Identifier
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Images
=>
Cc0005;cc-rep-0
[1,0,1,0]=>[1,2]=>1=>[1,1] [1,1,0,0]=>[2,1]=>0=>[2] [1,0,1,0,1,0]=>[1,2,3]=>11=>[1,1,1] [1,0,1,1,0,0]=>[1,3,2]=>10=>[1,2] [1,1,0,0,1,0]=>[2,1,3]=>01=>[2,1] [1,1,0,1,0,0]=>[2,3,1]=>00=>[3] [1,1,1,0,0,0]=>[3,2,1]=>00=>[3] [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>111=>[1,1,1,1] [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>110=>[1,1,2] [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>101=>[1,2,1] [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>100=>[1,3] [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>100=>[1,3] [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>011=>[2,1,1] [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>010=>[2,2] [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>001=>[3,1] [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>000=>[4] [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>000=>[4] [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>001=>[3,1] [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>000=>[4] [1,1,1,0,1,0,0,0]=>[4,2,3,1]=>000=>[4] [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>000=>[4] [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>1111=>[1,1,1,1,1] [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>1110=>[1,1,1,2] [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>1101=>[1,1,2,1] [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>1100=>[1,1,3] [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>1100=>[1,1,3] [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>1011=>[1,2,1,1] [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>1010=>[1,2,2] [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>1001=>[1,3,1] [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>1000=>[1,4] [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>1000=>[1,4] [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>1001=>[1,3,1] [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>1000=>[1,4] [1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>1000=>[1,4] [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>1000=>[1,4] [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>0111=>[2,1,1,1] [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>0110=>[2,1,2] [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>0101=>[2,2,1] [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>0100=>[2,3] [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>0100=>[2,3] [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>0011=>[3,1,1] [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>0010=>[3,2] [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>0001=>[4,1] [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>0000=>[5] [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>0000=>[5] [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>0001=>[4,1] [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>0000=>[5] [1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>0000=>[5] [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>0000=>[5] [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>0011=>[3,1,1] [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>0010=>[3,2] [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>0001=>[4,1] [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>0000=>[5] [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>0000=>[5] [1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>0001=>[4,1] [1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>0000=>[5] [1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>0000=>[5] [1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>0000=>[5] [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>0001=>[4,1] [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>0000=>[5] [1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>0000=>[5] [1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>0000=>[5] [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>0000=>[5] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>11111=>[1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>11110=>[1,1,1,1,2] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>11101=>[1,1,1,2,1] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>11100=>[1,1,1,3] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>11100=>[1,1,1,3] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>11011=>[1,1,2,1,1] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>11010=>[1,1,2,2] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>11001=>[1,1,3,1] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>11000=>[1,1,4] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>11000=>[1,1,4] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>11001=>[1,1,3,1] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>11000=>[1,1,4] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>11000=>[1,1,4] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>11000=>[1,1,4] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>10111=>[1,2,1,1,1] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>10110=>[1,2,1,2] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>10101=>[1,2,2,1] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>10100=>[1,2,3] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>10100=>[1,2,3] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>10011=>[1,3,1,1] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>10010=>[1,3,2] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>10001=>[1,4,1] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>10000=>[1,5] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>10000=>[1,5] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>10001=>[1,4,1] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>10000=>[1,5] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>10000=>[1,5] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>10000=>[1,5] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>10011=>[1,3,1,1] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>10010=>[1,3,2] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>10001=>[1,4,1] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>10000=>[1,5] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>10000=>[1,5] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>10001=>[1,4,1] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>10000=>[1,5] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>10000=>[1,5] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>10000=>[1,5] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>10001=>[1,4,1] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>10000=>[1,5] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>10000=>[1,5] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>10000=>[1,5] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>10000=>[1,5] [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>01111=>[2,1,1,1,1] [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>01110=>[2,1,1,2] [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>01101=>[2,1,2,1] [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>01100=>[2,1,3] [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>01100=>[2,1,3] [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>01011=>[2,2,1,1] [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>01010=>[2,2,2] [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>01001=>[2,3,1] [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>01000=>[2,4] [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>01000=>[2,4] [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>01001=>[2,3,1] [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>01000=>[2,4] [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>01000=>[2,4] [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>01000=>[2,4] [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>00111=>[3,1,1,1] [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>00110=>[3,1,2] [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>00101=>[3,2,1] [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>00100=>[3,3] [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>00100=>[3,3] [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>00011=>[4,1,1] [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>00010=>[4,2] [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>00001=>[5,1] [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>00000=>[6] [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>00000=>[6] [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>00001=>[5,1] [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>00000=>[6] [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>00000=>[6] [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>00000=>[6] [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>00011=>[4,1,1] [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>00010=>[4,2] [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>00001=>[5,1] [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>00000=>[6] [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>00000=>[6] [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>00001=>[5,1] [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>00000=>[6] [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>00000=>[6] [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>00000=>[6] [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>00001=>[5,1] [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>00000=>[6] [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>00000=>[6] [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>00000=>[6] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>00000=>[6] [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>00111=>[3,1,1,1] [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>00110=>[3,1,2] [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>00101=>[3,2,1] [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>00100=>[3,3] [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>00100=>[3,3] [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>00011=>[4,1,1] [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>00010=>[4,2] [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>00001=>[5,1] [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>00000=>[6] [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>00000=>[6] [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>00001=>[5,1] [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>00000=>[6] [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>00000=>[6] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>00000=>[6] [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>00011=>[4,1,1] [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>00010=>[4,2] [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>00001=>[5,1] [1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>00000=>[6] [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>00000=>[6] [1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>00001=>[5,1] [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>00000=>[6] [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>00000=>[6] [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>00000=>[6] [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>00001=>[5,1] [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>00000=>[6] [1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>00000=>[6] [1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>00000=>[6] [1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>00000=>[6] [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>00011=>[4,1,1] [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>00010=>[4,2] [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>00001=>[5,1] [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>00000=>[6] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>00000=>[6] [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>00001=>[5,1] [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>00000=>[6] [1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>00000=>[6] [1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>00000=>[6] [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>00001=>[5,1] [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>00000=>[6] [1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>00000=>[6] [1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>00000=>[6] [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>00000=>[6] [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>00001=>[5,1] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>00000=>[6] [1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>00000=>[6] [1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>00000=>[6] [1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>00000=>[6] [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>00000=>[6] [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>111111=>[1,1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>111110=>[1,1,1,1,1,2] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>111101=>[1,1,1,1,2,1] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>111100=>[1,1,1,1,3] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>111100=>[1,1,1,1,3] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>111011=>[1,1,1,2,1,1] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>111010=>[1,1,1,2,2] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>111001=>[1,1,1,3,1] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>111000=>[1,1,1,4] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>111000=>[1,1,1,4] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>111001=>[1,1,1,3,1] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>111000=>[1,1,1,4] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,7,5,6,4]=>111000=>[1,1,1,4] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>111000=>[1,1,1,4] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>110111=>[1,1,2,1,1,1] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>110110=>[1,1,2,1,2] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>110101=>[1,1,2,2,1] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>110100=>[1,1,2,3] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>110100=>[1,1,2,3] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>110011=>[1,1,3,1,1] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>110010=>[1,1,3,2] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>110001=>[1,1,4,1] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>110000=>[1,1,5] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>110000=>[1,1,5] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>110001=>[1,1,4,1] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>110000=>[1,1,5] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,7,5,6,3]=>110000=>[1,1,5] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>110000=>[1,1,5] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>110011=>[1,1,3,1,1] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>110010=>[1,1,3,2] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>110001=>[1,1,4,1] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>110000=>[1,1,5] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>110000=>[1,1,5] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,6,4,5,3,7]=>110001=>[1,1,4,1] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,6,4,5,7,3]=>110000=>[1,1,5] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,7,4,5,6,3]=>110000=>[1,1,5] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,7,4,6,5,3]=>110000=>[1,1,5] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>110001=>[1,1,4,1] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>110000=>[1,1,5] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,7,5,4,6,3]=>110000=>[1,1,5] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,7,5,6,4,3]=>110000=>[1,1,5] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>110000=>[1,1,5] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>101111=>[1,2,1,1,1,1] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>101110=>[1,2,1,1,2] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>101101=>[1,2,1,2,1] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>101100=>[1,2,1,3] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>101100=>[1,2,1,3] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>101011=>[1,2,2,1,1] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>101010=>[1,2,2,2] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>101001=>[1,2,3,1] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>101000=>[1,2,4] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>101000=>[1,2,4] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>101001=>[1,2,3,1] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>101000=>[1,2,4] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,7,5,6,4]=>101000=>[1,2,4] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>101000=>[1,2,4] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>100111=>[1,3,1,1,1] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>100110=>[1,3,1,2] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>100101=>[1,3,2,1] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>100100=>[1,3,3] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>100100=>[1,3,3] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>100011=>[1,4,1,1] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>100010=>[1,4,2] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>100001=>[1,5,1] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>100000=>[1,6] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>100000=>[1,6] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>100001=>[1,5,1] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>100000=>[1,6] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,7,5,6,2]=>100000=>[1,6] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>100000=>[1,6] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>100011=>[1,4,1,1] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>100010=>[1,4,2] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>100001=>[1,5,1] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>100000=>[1,6] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>100000=>[1,6] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,6,4,5,2,7]=>100001=>[1,5,1] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,6,4,5,7,2]=>100000=>[1,6] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,7,4,5,6,2]=>100000=>[1,6] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,7,4,6,5,2]=>100000=>[1,6] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>100001=>[1,5,1] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>100000=>[1,6] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,7,5,4,6,2]=>100000=>[1,6] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,7,5,6,4,2]=>100000=>[1,6] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>100000=>[1,6] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>100111=>[1,3,1,1,1] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>100110=>[1,3,1,2] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>100101=>[1,3,2,1] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>100100=>[1,3,3] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>100100=>[1,3,3] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>100011=>[1,4,1,1] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>100010=>[1,4,2] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>100001=>[1,5,1] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>100000=>[1,6] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>100000=>[1,6] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>100001=>[1,5,1] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>100000=>[1,6] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,7,5,6,2]=>100000=>[1,6] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>100000=>[1,6] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,3,4,2,6,7]=>100011=>[1,4,1,1] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,3,4,2,7,6]=>100010=>[1,4,2] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,3,4,6,2,7]=>100001=>[1,5,1] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,5,3,4,6,7,2]=>100000=>[1,6] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,5,3,4,7,6,2]=>100000=>[1,6] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,3,4,5,2,7]=>100001=>[1,5,1] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6,3,4,5,7,2]=>100000=>[1,6] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,7,3,4,5,6,2]=>100000=>[1,6] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,7,3,4,6,5,2]=>100000=>[1,6] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,3,5,4,2,7]=>100001=>[1,5,1] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6,3,5,4,7,2]=>100000=>[1,6] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,7,3,5,4,6,2]=>100000=>[1,6] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,7,3,5,6,4,2]=>100000=>[1,6] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,7,3,6,5,4,2]=>100000=>[1,6] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>100011=>[1,4,1,1] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>100010=>[1,4,2] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>100001=>[1,5,1] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>100000=>[1,6] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>100000=>[1,6] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,4,3,5,2,7]=>100001=>[1,5,1] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6,4,3,5,7,2]=>100000=>[1,6] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,7,4,3,5,6,2]=>100000=>[1,6] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,7,4,3,6,5,2]=>100000=>[1,6] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,4,5,3,2,7]=>100001=>[1,5,1] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6,4,5,3,7,2]=>100000=>[1,6] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,7,4,5,3,6,2]=>100000=>[1,6] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,7,4,5,6,3,2]=>100000=>[1,6] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,7,4,6,5,3,2]=>100000=>[1,6] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>100001=>[1,5,1] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>100000=>[1,6] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,7,5,4,3,6,2]=>100000=>[1,6] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,7,5,4,6,3,2]=>100000=>[1,6] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,7,6,4,5,3,2]=>100000=>[1,6] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>100000=>[1,6] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>011111=>[2,1,1,1,1,1] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>011110=>[2,1,1,1,2] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>011101=>[2,1,1,2,1] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>011100=>[2,1,1,3] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>011100=>[2,1,1,3] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>011011=>[2,1,2,1,1] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>011010=>[2,1,2,2] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>011001=>[2,1,3,1] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>011000=>[2,1,4] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>011000=>[2,1,4] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>011001=>[2,1,3,1] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>011000=>[2,1,4] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,7,5,6,4]=>011000=>[2,1,4] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>011000=>[2,1,4] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>010111=>[2,2,1,1,1] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>010110=>[2,2,1,2] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>010101=>[2,2,2,1] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>010100=>[2,2,3] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>010100=>[2,2,3] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>010011=>[2,3,1,1] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>010010=>[2,3,2] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>010001=>[2,4,1] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>010000=>[2,5] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>010000=>[2,5] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>010001=>[2,4,1] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>010000=>[2,5] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,7,5,6,3]=>010000=>[2,5] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>010000=>[2,5] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>010011=>[2,3,1,1] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>010010=>[2,3,2] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>010001=>[2,4,1] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>010000=>[2,5] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>010000=>[2,5] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,6,4,5,3,7]=>010001=>[2,4,1] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,6,4,5,7,3]=>010000=>[2,5] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,7,4,5,6,3]=>010000=>[2,5] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,7,4,6,5,3]=>010000=>[2,5] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>010001=>[2,4,1] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>010000=>[2,5] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,7,5,4,6,3]=>010000=>[2,5] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,7,5,6,4,3]=>010000=>[2,5] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>010000=>[2,5] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>001111=>[3,1,1,1,1] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>001110=>[3,1,1,2] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>001101=>[3,1,2,1] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>001100=>[3,1,3] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>001100=>[3,1,3] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>001011=>[3,2,1,1] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>001010=>[3,2,2] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>001001=>[3,3,1] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>001000=>[3,4] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>001000=>[3,4] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>001001=>[3,3,1] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>001000=>[3,4] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,7,5,6,4]=>001000=>[3,4] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>001000=>[3,4] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>000111=>[4,1,1,1] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>000110=>[4,1,2] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>000101=>[4,2,1] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>000100=>[4,3] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>000100=>[4,3] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>000011=>[5,1,1] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>000010=>[5,2] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>000001=>[6,1] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>000000=>[7] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>000000=>[7] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>000001=>[6,1] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>000000=>[7] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>000000=>[7] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>000000=>[7] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>000011=>[5,1,1] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>000010=>[5,2] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>000001=>[6,1] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>000000=>[7] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>000000=>[7] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,6,4,5,1,7]=>000001=>[6,1] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,6,4,5,7,1]=>000000=>[7] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>000000=>[7] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>000000=>[7] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>000001=>[6,1] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>000000=>[7] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,7,5,4,6,1]=>000000=>[7] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,7,5,6,4,1]=>000000=>[7] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>000000=>[7] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>000111=>[4,1,1,1] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>000110=>[4,1,2] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>000101=>[4,2,1] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>000100=>[4,3] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>000100=>[4,3] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>000011=>[5,1,1] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>000010=>[5,2] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>000001=>[6,1] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>000000=>[7] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>000000=>[7] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>000001=>[6,1] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>000000=>[7] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,7,5,6,1]=>000000=>[7] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>000000=>[7] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,3,4,1,6,7]=>000011=>[5,1,1] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,3,4,1,7,6]=>000010=>[5,2] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,3,4,6,1,7]=>000001=>[6,1] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,3,4,6,7,1]=>000000=>[7] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,3,4,7,6,1]=>000000=>[7] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,6,3,4,5,1,7]=>000001=>[6,1] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,6,3,4,5,7,1]=>000000=>[7] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,7,3,4,5,6,1]=>000000=>[7] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,7,3,4,6,5,1]=>000000=>[7] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,6,3,5,4,1,7]=>000001=>[6,1] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,6,3,5,4,7,1]=>000000=>[7] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,7,3,5,4,6,1]=>000000=>[7] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,7,3,5,6,4,1]=>000000=>[7] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,3,6,5,4,1]=>000000=>[7] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>000011=>[5,1,1] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>000010=>[5,2] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>000001=>[6,1] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>000000=>[7] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>000000=>[7] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,6,4,3,5,1,7]=>000001=>[6,1] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,6,4,3,5,7,1]=>000000=>[7] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,4,3,5,6,1]=>000000=>[7] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,7,4,3,6,5,1]=>000000=>[7] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,4,5,3,1,7]=>000001=>[6,1] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,4,5,3,7,1]=>000000=>[7] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,7,4,5,3,6,1]=>000000=>[7] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,7,4,5,6,3,1]=>000000=>[7] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,7,4,6,5,3,1]=>000000=>[7] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>000001=>[6,1] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>000000=>[7] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,7,5,4,3,6,1]=>000000=>[7] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,5,4,6,3,1]=>000000=>[7] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,6,4,5,3,1]=>000000=>[7] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>000000=>[7] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>001111=>[3,1,1,1,1] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>001110=>[3,1,1,2] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>001101=>[3,1,2,1] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>001100=>[3,1,3] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>001100=>[3,1,3] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>001011=>[3,2,1,1] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>001010=>[3,2,2] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>001001=>[3,3,1] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>001000=>[3,4] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>001000=>[3,4] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>001001=>[3,3,1] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>001000=>[3,4] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,7,5,6,4]=>001000=>[3,4] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>001000=>[3,4] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>000111=>[4,1,1,1] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>000110=>[4,1,2] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>000101=>[4,2,1] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>000100=>[4,3] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>000100=>[4,3] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>000011=>[5,1,1] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>000010=>[5,2] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>000001=>[6,1] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>000000=>[7] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>000000=>[7] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>000001=>[6,1] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>000000=>[7] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,7,5,6,1]=>000000=>[7] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>000000=>[7] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>000011=>[5,1,1] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>000010=>[5,2] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>000001=>[6,1] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>000000=>[7] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>000000=>[7] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,6,4,5,1,7]=>000001=>[6,1] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,6,4,5,7,1]=>000000=>[7] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,7,4,5,6,1]=>000000=>[7] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,7,4,6,5,1]=>000000=>[7] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>000001=>[6,1] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>000000=>[7] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,7,5,4,6,1]=>000000=>[7] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,7,5,6,4,1]=>000000=>[7] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>000000=>[7] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7]=>000111=>[4,1,1,1] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,2,3,1,5,7,6]=>000110=>[4,1,2] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,3,1,6,5,7]=>000101=>[4,2,1] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,2,3,1,6,7,5]=>000100=>[4,3] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,2,3,1,7,6,5]=>000100=>[4,3] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,2,3,5,1,6,7]=>000011=>[5,1,1] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,3,5,1,7,6]=>000010=>[5,2] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,2,3,5,6,1,7]=>000001=>[6,1] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,2,3,5,6,7,1]=>000000=>[7] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,2,3,5,7,6,1]=>000000=>[7] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,2,3,6,5,1,7]=>000001=>[6,1] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,3,6,5,7,1]=>000000=>[7] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,2,3,7,5,6,1]=>000000=>[7] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,2,3,7,6,5,1]=>000000=>[7] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,2,3,4,1,6,7]=>000011=>[5,1,1] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2,3,4,1,7,6]=>000010=>[5,2] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[5,2,3,4,6,1,7]=>000001=>[6,1] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,2,3,4,6,7,1]=>000000=>[7] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,2,3,4,7,6,1]=>000000=>[7] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,2,3,4,5,1,7]=>000001=>[6,1] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>000000=>[7] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,2,3,4,5,6,1]=>000000=>[7] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,2,3,4,6,5,1]=>000000=>[7] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,5,4,1,7]=>000001=>[6,1] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,2,3,5,4,7,1]=>000000=>[7] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7,2,3,5,4,6,1]=>000000=>[7] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,2,3,5,6,4,1]=>000000=>[7] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7,2,3,6,5,4,1]=>000000=>[7] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,2,4,3,1,6,7]=>000011=>[5,1,1] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,4,3,1,7,6]=>000010=>[5,2] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[5,2,4,3,6,1,7]=>000001=>[6,1] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,2,4,3,6,7,1]=>000000=>[7] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,2,4,3,7,6,1]=>000000=>[7] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,2,4,3,5,1,7]=>000001=>[6,1] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,2,4,3,5,7,1]=>000000=>[7] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,2,4,3,5,6,1]=>000000=>[7] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,2,4,3,6,5,1]=>000000=>[7] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,4,5,3,1,7]=>000001=>[6,1] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,2,4,5,3,7,1]=>000000=>[7] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,2,4,5,3,6,1]=>000000=>[7] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,2,4,5,6,3,1]=>000000=>[7] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,2,4,6,5,3,1]=>000000=>[7] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,2,5,4,3,1,7]=>000001=>[6,1] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,5,4,3,7,1]=>000000=>[7] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7,2,5,4,3,6,1]=>000000=>[7] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7,2,5,4,6,3,1]=>000000=>[7] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7,2,6,4,5,3,1]=>000000=>[7] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7,2,6,5,4,3,1]=>000000=>[7] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>000111=>[4,1,1,1] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>000110=>[4,1,2] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>000101=>[4,2,1] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>000100=>[4,3] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>000100=>[4,3] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>000011=>[5,1,1] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>000010=>[5,2] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>000001=>[6,1] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>000000=>[7] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>000000=>[7] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>000001=>[6,1] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>000000=>[7] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,7,5,6,1]=>000000=>[7] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>000000=>[7] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,3,2,4,1,6,7]=>000011=>[5,1,1] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,3,2,4,1,7,6]=>000010=>[5,2] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,3,2,4,6,1,7]=>000001=>[6,1] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,3,2,4,6,7,1]=>000000=>[7] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,3,2,4,7,6,1]=>000000=>[7] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1,7]=>000001=>[6,1] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>000000=>[7] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,2,4,5,6,1]=>000000=>[7] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,2,4,6,5,1]=>000000=>[7] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,3,2,5,4,1,7]=>000001=>[6,1] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,2,5,4,7,1]=>000000=>[7] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,2,5,4,6,1]=>000000=>[7] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,2,5,6,4,1]=>000000=>[7] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,2,6,5,4,1]=>000000=>[7] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,3,4,2,1,6,7]=>000011=>[5,1,1] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,3,4,2,1,7,6]=>000010=>[5,2] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,3,4,2,6,1,7]=>000001=>[6,1] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,3,4,2,6,7,1]=>000000=>[7] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,3,4,2,7,6,1]=>000000=>[7] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,4,2,5,1,7]=>000001=>[6,1] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>000000=>[7] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,4,2,5,6,1]=>000000=>[7] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,4,2,6,5,1]=>000000=>[7] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,3,4,5,2,1,7]=>000001=>[6,1] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>000000=>[7] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,3,4,5,2,6,1]=>000000=>[7] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,3,4,5,6,2,1]=>000000=>[7] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,3,4,6,5,2,1]=>000000=>[7] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,5,4,2,1,7]=>000001=>[6,1] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,3,5,4,2,7,1]=>000000=>[7] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7,3,5,4,2,6,1]=>000000=>[7] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,3,5,4,6,2,1]=>000000=>[7] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,3,6,4,5,2,1]=>000000=>[7] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,3,6,5,4,2,1]=>000000=>[7] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>000011=>[5,1,1] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>000010=>[5,2] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>000001=>[6,1] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>000000=>[7] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>000000=>[7] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,4,3,2,5,1,7]=>000001=>[6,1] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>000000=>[7] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7,4,3,2,5,6,1]=>000000=>[7] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7,4,3,2,6,5,1]=>000000=>[7] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,4,3,5,2,1,7]=>000001=>[6,1] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>000000=>[7] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7,4,3,5,2,6,1]=>000000=>[7] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7,4,3,5,6,2,1]=>000000=>[7] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7,4,3,6,5,2,1]=>000000=>[7] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,5,3,4,2,1,7]=>000001=>[6,1] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,5,3,4,2,7,1]=>000000=>[7] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7,5,3,4,2,6,1]=>000000=>[7] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7,5,3,4,6,2,1]=>000000=>[7] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7,6,3,4,5,2,1]=>000000=>[7] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,6,3,5,4,2,1]=>000000=>[7] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>000001=>[6,1] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>000000=>[7] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7,5,4,3,2,6,1]=>000000=>[7] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7,5,4,3,6,2,1]=>000000=>[7] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7,6,4,3,5,2,1]=>000000=>[7] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,6,4,5,3,2,1]=>000000=>[7] [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>000000=>[7] [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>1111111=>[1,1,1,1,1,1,1,1] [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>1111110=>[1,1,1,1,1,1,2] [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>1111101=>[1,1,1,1,1,2,1] [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>1111100=>[1,1,1,1,1,3] [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>1111100=>[1,1,1,1,1,3] [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>1111011=>[1,1,1,1,2,1,1] [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>1111010=>[1,1,1,1,2,2] [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>1111001=>[1,1,1,1,3,1] [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>1111000=>[1,1,1,1,4] [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>1111000=>[1,1,1,1,4] [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>1111001=>[1,1,1,1,3,1] [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>1111000=>[1,1,1,1,4] [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,8,6,7,5]=>1111000=>[1,1,1,1,4] [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>1111000=>[1,1,1,1,4] [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>1110111=>[1,1,1,2,1,1,1] [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>1110101=>[1,1,1,2,2,1] [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>1110100=>[1,1,1,2,3] [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>1110100=>[1,1,1,2,3] [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>1110011=>[1,1,1,3,1,1] [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>1110010=>[1,1,1,3,2] [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>1110001=>[1,1,1,4,1] [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,6,4,8]=>1110001=>[1,1,1,4,1] [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,8,6,7,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>1110010=>[1,1,1,3,2] [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,5,7,4,8]=>1110001=>[1,1,1,4,1] [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,7,5,6,4,8]=>1110001=>[1,1,1,4,1] [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,7,5,6,8,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,8,5,6,7,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,8,5,7,6,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>1110001=>[1,1,1,4,1] [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,8,6,5,7,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,8,6,7,5,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>1110000=>[1,1,1,5] [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>1101111=>[1,1,2,1,1,1,1] [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>1101110=>[1,1,2,1,1,2] [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,3,5,7,8,6]=>1101100=>[1,1,2,1,3] [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>1101011=>[1,1,2,2,1,1] [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>1101010=>[1,1,2,2,2] [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,3,6,7,5,8]=>1101001=>[1,1,2,3,1] [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>1101000=>[1,1,2,4] [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,7,5]=>1101000=>[1,1,2,4] [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>1101000=>[1,1,2,4] [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>1100100=>[1,1,3,3] [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>1100011=>[1,1,4,1,1] [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,8,6,7,3]=>1100000=>[1,1,6] [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,5,8,7,3]=>1100000=>[1,1,6] [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,4,7,6,5,8,3]=>1100000=>[1,1,6] [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,8,6,5,7,3]=>1100000=>[1,1,6] [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>1100000=>[1,1,6] [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,4,3,6,8,7]=>1100110=>[1,1,3,1,2] [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,4,3,7,8,6]=>1100100=>[1,1,3,3] [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,5,4,6,7,3,8]=>1100001=>[1,1,5,1] [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,5,4,6,8,7,3]=>1100000=>[1,1,6] [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,5,4,8,6,7,3]=>1100000=>[1,1,6] [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,4,8,7,6,3]=>1100000=>[1,1,6] [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,6,4,5,3,7,8]=>1100011=>[1,1,4,1,1] [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,8,4,5,6,7,3]=>1100000=>[1,1,6] [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>1100011=>[1,1,4,1,1] [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,5,4,8,7,3]=>1100000=>[1,1,6] [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,7,5,4,6,8,3]=>1100000=>[1,1,6] [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,8,5,4,6,7,3]=>1100000=>[1,1,6] [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,8,5,4,7,6,3]=>1100000=>[1,1,6] [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>1100000=>[1,1,6] [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>1011111=>[1,2,1,1,1,1,1] [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>1011101=>[1,2,1,1,2,1] [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>1011011=>[1,2,1,2,1,1] [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>1011010=>[1,2,1,2,2] [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>1011000=>[1,2,1,4] [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>1011000=>[1,2,1,4] [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,7,6,5,8]=>1011001=>[1,2,1,3,1] [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>1011000=>[1,2,1,4] [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>1010111=>[1,2,2,1,1,1] [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>1010101=>[1,2,2,2,1] [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>1010100=>[1,2,2,3] [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>1010100=>[1,2,2,3] [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,5,7,4,8]=>1010001=>[1,2,4,1] [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,5,8,7,4]=>1010000=>[1,2,5] [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,2,7,5,6,8,4]=>1010000=>[1,2,5] [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2,8,5,7,6,4]=>1010000=>[1,2,5] [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>1010000=>[1,2,5] [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>1001111=>[1,3,1,1,1,1] [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>1001100=>[1,3,1,3] [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>1001001=>[1,3,3,1] [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,7,5]=>1001000=>[1,3,4] [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>1001000=>[1,3,4] [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>1000001=>[1,6,1] [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,6,5,8,2]=>1000000=>[1,7] [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>1000000=>[1,7] [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,4,2,6,8,7]=>1000110=>[1,4,1,2] [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,4,7,6,2,8]=>1000001=>[1,6,1] [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,6,4,5,2,8,7]=>1000010=>[1,5,2] [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,6,4,5,7,2,8]=>1000001=>[1,6,1] [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,4,5,8,7,2]=>1000000=>[1,7] [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,8,4,5,6,7,2]=>1000000=>[1,7] [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,8,4,6,7,5,2]=>1000000=>[1,7] [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,6,5,4,2,8,7]=>1000010=>[1,5,2] [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,6,5,4,7,2,8]=>1000001=>[1,6,1] [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,5,4,8,7,2]=>1000000=>[1,7] [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,8,5,4,6,7,2]=>1000000=>[1,7] [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,8,5,6,7,4,2]=>1000000=>[1,7] [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,8,5,7,6,4,2]=>1000000=>[1,7] [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,8,6,5,7,4,2]=>1000000=>[1,7] [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,8,7,5,6,4,2]=>1000000=>[1,7] [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>1000000=>[1,7] [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>1001111=>[1,3,1,1,1,1] [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,3,2,5,6,8,7]=>1001110=>[1,3,1,1,2] [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,3,2,5,7,6,8]=>1001101=>[1,3,1,2,1] [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,3,2,5,8,7,6]=>1001100=>[1,3,1,3] [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,4,3,2,6,7,5,8]=>1001001=>[1,3,3,1] [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>1001000=>[1,3,4] [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>1001001=>[1,3,3,1] [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>1001000=>[1,3,4] [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,3,5,2,7,6,8]=>1000101=>[1,4,2,1] [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,3,5,7,6,2,8]=>1000001=>[1,6,1] [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,3,5,8,7,6,2]=>1000000=>[1,7] [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,3,6,5,2,7,8]=>1000011=>[1,5,1,1] [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,3,6,5,7,2,8]=>1000001=>[1,6,1] [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>1000000=>[1,7] [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,3,8,5,6,7,2]=>1000000=>[1,7] [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,3,8,5,7,6,2]=>1000000=>[1,7] [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,8,6,7,5,2]=>1000000=>[1,7] [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>1000000=>[1,7] [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,5,3,4,2,7,8,6]=>1000100=>[1,4,3] [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,5,3,4,2,8,7,6]=>1000100=>[1,4,3] [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,3,4,8,6,7,2]=>1000000=>[1,7] [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,8,3,4,6,7,5,2]=>1000000=>[1,7] [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,6,3,5,4,2,7,8]=>1000011=>[1,5,1,1] [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,6,3,5,4,8,7,2]=>1000000=>[1,7] [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,8,3,5,6,4,7,2]=>1000000=>[1,7] [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,8,3,5,7,6,4,2]=>1000000=>[1,7] [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,8,3,6,5,4,7,2]=>1000000=>[1,7] [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,8,3,7,6,5,4,2]=>1000000=>[1,7] [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,4,3,6,2,7,8]=>1000011=>[1,5,1,1] [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>1000000=>[1,7] [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>1000000=>[1,7] [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,6,4,3,5,2,7,8]=>1000011=>[1,5,1,1] [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,8,4,3,5,6,7,2]=>1000000=>[1,7] [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,8,4,3,5,7,6,2]=>1000000=>[1,7] [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,6,4,5,3,8,7,2]=>1000000=>[1,7] [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,8,4,5,6,7,3,2]=>1000000=>[1,7] [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,8,4,6,5,7,3,2]=>1000000=>[1,7] [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,8,4,7,6,5,3,2]=>1000000=>[1,7] [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>1000000=>[1,7] [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,7,5,4,3,6,8,2]=>1000000=>[1,7] [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,8,5,4,3,6,7,2]=>1000000=>[1,7] [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,8,5,4,6,3,7,2]=>1000000=>[1,7] [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,8,5,4,6,7,3,2]=>1000000=>[1,7] [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,8,5,4,7,6,3,2]=>1000000=>[1,7] [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,8,6,4,5,7,3,2]=>1000000=>[1,7] [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,8,6,5,4,7,3,2]=>1000000=>[1,7] [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,8,7,5,6,4,3,2]=>1000000=>[1,7] [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>1000000=>[1,7] [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>0111111=>[2,1,1,1,1,1,1] [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>0111110=>[2,1,1,1,1,2] [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>0111011=>[2,1,1,2,1,1] [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>0111010=>[2,1,1,2,2] [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>0111000=>[2,1,1,4] [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,8,6,7,5]=>0111000=>[2,1,1,4] [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>0111000=>[2,1,1,4] [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>0110110=>[2,1,2,1,2] [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>0110100=>[2,1,2,3] [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,5,4,8,7]=>0110010=>[2,1,3,2] [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>0110000=>[2,1,5] [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>0101111=>[2,2,1,1,1,1] [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>0101110=>[2,2,1,1,2] [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>0101011=>[2,2,2,1,1] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>0101010=>[2,2,2,2] [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,3,6,7,5,8]=>0101001=>[2,2,3,1] [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>0101000=>[2,2,4] [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>0101000=>[2,2,4] [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>0100010=>[2,4,2] [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,7,3]=>0100000=>[2,6] [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,5,3,7,8]=>0100011=>[2,4,1,1] [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>0100000=>[2,6] [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>0100000=>[2,6] [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,4,8,6,5,7,3]=>0100000=>[2,6] [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>0100000=>[2,6] [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>0100110=>[2,3,1,2] [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>0100000=>[2,6] [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,6,4,5,8,7,3]=>0100000=>[2,6] [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>0100010=>[2,4,2] [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,8,5,4,6,7,3]=>0100000=>[2,6] [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,8,5,4,7,6,3]=>0100000=>[2,6] [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,7,5,6,4,8,3]=>0100000=>[2,6] [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,8,7,5,6,4,3]=>0100000=>[2,6] [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>0100000=>[2,6] [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>0011111=>[3,1,1,1,1,1] [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>0011100=>[3,1,1,3] [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>0011000=>[3,1,4] [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>0010101=>[3,2,2,1] [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>0010000=>[3,5] [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,6,5,4,8,7]=>0010010=>[3,3,2] [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,5,7,4,8]=>0010001=>[3,4,1] [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>0010000=>[3,5] [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,8,6,7,5,4]=>0010000=>[3,5] [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>0010000=>[3,5] [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>0001111=>[4,1,1,1,1] [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>0001000=>[4,4] [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>0001000=>[4,4] [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>0000100=>[5,3] [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>0000000=>[8] [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>0000000=>[8] [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,1]=>0000000=>[8] [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,5,8,7,1]=>0000000=>[8] [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,6,5,1,8]=>0000001=>[7,1] [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>0000000=>[8] [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>0000000=>[8] [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>0000100=>[5,3] [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,4,8,7,6,1]=>0000000=>[8] [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,6,4,5,7,8,1]=>0000000=>[8] [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,7,4,5,6,8,1]=>0000000=>[8] [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,8,4,5,6,7,1]=>0000000=>[8] [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,7,4,6,5,8,1]=>0000000=>[8] [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,5,4,7,8,1]=>0000000=>[8] [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,7,5,4,6,8,1]=>0000000=>[8] [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,7,5,6,4,1,8]=>0000001=>[7,1] [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,7,5,6,4,8,1]=>0000000=>[8] [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,6,5,4,1,8]=>0000001=>[7,1] [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>0000000=>[8] [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>0000000=>[8] [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8]=>0001111=>[4,1,1,1,1] [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>0001000=>[4,4] [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>0001000=>[4,4] [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,3,5,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,3,5,1,7,6,8]=>0000101=>[5,2,1] [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,3,5,1,8,7,6]=>0000100=>[5,3] [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,1]=>0000000=>[8] [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>0000000=>[8] [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,7,6,8,1]=>0000000=>[8] [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,4,3,5,8,6,7,1]=>0000000=>[8] [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,6,5,7,1,8]=>0000001=>[7,1] [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>0000000=>[8] [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>0000000=>[8] [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>0000000=>[8] [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>0000000=>[8] [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,5,3,4,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,5,3,4,1,8,7,6]=>0000100=>[5,3] [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,5,3,4,6,7,1,8]=>0000001=>[7,1] [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,5,3,4,8,7,6,1]=>0000000=>[8] [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,6,3,4,5,7,8,1]=>0000000=>[8] [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,6,3,5,4,1,8,7]=>0000010=>[6,2] [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,6,3,5,4,7,8,1]=>0000000=>[8] [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,7,3,5,4,6,8,1]=>0000000=>[8] [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,7,3,5,6,4,8,1]=>0000000=>[8] [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,8,3,5,7,6,4,1]=>0000000=>[8] [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,7,3,6,5,4,1,8]=>0000001=>[7,1] [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,5,4,3,1,6,8,7]=>0000110=>[5,1,2] [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>0000100=>[5,3] [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,5,4,3,6,7,1,8]=>0000001=>[7,1] [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>0000000=>[8] [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>0000000=>[8] [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>0000000=>[8] [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,8,6,7,1]=>0000000=>[8] [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>0000000=>[8] [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,6,4,3,5,7,8,1]=>0000000=>[8] [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,8,4,3,5,6,7,1]=>0000000=>[8] [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,8,4,3,7,6,5,1]=>0000000=>[8] [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,6,4,5,3,1,7,8]=>0000011=>[6,1,1] [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,6,4,5,3,7,8,1]=>0000000=>[8] [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,6,5,4,3,7,8,1]=>0000000=>[8] [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,7,5,4,3,6,8,1]=>0000000=>[8] [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,7,5,4,6,3,8,1]=>0000000=>[8] [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,8,5,4,7,6,3,1]=>0000000=>[8] [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,8,7,5,4,6,3,1]=>0000000=>[8] [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,8,7,5,6,4,3,1]=>0000000=>[8] [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>0000000=>[8] [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>0011111=>[3,1,1,1,1,1] [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,5,7,8,6]=>0011100=>[3,1,1,3] [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>0011100=>[3,1,1,3] [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,2,1,4,6,8,7,5]=>0011000=>[3,1,4] [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>0011001=>[3,1,3,1] [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,8,6,7,5]=>0011000=>[3,1,4] [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>0011000=>[3,1,4] [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>0010101=>[3,2,2,1] [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,5,6,4,7,8]=>0010011=>[3,3,1,1] [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>0010000=>[3,5] [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>0010000=>[3,5] [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,5,7,6,4,8]=>0010001=>[3,4,1] [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>0010000=>[3,5] [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,8,6,7,4]=>0010000=>[3,5] [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>0010000=>[3,5] [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,2,1,6,5,7,4,8]=>0010001=>[3,4,1] [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>0010000=>[3,5] [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>0010000=>[3,5] [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,2,1,7,5,6,4,8]=>0010001=>[3,4,1] [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,7,5,6,8,4]=>0010000=>[3,5] [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,8,5,6,7,4]=>0010000=>[3,5] [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,8,5,7,6,4]=>0010000=>[3,5] [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>0010000=>[3,5] [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,8,6,5,7,4]=>0010000=>[3,5] [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,8,6,7,5,4]=>0010000=>[3,5] [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>0010000=>[3,5] [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>0001111=>[4,1,1,1,1] [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>0001100=>[4,1,3] [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>0001011=>[4,2,1,1] [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>0001010=>[4,2,2] [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>0001000=>[4,4] [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,8,6,7,5]=>0001000=>[4,4] [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>0001000=>[4,4] [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,5,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,5,1,8,7,6]=>0000100=>[5,3] [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>0000000=>[8] [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>0000000=>[8] [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,5,4,1,6,8,7]=>0000110=>[5,1,2] [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,5,4,1,7,6,8]=>0000101=>[5,2,1] [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,5,4,1,7,8,6]=>0000100=>[5,3] [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>0000100=>[5,3] [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>0000001=>[7,1] [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,7,4,6,5,1,8]=>0000001=>[7,1] [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,7,4,6,5,8,1]=>0000000=>[8] [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,2,6,5,4,7,1,8]=>0000001=>[7,1] [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,2,8,5,4,6,7,1]=>0000000=>[8] [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,7,5,6,4,1,8]=>0000001=>[7,1] [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,8,5,7,6,4,1]=>0000000=>[8] [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>0000001=>[7,1] [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>0000000=>[8] [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7,8]=>0001111=>[4,1,1,1,1] [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,2,3,1,8,6,7,5]=>0001000=>[4,4] [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,2,3,1,8,7,6,5]=>0001000=>[4,4] [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,2,3,5,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,2,3,5,1,7,8,6]=>0000100=>[5,3] [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,2,3,5,1,8,7,6]=>0000100=>[5,3] [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,2,3,5,6,8,7,1]=>0000000=>[8] [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,3,7,5,6,1,8]=>0000001=>[7,1] [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,3,8,5,6,7,1]=>0000000=>[8] [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[4,2,3,7,6,5,8,1]=>0000000=>[8] [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,2,3,8,7,6,5,1]=>0000000=>[8] [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[5,2,3,4,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,2,3,4,1,8,7,6]=>0000100=>[5,3] [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,2,3,4,8,7,6,1]=>0000000=>[8] [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,2,3,4,5,7,1,8]=>0000001=>[7,1] [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,2,3,5,4,1,7,8]=>0000011=>[6,1,1] [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,2,3,5,4,1,8,7]=>0000010=>[6,2] [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,2,3,5,4,7,1,8]=>0000001=>[7,1] [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,2,3,5,6,4,1,8]=>0000001=>[7,1] [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,6,5,4,1,8]=>0000001=>[7,1] [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,2,4,3,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,2,4,3,1,6,8,7]=>0000110=>[5,1,2] [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,4,3,1,7,6,8]=>0000101=>[5,2,1] [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,2,4,3,1,8,7,6]=>0000100=>[5,3] [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,2,4,3,6,1,7,8]=>0000011=>[6,1,1] [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,2,4,3,6,1,8,7]=>0000010=>[6,2] [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,2,4,3,7,6,1,8]=>0000001=>[7,1] [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,2,4,3,7,6,8,1]=>0000000=>[8] [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,2,4,3,6,5,1,8]=>0000001=>[7,1] [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,2,4,3,6,5,8,1]=>0000000=>[8] [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,2,4,5,3,1,7,8]=>0000011=>[6,1,1] [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,2,4,5,3,6,1,8]=>0000001=>[7,1] [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,2,4,5,3,6,8,1]=>0000000=>[8] [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[8,2,4,7,6,5,3,1]=>0000000=>[8] [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,2,5,4,3,1,8,7]=>0000010=>[6,2] [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,2,5,4,3,6,1,8]=>0000001=>[7,1] [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,2,6,4,5,7,3,1]=>0000000=>[8] [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[8,2,7,5,6,4,3,1]=>0000000=>[8] [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[8,2,7,6,5,4,3,1]=>0000000=>[8] [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>0001111=>[4,1,1,1,1] [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>0001110=>[4,1,1,2] [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>0001101=>[4,1,2,1] [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>0001100=>[4,1,3] [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>0001100=>[4,1,3] [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>0001011=>[4,2,1,1] [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>0001010=>[4,2,2] [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>0001001=>[4,3,1] [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>0001000=>[4,4] [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>0001000=>[4,4] [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>0001001=>[4,3,1] [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>0001000=>[4,4] [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,8,6,7,5]=>0001000=>[4,4] [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>0001000=>[4,4] [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>0000100=>[5,3] [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,3,2,5,6,8,7,1]=>0000000=>[8] [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,3,2,5,8,7,6,1]=>0000000=>[8] [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,3,2,6,5,1,7,8]=>0000011=>[6,1,1] [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,1]=>0000000=>[8] [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,3,2,6,5,8,7,1]=>0000000=>[8] [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,3,2,7,5,6,8,1]=>0000000=>[8] [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,8,5,6,7,1]=>0000000=>[8] [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>0000000=>[8] [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,2,8,6,7,5,1]=>0000000=>[8] [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>0000000=>[8] [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,3,2,4,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[5,3,2,4,1,6,8,7]=>0000110=>[5,1,2] [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,3,2,4,1,8,7,6]=>0000100=>[5,3] [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,3,2,4,6,1,7,8]=>0000011=>[6,1,1] [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,3,2,4,6,1,8,7]=>0000010=>[6,2] [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[6,3,2,4,5,7,1,8]=>0000001=>[7,1] [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[6,3,2,5,4,1,7,8]=>0000011=>[6,1,1] [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,3,2,5,4,1,8,7]=>0000010=>[6,2] [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[6,3,2,5,4,7,1,8]=>0000001=>[7,1] [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[8,3,2,5,4,7,6,1]=>0000000=>[8] [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[8,3,2,5,6,4,7,1]=>0000000=>[8] [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8,3,2,7,6,5,4,1]=>0000000=>[8] [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,3,4,2,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,3,4,2,1,7,8,6]=>0000100=>[5,3] [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,3,4,2,1,8,7,6]=>0000100=>[5,3] [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,3,4,2,7,6,1,8]=>0000001=>[7,1] [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,6,5,1,8]=>0000001=>[7,1] [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[7,3,4,2,6,5,8,1]=>0000000=>[8] [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[6,3,4,5,2,7,1,8]=>0000001=>[7,1] [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1,8]=>0000001=>[7,1] [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,3,4,6,5,2,1,8]=>0000001=>[7,1] [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[6,3,5,4,2,7,1,8]=>0000001=>[7,1] [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,5,4,6,2,1,8]=>0000001=>[7,1] [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,3,6,4,5,2,1,8]=>0000001=>[7,1] [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,3,6,5,4,2,1,8]=>0000001=>[7,1] [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>0000111=>[5,1,1,1] [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>0000110=>[5,1,2] [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>0000101=>[5,2,1] [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>0000100=>[5,3] [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>0000100=>[5,3] [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>0000011=>[6,1,1] [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>0000010=>[6,2] [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>0000001=>[7,1] [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>0000000=>[8] [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>0000000=>[8] [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>0000001=>[7,1] [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>0000000=>[8] [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,8,6,7,1]=>0000000=>[8] [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>0000000=>[8] [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[6,4,3,2,5,1,7,8]=>0000011=>[6,1,1] [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,4,3,5,2,1,8,7]=>0000010=>[6,2] [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1,8]=>0000001=>[7,1] [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,4,3,6,5,2,1,8]=>0000001=>[7,1] [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[7,4,3,6,5,2,8,1]=>0000000=>[8] [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,5,3,4,2,1,8,7]=>0000010=>[6,2] [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[8,5,3,4,7,6,2,1]=>0000000=>[8] [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,6,3,4,5,2,1,8]=>0000001=>[7,1] [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[8,7,3,6,5,4,2,1]=>0000000=>[8] [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>0000010=>[6,2] [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]=>0000000=>[8] [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>0000000=>[8] [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8,5,4,3,2,7,6,1]=>0000000=>[8] [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[8,7,4,3,6,5,2,1]=>0000000=>[8] [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,6,4,5,3,2,1,8]=>0000001=>[7,1] [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>0000001=>[7,1] [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[8,7,5,4,3,6,2,1]=>0000000=>[8] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>0000000=>[8] [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5,10,9,8,7,6]=>111110000=>[1,1,1,1,1,5]
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
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.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.