
{{1,6},{2,3,4,7},{5}}=>{{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000
{{1,6},{2,3,4},{5,7}}=>{{1,6},{2,3,4},{5,7}}=>[6,3,4,2,7,1,5]=>000000
{{1,6},{2,3,4},{5},{7}}=>{{1,6},{2,3,4},{5},{7}}=>[6,3,4,2,5,1,7]=>000001
{{1,7},{2,3,4,6},{5}}=>{{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000
{{1},{2,3,4,6,7},{5}}=>{{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000
{{1},{2,3,4,6},{5,7}}=>{{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>100000
{{1},{2,3,4,6},{5},{7}}=>{{1},{2,3,4,6},{5},{7}}=>[1,3,4,6,5,2,7]=>100001
{{1,7},{2,3,4},{5,6}}=>{{1,7},{2,3,4},{5,6}}=>[7,3,4,2,6,5,1]=>000000
{{1},{2,3,4,7},{5,6}}=>{{1},{2,3,4,7},{5,6}}=>[1,3,4,7,6,5,2]=>100000
{{1},{2,3,4},{5,6,7}}=>{{1},{2,3,4},{5,6,7}}=>[1,3,4,2,6,7,5]=>100100
{{1},{2,3,4},{5,6},{7}}=>{{1},{2,3,4},{5,6},{7}}=>[1,3,4,2,6,5,7]=>100101
{{1,7},{2,3,4},{5},{6}}=>{{1,7},{2,3,4},{5},{6}}=>[7,3,4,2,5,6,1]=>000000
{{1},{2,3,4,7},{5},{6}}=>{{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>100000
{{1},{2,3,4},{5,7},{6}}=>{{1},{2,3,4},{5,7},{6}}=>[1,3,4,2,7,6,5]=>100100
{{1},{2,3,4},{5},{6,7}}=>{{1},{2,3,4},{5},{6,7}}=>[1,3,4,2,5,7,6]=>100110
{{1},{2,3,4},{5},{6},{7}}=>{{1},{2,3,4},{5},{6},{7}}=>[1,3,4,2,5,6,7]=>100111
{{1,5,6,7},{2,3},{4}}=>{{1,5,6,7},{2,3},{4}}=>[5,3,2,4,6,7,1]=>000000
{{1,5,6},{2,3,7},{4}}=>{{1,4,6},{2,3,7},{5}}=>[4,3,7,6,5,1,2]=>000000
{{1,5,6},{2,3},{4,7}}=>{{1,5,6},{2,3},{4,7}}=>[5,3,2,7,6,1,4]=>000000
{{1,5,6},{2,3},{4},{7}}=>{{1,5,6},{2,3},{4},{7}}=>[5,3,2,4,6,1,7]=>000001
{{1,5,7},{2,3,6},{4}}=>{{1,4,7},{2,3,6},{5}}=>[4,3,6,7,5,2,1]=>000000
{{1,5},{2,3,6,7},{4}}=>{{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000
{{1,5},{2,3,6},{4,7}}=>{{1,5},{2,3,6},{4,7}}=>[5,3,6,7,1,2,4]=>000000
{{1,5},{2,3,6},{4},{7}}=>{{1,4,5},{2,3,6},{7}}=>[4,3,6,5,1,2,7]=>000001
{{1,5,7},{2,3},{4,6}}=>{{1,5,7},{2,3},{4,6}}=>[5,3,2,6,7,4,1]=>000000
{{1,5},{2,3,7},{4,6}}=>{{1,5},{2,3,7},{4,6}}=>[5,3,7,6,1,4,2]=>000000
{{1,5},{2,3},{4,6,7}}=>{{1,5},{2,3},{4,6,7}}=>[5,3,2,6,1,7,4]=>000000
{{1,5},{2,3},{4,6},{7}}=>{{1,5},{2,3},{4,6},{7}}=>[5,3,2,6,1,4,7]=>000001
{{1,5,7},{2,3},{4},{6}}=>{{1,5,7},{2,3},{4},{6}}=>[5,3,2,4,7,6,1]=>000000
{{1,5},{2,3,7},{4},{6}}=>{{1,4,5},{2,3,7},{6}}=>[4,3,7,5,1,6,2]=>000000
{{1,5},{2,3},{4,7},{6}}=>{{1,5},{2,3},{4,7},{6}}=>[5,3,2,7,1,6,4]=>000000
{{1,5},{2,3},{4},{6,7}}=>{{1,5},{2,3},{4},{6,7}}=>[5,3,2,4,1,7,6]=>000010
{{1,5},{2,3},{4},{6},{7}}=>{{1,5},{2,3},{4},{6},{7}}=>[5,3,2,4,1,6,7]=>000011
{{1,6,7},{2,3,5},{4}}=>{{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000
{{1,6},{2,3,5,7},{4}}=>{{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000
{{1,6},{2,3,5},{4,7}}=>{{1,6},{2,3,5},{4,7}}=>[6,3,5,7,2,1,4]=>000000
{{1,6},{2,3,5},{4},{7}}=>{{1,4,6},{2,3,5},{7}}=>[4,3,5,6,2,1,7]=>000001
{{1,7},{2,3,5,6},{4}}=>{{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000
{{1},{2,3,5,6,7},{4}}=>{{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000
{{1},{2,3,5,6},{4,7}}=>{{1},{2,3,5,6},{4,7}}=>[1,3,5,7,6,2,4]=>100000
{{1},{2,3,5,6},{4},{7}}=>{{1},{2,3,5,6},{4},{7}}=>[1,3,5,4,6,2,7]=>100001
{{1,7},{2,3,5},{4,6}}=>{{1,7},{2,3,5},{4,6}}=>[7,3,5,6,2,4,1]=>000000
{{1},{2,3,5,7},{4,6}}=>{{1},{2,3,5,7},{4,6}}=>[1,3,5,6,7,4,2]=>100000
{{1},{2,3,5},{4,6,7}}=>{{1},{2,3,5},{4,6,7}}=>[1,3,5,6,2,7,4]=>100000
{{1},{2,3,5},{4,6},{7}}=>{{1},{2,3,5},{4,6},{7}}=>[1,3,5,6,2,4,7]=>100001
{{1,7},{2,3,5},{4},{6}}=>{{1,4,7},{2,3,5},{6}}=>[4,3,5,7,2,6,1]=>000000
{{1},{2,3,5,7},{4},{6}}=>{{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>100000
{{1},{2,3,5},{4,7},{6}}=>{{1},{2,3,5},{4,7},{6}}=>[1,3,5,7,2,6,4]=>100000
{{1},{2,3,5},{4},{6,7}}=>{{1},{2,3,5},{4},{6,7}}=>[1,3,5,4,2,7,6]=>100010
{{1},{2,3,5},{4},{6},{7}}=>{{1},{2,3,5},{4},{6},{7}}=>[1,3,5,4,2,6,7]=>100011
{{1,6,7},{2,3},{4,5}}=>{{1,6,7},{2,3},{4,5}}=>[6,3,2,5,4,7,1]=>000000
{{1,6},{2,3,7},{4,5}}=>{{1,6},{2,3,7},{4,5}}=>[6,3,7,5,4,1,2]=>000000
{{1,6},{2,3},{4,5,7}}=>{{1,6},{2,3},{4,5,7}}=>[6,3,2,5,7,1,4]=>000000
{{1,6},{2,3},{4,5},{7}}=>{{1,6},{2,3},{4,5},{7}}=>[6,3,2,5,4,1,7]=>000001
{{1,7},{2,3,6},{4,5}}=>{{1,7},{2,3,6},{4,5}}=>[7,3,6,5,4,2,1]=>000000
{{1},{2,3,6,7},{4,5}}=>{{1},{2,3,6,7},{4,5}}=>[1,3,6,5,4,7,2]=>100000
{{1},{2,3,6},{4,5,7}}=>{{1},{2,3,6},{4,5,7}}=>[1,3,6,5,7,2,4]=>100000
{{1},{2,3,6},{4,5},{7}}=>{{1},{2,3,6},{4,5},{7}}=>[1,3,6,5,4,2,7]=>100001
{{1,7},{2,3},{4,5,6}}=>{{1,7},{2,3},{4,5,6}}=>[7,3,2,5,6,4,1]=>000000
{{1},{2,3,7},{4,5,6}}=>{{1},{2,3,7},{4,5,6}}=>[1,3,7,5,6,4,2]=>100000
{{1},{2,3},{4,5,6,7}}=>{{1},{2,3},{4,5,6,7}}=>[1,3,2,5,6,7,4]=>101000
{{1},{2,3},{4,5,6},{7}}=>{{1},{2,3},{4,5,6},{7}}=>[1,3,2,5,6,4,7]=>101001
{{1,7},{2,3},{4,5},{6}}=>{{1,7},{2,3},{4,5},{6}}=>[7,3,2,5,4,6,1]=>000000
{{1},{2,3,7},{4,5},{6}}=>{{1},{2,3,7},{4,5},{6}}=>[1,3,7,5,4,6,2]=>100000
{{1},{2,3},{4,5,7},{6}}=>{{1},{2,3},{4,5,7},{6}}=>[1,3,2,5,7,6,4]=>101000
{{1},{2,3},{4,5},{6,7}}=>{{1},{2,3},{4,5},{6,7}}=>[1,3,2,5,4,7,6]=>101010
{{1},{2,3},{4,5},{6},{7}}=>{{1},{2,3},{4,5},{6},{7}}=>[1,3,2,5,4,6,7]=>101011
{{1,6,7},{2,3},{4},{5}}=>{{1,6,7},{2,3},{4},{5}}=>[6,3,2,4,5,7,1]=>000000
{{1,6},{2,3,7},{4},{5}}=>{{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000
{{1,6},{2,3},{4,7},{5}}=>{{1,6},{2,3},{4,7},{5}}=>[6,3,2,7,5,1,4]=>000000
{{1,6},{2,3},{4},{5,7}}=>{{1,6},{2,3},{4},{5,7}}=>[6,3,2,4,7,1,5]=>000000
{{1,6},{2,3},{4},{5},{7}}=>{{1,6},{2,3},{4},{5},{7}}=>[6,3,2,4,5,1,7]=>000001
{{1,7},{2,3,6},{4},{5}}=>{{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000
{{1},{2,3,6,7},{4},{5}}=>{{1},{2,3,6,7},{4},{5}}=>[1,3,6,4,5,7,2]=>100000
{{1},{2,3,6},{4,7},{5}}=>{{1},{2,3,6},{4,7},{5}}=>[1,3,6,7,5,2,4]=>100000
{{1},{2,3,6},{4},{5,7}}=>{{1},{2,3,6},{4},{5,7}}=>[1,3,6,4,7,2,5]=>100000
{{1},{2,3,6},{4},{5},{7}}=>{{1},{2,3,6},{4},{5},{7}}=>[1,3,6,4,5,2,7]=>100001
{{1,7},{2,3},{4,6},{5}}=>{{1,7},{2,3},{4,6},{5}}=>[7,3,2,6,5,4,1]=>000000
{{1},{2,3,7},{4,6},{5}}=>{{1},{2,3,7},{4,6},{5}}=>[1,3,7,6,5,4,2]=>100000
{{1},{2,3},{4,6,7},{5}}=>{{1},{2,3},{4,6,7},{5}}=>[1,3,2,6,5,7,4]=>101000
{{1},{2,3},{4,6},{5,7}}=>{{1},{2,3},{4,6},{5,7}}=>[1,3,2,6,7,4,5]=>101000
{{1},{2,3},{4,6},{5},{7}}=>{{1},{2,3},{4,6},{5},{7}}=>[1,3,2,6,5,4,7]=>101001
{{1,7},{2,3},{4},{5,6}}=>{{1,7},{2,3},{4},{5,6}}=>[7,3,2,4,6,5,1]=>000000
{{1},{2,3,7},{4},{5,6}}=>{{1},{2,3,7},{4},{5,6}}=>[1,3,7,4,6,5,2]=>100000
{{1},{2,3},{4,7},{5,6}}=>{{1},{2,3},{4,7},{5,6}}=>[1,3,2,7,6,5,4]=>101000
{{1},{2,3},{4},{5,6,7}}=>{{1},{2,3},{4},{5,6,7}}=>[1,3,2,4,6,7,5]=>101100
{{1},{2,3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5,6},{7}}=>[1,3,2,4,6,5,7]=>101101
{{1,7},{2,3},{4},{5},{6}}=>{{1,7},{2,3},{4},{5},{6}}=>[7,3,2,4,5,6,1]=>000000
{{1},{2,3,7},{4},{5},{6}}=>{{1},{2,3,7},{4},{5},{6}}=>[1,3,7,4,5,6,2]=>100000
{{1},{2,3},{4,7},{5},{6}}=>{{1},{2,3},{4,7},{5},{6}}=>[1,3,2,7,5,6,4]=>101000
{{1},{2,3},{4},{5,7},{6}}=>{{1},{2,3},{4},{5,7},{6}}=>[1,3,2,4,7,6,5]=>101100
{{1},{2,3},{4},{5},{6,7}}=>{{1},{2,3},{4},{5},{6,7}}=>[1,3,2,4,5,7,6]=>101110
{{1},{2,3},{4},{5},{6},{7}}=>{{1},{2,3},{4},{5},{6},{7}}=>[1,3,2,4,5,6,7]=>101111
{{1,4,5,6,7},{2},{3}}=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000
{{1,4,5,6},{2,7},{3}}=>{{1,3,5,6},{2,7},{4}}=>[3,7,5,4,6,1,2]=>000000
{{1,4,5,6},{2},{3,7}}=>{{1,2,5,6},{3,7},{4}}=>[2,5,7,4,6,1,3]=>000000
{{1,4,5,6},{2},{3},{7}}=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001
{{1,4,5,7},{2,6},{3}}=>{{1,3,5,7},{2,6},{4}}=>[3,6,5,4,7,2,1]=>000000
{{1,4,5},{2,6,7},{3}}=>{{1,3,5},{2,6,7},{4}}=>[3,6,5,4,1,7,2]=>000000
{{1,4,5},{2,6},{3,7}}=>{{1,5},{2,6},{3,7},{4}}=>[5,6,7,4,1,2,3]=>000000
{{1,4,5},{2,6},{3},{7}}=>{{1,3,5},{2,6},{4},{7}}=>[3,6,5,4,1,2,7]=>000001
{{1,4,5,7},{2},{3,6}}=>{{1,2,5,7},{3,6},{4}}=>[2,5,6,4,7,3,1]=>000000
{{1,4,5},{2,7},{3,6}}=>{{1,5},{2,7},{3,6},{4}}=>[5,7,6,4,1,3,2]=>000000
{{1,4,5},{2},{3,6,7}}=>{{1,2,5},{3,6,7},{4}}=>[2,5,6,4,1,7,3]=>000000
{{1,4,5},{2},{3,6},{7}}=>{{1,2,5},{3,6},{4},{7}}=>[2,5,6,4,1,3,7]=>000001
{{1,4,5,7},{2},{3},{6}}=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000
{{1,4,5},{2,7},{3},{6}}=>{{1,3,5},{2,7},{4},{6}}=>[3,7,5,4,1,6,2]=>000000
{{1,4,5},{2},{3,7},{6}}=>{{1,2,5},{3,7},{4},{6}}=>[2,5,7,4,1,6,3]=>000000
{{1,4,5},{2},{3},{6,7}}=>{{1,2,3,5},{4},{6,7}}=>[2,3,5,4,1,7,6]=>000010
{{1,4,5},{2},{3},{6},{7}}=>{{1,2,3,5},{4},{6},{7}}=>[2,3,5,4,1,6,7]=>000011
{{1,4,6,7},{2,5},{3}}=>{{1,3,6,7},{2,5},{4}}=>[3,5,6,4,2,7,1]=>000000
{{1,4,6},{2,5,7},{3}}=>{{1,3,6},{2,5,7},{4}}=>[3,5,6,4,7,1,2]=>000000
{{1,4,6},{2,5},{3,7}}=>{{1,6},{2,5},{3,7},{4}}=>[6,5,7,4,2,1,3]=>000000
{{1,4,6},{2,5},{3},{7}}=>{{1,3,6},{2,5},{4},{7}}=>[3,5,6,4,2,1,7]=>000001
{{1,4,7},{2,5,6},{3}}=>{{1,3,7},{2,5,6},{4}}=>[3,5,7,4,6,2,1]=>000000
{{1,4},{2,5,6,7},{3}}=>{{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000
{{1,4},{2,5,6},{3,7}}=>{{1,4},{2,5,6},{3,7}}=>[4,5,7,1,6,2,3]=>000000
{{1,4},{2,5,6},{3},{7}}=>{{1,3,4},{2,5,6},{7}}=>[3,5,4,1,6,2,7]=>000001
{{1,4,7},{2,5},{3,6}}=>{{1,7},{2,5},{3,6},{4}}=>[7,5,6,4,2,3,1]=>000000
{{1,4},{2,5,7},{3,6}}=>{{1,4},{2,5,7},{3,6}}=>[4,5,6,1,7,3,2]=>000000
{{1,4},{2,5},{3,6,7}}=>{{1,4},{2,5},{3,6,7}}=>[4,5,6,1,2,7,3]=>000000
{{1,4},{2,5},{3,6},{7}}=>{{1,4},{2,5},{3,6},{7}}=>[4,5,6,1,2,3,7]=>000001
{{1,4,7},{2,5},{3},{6}}=>{{1,3,7},{2,5},{4},{6}}=>[3,5,7,4,2,6,1]=>000000
{{1,4},{2,5,7},{3},{6}}=>{{1,3,4},{2,5,7},{6}}=>[3,5,4,1,7,6,2]=>000000
{{1,4},{2,5},{3,7},{6}}=>{{1,4},{2,5},{3,7},{6}}=>[4,5,7,1,2,6,3]=>000000
{{1,4},{2,5},{3},{6,7}}=>{{1,3,4},{2,5},{6,7}}=>[3,5,4,1,2,7,6]=>000010
{{1,4},{2,5},{3},{6},{7}}=>{{1,3,4},{2,5},{6},{7}}=>[3,5,4,1,2,6,7]=>000011
{{1,4,6,7},{2},{3,5}}=>{{1,2,6,7},{3,5},{4}}=>[2,6,5,4,3,7,1]=>000000
{{1,4,6},{2,7},{3,5}}=>{{1,6},{2,7},{3,5},{4}}=>[6,7,5,4,3,1,2]=>000000
{{1,4,6},{2},{3,5,7}}=>{{1,2,6},{3,5,7},{4}}=>[2,6,5,4,7,1,3]=>000000
{{1,4,6},{2},{3,5},{7}}=>{{1,2,6},{3,5},{4},{7}}=>[2,6,5,4,3,1,7]=>000001
{{1,4,7},{2,6},{3,5}}=>{{1,7},{2,6},{3,5},{4}}=>[7,6,5,4,3,2,1]=>000000
{{1,4},{2,6,7},{3,5}}=>{{1,4},{2,6,7},{3,5}}=>[4,6,5,1,3,7,2]=>000000
{{1,4},{2,6},{3,5,7}}=>{{1,4},{2,6},{3,5,7}}=>[4,6,5,1,7,2,3]=>000000
{{1,4},{2,6},{3,5},{7}}=>{{1,4},{2,6},{3,5},{7}}=>[4,6,5,1,3,2,7]=>000001
{{1,4,7},{2},{3,5,6}}=>{{1,2,7},{3,5,6},{4}}=>[2,7,5,4,6,3,1]=>000000
{{1,4},{2,7},{3,5,6}}=>{{1,4},{2,7},{3,5,6}}=>[4,7,5,1,6,3,2]=>000000
{{1,4},{2},{3,5,6,7}}=>{{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000
{{1,4},{2},{3,5,6},{7}}=>{{1,2,4},{3,5,6},{7}}=>[2,4,5,1,6,3,7]=>000001
{{1,4,7},{2},{3,5},{6}}=>{{1,2,7},{3,5},{4},{6}}=>[2,7,5,4,3,6,1]=>000000
{{1,4},{2,7},{3,5},{6}}=>{{1,4},{2,7},{3,5},{6}}=>[4,7,5,1,3,6,2]=>000000
{{1,4},{2},{3,5,7},{6}}=>{{1,2,4},{3,5,7},{6}}=>[2,4,5,1,7,6,3]=>000000
{{1,4},{2},{3,5},{6,7}}=>{{1,2,4},{3,5},{6,7}}=>[2,4,5,1,3,7,6]=>000010
{{1,4},{2},{3,5},{6},{7}}=>{{1,2,4},{3,5},{6},{7}}=>[2,4,5,1,3,6,7]=>000011
{{1,4,6,7},{2},{3},{5}}=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000
{{1,4,6},{2,7},{3},{5}}=>{{1,3,6},{2,7},{4},{5}}=>[3,7,6,4,5,1,2]=>000000
{{1,4,6},{2},{3,7},{5}}=>{{1,2,6},{3,7},{4},{5}}=>[2,6,7,4,5,1,3]=>000000
{{1,4,6},{2},{3},{5,7}}=>{{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>000000
{{1,4,6},{2},{3},{5},{7}}=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>000001
{{1,4,7},{2,6},{3},{5}}=>{{1,3,7},{2,6},{4},{5}}=>[3,6,7,4,5,2,1]=>000000
{{1,4},{2,6,7},{3},{5}}=>{{1,3,4},{2,6,7},{5}}=>[3,6,4,1,5,7,2]=>000000
{{1,4},{2,6},{3,7},{5}}=>{{1,4},{2,6},{3,7},{5}}=>[4,6,7,1,5,2,3]=>000000
{{1,4},{2,6},{3},{5,7}}=>{{1,3,4},{2,6},{5,7}}=>[3,6,4,1,7,2,5]=>000000
{{1,4},{2,6},{3},{5},{7}}=>{{1,3,4},{2,6},{5},{7}}=>[3,6,4,1,5,2,7]=>000001
{{1,4,7},{2},{3,6},{5}}=>{{1,2,7},{3,6},{4},{5}}=>[2,7,6,4,5,3,1]=>000000
{{1,4},{2,7},{3,6},{5}}=>{{1,4},{2,7},{3,6},{5}}=>[4,7,6,1,5,3,2]=>000000
{{1,4},{2},{3,6,7},{5}}=>{{1,2,4},{3,6,7},{5}}=>[2,4,6,1,5,7,3]=>000000
{{1,4},{2},{3,6},{5,7}}=>{{1,2,4},{3,6},{5,7}}=>[2,4,6,1,7,3,5]=>000000
{{1,4},{2},{3,6},{5},{7}}=>{{1,2,4},{3,6},{5},{7}}=>[2,4,6,1,5,3,7]=>000001
{{1,4,7},{2},{3},{5,6}}=>{{1,2,3,7},{4},{5,6}}=>[2,3,7,4,6,5,1]=>000000
{{1,4},{2,7},{3},{5,6}}=>{{1,3,4},{2,7},{5,6}}=>[3,7,4,1,6,5,2]=>000000
{{1,4},{2},{3,7},{5,6}}=>{{1,2,4},{3,7},{5,6}}=>[2,4,7,1,6,5,3]=>000000
{{1,4},{2},{3},{5,6,7}}=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100
{{1,4},{2},{3},{5,6},{7}}=>{{1,2,3,4},{5,6},{7}}=>[2,3,4,1,6,5,7]=>000101
{{1,4,7},{2},{3},{5},{6}}=>{{1,2,3,7},{4},{5},{6}}=>[2,3,7,4,5,6,1]=>000000
{{1,4},{2,7},{3},{5},{6}}=>{{1,3,4},{2,7},{5},{6}}=>[3,7,4,1,5,6,2]=>000000
{{1,4},{2},{3,7},{5},{6}}=>{{1,2,4},{3,7},{5},{6}}=>[2,4,7,1,5,6,3]=>000000
{{1,4},{2},{3},{5,7},{6}}=>{{1,2,3,4},{5,7},{6}}=>[2,3,4,1,7,6,5]=>000100
{{1,4},{2},{3},{5},{6,7}}=>{{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>000110
{{1,4},{2},{3},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>000111
{{1,5,6,7},{2,4},{3}}=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000
{{1,5,6},{2,4,7},{3}}=>{{1,3,6},{2,4,7},{5}}=>[3,4,6,7,5,1,2]=>000000
{{1,5,6},{2,4},{3,7}}=>{{1,5,6},{2,4},{3,7}}=>[5,4,7,2,6,1,3]=>000000
{{1,5,6},{2,4},{3},{7}}=>{{1,3,5,6},{2,4},{7}}=>[3,4,5,2,6,1,7]=>000001
{{1,5,7},{2,4,6},{3}}=>{{1,3,7},{2,4,6},{5}}=>[3,4,7,6,5,2,1]=>000000
{{1,5},{2,4,6,7},{3}}=>{{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000
{{1,5},{2,4,6},{3,7}}=>{{1,5},{2,4,6},{3,7}}=>[5,4,7,6,1,2,3]=>000000
{{1,5},{2,4,6},{3},{7}}=>{{1,3,5},{2,4,6},{7}}=>[3,4,5,6,1,2,7]=>000001
{{1,5,7},{2,4},{3,6}}=>{{1,5,7},{2,4},{3,6}}=>[5,4,6,2,7,3,1]=>000000
{{1,5},{2,4,7},{3,6}}=>{{1,5},{2,4,7},{3,6}}=>[5,4,6,7,1,3,2]=>000000
{{1,5},{2,4},{3,6,7}}=>{{1,5},{2,4},{3,6,7}}=>[5,4,6,2,1,7,3]=>000000
{{1,5},{2,4},{3,6},{7}}=>{{1,5},{2,4},{3,6},{7}}=>[5,4,6,2,1,3,7]=>000001
{{1,5,7},{2,4},{3},{6}}=>{{1,3,5,7},{2,4},{6}}=>[3,4,5,2,7,6,1]=>000000
{{1,5},{2,4,7},{3},{6}}=>{{1,3,5},{2,4,7},{6}}=>[3,4,5,7,1,6,2]=>000000
{{1,5},{2,4},{3,7},{6}}=>{{1,5},{2,4},{3,7},{6}}=>[5,4,7,2,1,6,3]=>000000
{{1,5},{2,4},{3},{6,7}}=>{{1,3,5},{2,4},{6,7}}=>[3,4,5,2,1,7,6]=>000010
{{1,5},{2,4},{3},{6},{7}}=>{{1,3,5},{2,4},{6},{7}}=>[3,4,5,2,1,6,7]=>000011
{{1,6,7},{2,4,5},{3}}=>{{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000
{{1,6},{2,4,5,7},{3}}=>{{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000
{{1,6},{2,4,5},{3,7}}=>{{1,6},{2,4,5},{3,7}}=>[6,4,7,5,2,1,3]=>000000
{{1,6},{2,4,5},{3},{7}}=>{{1,3,6},{2,4,5},{7}}=>[3,4,6,5,2,1,7]=>000001
{{1,7},{2,4,5,6},{3}}=>{{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000
{{1},{2,4,5,6,7},{3}}=>{{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000
{{1},{2,4,5,6},{3,7}}=>{{1},{2,4,5,6},{3,7}}=>[1,4,7,5,6,2,3]=>100000
{{1},{2,4,5,6},{3},{7}}=>{{1},{2,4,5,6},{3},{7}}=>[1,4,3,5,6,2,7]=>100001
{{1,7},{2,4,5},{3,6}}=>{{1,7},{2,4,5},{3,6}}=>[7,4,6,5,2,3,1]=>000000
{{1},{2,4,5,7},{3,6}}=>{{1},{2,4,5,7},{3,6}}=>[1,4,6,5,7,3,2]=>100000
{{1},{2,4,5},{3,6,7}}=>{{1},{2,4,5},{3,6,7}}=>[1,4,6,5,2,7,3]=>100000
{{1},{2,4,5},{3,6},{7}}=>{{1},{2,4,5},{3,6},{7}}=>[1,4,6,5,2,3,7]=>100001
{{1,7},{2,4,5},{3},{6}}=>{{1,3,7},{2,4,5},{6}}=>[3,4,7,5,2,6,1]=>000000
{{1},{2,4,5,7},{3},{6}}=>{{1},{2,4,5,7},{3},{6}}=>[1,4,3,5,7,6,2]=>100000
{{1},{2,4,5},{3,7},{6}}=>{{1},{2,4,5},{3,7},{6}}=>[1,4,7,5,2,6,3]=>100000
{{1},{2,4,5},{3},{6,7}}=>{{1},{2,4,5},{3},{6,7}}=>[1,4,3,5,2,7,6]=>100010
{{1},{2,4,5},{3},{6},{7}}=>{{1},{2,4,5},{3},{6},{7}}=>[1,4,3,5,2,6,7]=>100011
{{1,6,7},{2,4},{3,5}}=>{{1,6,7},{2,4},{3,5}}=>[6,4,5,2,3,7,1]=>000000
{{1,6},{2,4,7},{3,5}}=>{{1,6},{2,4,7},{3,5}}=>[6,4,5,7,3,1,2]=>000000
{{1,6},{2,4},{3,5,7}}=>{{1,6},{2,4},{3,5,7}}=>[6,4,5,2,7,1,3]=>000000
{{1,6},{2,4},{3,5},{7}}=>{{1,6},{2,4},{3,5},{7}}=>[6,4,5,2,3,1,7]=>000001
{{1,7},{2,4,6},{3,5}}=>{{1,7},{2,4,6},{3,5}}=>[7,4,5,6,3,2,1]=>000000
{{1},{2,4,6,7},{3,5}}=>{{1},{2,4,6,7},{3,5}}=>[1,4,5,6,3,7,2]=>100000
{{1},{2,4,6},{3,5,7}}=>{{1},{2,4,6},{3,5,7}}=>[1,4,5,6,7,2,3]=>100000
{{1},{2,4,6},{3,5},{7}}=>{{1},{2,4,6},{3,5},{7}}=>[1,4,5,6,3,2,7]=>100001
{{1,7},{2,4},{3,5,6}}=>{{1,7},{2,4},{3,5,6}}=>[7,4,5,2,6,3,1]=>000000
{{1},{2,4,7},{3,5,6}}=>{{1},{2,4,7},{3,5,6}}=>[1,4,5,7,6,3,2]=>100000
{{1},{2,4},{3,5,6,7}}=>{{1},{2,4},{3,5,6,7}}=>[1,4,5,2,6,7,3]=>100000
{{1},{2,4},{3,5,6},{7}}=>{{1},{2,4},{3,5,6},{7}}=>[1,4,5,2,6,3,7]=>100001
{{1,7},{2,4},{3,5},{6}}=>{{1,7},{2,4},{3,5},{6}}=>[7,4,5,2,3,6,1]=>000000
{{1},{2,4,7},{3,5},{6}}=>{{1},{2,4,7},{3,5},{6}}=>[1,4,5,7,3,6,2]=>100000
{{1},{2,4},{3,5,7},{6}}=>{{1},{2,4},{3,5,7},{6}}=>[1,4,5,2,7,6,3]=>100000
{{1},{2,4},{3,5},{6,7}}=>{{1},{2,4},{3,5},{6,7}}=>[1,4,5,2,3,7,6]=>100010
{{1},{2,4},{3,5},{6},{7}}=>{{1},{2,4},{3,5},{6},{7}}=>[1,4,5,2,3,6,7]=>100011
{{1,6,7},{2,4},{3},{5}}=>{{1,3,6,7},{2,4},{5}}=>[3,4,6,2,5,7,1]=>000000
{{1,6},{2,4,7},{3},{5}}=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000
{{1,6},{2,4},{3,7},{5}}=>{{1,6},{2,4},{3,7},{5}}=>[6,4,7,2,5,1,3]=>000000
{{1,6},{2,4},{3},{5,7}}=>{{1,3,6},{2,4},{5,7}}=>[3,4,6,2,7,1,5]=>000000
{{1,6},{2,4},{3},{5},{7}}=>{{1,3,6},{2,4},{5},{7}}=>[3,4,6,2,5,1,7]=>000001
{{1,7},{2,4,6},{3},{5}}=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000
{{1},{2,4,6,7},{3},{5}}=>{{1},{2,4,6,7},{3},{5}}=>[1,4,3,6,5,7,2]=>100000
{{1},{2,4,6},{3,7},{5}}=>{{1},{2,4,6},{3,7},{5}}=>[1,4,7,6,5,2,3]=>100000
{{1},{2,4,6},{3},{5,7}}=>{{1},{2,4,6},{3},{5,7}}=>[1,4,3,6,7,2,5]=>100000
{{1},{2,4,6},{3},{5},{7}}=>{{1},{2,4,6},{3},{5},{7}}=>[1,4,3,6,5,2,7]=>100001
{{1,7},{2,4},{3,6},{5}}=>{{1,7},{2,4},{3,6},{5}}=>[7,4,6,2,5,3,1]=>000000
{{1},{2,4,7},{3,6},{5}}=>{{1},{2,4,7},{3,6},{5}}=>[1,4,6,7,5,3,2]=>100000
{{1},{2,4},{3,6,7},{5}}=>{{1},{2,4},{3,6,7},{5}}=>[1,4,6,2,5,7,3]=>100000
{{1},{2,4},{3,6},{5,7}}=>{{1},{2,4},{3,6},{5,7}}=>[1,4,6,2,7,3,5]=>100000
{{1},{2,4},{3,6},{5},{7}}=>{{1},{2,4},{3,6},{5},{7}}=>[1,4,6,2,5,3,7]=>100001
{{1,7},{2,4},{3},{5,6}}=>{{1,3,7},{2,4},{5,6}}=>[3,4,7,2,6,5,1]=>000000
{{1},{2,4,7},{3},{5,6}}=>{{1},{2,4,7},{3},{5,6}}=>[1,4,3,7,6,5,2]=>100000
{{1},{2,4},{3,7},{5,6}}=>{{1},{2,4},{3,7},{5,6}}=>[1,4,7,2,6,5,3]=>100000
{{1},{2,4},{3},{5,6,7}}=>{{1},{2,4},{3},{5,6,7}}=>[1,4,3,2,6,7,5]=>100100
{{1},{2,4},{3},{5,6},{7}}=>{{1},{2,4},{3},{5,6},{7}}=>[1,4,3,2,6,5,7]=>100101
{{1,7},{2,4},{3},{5},{6}}=>{{1,3,7},{2,4},{5},{6}}=>[3,4,7,2,5,6,1]=>000000
{{1},{2,4,7},{3},{5},{6}}=>{{1},{2,4,7},{3},{5},{6}}=>[1,4,3,7,5,6,2]=>100000
{{1},{2,4},{3,7},{5},{6}}=>{{1},{2,4},{3,7},{5},{6}}=>[1,4,7,2,5,6,3]=>100000
{{1},{2,4},{3},{5,7},{6}}=>{{1},{2,4},{3},{5,7},{6}}=>[1,4,3,2,7,6,5]=>100100
{{1},{2,4},{3},{5},{6,7}}=>{{1},{2,4},{3},{5},{6,7}}=>[1,4,3,2,5,7,6]=>100110
{{1},{2,4},{3},{5},{6},{7}}=>{{1},{2,4},{3},{5},{6},{7}}=>[1,4,3,2,5,6,7]=>100111
{{1,5,6,7},{2},{3,4}}=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000
{{1,5,6},{2,7},{3,4}}=>{{1,5,6},{2,7},{3,4}}=>[5,7,4,3,6,1,2]=>000000
{{1,5,6},{2},{3,4,7}}=>{{1,2,6},{3,4,7},{5}}=>[2,6,4,7,5,1,3]=>000000
{{1,5,6},{2},{3,4},{7}}=>{{1,2,5,6},{3,4},{7}}=>[2,5,4,3,6,1,7]=>000001
{{1,5,7},{2,6},{3,4}}=>{{1,5,7},{2,6},{3,4}}=>[5,6,4,3,7,2,1]=>000000
{{1,5},{2,6,7},{3,4}}=>{{1,5},{2,6,7},{3,4}}=>[5,6,4,3,1,7,2]=>000000
{{1,5},{2,6},{3,4,7}}=>{{1,5},{2,6},{3,4,7}}=>[5,6,4,7,1,2,3]=>000000
{{1,5},{2,6},{3,4},{7}}=>{{1,5},{2,6},{3,4},{7}}=>[5,6,4,3,1,2,7]=>000001
{{1,5,7},{2},{3,4,6}}=>{{1,2,7},{3,4,6},{5}}=>[2,7,4,6,5,3,1]=>000000
{{1,5},{2,7},{3,4,6}}=>{{1,5},{2,7},{3,4,6}}=>[5,7,4,6,1,3,2]=>000000
{{1,5},{2},{3,4,6,7}}=>{{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000
{{1,5},{2},{3,4,6},{7}}=>{{1,2,5},{3,4,6},{7}}=>[2,5,4,6,1,3,7]=>000001
{{1,5,7},{2},{3,4},{6}}=>{{1,2,5,7},{3,4},{6}}=>[2,5,4,3,7,6,1]=>000000
{{1,5},{2,7},{3,4},{6}}=>{{1,5},{2,7},{3,4},{6}}=>[5,7,4,3,1,6,2]=>000000
{{1,5},{2},{3,4,7},{6}}=>{{1,2,5},{3,4,7},{6}}=>[2,5,4,7,1,6,3]=>000000
{{1,5},{2},{3,4},{6,7}}=>{{1,2,5},{3,4},{6,7}}=>[2,5,4,3,1,7,6]=>000010
{{1,5},{2},{3,4},{6},{7}}=>{{1,2,5},{3,4},{6},{7}}=>[2,5,4,3,1,6,7]=>000011
{{1,6,7},{2,5},{3,4}}=>{{1,6,7},{2,5},{3,4}}=>[6,5,4,3,2,7,1]=>000000
{{1,6},{2,5,7},{3,4}}=>{{1,6},{2,5,7},{3,4}}=>[6,5,4,3,7,1,2]=>000000
{{1,6},{2,5},{3,4,7}}=>{{1,6},{2,5},{3,4,7}}=>[6,5,4,7,2,1,3]=>000000
{{1,6},{2,5},{3,4},{7}}=>{{1,6},{2,5},{3,4},{7}}=>[6,5,4,3,2,1,7]=>000001
{{1,7},{2,5,6},{3,4}}=>{{1,7},{2,5,6},{3,4}}=>[7,5,4,3,6,2,1]=>000000
{{1},{2,5,6,7},{3,4}}=>{{1},{2,5,6,7},{3,4}}=>[1,5,4,3,6,7,2]=>100000
{{1},{2,5,6},{3,4,7}}=>{{1},{2,5,6},{3,4,7}}=>[1,5,4,7,6,2,3]=>100000
{{1},{2,5,6},{3,4},{7}}=>{{1},{2,5,6},{3,4},{7}}=>[1,5,4,3,6,2,7]=>100001
{{1,7},{2,5},{3,4,6}}=>{{1,7},{2,5},{3,4,6}}=>[7,5,4,6,2,3,1]=>000000
{{1},{2,5,7},{3,4,6}}=>{{1},{2,5,7},{3,4,6}}=>[1,5,4,6,7,3,2]=>100000
{{1},{2,5},{3,4,6,7}}=>{{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>100000
{{1},{2,5},{3,4,6},{7}}=>{{1},{2,5},{3,4,6},{7}}=>[1,5,4,6,2,3,7]=>100001
{{1,7},{2,5},{3,4},{6}}=>{{1,7},{2,5},{3,4},{6}}=>[7,5,4,3,2,6,1]=>000000
{{1},{2,5,7},{3,4},{6}}=>{{1},{2,5,7},{3,4},{6}}=>[1,5,4,3,7,6,2]=>100000
{{1},{2,5},{3,4,7},{6}}=>{{1},{2,5},{3,4,7},{6}}=>[1,5,4,7,2,6,3]=>100000
{{1},{2,5},{3,4},{6,7}}=>{{1},{2,5},{3,4},{6,7}}=>[1,5,4,3,2,7,6]=>100010
{{1},{2,5},{3,4},{6},{7}}=>{{1},{2,5},{3,4},{6},{7}}=>[1,5,4,3,2,6,7]=>100011
{{1,6,7},{2},{3,4,5}}=>{{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000
{{1,6},{2,7},{3,4,5}}=>{{1,6},{2,7},{3,4,5}}=>[6,7,4,5,3,1,2]=>000000
{{1,6},{2},{3,4,5,7}}=>{{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000
{{1,6},{2},{3,4,5},{7}}=>{{1,2,6},{3,4,5},{7}}=>[2,6,4,5,3,1,7]=>000001
{{1,7},{2,6},{3,4,5}}=>{{1,7},{2,6},{3,4,5}}=>[7,6,4,5,3,2,1]=>000000
{{1},{2,6,7},{3,4,5}}=>{{1},{2,6,7},{3,4,5}}=>[1,6,4,5,3,7,2]=>100000
{{1},{2,6},{3,4,5,7}}=>{{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>100000
{{1},{2,6},{3,4,5},{7}}=>{{1},{2,6},{3,4,5},{7}}=>[1,6,4,5,3,2,7]=>100001
{{1,7},{2},{3,4,5,6}}=>{{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000
{{1},{2,7},{3,4,5,6}}=>{{1},{2,7},{3,4,5,6}}=>[1,7,4,5,6,3,2]=>100000
{{1},{2},{3,4,5,6,7}}=>{{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000
{{1},{2},{3,4,5,6},{7}}=>{{1},{2},{3,4,5,6},{7}}=>[1,2,4,5,6,3,7]=>110001
{{1,7},{2},{3,4,5},{6}}=>{{1,2,7},{3,4,5},{6}}=>[2,7,4,5,3,6,1]=>000000
{{1},{2,7},{3,4,5},{6}}=>{{1},{2,7},{3,4,5},{6}}=>[1,7,4,5,3,6,2]=>100000
{{1},{2},{3,4,5,7},{6}}=>{{1},{2},{3,4,5,7},{6}}=>[1,2,4,5,7,6,3]=>110000
{{1},{2},{3,4,5},{6,7}}=>{{1},{2},{3,4,5},{6,7}}=>[1,2,4,5,3,7,6]=>110010
{{1},{2},{3,4,5},{6},{7}}=>{{1},{2},{3,4,5},{6},{7}}=>[1,2,4,5,3,6,7]=>110011
{{1,6,7},{2},{3,4},{5}}=>{{1,2,6,7},{3,4},{5}}=>[2,6,4,3,5,7,1]=>000000
{{1,6},{2,7},{3,4},{5}}=>{{1,6},{2,7},{3,4},{5}}=>[6,7,4,3,5,1,2]=>000000
{{1,6},{2},{3,4,7},{5}}=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000
{{1,6},{2},{3,4},{5,7}}=>{{1,2,6},{3,4},{5,7}}=>[2,6,4,3,7,1,5]=>000000
{{1,6},{2},{3,4},{5},{7}}=>{{1,2,6},{3,4},{5},{7}}=>[2,6,4,3,5,1,7]=>000001
{{1,7},{2,6},{3,4},{5}}=>{{1,7},{2,6},{3,4},{5}}=>[7,6,4,3,5,2,1]=>000000
{{1},{2,6,7},{3,4},{5}}=>{{1},{2,6,7},{3,4},{5}}=>[1,6,4,3,5,7,2]=>100000
{{1},{2,6},{3,4,7},{5}}=>{{1},{2,6},{3,4,7},{5}}=>[1,6,4,7,5,2,3]=>100000
{{1},{2,6},{3,4},{5,7}}=>{{1},{2,6},{3,4},{5,7}}=>[1,6,4,3,7,2,5]=>100000
{{1},{2,6},{3,4},{5},{7}}=>{{1},{2,6},{3,4},{5},{7}}=>[1,6,4,3,5,2,7]=>100001
{{1,7},{2},{3,4,6},{5}}=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000
{{1},{2,7},{3,4,6},{5}}=>{{1},{2,7},{3,4,6},{5}}=>[1,7,4,6,5,3,2]=>100000
{{1},{2},{3,4,6,7},{5}}=>{{1},{2},{3,4,6,7},{5}}=>[1,2,4,6,5,7,3]=>110000
{{1},{2},{3,4,6},{5,7}}=>{{1},{2},{3,4,6},{5,7}}=>[1,2,4,6,7,3,5]=>110000
{{1},{2},{3,4,6},{5},{7}}=>{{1},{2},{3,4,6},{5},{7}}=>[1,2,4,6,5,3,7]=>110001
{{1,7},{2},{3,4},{5,6}}=>{{1,2,7},{3,4},{5,6}}=>[2,7,4,3,6,5,1]=>000000
{{1},{2,7},{3,4},{5,6}}=>{{1},{2,7},{3,4},{5,6}}=>[1,7,4,3,6,5,2]=>100000
{{1},{2},{3,4,7},{5,6}}=>{{1},{2},{3,4,7},{5,6}}=>[1,2,4,7,6,5,3]=>110000
{{1},{2},{3,4},{5,6,7}}=>{{1},{2},{3,4},{5,6,7}}=>[1,2,4,3,6,7,5]=>110100
{{1},{2},{3,4},{5,6},{7}}=>{{1},{2},{3,4},{5,6},{7}}=>[1,2,4,3,6,5,7]=>110101
{{1,7},{2},{3,4},{5},{6}}=>{{1,2,7},{3,4},{5},{6}}=>[2,7,4,3,5,6,1]=>000000
{{1},{2,7},{3,4},{5},{6}}=>{{1},{2,7},{3,4},{5},{6}}=>[1,7,4,3,5,6,2]=>100000
{{1},{2},{3,4,7},{5},{6}}=>{{1},{2},{3,4,7},{5},{6}}=>[1,2,4,7,5,6,3]=>110000
{{1},{2},{3,4},{5,7},{6}}=>{{1},{2},{3,4},{5,7},{6}}=>[1,2,4,3,7,6,5]=>110100
{{1},{2},{3,4},{5},{6,7}}=>{{1},{2},{3,4},{5},{6,7}}=>[1,2,4,3,5,7,6]=>110110
{{1},{2},{3,4},{5},{6},{7}}=>{{1},{2},{3,4},{5},{6},{7}}=>[1,2,4,3,5,6,7]=>110111
{{1,5,6,7},{2},{3},{4}}=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000
{{1,5,6},{2,7},{3},{4}}=>{{1,3,4,6},{2,7},{5}}=>[3,7,4,6,5,1,2]=>000000
{{1,5,6},{2},{3,7},{4}}=>{{1,2,4,6},{3,7},{5}}=>[2,4,7,6,5,1,3]=>000000
{{1,5,6},{2},{3},{4,7}}=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>000000
{{1,5,6},{2},{3},{4},{7}}=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001
{{1,5,7},{2,6},{3},{4}}=>{{1,3,4,7},{2,6},{5}}=>[3,6,4,7,5,2,1]=>000000
{{1,5},{2,6,7},{3},{4}}=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000
{{1,5},{2,6},{3,7},{4}}=>{{1,4,5},{2,6},{3,7}}=>[4,6,7,5,1,2,3]=>000000
{{1,5},{2,6},{3},{4,7}}=>{{1,3,5},{2,6},{4,7}}=>[3,6,5,7,1,2,4]=>000000
{{1,5},{2,6},{3},{4},{7}}=>{{1,3,4,5},{2,6},{7}}=>[3,6,4,5,1,2,7]=>000001
{{1,5,7},{2},{3,6},{4}}=>{{1,2,4,7},{3,6},{5}}=>[2,4,6,7,5,3,1]=>000000
{{1,5},{2,7},{3,6},{4}}=>{{1,4,5},{2,7},{3,6}}=>[4,7,6,5,1,3,2]=>000000
{{1,5},{2},{3,6,7},{4}}=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000
{{1,5},{2},{3,6},{4,7}}=>{{1,2,5},{3,6},{4,7}}=>[2,5,6,7,1,3,4]=>000000
{{1,5},{2},{3,6},{4},{7}}=>{{1,2,4,5},{3,6},{7}}=>[2,4,6,5,1,3,7]=>000001
{{1,5,7},{2},{3},{4,6}}=>{{1,2,3,7},{4,6},{5}}=>[2,3,7,6,5,4,1]=>000000
{{1,5},{2,7},{3},{4,6}}=>{{1,3,5},{2,7},{4,6}}=>[3,7,5,6,1,4,2]=>000000
{{1,5},{2},{3,7},{4,6}}=>{{1,2,5},{3,7},{4,6}}=>[2,5,7,6,1,4,3]=>000000
{{1,5},{2},{3},{4,6,7}}=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000
{{1,5},{2},{3},{4,6},{7}}=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>000001
{{1,5,7},{2},{3},{4},{6}}=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000
{{1,5},{2,7},{3},{4},{6}}=>{{1,3,4,5},{2,7},{6}}=>[3,7,4,5,1,6,2]=>000000
{{1,5},{2},{3,7},{4},{6}}=>{{1,2,4,5},{3,7},{6}}=>[2,4,7,5,1,6,3]=>000000
{{1,5},{2},{3},{4,7},{6}}=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>000000
{{1,5},{2},{3},{4},{6,7}}=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010
{{1,5},{2},{3},{4},{6},{7}}=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011
{{1,6,7},{2,5},{3},{4}}=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000
{{1,6},{2,5,7},{3},{4}}=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000
{{1,6},{2,5},{3,7},{4}}=>{{1,4,6},{2,5},{3,7}}=>[4,5,7,6,2,1,3]=>000000
{{1,6},{2,5},{3},{4,7}}=>{{1,3,6},{2,5},{4,7}}=>[3,5,6,7,2,1,4]=>000000
{{1,6},{2,5},{3},{4},{7}}=>{{1,3,4,6},{2,5},{7}}=>[3,5,4,6,2,1,7]=>000001
{{1,7},{2,5,6},{3},{4}}=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000
{{1},{2,5,6,7},{3},{4}}=>{{1},{2,5,6,7},{3},{4}}=>[1,5,3,4,6,7,2]=>100000
{{1},{2,5,6},{3,7},{4}}=>{{1},{2,5,6},{3,7},{4}}=>[1,5,7,4,6,2,3]=>100000
{{1},{2,5,6},{3},{4,7}}=>{{1},{2,5,6},{3},{4,7}}=>[1,5,3,7,6,2,4]=>100000
{{1},{2,5,6},{3},{4},{7}}=>{{1},{2,5,6},{3},{4},{7}}=>[1,5,3,4,6,2,7]=>100001
{{1,7},{2,5},{3,6},{4}}=>{{1,4,7},{2,5},{3,6}}=>[4,5,6,7,2,3,1]=>000000
{{1},{2,5,7},{3,6},{4}}=>{{1},{2,5,7},{3,6},{4}}=>[1,5,6,4,7,3,2]=>100000
{{1},{2,5},{3,6,7},{4}}=>{{1},{2,5},{3,6,7},{4}}=>[1,5,6,4,2,7,3]=>100000
{{1},{2,5},{3,6},{4,7}}=>{{1},{2,5},{3,6},{4,7}}=>[1,5,6,7,2,3,4]=>100000
{{1},{2,5},{3,6},{4},{7}}=>{{1},{2,5},{3,6},{4},{7}}=>[1,5,6,4,2,3,7]=>100001
{{1,7},{2,5},{3},{4,6}}=>{{1,3,7},{2,5},{4,6}}=>[3,5,7,6,2,4,1]=>000000
{{1},{2,5,7},{3},{4,6}}=>{{1},{2,5,7},{3},{4,6}}=>[1,5,3,6,7,4,2]=>100000
{{1},{2,5},{3,7},{4,6}}=>{{1},{2,5},{3,7},{4,6}}=>[1,5,7,6,2,4,3]=>100000
{{1},{2,5},{3},{4,6,7}}=>{{1},{2,5},{3},{4,6,7}}=>[1,5,3,6,2,7,4]=>100000
{{1},{2,5},{3},{4,6},{7}}=>{{1},{2,5},{3},{4,6},{7}}=>[1,5,3,6,2,4,7]=>100001
{{1,7},{2,5},{3},{4},{6}}=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>000000
{{1},{2,5,7},{3},{4},{6}}=>{{1},{2,5,7},{3},{4},{6}}=>[1,5,3,4,7,6,2]=>100000
{{1},{2,5},{3,7},{4},{6}}=>{{1},{2,5},{3,7},{4},{6}}=>[1,5,7,4,2,6,3]=>100000
{{1},{2,5},{3},{4,7},{6}}=>{{1},{2,5},{3},{4,7},{6}}=>[1,5,3,7,2,6,4]=>100000
{{1},{2,5},{3},{4},{6,7}}=>{{1},{2,5},{3},{4},{6,7}}=>[1,5,3,4,2,7,6]=>100010
{{1},{2,5},{3},{4},{6},{7}}=>{{1},{2,5},{3},{4},{6},{7}}=>[1,5,3,4,2,6,7]=>100011
{{1,6,7},{2},{3,5},{4}}=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000
{{1,6},{2,7},{3,5},{4}}=>{{1,4,6},{2,7},{3,5}}=>[4,7,5,6,3,1,2]=>000000
{{1,6},{2},{3,5,7},{4}}=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000
{{1,6},{2},{3,5},{4,7}}=>{{1,2,6},{3,5},{4,7}}=>[2,6,5,7,3,1,4]=>000000
{{1,6},{2},{3,5},{4},{7}}=>{{1,2,4,6},{3,5},{7}}=>[2,4,5,6,3,1,7]=>000001
{{1,7},{2,6},{3,5},{4}}=>{{1,4,7},{2,6},{3,5}}=>[4,6,5,7,3,2,1]=>000000
{{1},{2,6,7},{3,5},{4}}=>{{1},{2,6,7},{3,5},{4}}=>[1,6,5,4,3,7,2]=>100000
{{1},{2,6},{3,5,7},{4}}=>{{1},{2,6},{3,5,7},{4}}=>[1,6,5,4,7,2,3]=>100000
{{1},{2,6},{3,5},{4,7}}=>{{1},{2,6},{3,5},{4,7}}=>[1,6,5,7,3,2,4]=>100000
{{1},{2,6},{3,5},{4},{7}}=>{{1},{2,6},{3,5},{4},{7}}=>[1,6,5,4,3,2,7]=>100001
{{1,7},{2},{3,5,6},{4}}=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000
{{1},{2,7},{3,5,6},{4}}=>{{1},{2,7},{3,5,6},{4}}=>[1,7,5,4,6,3,2]=>100000
{{1},{2},{3,5,6,7},{4}}=>{{1},{2},{3,5,6,7},{4}}=>[1,2,5,4,6,7,3]=>110000
{{1},{2},{3,5,6},{4,7}}=>{{1},{2},{3,5,6},{4,7}}=>[1,2,5,7,6,3,4]=>110000
{{1},{2},{3,5,6},{4},{7}}=>{{1},{2},{3,5,6},{4},{7}}=>[1,2,5,4,6,3,7]=>110001
{{1,7},{2},{3,5},{4,6}}=>{{1,2,7},{3,5},{4,6}}=>[2,7,5,6,3,4,1]=>000000
{{1},{2,7},{3,5},{4,6}}=>{{1},{2,7},{3,5},{4,6}}=>[1,7,5,6,3,4,2]=>100000
{{1},{2},{3,5,7},{4,6}}=>{{1},{2},{3,5,7},{4,6}}=>[1,2,5,6,7,4,3]=>110000
{{1},{2},{3,5},{4,6,7}}=>{{1},{2},{3,5},{4,6,7}}=>[1,2,5,6,3,7,4]=>110000
{{1},{2},{3,5},{4,6},{7}}=>{{1},{2},{3,5},{4,6},{7}}=>[1,2,5,6,3,4,7]=>110001
{{1,7},{2},{3,5},{4},{6}}=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>000000
{{1},{2,7},{3,5},{4},{6}}=>{{1},{2,7},{3,5},{4},{6}}=>[1,7,5,4,3,6,2]=>100000
{{1},{2},{3,5,7},{4},{6}}=>{{1},{2},{3,5,7},{4},{6}}=>[1,2,5,4,7,6,3]=>110000
{{1},{2},{3,5},{4,7},{6}}=>{{1},{2},{3,5},{4,7},{6}}=>[1,2,5,7,3,6,4]=>110000
{{1},{2},{3,5},{4},{6,7}}=>{{1},{2},{3,5},{4},{6,7}}=>[1,2,5,4,3,7,6]=>110010
{{1},{2},{3,5},{4},{6},{7}}=>{{1},{2},{3,5},{4},{6},{7}}=>[1,2,5,4,3,6,7]=>110011
{{1,6,7},{2},{3},{4,5}}=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000
{{1,6},{2,7},{3},{4,5}}=>{{1,3,6},{2,7},{4,5}}=>[3,7,6,5,4,1,2]=>000000
{{1,6},{2},{3,7},{4,5}}=>{{1,2,6},{3,7},{4,5}}=>[2,6,7,5,4,1,3]=>000000
{{1,6},{2},{3},{4,5,7}}=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000
{{1,6},{2},{3},{4,5},{7}}=>{{1,2,3,6},{4,5},{7}}=>[2,3,6,5,4,1,7]=>000001
{{1,7},{2,6},{3},{4,5}}=>{{1,3,7},{2,6},{4,5}}=>[3,6,7,5,4,2,1]=>000000
{{1},{2,6,7},{3},{4,5}}=>{{1},{2,6,7},{3},{4,5}}=>[1,6,3,5,4,7,2]=>100000
{{1},{2,6},{3,7},{4,5}}=>{{1},{2,6},{3,7},{4,5}}=>[1,6,7,5,4,2,3]=>100000
{{1},{2,6},{3},{4,5,7}}=>{{1},{2,6},{3},{4,5,7}}=>[1,6,3,5,7,2,4]=>100000
{{1},{2,6},{3},{4,5},{7}}=>{{1},{2,6},{3},{4,5},{7}}=>[1,6,3,5,4,2,7]=>100001
{{1,7},{2},{3,6},{4,5}}=>{{1,2,7},{3,6},{4,5}}=>[2,7,6,5,4,3,1]=>000000
{{1},{2,7},{3,6},{4,5}}=>{{1},{2,7},{3,6},{4,5}}=>[1,7,6,5,4,3,2]=>100000
{{1},{2},{3,6,7},{4,5}}=>{{1},{2},{3,6,7},{4,5}}=>[1,2,6,5,4,7,3]=>110000
{{1},{2},{3,6},{4,5,7}}=>{{1},{2},{3,6},{4,5,7}}=>[1,2,6,5,7,3,4]=>110000
{{1},{2},{3,6},{4,5},{7}}=>{{1},{2},{3,6},{4,5},{7}}=>[1,2,6,5,4,3,7]=>110001
{{1,7},{2},{3},{4,5,6}}=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000
{{1},{2,7},{3},{4,5,6}}=>{{1},{2,7},{3},{4,5,6}}=>[1,7,3,5,6,4,2]=>100000
{{1},{2},{3,7},{4,5,6}}=>{{1},{2},{3,7},{4,5,6}}=>[1,2,7,5,6,4,3]=>110000
{{1},{2},{3},{4,5,6,7}}=>{{1},{2},{3},{4,5,6,7}}=>[1,2,3,5,6,7,4]=>111000
{{1},{2},{3},{4,5,6},{7}}=>{{1},{2},{3},{4,5,6},{7}}=>[1,2,3,5,6,4,7]=>111001
{{1,7},{2},{3},{4,5},{6}}=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>000000
{{1},{2,7},{3},{4,5},{6}}=>{{1},{2,7},{3},{4,5},{6}}=>[1,7,3,5,4,6,2]=>100000
{{1},{2},{3,7},{4,5},{6}}=>{{1},{2},{3,7},{4,5},{6}}=>[1,2,7,5,4,6,3]=>110000
{{1},{2},{3},{4,5,7},{6}}=>{{1},{2},{3},{4,5,7},{6}}=>[1,2,3,5,7,6,4]=>111000
{{1},{2},{3},{4,5},{6,7}}=>{{1},{2},{3},{4,5},{6,7}}=>[1,2,3,5,4,7,6]=>111010
{{1},{2},{3},{4,5},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7}}=>[1,2,3,5,4,6,7]=>111011
{{1,6,7},{2},{3},{4},{5}}=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000
{{1,6},{2,7},{3},{4},{5}}=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000
{{1,6},{2},{3,7},{4},{5}}=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000
{{1,6},{2},{3},{4,7},{5}}=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000
{{1,6},{2},{3},{4},{5,7}}=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000
{{1,6},{2},{3},{4},{5},{7}}=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001
{{1,7},{2,6},{3},{4},{5}}=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000
{{1},{2,6,7},{3},{4},{5}}=>{{1},{2,6,7},{3},{4},{5}}=>[1,6,3,4,5,7,2]=>100000
{{1},{2,6},{3,7},{4},{5}}=>{{1},{2,6},{3,7},{4},{5}}=>[1,6,7,4,5,2,3]=>100000
{{1},{2,6},{3},{4,7},{5}}=>{{1},{2,6},{3},{4,7},{5}}=>[1,6,3,7,5,2,4]=>100000
{{1},{2,6},{3},{4},{5,7}}=>{{1},{2,6},{3},{4},{5,7}}=>[1,6,3,4,7,2,5]=>100000
{{1},{2,6},{3},{4},{5},{7}}=>{{1},{2,6},{3},{4},{5},{7}}=>[1,6,3,4,5,2,7]=>100001
{{1,7},{2},{3,6},{4},{5}}=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000
{{1},{2,7},{3,6},{4},{5}}=>{{1},{2,7},{3,6},{4},{5}}=>[1,7,6,4,5,3,2]=>100000
{{1},{2},{3,6,7},{4},{5}}=>{{1},{2},{3,6,7},{4},{5}}=>[1,2,6,4,5,7,3]=>110000
{{1},{2},{3,6},{4,7},{5}}=>{{1},{2},{3,6},{4,7},{5}}=>[1,2,6,7,5,3,4]=>110000
{{1},{2},{3,6},{4},{5,7}}=>{{1},{2},{3,6},{4},{5,7}}=>[1,2,6,4,7,3,5]=>110000
{{1},{2},{3,6},{4},{5},{7}}=>{{1},{2},{3,6},{4},{5},{7}}=>[1,2,6,4,5,3,7]=>110001
{{1,7},{2},{3},{4,6},{5}}=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000
{{1},{2,7},{3},{4,6},{5}}=>{{1},{2,7},{3},{4,6},{5}}=>[1,7,3,6,5,4,2]=>100000
{{1},{2},{3,7},{4,6},{5}}=>{{1},{2},{3,7},{4,6},{5}}=>[1,2,7,6,5,4,3]=>110000
{{1},{2},{3},{4,6,7},{5}}=>{{1},{2},{3},{4,6,7},{5}}=>[1,2,3,6,5,7,4]=>111000
{{1},{2},{3},{4,6},{5,7}}=>{{1},{2},{3},{4,6},{5,7}}=>[1,2,3,6,7,4,5]=>111000
{{1},{2},{3},{4,6},{5},{7}}=>{{1},{2},{3},{4,6},{5},{7}}=>[1,2,3,6,5,4,7]=>111001
{{1,7},{2},{3},{4},{5,6}}=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000
{{1},{2,7},{3},{4},{5,6}}=>{{1},{2,7},{3},{4},{5,6}}=>[1,7,3,4,6,5,2]=>100000
{{1},{2},{3,7},{4},{5,6}}=>{{1},{2},{3,7},{4},{5,6}}=>[1,2,7,4,6,5,3]=>110000
{{1},{2},{3},{4,7},{5,6}}=>{{1},{2},{3},{4,7},{5,6}}=>[1,2,3,7,6,5,4]=>111000
{{1},{2},{3},{4},{5,6,7}}=>{{1},{2},{3},{4},{5,6,7}}=>[1,2,3,4,6,7,5]=>111100
{{1},{2},{3},{4},{5,6},{7}}=>{{1},{2},{3},{4},{5,6},{7}}=>[1,2,3,4,6,5,7]=>111101
{{1,7},{2},{3},{4},{5},{6}}=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000
{{1},{2,7},{3},{4},{5},{6}}=>{{1},{2,7},{3},{4},{5},{6}}=>[1,7,3,4,5,6,2]=>100000
{{1},{2},{3,7},{4},{5},{6}}=>{{1},{2},{3,7},{4},{5},{6}}=>[1,2,7,4,5,6,3]=>110000
{{1},{2},{3},{4,7},{5},{6}}=>{{1},{2},{3},{4,7},{5},{6}}=>[1,2,3,7,5,6,4]=>111000
{{1},{2},{3},{4},{5,7},{6}}=>{{1},{2},{3},{4},{5,7},{6}}=>[1,2,3,4,7,6,5]=>111100
{{1},{2},{3},{4},{5},{6,7}}=>{{1},{2},{3},{4},{5},{6,7}}=>[1,2,3,4,5,7,6]=>111110
{{1},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7}}=>[1,2,3,4,5,6,7]=>111111
{{1,2},{3,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,6},{7,8}}=>[2,1,4,3,6,5,8,7]=>0101010
{{1,3},{2,4},{5,6},{7,8}}=>{{1,3},{2,4},{5,6},{7,8}}=>[3,4,1,2,6,5,8,7]=>0001010
{{1,4},{2,3},{5,6},{7,8}}=>{{1,4},{2,3},{5,6},{7,8}}=>[4,3,2,1,6,5,8,7]=>0001010
{{1,5},{2,3},{4,6},{7,8}}=>{{1,5},{2,3},{4,6},{7,8}}=>[5,3,2,6,1,4,8,7]=>0000010
{{1,6},{2,3},{4,5},{7,8}}=>{{1,6},{2,3},{4,5},{7,8}}=>[6,3,2,5,4,1,8,7]=>0000010
{{1,7},{2,3},{4,5},{6,8}}=>{{1,7},{2,3},{4,5},{6,8}}=>[7,3,2,5,4,8,1,6]=>0000000
{{1,8},{2,3},{4,5},{6,7}}=>{{1,8},{2,3},{4,5},{6,7}}=>[8,3,2,5,4,7,6,1]=>0000000
{{1,8},{2,4},{3,5},{6,7}}=>{{1,8},{2,4},{3,5},{6,7}}=>[8,4,5,2,3,7,6,1]=>0000000
{{1,7},{2,4},{3,5},{6,8}}=>{{1,7},{2,4},{3,5},{6,8}}=>[7,4,5,2,3,8,1,6]=>0000000
{{1,6},{2,4},{3,5},{7,8}}=>{{1,6},{2,4},{3,5},{7,8}}=>[6,4,5,2,3,1,8,7]=>0000010
{{1,5},{2,4},{3,6},{7,8}}=>{{1,5},{2,4},{3,6},{7,8}}=>[5,4,6,2,1,3,8,7]=>0000010
{{1,4},{2,5},{3,6},{7,8}}=>{{1,4},{2,5},{3,6},{7,8}}=>[4,5,6,1,2,3,8,7]=>0000010
{{1,3},{2,5},{4,6},{7,8}}=>{{1,3},{2,5},{4,6},{7,8}}=>[3,5,1,6,2,4,8,7]=>0000010
{{1,2},{3,5},{4,6},{7,8}}=>{{1,2},{3,5},{4,6},{7,8}}=>[2,1,5,6,3,4,8,7]=>0100010
{{1,2},{3,6},{4,5},{7,8}}=>{{1,2},{3,6},{4,5},{7,8}}=>[2,1,6,5,4,3,8,7]=>0100010
{{1,3},{2,6},{4,5},{7,8}}=>{{1,3},{2,6},{4,5},{7,8}}=>[3,6,1,5,4,2,8,7]=>0000010
{{1,4},{2,6},{3,5},{7,8}}=>{{1,4},{2,6},{3,5},{7,8}}=>[4,6,5,1,3,2,8,7]=>0000010
{{1,5},{2,6},{3,4},{7,8}}=>{{1,5},{2,6},{3,4},{7,8}}=>[5,6,4,3,1,2,8,7]=>0000010
{{1,6},{2,5},{3,4},{7,8}}=>{{1,6},{2,5},{3,4},{7,8}}=>[6,5,4,3,2,1,8,7]=>0000010
{{1,7},{2,5},{3,4},{6,8}}=>{{1,7},{2,5},{3,4},{6,8}}=>[7,5,4,3,2,8,1,6]=>0000000
{{1,8},{2,5},{3,4},{6,7}}=>{{1,8},{2,5},{3,4},{6,7}}=>[8,5,4,3,2,7,6,1]=>0000000
{{1,8},{2,6},{3,4},{5,7}}=>{{1,8},{2,6},{3,4},{5,7}}=>[8,6,4,3,7,2,5,1]=>0000000
{{1,7},{2,6},{3,4},{5,8}}=>{{1,7},{2,6},{3,4},{5,8}}=>[7,6,4,3,8,2,1,5]=>0000000
{{1,6},{2,7},{3,4},{5,8}}=>{{1,6},{2,7},{3,4},{5,8}}=>[6,7,4,3,8,1,2,5]=>0000000
{{1,5},{2,7},{3,4},{6,8}}=>{{1,5},{2,7},{3,4},{6,8}}=>[5,7,4,3,1,8,2,6]=>0000000
{{1,4},{2,7},{3,5},{6,8}}=>{{1,4},{2,7},{3,5},{6,8}}=>[4,7,5,1,3,8,2,6]=>0000000
{{1,3},{2,7},{4,5},{6,8}}=>{{1,3},{2,7},{4,5},{6,8}}=>[3,7,1,5,4,8,2,6]=>0000000
{{1,2},{3,7},{4,5},{6,8}}=>{{1,2},{3,7},{4,5},{6,8}}=>[2,1,7,5,4,8,3,6]=>0100000
{{1,2},{3,8},{4,5},{6,7}}=>{{1,2},{3,8},{4,5},{6,7}}=>[2,1,8,5,4,7,6,3]=>0100000
{{1,3},{2,8},{4,5},{6,7}}=>{{1,3},{2,8},{4,5},{6,7}}=>[3,8,1,5,4,7,6,2]=>0000000
{{1,4},{2,8},{3,5},{6,7}}=>{{1,4},{2,8},{3,5},{6,7}}=>[4,8,5,1,3,7,6,2]=>0000000
{{1,5},{2,8},{3,4},{6,7}}=>{{1,5},{2,8},{3,4},{6,7}}=>[5,8,4,3,1,7,6,2]=>0000000
{{1,6},{2,8},{3,4},{5,7}}=>{{1,6},{2,8},{3,4},{5,7}}=>[6,8,4,3,7,1,5,2]=>0000000
{{1,7},{2,8},{3,4},{5,6}}=>{{1,7},{2,8},{3,4},{5,6}}=>[7,8,4,3,6,5,1,2]=>0000000
{{1,8},{2,7},{3,4},{5,6}}=>{{1,8},{2,7},{3,4},{5,6}}=>[8,7,4,3,6,5,2,1]=>0000000
{{1,8},{2,7},{3,5},{4,6}}=>{{1,8},{2,7},{3,5},{4,6}}=>[8,7,5,6,3,4,2,1]=>0000000
{{1,7},{2,8},{3,5},{4,6}}=>{{1,7},{2,8},{3,5},{4,6}}=>[7,8,5,6,3,4,1,2]=>0000000
{{1,6},{2,8},{3,5},{4,7}}=>{{1,6},{2,8},{3,5},{4,7}}=>[6,8,5,7,3,1,4,2]=>0000000
{{1,5},{2,8},{3,6},{4,7}}=>{{1,5},{2,8},{3,6},{4,7}}=>[5,8,6,7,1,3,4,2]=>0000000
{{1,4},{2,8},{3,6},{5,7}}=>{{1,4},{2,8},{3,6},{5,7}}=>[4,8,6,1,7,3,5,2]=>0000000
{{1,3},{2,8},{4,6},{5,7}}=>{{1,3},{2,8},{4,6},{5,7}}=>[3,8,1,6,7,4,5,2]=>0000000
{{1,2},{3,8},{4,6},{5,7}}=>{{1,2},{3,8},{4,6},{5,7}}=>[2,1,8,6,7,4,5,3]=>0100000
{{1,2},{3,7},{4,6},{5,8}}=>{{1,2},{3,7},{4,6},{5,8}}=>[2,1,7,6,8,4,3,5]=>0100000
{{1,3},{2,7},{4,6},{5,8}}=>{{1,3},{2,7},{4,6},{5,8}}=>[3,7,1,6,8,4,2,5]=>0000000
{{1,4},{2,7},{3,6},{5,8}}=>{{1,4},{2,7},{3,6},{5,8}}=>[4,7,6,1,8,3,2,5]=>0000000
{{1,5},{2,7},{3,6},{4,8}}=>{{1,5},{2,7},{3,6},{4,8}}=>[5,7,6,8,1,3,2,4]=>0000000
{{1,6},{2,7},{3,5},{4,8}}=>{{1,6},{2,7},{3,5},{4,8}}=>[6,7,5,8,3,1,2,4]=>0000000
{{1,7},{2,6},{3,5},{4,8}}=>{{1,7},{2,6},{3,5},{4,8}}=>[7,6,5,8,3,2,1,4]=>0000000
{{1,8},{2,6},{3,5},{4,7}}=>{{1,8},{2,6},{3,5},{4,7}}=>[8,6,5,7,3,2,4,1]=>0000000
{{1,8},{2,5},{3,6},{4,7}}=>{{1,8},{2,5},{3,6},{4,7}}=>[8,5,6,7,2,3,4,1]=>0000000
{{1,7},{2,5},{3,6},{4,8}}=>{{1,7},{2,5},{3,6},{4,8}}=>[7,5,6,8,2,3,1,4]=>0000000
{{1,6},{2,5},{3,7},{4,8}}=>{{1,6},{2,5},{3,7},{4,8}}=>[6,5,7,8,2,1,3,4]=>0000000
{{1,5},{2,6},{3,7},{4,8}}=>{{1,5},{2,6},{3,7},{4,8}}=>[5,6,7,8,1,2,3,4]=>0000000
{{1,4},{2,6},{3,7},{5,8}}=>{{1,4},{2,6},{3,7},{5,8}}=>[4,6,7,1,8,2,3,5]=>0000000
{{1,3},{2,6},{4,7},{5,8}}=>{{1,3},{2,6},{4,7},{5,8}}=>[3,6,1,7,8,2,4,5]=>0000000
{{1,2},{3,6},{4,7},{5,8}}=>{{1,2},{3,6},{4,7},{5,8}}=>[2,1,6,7,8,3,4,5]=>0100000
{{1,2},{3,5},{4,7},{6,8}}=>{{1,2},{3,5},{4,7},{6,8}}=>[2,1,5,7,3,8,4,6]=>0100000
{{1,3},{2,5},{4,7},{6,8}}=>{{1,3},{2,5},{4,7},{6,8}}=>[3,5,1,7,2,8,4,6]=>0000000
{{1,4},{2,5},{3,7},{6,8}}=>{{1,4},{2,5},{3,7},{6,8}}=>[4,5,7,1,2,8,3,6]=>0000000
{{1,5},{2,4},{3,7},{6,8}}=>{{1,5},{2,4},{3,7},{6,8}}=>[5,4,7,2,1,8,3,6]=>0000000
{{1,6},{2,4},{3,7},{5,8}}=>{{1,6},{2,4},{3,7},{5,8}}=>[6,4,7,2,8,1,3,5]=>0000000
{{1,7},{2,4},{3,6},{5,8}}=>{{1,7},{2,4},{3,6},{5,8}}=>[7,4,6,2,8,3,1,5]=>0000000
{{1,8},{2,4},{3,6},{5,7}}=>{{1,8},{2,4},{3,6},{5,7}}=>[8,4,6,2,7,3,5,1]=>0000000
{{1,8},{2,3},{4,6},{5,7}}=>{{1,8},{2,3},{4,6},{5,7}}=>[8,3,2,6,7,4,5,1]=>0000000
{{1,7},{2,3},{4,6},{5,8}}=>{{1,7},{2,3},{4,6},{5,8}}=>[7,3,2,6,8,4,1,5]=>0000000
{{1,6},{2,3},{4,7},{5,8}}=>{{1,6},{2,3},{4,7},{5,8}}=>[6,3,2,7,8,1,4,5]=>0000000
{{1,5},{2,3},{4,7},{6,8}}=>{{1,5},{2,3},{4,7},{6,8}}=>[5,3,2,7,1,8,4,6]=>0000000
{{1,4},{2,3},{5,7},{6,8}}=>{{1,4},{2,3},{5,7},{6,8}}=>[4,3,2,1,7,8,5,6]=>0001000
{{1,3},{2,4},{5,7},{6,8}}=>{{1,3},{2,4},{5,7},{6,8}}=>[3,4,1,2,7,8,5,6]=>0001000
{{1,2},{3,4},{5,7},{6,8}}=>{{1,2},{3,4},{5,7},{6,8}}=>[2,1,4,3,7,8,5,6]=>0101000
{{1,2},{3,4},{5,8},{6,7}}=>{{1,2},{3,4},{5,8},{6,7}}=>[2,1,4,3,8,7,6,5]=>0101000
{{1,3},{2,4},{5,8},{6,7}}=>{{1,3},{2,4},{5,8},{6,7}}=>[3,4,1,2,8,7,6,5]=>0001000
{{1,4},{2,3},{5,8},{6,7}}=>{{1,4},{2,3},{5,8},{6,7}}=>[4,3,2,1,8,7,6,5]=>0001000
{{1,5},{2,3},{4,8},{6,7}}=>{{1,5},{2,3},{4,8},{6,7}}=>[5,3,2,8,1,7,6,4]=>0000000
{{1,6},{2,3},{4,8},{5,7}}=>{{1,6},{2,3},{4,8},{5,7}}=>[6,3,2,8,7,1,5,4]=>0000000
{{1,7},{2,3},{4,8},{5,6}}=>{{1,7},{2,3},{4,8},{5,6}}=>[7,3,2,8,6,5,1,4]=>0000000
{{1,8},{2,3},{4,7},{5,6}}=>{{1,8},{2,3},{4,7},{5,6}}=>[8,3,2,7,6,5,4,1]=>0000000
{{1,8},{2,4},{3,7},{5,6}}=>{{1,8},{2,4},{3,7},{5,6}}=>[8,4,7,2,6,5,3,1]=>0000000
{{1,7},{2,4},{3,8},{5,6}}=>{{1,7},{2,4},{3,8},{5,6}}=>[7,4,8,2,6,5,1,3]=>0000000
{{1,6},{2,4},{3,8},{5,7}}=>{{1,6},{2,4},{3,8},{5,7}}=>[6,4,8,2,7,1,5,3]=>0000000
{{1,5},{2,4},{3,8},{6,7}}=>{{1,5},{2,4},{3,8},{6,7}}=>[5,4,8,2,1,7,6,3]=>0000000
{{1,4},{2,5},{3,8},{6,7}}=>{{1,4},{2,5},{3,8},{6,7}}=>[4,5,8,1,2,7,6,3]=>0000000
{{1,3},{2,5},{4,8},{6,7}}=>{{1,3},{2,5},{4,8},{6,7}}=>[3,5,1,8,2,7,6,4]=>0000000
{{1,2},{3,5},{4,8},{6,7}}=>{{1,2},{3,5},{4,8},{6,7}}=>[2,1,5,8,3,7,6,4]=>0100000
{{1,2},{3,6},{4,8},{5,7}}=>{{1,2},{3,6},{4,8},{5,7}}=>[2,1,6,8,7,3,5,4]=>0100000
{{1,3},{2,6},{4,8},{5,7}}=>{{1,3},{2,6},{4,8},{5,7}}=>[3,6,1,8,7,2,5,4]=>0000000
{{1,4},{2,6},{3,8},{5,7}}=>{{1,4},{2,6},{3,8},{5,7}}=>[4,6,8,1,7,2,5,3]=>0000000
{{1,5},{2,6},{3,8},{4,7}}=>{{1,5},{2,6},{3,8},{4,7}}=>[5,6,8,7,1,2,4,3]=>0000000
{{1,6},{2,5},{3,8},{4,7}}=>{{1,6},{2,5},{3,8},{4,7}}=>[6,5,8,7,2,1,4,3]=>0000000
{{1,7},{2,5},{3,8},{4,6}}=>{{1,7},{2,5},{3,8},{4,6}}=>[7,5,8,6,2,4,1,3]=>0000000
{{1,8},{2,5},{3,7},{4,6}}=>{{1,8},{2,5},{3,7},{4,6}}=>[8,5,7,6,2,4,3,1]=>0000000
{{1,8},{2,6},{3,7},{4,5}}=>{{1,8},{2,6},{3,7},{4,5}}=>[8,6,7,5,4,2,3,1]=>0000000
{{1,7},{2,6},{3,8},{4,5}}=>{{1,7},{2,6},{3,8},{4,5}}=>[7,6,8,5,4,2,1,3]=>0000000
{{1,6},{2,7},{3,8},{4,5}}=>{{1,6},{2,7},{3,8},{4,5}}=>[6,7,8,5,4,1,2,3]=>0000000
{{1,5},{2,7},{3,8},{4,6}}=>{{1,5},{2,7},{3,8},{4,6}}=>[5,7,8,6,1,4,2,3]=>0000000
{{1,4},{2,7},{3,8},{5,6}}=>{{1,4},{2,7},{3,8},{5,6}}=>[4,7,8,1,6,5,2,3]=>0000000
{{1,3},{2,7},{4,8},{5,6}}=>{{1,3},{2,7},{4,8},{5,6}}=>[3,7,1,8,6,5,2,4]=>0000000
{{1,2},{3,7},{4,8},{5,6}}=>{{1,2},{3,7},{4,8},{5,6}}=>[2,1,7,8,6,5,3,4]=>0100000
{{1,2},{3,8},{4,7},{5,6}}=>{{1,2},{3,8},{4,7},{5,6}}=>[2,1,8,7,6,5,4,3]=>0100000
{{1,3},{2,8},{4,7},{5,6}}=>{{1,3},{2,8},{4,7},{5,6}}=>[3,8,1,7,6,5,4,2]=>0000000
{{1,4},{2,8},{3,7},{5,6}}=>{{1,4},{2,8},{3,7},{5,6}}=>[4,8,7,1,6,5,3,2]=>0000000
{{1,5},{2,8},{3,7},{4,6}}=>{{1,5},{2,8},{3,7},{4,6}}=>[5,8,7,6,1,4,3,2]=>0000000
{{1,6},{2,8},{3,7},{4,5}}=>{{1,6},{2,8},{3,7},{4,5}}=>[6,8,7,5,4,1,3,2]=>0000000
{{1,7},{2,8},{3,6},{4,5}}=>{{1,7},{2,8},{3,6},{4,5}}=>[7,8,6,5,4,3,1,2]=>0000000
{{1,8},{2,7},{3,6},{4,5}}=>{{1,8},{2,7},{3,6},{4,5}}=>[8,7,6,5,4,3,2,1]=>0000000
{{1,2},{3,4,5,6},{7,8}}=>{{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>0100010
{{1,4},{2,3,5,7},{6,8}}=>{{1,4},{2,3,5,7},{6,8}}=>[4,3,5,1,7,8,2,6]=>0000000
{{1,3},{2,4,5,7},{6,8}}=>{{1,3},{2,4,5,7},{6,8}}=>[3,4,1,5,7,8,2,6]=>0000000
{{1,2,3,6},{4,7},{5,8}}=>{{1,6},{2},{3},{4,7},{5,8}}=>[6,2,3,7,8,1,4,5]=>0000000
{{1,3},{2,4},{5,6,7,8}}=>{{1,3},{2,4},{5,6,7,8}}=>[3,4,1,2,6,7,8,5]=>0001000
{{1,3},{2,5},{4,6,7,8}}=>{{1,3},{2,5},{4,6,7,8}}=>[3,5,1,6,2,7,8,4]=>0000000
{{1,2},{3,5},{4,6,7,8}}=>{{1,2},{3,5},{4,6,7,8}}=>[2,1,5,6,3,7,8,4]=>0100000
{{1,5},{2,4,6,8},{3,7}}=>{{1,5},{2,4,6,8},{3,7}}=>[5,4,7,6,1,8,3,2]=>0000000
Map
Callan switch
Description
Switch the first closer and the minimum of the smallest closer and the second element of the block containing 1 in a set partition.
More precisely, this involution implements a joint symmetry between St000971The smallest closer of a set partition. and St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition..
More precisely, this involution implements a joint symmetry between St000971The smallest closer of a set partition. and St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition..
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
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